IDEALIZATION XII: CORRECTING THE MODEL
POZNAŃ STUDIES IN THE PHILOSOPHY OF THE SCIENCES AND THE HUMANITIES VOLUME 86
EDITORS Jerzy Brzeziński Andrzej Klawiter Piotr Kwieciński (assistant editor) Krzysztof Łastowski Leszek Nowak (editor-in-chief)
Izabella Nowakowa Katarzyna Paprzycka (managing editor) Marcin Paprzycki Piotr Przybysz (assistant editor) Michael J. Shaffer
ADVISORY COMMITTEE Joseph Agassi (Tel-Aviv) Étienne Balibar (Paris) Wolfgang Balzer (München) Mario Bunge (Montreal) Nancy Cartwright (London) Robert S. Cohen (Boston) Francesco Coniglione (Catania) Andrzej Falkiewicz (Wrocław) Dagfinn Føllesdal (Oslo) Bert Hamminga (Tilburg) Jaakko Hintikka (Boston) Jacek J. Jadacki (Warszawa) Jerzy Kmita (Poznań)
Leon Koj (Lublin) Władysław Krajewski (Warszawa) Theo A.F. Kuipers (Groningen) Witold Marciszewski (Warszawa) Ilkka Niiniluoto (Helsinki) Günter Patzig (Göttingen) Jerzy Perzanowski (Toruń) Marian Przełęcki (Warszawa) Jan Such (Poznań) Max Urchs (Konstanz) Jan Woleński (Kraków) Ryszard Wójcicki (Warszawa)
Poznań Studies in the Philosophy of the Sciences and the Humanities is partly sponsored by SWPS and Adam Mickiewicz University
Address:
dr Katarzyna Paprzycka . Instytut Filozofii . SWPS . ul. Chodakowska 19/31 03-815 Warszawa . Poland . fax: ++48 22 517-9625 E-mail:
[email protected] . Website: http://PoznanStudies.swps.edu.pl
IDEALIZATION XII: CORRECTING THE MODEL IDEALIZATION AND ABSTRACTION IN THE SCIENCES
Edited by Martin R. Jones and Nancy Cartwright
Amsterdam - New York, NY 2005
The paper on which this book is printed meets the requirements of "ISO 9706:1994, Information and documentation - Paper for documents Requirements for permanence". ISSN 0303-8157 ISBN: 90-420-1955-7 ©Editions Rodopi B.V., Amsterdam - New York, NY 2005 Printed in The Netherlands
Science at its best seeks most to keep us in this simplified, thoroughly artificial world, suitably constructed and suitably falsified world . . . willy-nilly, it loves error, because, being alive, it loves life. Friedrich Nietzsche, Beyond Good and Evil
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CONTENTS
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
Analytical Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11
Kevin D. Hoover, Quantitative Evaluation of Idealized Models in the New Classical Macroeconomics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15
John Pemberton, Why Idealized Models in Economics Have Limited Use. .
35
Amos Funkenstein, The Revival of Aristotle’s Nature . . . . . . . . . . . . . . . . . .
47
James R. Griesemer, The Informational Gene and the Substantial Body: On the Generalization of Evolutionary Theory by Abstraction . . . . . . .
59
Nancy J. Nersessian, Abstraction via Generic Modeling in Concept Formation in Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117
Margaret Morrison, Approximating the Real: The Role of Idealizations in Physical Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
145
Martin R. Jones, Idealization and Abstraction: A Framework . . . . . . . . . . .
173
David S. Nivison, Standard Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
219
James Bogen and James Woodward, Evading the IRS . . . . . . . . . . . . . . . . .
233
M. Norton Wise, Realism Is Dead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
269
Ronald N. Giere, Is Realism Dead? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
287
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PREFACE
This volume was conceived over a dozen years ago in Stanford, California when Cartwright and Jones were both grappling – each for their own reasons – with questions about idealization in science. There was already a rich European literature on the subject, much of it represented in this series; and there was a growing interest in the United States, prompted in part by new work on approximation and in part by problems encountered within the American versions of the semantic view of theories about the fit of models to the world. At the time, tuned to questions about idealization and abstraction, we began to see elements of the problem and lessons to be learned about it everywhere, in papers and lectures on vastly different subjects, from Chinese calendars to nineteenth century electrodynamics to options pricing. Each – usually unintentionally and not explicitly – gave some new slant, some new insight, into the problems about idealization, abstraction, approximation, and modeling; and we thought it would be valuable to the philosophical and scientific communities to make these kinds of discussions available to all, specifically earmarked as discussions that can teach us about idealization. This volume is the result. We asked the contributors to write about some aspect of idealization or abstraction in a subject they were studying – “idealization” as they found it useful to think about it, without trying to fit their discussion into some categories already available. As a consequence, most of the authors in this volume are not grappling directly with the standard philosophical literature on the problems; indeed, several are not philosophers – we have a distinguished historian of ideas who specialized in the medieval period, a renowned historian of physics, an eminent economic methodologist, and an investment director for one of the largest insurance companies in the world. The volume has unfortunately been a long time in the making; many of the papers were written a decade ago. We apologize to the authors for this long delay. Still, for thinking about abstraction and idealization, the material remains fresh and original. We hope that readers of this volume will find this diverse collection as rewarding a source of new ideas and new materials as we ourselves have. Two of the papers in particular need to be set in context. Norton Wise’s contribution, “Realism is Dead,” was given at the 1989 Pacific Division Meetings of the American Philosophical Association, in Berkeley, California, as part of an “Author Meets the Critics” session devoted to Ronald Giere’s book Explaining Science, which was hot off the presses at the time. (The other
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Preface
speaker was Bas van Fraassen.) Giere’s contribution, “Is Realism Dead?”, is based on his response to Wise’s comments on that occasion. Sadly, Amos Funkenstein died during the production of the volume. As a result, we have had to make several decisions during the editing of his paper without being able to confirm our judgements with the author. Some of these decisions concerned the right way to correct apparent typographical error, some the filling-in of bibliographical gaps, and some the fine points of various languages. Thanks in that connection to James Helm of the Classics Department of Oberlin, who helped us to get the Greek right. We hope we have been true to Professor Funkenstein’s original intentions. Any errors which remain are, no doubt, the fault of the editors. Nancy Nersessian’s paper has also been published in Mind and Society, vol. 3, no. 5, and we thank Fondazione Roselli for permission to reprint it here. We also thank the various publishers for their permission to reprint the following figures: figure 2 in James Bogen and James Woodward’s paper, from John Earman and Clark Glymour’s “Relativity and Eclipses: The British Eclipse Expeditions of 1919 and their Predecessors,” Historical Studies in the Physical Sciences, 11:1 (1980), p. 67 (University of California Press); figure 2 in James Griesemer’s paper, reprinted by permission from Nature vol. 227, p. 561 (copyright © 1970 MacMillan Magazines Limited); and figure 3 in James Griesemer’s paper, from John Maynard Smith’s The Theory of Evolution, 3rd ed., 1975 (copyright © John Maynard Smith, 1985, 1966, 1975, reproduced by permission of Penguin Books, Middlesex). In the process of putting the volume together, we have benefited from the help of many people. Particular thanks are due to Jon Ellis, Ursula Coope, Cheryl Chen, Mary Conger, Lan Sasa, George Zouros, and especially to Brendan O’Sullivan, for their careful, thorough, and diligent assistance with various sorts of editorial and bibliographical work. Thanks to Ned Hall for suggesting that we use the phrase “correcting the model” in the title of the book, to Leszek Nowak as series editor, and to Fred van der Zee at Rodopi. We (and especially MRJ) would also like to thank the authors for their patience in the face of delay. Martin Jones’s work on the volume was assisted at various points, and in various ways, by: a President’s Research Fellowship in the Humanities from the University of California; a Humanities Research Fellowship from the University of California, Berkeley; and a Hellman Family Faculty Fund Award, also at the University of California, Berkeley. In addition, H. H. Powers Travel Grants from Oberlin College made it much easier for the editors to meet during two recent summers. M.R.J. N.C.
ANALYTICAL TABLE OF CONTENTS
Kevin D. Hoover, Quantitative Evaluation of Idealized Models in the New Classical Macroeconomics The new classical macroeconomics responds to the “Lucas critique” by providing microfoundations for macroeconomic relationships. There is disagreement, however, about how best to conduct quantitative policy evaluation, given the idealized nature of the models in question. An examination of whether a coherent methodological basis can be found for one method – the calibration strategy – and an assessment of the limits of quantitative analysis within idealized macroeconomic models, with special attention to the work of Herbert Simon.
John Pemberton, Why Idealized Models in Economics Have Limited Use A distinction is drawn between causal and non-causal idealized models. Models of the second sort, which include those specified by means of restrictive antecedent clauses, are widely used in economics, but do not provide generally reliable predictions; moreover, they contain no clues as to when their reliability will fail.This is illustrated by a critique of the Black and Scholes option pricing model. The high degree of causal complexity of economic systems means that causal idealized models are also of limited value.
Amos Funkenstein, The Revival of Aristotle’s Nature A response to Nancy Cartwright’s arguments for the primacy of the notion of capacity. Explores the question of why, historically, capacities were seemingly set aside in the physics of the Scientific Revolution, and suggests some doubts about the fit between the notion of capacity and post-Galilean natural science. Connections between the putative abandonment of capacities and the move to seeing nature as uniform, and implications for the correct understanding of idealization as a method.
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Analytical Table of Contents
James R. Griesemer, The Informational Gene and the Substantial Body: On the Generalization of Evolutionary Theory by Abstraction Darwin’s theory of evolution dealt only with organisms in populations. Problems are raised for two central strategies for generalization by abstraction, including, in one case, contamination of the abstract theory by assumptions specific to particular mechanisms operating in particular sorts of material. A different foundation is needed for the generalization of evolutionary theory; and there are ramifications for the “units of selection” debate. A modification of Cartwright and Mendell’s account of abstraction is also proposed.
Nancy J. Nersessian, Abstraction via Generic Modeling in Concept Formation in Science Conceptual innovation in science often involves analogical reasoning. The notion of abstraction via generic modeling casts light on this process; generic modeling is the process of constructing a model which represents features common to a class of phenomena. Maxwell’s development of a model of the electromagnetic field as a state of a mechanical aether involved just this strategy. The study of generic modeling also yields insights into abstraction and idealization, and their roles in mathematization.
Margaret Morrison, Approximating the Real: The Role of Idealizations in Physical Theory An examination of the role and nature of idealization and abstraction in model construction and theory development. Parallels between current debates about the role of models and nineteenth-century debates surrounding Maxwellian electrodynamics. Response to realist claims that abstract models can be made representationally accurate by “adding back” parameters. Problems with the standard philosophical distinction between realistic and heuristic models. Two levels at which idealization operates, and the differing implications for the attempt to connect models to real systems.
Martin R. Jones, Idealization and Abstraction: A Framework A fundamental distinction is between idealizations as misrepresentations, and abstractions as mere omissions; other characteristic features of idealizations and abstractions are considered. A systematic proposal for clarifying talk of
Analytical Table of Contents
13
idealization and abstraction in both models and laws, degrees of idealization and abstraction, and idealization and abstraction as processes. Relations to the work of Cartwright and McMullin. Three ways in which idealization can occur in laws and our employment of them – there are quasi-laws, idealized laws, and ideal laws.
David S. Nivison, Standard Time Ancient Chinese astronomy and calendary divided time in simple, idealized ways with respect to, for example, lunar cycles, the seasons, and the period of Jupiter. The resulting schemes do not fit the data exactly, and astronomers employed complex rules of adjustment to correct for the mismatch. Nonetheless, the simpler picture was often treated as ideally true, and as capturing an order which was supposed to underlie the untidiness of observed reality.
James Bogen and James Woodward, Evading the IRS Critique of, and an alternative to, the view that the epistemic bearing of observational evidence on theory is best understood by examining Inferential Relations between Sentences (‘IRS’). Instead, we should attend to empirical facts about particular causal connections and about the error characteristics of detection processes. Both the general and the local reliability of detection procedures must be evaluated. Case studies, including attempts to confirm General Relativity by observing the bending of light, and by detecting gravity waves.
M. Norton Wise, Realism Is Dead An evaluation of Giere’s views of theory structure and representation in Explaining Science, and objections to his “constructive realism”: focus on the Hamiltonian version of classical mechanics shows that the theory should not be seen as a collection of abstract and idealized models; many nineteenth-century figures in classical physics did not treat mechanics as realistic, seeing its models as merely structurally analogous to real systems; a naturalistic theory of science ought to reflect that historical fact; and Giere’s realism does not take sufficient account of the social. Constrained social constructionism is the better view.
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Analytical Table of Contents
Ronald N. Giere, Is Realism Dead? Response to Wise, defending an “enlightened post-modernism”: the Hamiltonian version of classical mechanics simply provides more general recipes for model building; structural analogy is a kind of similarity, and so fits with constructive realism; scientists’ own theories of science are not privileged; and although constructive realism makes room for the social, strategies of experimentation can overwhelm social factors, and individuals are basic. We should start with a minimal realism, and focus on the task of explaining how science has led to an increase in our knowledge of the world.
Kevin D. Hoover QUANTITATIVE EVALUATION OF IDEALIZED MODELS IN THE NEW CLASSICAL MACROECONOMICS
The new classical macroeconomics is today certainly the most coherent, if not the dominant, school of macroeconomic thought. The pivotal document in its two decades of development is Robert Lucas’s 1976 paper, “Econometric Policy Evaluation: A Critique.”1 Lucas argued against the then reigning methods of evaluating the quantitative effects of economic policies on the grounds that the models used to conduct policy evaluation were not themselves invariant with respect to changes in policy.2 In the face of the Lucas critique, the new classical economics is divided in its view of how to conduct quantitative policy analysis between those who take the critique as a call for better methods of employing theoretical knowledge in the direct empirical estimation of macroeconomic models, and those who believe that it shows that estimation is hopeless and that quantitative assessment must be conducted using idealized models. Assessing the soundness of the views of the latter camp is the main focus of this essay.
1. The Lucas Critique The Lucas critique is usually seen as a pressing problem for macroeconomics, the study of aggregate economic activity (GNP, inflation, unemployment, interest rates, etc.). Economists typically envisage individual consumers, workers, or firms as choosing the best arrangement of their affairs, given their preferences, subject to constraints imposed by limited resources. Moving up from an account of individual behavior to an account of economy-wide aggregates is problematic. Typical macroeconometric models before Lucas’s ⎯⎯⎯⎯⎯⎯⎯
1
See Hoover (1988), (1991) and (1992) for accounts of the development of new classical thinking. The “Lucas critique,” as it is always known, is older than Lucas’s paper, going back at least to the work of Frisch and Haavelmo in the 1930s; see Morgan (1990), Hoover (1994).
2
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 15-33. Amsterdam/New York, NY: Rodopi, 2005.
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paper consisted of a set of aggregate variables to be explained (endogenous variables). Each was expressed as a (typically, but not necessarily, linear) function of other endogenous variables and of variables taken to be given from outside the model (exogenous variables). The functional forms were generally suggested by economic theory. The functions usually contained free parameters; thus, in practice, no one believed that these functions held exactly. Consequently, the parameters were usually estimated using statistical techniques such as multivariate regression. The consumption function provides a typical example of a function of a macromodel. The permanent income hypothesis (Friedman 1957) suggests that consumption at time t (Ct) should be related to income at t (Yt) and consumption at t-1 as follows: C t = k(1 – µ)Y t + µC t–1 + e
(1)
where k is a parameter based on people’s tastes for saving, µ is a parameter based on the process by which they form their expectations of future income, and e is an unobservable random error indicating that the relationship is not exact. One issue with a long pedigree in econometrics is whether the underlying parameters can be recovered from an econometric estimation.3 This is called the identification problem. For example, suppose that what we want to know is the true relationship between savings and permanent income, k. If the theory that generated equation (1) is correct, then we would estimate a linear regression of the form C t = π1Y t + π2C t–1 + w
(2)
where w is a random error and π1 and π2 are free parameters to be estimated. We may then calculate k = π1 / (1– π2). The Lucas critique suggested that it was wrong to take an equation such as (1) in isolation. Rather, it had to be considered in the context of the whole system of related equations. What is more, given that economic agents were optimizers, it was wrong to treat µ as a fixed parameter, because people’s estimates of future income would depend in part on government policies that alter the course of the economy and, therefore, on GNP, unemployment, and other influences on personal income. The parameter itself would have to be modeled something like this: µ = f (Yt, Y t–1, C t–1, G)
⎯⎯⎯⎯⎯⎯⎯ 3
See Morgan (1990), ch. 6, for a history of this problem.
(3)
Quantitative Evaluation of Idealized Models in the New Classical Macroeconomics
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where G is a variable indicating the stance of government policy. Every time government policy changes, µ changes. If equation (1) were a true representation of economic reality, the estimates of π1 and π2 in equation (2) would alter with every change in µ: they would not be autonomous.4 The absence of autonomy, in turn, plays havoc with identification: the true k can be recovered from π1 and π2 only if they are stable. Identification and autonomy are distinct streams in the history of econometrics; the Lucas critique stands at their confluence. Autonomy had been a neglected issue in econometrics for over forty years. Identification, in contrast, is a central part of every econometrics course.
2. Calibration versus Estimation New classical macroeconomists are radical advocates of microfoundations for macroeconomics. Explanations of all aggregate economic phenomena must be based upon, or at least consistent with, the microeconomics of rational economic agents. The new classicals stress constrained optimization and general equilibrium. A characteristic feature of new classical models is the rational expectations hypothesis. Expectations are said to be formed rationally if they are consistent with the forecasts of the model itself. This is usually seen to be a requirement of rationality, since, if the model is correct, expectations that are not rational would be systematically incorrect, and rational agents would not persist in forming them in such an inferior manner.5 All new classicals share these theoretical commitments, yet they do not all draw the same implications for quantitative policy evaluation. One approach stresses the identification aspects of the Lucas critique. Hansen and Sargent (1980), for instance, recommend starting with a model of individual preferences and constraints (i.e., “taking only tastes and technology as given,” to use the jargon). From this they derive the analogs of equations (1)-(3). In particular, using the rational expectations hypothesis, they derive the correctly parameterized analog to (3). They then estimate the reduced forms, the analogs to equation (2) (which may, in fact, be a system of equations). Statistical tests are used to determine whether the restrictions implied by the theory and represented in the analogs to equations (1) and (3) hold. In the current example, since we have not specified (3) more definitely, there is nothing to test in equation (1). This is because equation (1) is just identified; i.e., there is only one way to calculate its parameters from the estimated coefficients of equation (2). Nonetheless, in many cases, there is more than one way to ⎯⎯⎯⎯⎯⎯⎯
4
For the history of autonomy, see Morgan (1990), chs. 4 and 8. See Sheffrin (1983) for a general account of the rational expectations hypothesis, and Hoover (1988), ch. 1, for a discussion of the weaknesses of the hypothesis.
5
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calculate these parameters; the equation is then said to be overidentified. A statistical test of whether, within some acceptable margin, all of these ways yield the same estimated parameters is a test of overidentifying restrictions and is the standard method of judging the success of the theoretical model in matching the actual data. Hansen and Sargent’s approach assumes that the underlying theory is (or could be or should be) adequate, and that the important problem is to obtain accurate estimates of the underlying free parameters. Once these are known, they can be used to conduct policy analysis. Lucas (1987, p. 45) and Kydland and Prescott (1991) argue that Hansen and Sargent’s approach is inappropriate for macroeconomics. They do not dissent from the underlying theory used to derive the overidentifying restrictions. Instead, they argue that reality is sufficiently complex that no tractable theory can preserve a close mapping with all of the nuances of the data that might be reflected in the reduced forms. Sufficiently general reduced forms will pick up many aspects of the data that are not captured in the theory, and the overidentifying restrictions will almost surely be rejected. Lucas and Prescott counsel not attempting to estimate or test macroeconomic theories directly. Instead, they argue that macroeconomists should build idealized models that are consistent with microeconomic theory and that mimic certain key aspects of aggregate economic behavior. These may then be used to simulate the effects of policy. Of course, theory leaves free parameters undetermined for Lucas and Prescott, just as it does for Hansen and Sargent. Lucas and Prescott suggest that these may be supplied either from independently conducted microeconomic econometric studies, which do not suffer from the aggregation problems of macroeconomic estimation, or from searches over the range of possible parameter values for a combination of values that well matches the features of the economy most important for the problem at hand. Their procedure is known as calibration.6 In a sense, advocacy of calibration downplays the identification problem in the Lucas critique and emphasizes autonomy. Estimation in the manner of Hansen and Sargent is an extension of standard and well-established practices in econometrics. When the type of models routinely advocated by Prescott (e.g., Kydland and Prescott 1982) are estimated, they are rejected statistically (e.g., Altug 1989). Prescott simply dismisses such rejections as applying an inappropriate standard. Lucas and Prescott argue that models that are idealized to the point of being incapable of passing such statistical tests are nonetheless the preferred method for generating quantitative ⎯⎯⎯⎯⎯⎯⎯ 6
Calibration is not unique to the new classical macroeconomics, but is well established in the context of “computable general equilibrium” models common in the analysis of taxation and international trade; see Shoven and Whalley (1984). All the methodological issues that arise over calibration of new classical macromodels must arise with respect to computable general equilibrium models as well.
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evaluations of policies. The central issue now before us is: can models which clearly do not fit the data be useful as quantitative guides to policy? Who is right – Lucas and Prescott or Hansen and Sargent?
3. Models and Artifacts “Model” is a ubiquitous term in economics, and a term with a variety of meanings. One commonly speaks of an econometric model. Here one means the concrete specification of functional forms for estimation: equation (2) is a typical example. I call these observational models. The second main class of models are evaluative or interpretive models. An obvious subclass of interpretive/evaluative models are toy models. A toy model exists merely to illustrate or to check the coherence of principles or their interaction. An example of such a model is the simple exchange model with two goods and two agents (people or countries). Adam Smith’s famous “invisible hand” suggests that a price system can coordinate trade and improve welfare. In this simple model, agents are characterized by functions that rank their preferences over different combinations of goods and by initial endowments of the goods. One can check, first, whether there is a relative price between the two goods and a set of trades at that price that makes both agents satisfied with the arrangement; and, second, given such a price, whether agents are better off in their own estimation than they would have been in the absence of trade. No one would think of drawing quantitative conclusions about the working of the economy from this model. Instead, one uses it to verify in a tractable and transparent case that certain qualitative results obtain. Such models may also suggest other qualitative features that may not have been known or sufficiently appreciated.7 The utter lack of descriptive realism of such models is no reason to abandon them as test beds for general principles. Is there another subclass of interpretive/evaluative models – one that involves quantification? Lucas seems to think so: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that can serve as laboratories in which policies that would be prohibitively expensive to experiment with in actual economies can be tested out at much lower cost (Lucas 1980, p. 271).
Let us call such models benchmark models. Benchmark models must be abstract enough and precise enough to permit incontrovertible answers to the questions put to them. Therefore, ⎯⎯⎯⎯⎯⎯⎯ 7
Cf. Diamond (1984), p. 47.
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. . . insistence on the “realism” of an economic model subverts its potential usefulness in thinking about reality. Any model that is well enough articulated to give clear answers to the questions we put to it will necessarily be artificial, abstract, patently unreal (Lucas 1980, p. 271).
On the other hand, only models that mimic reality in important respects will be useful in analyzing actual economies. The more dimensions in which the model mimics the answers actual economies give to simple questions, the more we trust its answers to harder questions. This is the sense in which more “realism” in a model is clearly preferred to less (Lucas 1980, p. 272).
Later in the same essay, Lucas emphasizes the quantitative nature of such model building: Our task . . . is to write a FORTRAN program that will accept specific economic policy rules as “input” and will generate as “output” statistics describing the operating characteristics of time series we care about, which are predicted to result from these policies (Lucas 1980, p. 288).
For Lucas, Kydland and Prescott’s model is precisely such a program.8 One might interpret Lucas’s remarks as making a superficial contribution to the debate over Milton Friedman’s “Methodology of Positive Economics” (1953): must the assumptions on which a theory is constructed be true or realistic or is it enough that the theory predicts “as if” they were true? But this would be a mistake. Lucas is making a point about the architecture of models and not about the foundations of secure prediction. To make this clear, consider Lucas’s (1987, pp. 20-31) cost-benefit analysis of the policies to raise GNP growth and to damp the business cycle. Lucas’s model considers a single representative consumer with a constant-relative-riskaversion utility function facing an exogenous consumption stream. The model is calibrated by picking reasonable values for the mean and variance of consumption, the subjective rate of discount, and the constant coefficient of relative risk aversion. Lucas then calculates how much extra consumption consumers would require to compensate them in terms of utility for a cut in the growth rate of consumption and how much consumption they would be willing to give up to secure smoother consumption streams. Although the answers that Lucas seeks are quantitative, the model is not used to make predictions that might be subjected to statistical tests. Rather, it is used to set upper bounds to the benefits that might conceivably be gained in the real world. Its parameters must reflect some truth about the world if it is to be useful, but they could not be easily directly estimated. In that sense, the model is unrealistic. ⎯⎯⎯⎯⎯⎯⎯ 8
They do not say, however, whether it is actually written in FORTRAN.
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In a footnote, Lucas (1980, p. 272, fn. 1) cites Herbert Simon’s Sciences of the Artificial (1969) as an “immediate ancestor” of his “condensed” account. To uncover a more fully articulated argument for Lucas’s approach to modeling, it is worth following up the reference. For Simon, human artifacts, among which he must count economic models, can be thought of as a meeting point – an “interface” . . . – between an “inner” environment, the substance and organization of the artifact itself, and an “outer” environment, the surroundings in which it operates (Simon 1969, pp. 6, 7).
An artifact is useful, it achieves its goals, if its inner environment is appropriate to its outer environment. Simon’s distinction can be illustrated in the exceedingly simplified macroeconomic model represented by equations (1) and (3). The model converts inputs (Y t and G) into an output C t. Both the inputs and outputs, as well as the entire context in which such a model might be useful, can be considered parts of the outer environment. The inner environment includes the structure of the model – i.e., the particular functional forms – and the parameters, µ and k.9 The inner environment controls the manner in which the inputs are processed into outputs. The distinction between the outer and inner environments is important because there is some degree of independence between them. Clocks tell time for the outer environment. Although they may indicate the time in precisely the same way, say with identical hands on identical faces, the mechanisms of different clocks, their inner environments, may be constructed very differently. For determining when to leave to catch a plane, such differences are irrelevant. Equally, the inner environments may be isolated from all but a few key features of the outer environment. Only light entering through the lens for the short time that its shutter is open impinges on the inner environment of the camera. The remaining light is screened out by the opaque body of the camera, which is an essential part of its design. Our simple economic model demonstrates the same properties. If the goal is to predict the level of consumption within some statistical margin of error, then like the clock, other models with quite different functional forms may be (approximately) observationally equivalent. Equally, part of the point of the functional forms of the model is to isolate features which are relevant to achieving the goal of predicting C t – namely, Y t and G – and screening out irrelevant features of the outer environment, impounding any relevant but ignorable influences in the error term. Just as the camera is an opaque barrier to ambient light, the functional form of the consumption model is an opaque barrier to economic influences other than income and government policy. ⎯⎯⎯⎯⎯⎯⎯ 9
One might also include Ct-l, because, even though it is the lagged value of Ct (the output), it may be thought of as being stored “within” the model as time progresses.
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Simon factors adaptive systems into goals, outer environments, and inner environments. The relative independence of the outer and inner environments means that [w]e might hope to characterize the main properties of the system and its behavior without elaborating the detail of either the outer or the inner environments. We might look toward a science of the artificial that would depend on the relative simplicity of the interface as its primary source of abstraction and generality (Simon 1969, p. 9).
Simon’s views reinforce Lucas’s discussion of models. A model is useful only if it foregoes descriptive realism and selects limited features of reality to reproduce. The assumptions upon which the model is based do not matter, so long as the model succeeds in reproducing the selected features. Friedman’s “as if” methodology appears vindicated. But this is to move too fast. The inner environment is only relatively independent of the outer environment. Adaptation has its limits. In a benign environment we would learn from the motor only what it had been called upon to do; in a taxing environment we would learn something about its internal structure – specifically, about those aspects of the internal structure that were chiefly instrumental in limiting performance (Simon 1969, p. 13).
This is a more general statement of principles underlying Lucas’s (1976) critique of macroeconometric models. A benign outer environment for econometric models is one in which policy does not change. Changes of policy produce structural breaks in estimated equations: disintegration of the inner environment of the models. Economic models must be constructed like a ship’s chronometer, insulated from the outer environment so that . . . it reacts to the pitching of the ship only in the negative sense of maintaining an invariant relation of the hands on its dial to real time, independently of the ship’s motions (Simon 1969, p. 9).
Insulation in economic models is achieved by specifying functions whose parameters are invariant to policy. Again, this is easily clarified with the simple consumption model. If µ were a fixed parameter, as it might be in a stable environment in which government policy never changed, then equation (1) might yield an acceptable model of consumption. But in a world in which government policy changes, µ will also change constantly (the ship pitches, tilting the compass that is fastened securely to the deck). The role of equation (3) is precisely to isolate the model from changes in the outer environment by rendering µ a stable function of changing policy; µ changes, but in predictable and accountable ways (the compass mounted in a gimbal continually turns relative to the deck in just such a way as to maintain its orientation with the earth’s magnetic field).
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The independence of the inner and outer environments is not something that is true of arbitrary models; rather it must be built into models. While it may be enough in hostile environments for models to reproduce key features of the outer environment “as if” reality were described by their inner environments, it is not enough if they can do this only in benign environments. Thus, for Lucas, the “as if” methodology interpreted as an excuse for complacency with respect to modeling assumptions must be rejected. New classical economists argue that only through carefully constructing the model from invariants – tastes and technology, in Lucas’s usual phrase – can the model secure the benefits of a useful abstraction and generality. This is again an appeal to found macroeconomics in standard microeconomics. Here preferences and the production possibilities (tastes and technology) are presumed to be fixed, and the economic agent’s problem is to select the optimal combination of inputs and outputs. Tastes and technology are regarded as invariant partly because economists regard their formation as largely outside the domain of economics: de gustibus non est disputandum. Not all economists, however, would rule out modeling the formation of tastes or technological change. But for such models to be useful, they would themselves have to have parameters to govern the selection among possible preference orderings or the evolution of technology. These parameters would be the ultimate invariants from which a model immune to the Lucas critique would have to be constructed.
4. Quantification and Idealization Economic models are idealizations of the economy. The issue at hand, is whether, as idealizations, models can be held to a quantitative standard. Can idealized models convey useful quantitative information? The reason why one is inclined to answer these questions negatively is that models patently leave things out. Simon’s analysis, however, suggests that even on a quantitative standard that may be their principal advantage. To see this better, consider the analogy of physical laws. Nancy Cartwright (1983, esp. essays 3 and 6) argues that physical laws are instruments, human artifacts in precisely the sense of Simon and Lucas, the principal use of which is to permit calculations that would otherwise be impossible. The power of laws to rationalize the world and to permit complex calculation comes from their abstractness, definitiveness, and tractability. Lucas (1980, pp. 271, 272) says essentially the same thing about the power of economic models. The problem with laws for Cartwright (1989), however, is that they work only in ideal circumstances. Scientists must experiment to identify the actual working of a physical law: the book of nature is written in code or, more aptly
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perhaps, covered in rubbish. To break the code or clear the rubbish, the experimenter must either insulate the experiment from countervailing effects or must account for and, in essence, subtract away the influence of countervailing effects.10 What is left at the end of the well-run experiment is a measurement supporting the law – a quantification of the law. Despite its tenuousness in laboratory practice, the quantified law remains of the utmost importance. To illustrate, consider an experiment in introductory physics. To investigate the behavior of falling objects, a metal weight is dropped down a vertical track lined with a paper tape. An electric current is periodically sent through the track. The arcing of the electricity from the track to the weight burns a sequence of holes in the tape. These mark out equal times, and the experimenter measures the distances between the holes to determine the relation between time and distance. This experiment is crude. When, as a college freshman, I performed it, I proceeded as a purely empirically – minded economist might in what I thought was a true scientific spirit: I fitted the best line to the data. I tried linear, loglinear, exponential and quadratic forms. Linear fit best, and I got a C – on the experiment. The problem was not just that I did not get the right answer, although I felt it unjust at the time that scientific honesty was not rewarded. The problem was that many factors unrelated to the law of gravity combined to mask its operation – conditions were far from ideal. A truer scientific method would attempt to minimize or take account of those factors. Thus, had I not regarded the experiment as a naive attempt to infer the law of gravity empirically, but as an attempt to quantify a parameter in a model, I would have gotten a better grade. The model says that distance under the uniform acceleration of gravity is gt2 / 2. I suspect that given calculable margins of error, not only would my experiment have assigned a value to g, but that textbook values of g would have fallen within the range of experimental error – despite the apparent better fit of the linear curve.11 Even though the data had to be fudged and discounted to force it into the mold of the gravitational model, it would have been sensible to do so, because we know from unrelated experiments – the data from which also had to be fudged and discounted – that the quadratic law is more general. The law is right, and must be quantified, even though it is an idealization. Confirmation by practical application is important, although sometimes the confirmation is exceedingly indirect. Engineers would often not know where to begin if they did not have quantified physical laws to work with. But laws as ⎯⎯⎯⎯⎯⎯⎯
10
Cartwright (1989, secs. 2.3, 2.4), discusses the logic and methods of accounting for such countervailing effects. 11 An explicit analog to this problem is found in Sargent (1989), in which he shows that the presence of measurement error can make an investment-accelerator model of investment, which is incompatible with new classical theory, fit the data better, even when the data were in fact generated according to Tobin’s q-theory, which is in perfect harmony with new classical theory.
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idealizations leave important factors out. Thus, an engineer uses elementary physics to calculate loadings for an ideal bridge. Knowing that these laws fail to account for many critical factors, the engineer then specifies material strengths two, four, or ten times what the calculations showed was needed. Error is inevitable, so err on the side of caution. Better models reduce the margins of error. It is said that the Golden Gate Bridge could easily take a second deck because it was designed with pencil, paper, and slide rule, with simple models, and consequently greatly overbuilt. England’s Humber River Bridge, designed some forty years later with digital computers and more complex models is built to much closer tolerances and could not take a similar addition. The only confirmation that the bridges give of the models underlying their design is that they do not fall down. Overbuilding a bridge is one thing, overbuilding a fine watch is quite another: here close tolerances are essential. An engineer still begins with an idealized model, but the effects ignored by the model now have to be accounted for. Specific, unidealized knowledge of materials and their behavior is needed to correct the idealized model for departures from ideal conditions. Such knowledge is often based on the same sort of extrapolations that I rejected in the gravity experiment. Cartwright (1983, essay 6) refers to these extrapolations as “phenomenal laws.” So long as these extrapolations are restricted to the range of actual experience, they often prove useful in refining the fudge factors. Even though the phenomenal laws prove essential in design, the generality of idealized laws is a great source of efficiency: it is easier to use phenomenal laws to calculate departures from the ideal, than to attempt to work up from highly specific phenomenal laws. Again, the ideal laws find their only confirmation in the watch working as designed. Laws do not constitute all of physics: It is hard to find them in nature and we are always having to make excuses for them: why they have exceptions – big or little; why they only work for models in the head; why it takes an engineer with a special knowledge of materials and a not too literal mind to apply physics to reality (Cartwright 1989, p. 8).
Neither do formal models constitute all of economics. Yet despite the shortcomings of idealized laws, we know from practical applications, such as shooting artillery or sending rockets to the moon, that calculations based on the law of gravity get it nearly right and calculations based on linear extrapolation go hopelessly wrong. Cartwright (1989, ch. 4) argues that “capacities” are more fundamental than laws. Capacities are the invariant dispositions of the components of reality. Something like the notion of capacities must lie behind the proposal to set up “elasticity banks” to which researchers could turn when calibrating computable general equilibrium models (Shoven and Whalley 1984, p. 1047). An elasticity
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is the proportionate change of one variable with respect to another.12 Estimated elasticities vary according to the methods of estimation employed (e.g., functional forms, other controlling variables, and estimation procedures such as ordinary least squares regression or maximum likelihood estimation) and the set of data used. To “bank” disparate estimates is to assume that such different measures of elasticities somehow bracket or concentrate on a “true” value that is independent of the context of estimation. Laws, at best, describe how capacities compose under ideal circumstances. That models should represent the ways in which invariant capacities compose is, of course, the essence of the Lucas critique. Recognizing that models must be constructed from invariants does not itself tell us how to measure the strengths of the component capacities.
5. Aggregation and General Equilibrium Whether calibrated or estimated, real-business-cycle models are idealizations along many dimensions. The most important dimension of idealization is that the models deal in aggregates while the economy is composed of individuals. After all, the distinction between microeconomics and macroeconomics is the distinction between the individual actor and the economy as a whole. All new classical economists believe that one understands macroeconomic behavior only as an outcome of individual rationality. Lucas (1987, p. 57) comes close to adopting the Verstehen approach of the Austrians.13 The difficulty with this approach is that there are millions of people in an economy and it is not practical – nor is it ever likely to become practical – to model the behavior of each of them.14 Universally, new classical economists adopt representativeagent models, in which one agent or a few types of agents, stand in for the behavior of all agents.15 The conditions under which a single agent’s behavior can accurately represent the behavior of an entire class are onerous. Strict ⎯⎯⎯⎯⎯⎯⎯ 12
In a regression of the logarithm of one variable on the logarithms of others, the elasticities can be read directly as the value of the estimated coefficients. 13 For a full discussion of the relationship between new classical and Austrian economics see Hoover (1988), ch. 10. 14 In (Hoover 1984, pp. 64-66), and (Hoover 1988, pp. 218-220), I refer to this as the “Cournot problem,” since it was first articulated by Augustine Cournot (1927, p. 127). 15 Some economists reserve the term “representative-agent models” for models with a single, infinitely-lived agent. In a typical overlapping-generations model the new young are born at the start of every period, and the old die at the end of every period, and the model has infinitely many periods; so there are infinitely many agents. On this view, the overlapping-generations model is not a representative-agent model. I, however, regard it as one, because within any period one type of young agent and one type of old agent stand in for the enormous variety of people, and the same types are repeated period after period.
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aggregation requires not only that every economic agent have identical preferences but that these preferences are such that any individual agent would like to consume goods in the same ratios whatever their levels of wealth. The reason is straightforward: if agents with the same wealth have different preferences, then a transfer from one to the other will leave aggregate wealth unchanged but will change the pattern of consumption and possibly aggregate consumption as well; if all agents have identical preferences but prefer different combinations of goods when rich than when poor, transfers that make some richer and some poorer will again change the pattern of consumption and possibly aggregate consumption as well (Gorman 1953). The slightest reflection confirms that such conditions are never fulfilled in an actual economy. New classical macroeconomists insist on general equilibrium models. A fully elaborated general equilibrium model would represent each producer and each consumer and the whole range of goods and financial assets available in the economy. Agents would be modeled as making their decisions jointly so that, in the final equilibrium, production and consumption plans are individually optimal and jointly feasible. Such a detailed model is completely intractable. The new classicals usually obtain tractability by repairing to representativeagent models, modeling a single worker/consumer, who supplies labor in exchange for wages, and a single firm, which uses this labor to produce a single good that may be used indifferently for consumption or as a capital input into the production process. Labor, consumption, and capital are associated empirically with their aggregate counterparts. Although these models omit most of the details of the fully elaborated general equilibrium model, they nonetheless model firms and worker/consumers as making individually optimally and jointly consistent decisions about the demands for and supplies of labor and goods. They remain stripped-down general equilibrium models. One interpretation of the use of calibration methods in macroeconomics is that the practitioners recognize that highly aggregated, theoretical representative-agent models must be descriptively false, so that estimates of them are bound to fit badly in comparison to atheoretical (phenomenal) econometric models. The theoretical models are nonetheless to be preferred because useful policy evaluation is possible only within tractable models. In this, they are exactly like Lucas’s benchmark consumption model (see section III above). Calibrators appeal to microeconomic estimates of key parameters because information about individual agents is lost in the aggregation process. In general, these microeconomic estimates are not obtained using methods that impose the discipline of individual optimality and joint feasibility implicit in the general equilibrium model. Lucas (1987, pp. 46, 47) and Prescott (1986, p. 15) argue that the strength of calibration is that it uses multiple sources of information, supporting the belief that it is structured around true invariants. Again this
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comes close to endorsing a view of capacities as invariant dispositions independent of context. In contrast, advocates of direct estimation could argue that the idealized representative-agent model permits better use of other information not employed in microeconomic studies. Hansen and Sargent (1980, pp. 91, 92), for example, argue that the strength of their estimation method is that it accounts consistently for the interrelationships between constituent parts of the model; i.e., it enforces the discipline of the general equilibrium method – individual optimality and especially joint feasibility. The tradeoff between these gains and losses is not clear cut. Since both approaches share the representative-agent model, they also share a common disability: using the representative-agent model in any form begs the question by assuming that aggregation does not fundamentally alter the structure of the aggregate model. Physics may again provide a useful analogy. The laws that relate the pressures, temperatures and volumes of gases are macrophysics. The ideal laws can be derived from a micromodel: gas molecules are assumed to be point masses, subject to conservation of momentum, with a distribution of velocities. An aggregation assumption is also needed: the probability of the gas molecules moving in any direction is taken to be equal. Direct estimation of the ideal gas laws shows that they tend to break down – and must be corrected with fudge factors – when pushed to extremes. For example, under high pressures or low temperatures the ideal laws must be corrected according to van der Waals’s equation. This phenomenal law, a law in macrophysics, is used to justify alterations of the micromodel: when pressures are high one must recognize that forces operate between individual molecules. Despite some examples of macro-to-micro inferences analogous to the gas laws, Lucas’s (1980, p. 291) more typical view is that we must build our models up from the microeconomic to the macroeconomic. Unlike gases, human society does not comprise homogeneous molecules, but rational people, each choosing continually. To understand (verstehen) their behavior, one must model the individual and his situation. This insight is clearly correct. It is not clear in the least that it is adequately captured in the heroic aggregation assumptions of the representative-agent model. The analog for physics would be to model the behavior of gases at the macrophysical level, not as derived from the aggregation of molecules of randomly distributed momenta, but as a single molecule scaled up to observable volume – a thing corresponding to nothing ever known to nature.16
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A notable, non-new classical attempt to derive macroeconomic behavior from microeconomic behavior with appropriate aggregation assumptions is ( Durlauf 1989).
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6. Lessons for Econometrics Does the calibration methodology amount to a repudiation of econometrics? Clearly not. At some level, econometrics still helps to supply the values of the parameters of the models. Beyond that, whatever I have said in favor of calibration methods notwithstanding, the misgivings of econometricians such as Sargent are genuine. The calibration methodology, to date, lacks any discipline as stern as that imposed by econometric methods. For Lucas (1980, p. 288) and Prescott (1983, p. 11), the discipline of the calibration method comes from the paucity of free parameters. But one should note that theory places only loose restrictions on the values of key parameters. In the practice of the new classical calibrators, they are actually pinned down from econometric estimation at the microeconomic level or accounting considerations. In some sense, then, the calibration method would appear to be a kind of indirect estimation. Thus, it would be a mistake to treat calibration as simply an alternative form of estimation, although it is easy to understand why some critics interpret it that way. Even were there less flexibility in the parameterizations, the properties ascribed to the underlying components of the idealized representative-agent models – the agents, their utility functions, production functions, and constraints – are not subject to as convincing cross-checking as the analogous components in physical models usually are. The fudge factors that account for the discrepancies between the ideal model and the data look less like van der Waals’s equation, less like phenomenal laws, than like special pleading. Above all, it is not clear on what standards competing but contradictory models are to be compared and adjudicated.17 Some such standards are essential if any objective progress is to be made in economics.18 The calibration methodology is not, then, a repudiation of econometrics; yet it does contain some lessons for econometrics. In (Hoover 1994), I distinguish between two types of econometrics. Econometrics as observation treats econometric procedures as filters that process raw data into statistics. On this view, econometric calculations are not valid or ⎯⎯⎯⎯⎯⎯⎯ 17
Prescott (1983, p. 12), seems, oddly, to claim that the inability of a model to account for some real events is a positive virtue – in particular, that the inability of real-business-cycle models to account for the Great Depression is a point in their favor. He writes: “If any observation can be rationalized with some approach, then that approach is not scientific.” This seems to be a confused rendition of the respectable Popperian notion that a theory is more powerful the more things it rules out. But one must not mistake the power of a theory with its truth. Aside from issues of tractability, a theory that rationalizes only and exactly those events that actually occur, while ruling out exactly those events that do not occur is the perfect theory. In contrast, Prescott seems inadvertently to support the view that the more exceptions, the better the rule. 18 Watson (1993) develops a goodness-of-fit measure for calibrated models. It takes into account that, since idealization implies differences between model and reality that may be systematic, the errors-in-variables and errors-in-equations statistical models are probably not appropriate.
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invalid, but useful if they reveal theoretically interpretable facts about the world and not useful if they do not. Econometrics as measurement treats econometric procedures as direct measurements of theoretically articulated structures. This view is the classic Cowles Commission approach to structural estimation that concentrates on testing identified models specified from a priori theory.19 Many new classicals, such as Cooley and LeRoy (1985) and Sargent (1989), advocate econometrics as measurement. From a fundamental new classical perspective, they seem to have drawn the wrong lesson from the Lucas critique. Recall that the Lucas critique links traditional econometric concerns about identification and autonomy. New classical advocates of economics as observation overemphasize identification. Identification is achieved through prior theoretical commitment. The only meaning they allow for “theory” is general equilibrium microeconomics. Because such theory is intractable, they repair to the representative-agent model. Unfortunately, because of the failure of the conditions for exact aggregation to obtain, the representative-agent model does not represent the actual choices of any individual agent. The representative-agent model applies the mathematics of microeconomics, but in the context of econometrics as measurement it is only a simulacrum of microeconomics. The representative-agent model does not solve the aggregation problem; it ignores it. There is no reason to think that direct estimation will capture an accurate measurement of even the average behavior of the individuals who make up the economy. In contrast, calibrators use the representative-agent model precisely to represent average or typical behavior, but quantify that behavior independently of the representative-agent model. Thus, while it is problematic at the aggregate level, calibration can use econometrics as measurement, when it is truly microeconometric – the estimation of fundamental parameters from cross-section or panel data sets. Calibrators want their models to mimic the behavior of the economy; but they do not expect economic data to parameterize those models directly. Instead, they are likely to use various atheoretical statistical techniques to establish facts about the economy that they hope their models will ultimately imitate. Kydland and Prescott (1990, pp. 3, 4) self-consciously advocate a modern version of Burns and Mitchell’s “measurement without theory” – i.e., econometrics as observation. Econometrics as observation does not attempt to quantify fundamental invariants. Instead it repackages the facts already present in the data in a manner that a well calibrated model may successfully explain.
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19
For a general history of the Cowles Commission approach, see Epstein (1987), ch. 2.
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7. Conclusion The calibration methodology has both a wide following and a substantial opposition within the new classical school. I have attempted to give it a sympathetic reading. I have concentrated on Prescott and Lucas, as its most articulate advocates. Calibration is consistent with appealing accounts of the nature and role of models in science and economics, of quantification and idealization. The practical implementation of calibration methods typical of new classical representative-agent models is less convincing. The calibration methodology stresses that one might not wish to apply standard measures of goodness-of-fit (e.g., R2 or tests of overidentifying restrictions) such as are commonly applied with the usual econometric estimation techniques, because it is along only selected dimensions that one cares about the model’s performance at all. This is completely consistent with Simon’s account of artifacts. New classical economics has traditionally been skeptical about discretionary economic policies. They are therefore more concerned to evaluate the operating characteristics of policy rules. For this, the fit of the model to a particular historical realization is largely irrelevant, unless it assures that the model will also characterize the future distribution of outcomes. The implicit claim of most econometrics is that it does assure a good characterization. Probably most econometricians would reject calibration methods as coming nowhere close to providing such assurance. Substantial work remains to be done in establishing objective, comparative standards for judging competing models. Fortunately, even those converted to the method need not become Lucasians: methodology underdetermines substance. Simon, while providing Lucas with a foundation for his views on modeling, nonetheless prefers a notion of “bounded rationality” that is inconsistent with the rational expectations hypothesis or Lucas’s general view of humans as efficient optimizers.20 Favero and Hendry (1989) agree with Lucas over the importance of invariance, but seek to show that not only can invariance be found at the level of aggregate econometric relations (e.g., in the demand-for-money function), but that this rules out rational expectations as a source of noninvariance.21 Finally, to return to a physical analog, economic modeling is like the study of cosmology. Substantial empirical work helps to determine the values of key constants; their true values nonetheless remain doubtful. Different values within the margins of error, even given similarly structured models, may result in very ⎯⎯⎯⎯⎯⎯⎯ 20
E.g., Simon (1969, p. 33) writes: “What do these experiments tell us? First, they tell us that human beings do not always discover for themselves clever strategies that they could readily be taught (watching a chess master play a duffer should also convince us of that).” 21 Favero and Hendry (1989) reject the practical applicability of the Lucas critique for the demand for money in the U.K.; Campos and Ericsson (1988) reject it for the consumption function in Venezuela.
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different conclusions (e.g., that the universe expands forever or that it expands and then collapses). Equally, the same values, given the range of competing models, may result in very different conclusions. Nevertheless, we may all agree on the form that answers to cosmological or economic questions must take, without agreeing on the answers themselves.* Kevin D. Hoover Department of Economics University of California, Davis
[email protected]
REFERENCES Altug, S. (1989). Time-to-Build and Aggregate Fluctuations: Some New Evidence. International Economic Review 30, 889-920. Campos, J. and Ericsson, N. R. (1988). Econometric Modeling of Consumers’ Expenditure in Venezuela. Board of Governors of the Federal Reserve System International Finance Discussion Paper, no. 325. Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon Press. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Cooley, T. F. and LeRoy, S. F. (1985). Atheoretical Macroeconometrics: A Critique. Journal of Monetary Economics 16, 283-308. Cournot, A. ([1838] 1927). Researches into the Mathematical Principles of the Theory of Wealth. Translated by Nathaniel T. Bacon. New York: Macmillan. Diamond, P. A. (1984). A Search-Equilibrium Approach to the Micro Foundations of Macroeconomics: The Wicksell Lectures, 1982. Cambridge, Mass.: MIT Press. Durlauf, S. N. (1989). Locally Interacting Systems, Coordination Failure, and the Behavior of Aggregate Activity. Unpublished typescript, November 5th. Epstein, R. J. (1987). A History of Econometrics. Amsterdam: North-Holland. Favero, C. and Hendry, D. F. (1989). Testing the Lucas Critique: A Review. Unpublished typescript. Friedman, M. (1953). The Methodology of Positive Economics. In: Essays in Positive Economics. Chicago: Chicago University Press. Friedman, M. (1957). A Theory of the Consumption Function. Princeton: Princeton University Press. Gorman, W. M. (1953). Community Preference Fields. Econometrica 21, 63-80. Hansen, L. P. and Sargent, T. J. (1980). Formulating and Estimating Dynamic Linear Rational Expectations Models. In R. E. Lucas, Jr. and T. J. Sargent (eds.), Rational Expectations and Econometric Practice. London: George Allen & Unwin. Hoover, K. D. (1984). Two Types of Monetarism. Journal of Economic Literature 22, 58-76. Hoover, K. D. (1988). The New Classical Macroeconomics: A Skeptical Inquiry. Oxford: Blackwell.
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I thank Thomas Mayer, Kevin Salyer, Judy Klein, Roy Epstein, Nancy Cartwright, and Steven Sheffrin for many helpful comments on an earlier version of this paper.
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Hoover, K. D. (1991). Scientific Research Program or Tribe? A Joint Appraisal of Lakatos and the New Classical Macroeconomics. In M. Blaug and N. de Marchi (eds.), Appraising Economic Theories: Studies in the Application of the Methodology of Research Programs. Aldershot: Edward Elgar. Hoover, K. D. (1992). Reflections on the Rational Expectations Revolution in Macroeconomics. Cato Journal 12, 81-96. Hoover, K. D. (1994). Econometrics as Observation: The Lucas Critique and the Nature of Econometric Inference. Journal of Economic Methodology 1, 65-80. Kydland, F. E. and Prescott, E. C. (1982). Time to Build and Aggregate Fluctuations. Econometrica 50, 1345-1370. Kydland, F. E. and Prescott, E. C. (1990). Business Cycles: Real Facts and a Monetary Myth. Federal Reserve Bank of Minneapolis Quarterly Review 14, 3-18. Kydland, F. E. and Prescott, E. C. (1991). The Econometrics of the General Equilibrium Approach to Business Cycles. Scandinavian Journal of Economics 93, 161-78. Lucas, R. E., Jr. (1976). Econometric Policy Evaluation: A Critique. Reprinted in Lucas (1981). Lucas, R. E., Jr. (1980). Methods and Problems in Business Cycle Theory. Reprinted in Lucas (1981). Lucas, R. E., Jr. (1981). Studies in Business-Cycle Theory. Oxford: Blackwell. Lucas, R. E., Jr. (1987). Models of Business Cycles. Oxford: Blackwell. Morgan, M. S. (1990). The History of Econometric Ideas. Cambridge: Cambridge University Press. Prescott, E. C. (1983). ‘Can the Cycle be Reconciled with a Consistent Theory of Expectations?’ or A Progress Report on Business Cycle Theory. Federal Reserve Bank of Minneapolis Research Department Working Paper, No. 239. Prescott, E. C Prescott, E. C. (1986). Theory Ahead of Business Cycle Measurement. Federal Reserve Bank of Minneapolis Quarterly Review 10, 9-22. Sargent, T. J. (1989). Two Models of Measurements and the Investment Accelerator. Journal of Political Economy 97, 251-287. Sheffrin, S. M. (1983). Rational Expectations. Cambridge: Cambridge University Press. Shoven, J. B. and Whalley, J. (1984). Applied General-equilibrium Models of Taxation and International Trade. Journal of Economic Literature 22, 1007-1051. Simon, H. A. (1969). The Sciences of the Artificial. Cambridge, Mass.: The MIT Press. Watson, M. W. (1993). Measures of Fit for Calibrated Models. Journal of Political Economy 101, 1011-41.
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John Pemberton WHY IDEALIZED MODELS IN ECONOMICS HAVE LIMITED USE
1. Introduction This paper divides idealized models into two classes – causal and non-causal – according to whether the idealized model represents causes or not. Although the characterization of a causal idealized model may be incomplete, it is sufficiently well-defined to ensure that idealized models specified using restrictive antecedent clauses are non-causal. The contention of this paper is that whilst such idealized models are commonly used in economics, they are unsatisfactory; they do not predict reliably. Moreover, notions of causation that cut across such models are required to suggest when the idealized model will provide a sufficiently good approximation and when it will not. Doubt is cast on the ability of simple causal idealized models to capture sufficiently the causal complexity of economics in such a way as to provide useful predictions. The causalist philosophical standpoint of this paper is close to that of Nancy Cartwright.
2. Causal and Non-Causal Idealized Models For the purposes of this paper a “causal idealized model” is an idealized model that rests on simple idealized causes. The idealized models represent causes, or the effects of causes, that operate in reality. The inverse square law of gravitational attraction has an associated idealized model consisting of forces operating on point masses, and this is a causal idealized model by virtue of the fact that the forces of the model are causes. The standard idealized models of the operation of a spring, a pendulum or an ideal gas are causal by virtue of the fact that there are immediately identifiable causes that underpin these models. Cartwright shows, in Nature’s Capacities and their In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 35-46. Amsterdam/New York, NY: Rodopi, 2005.
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Measurement, how certain idealized models of the operation of lasers were shown to be causal (Cartwright 1989, pp. 41-55). Causal idealized models can on occasion tell us what happens in real, nonideal situations when the causes identified in the idealized model are modeled sufficiently accurately and operate in a sufficiently undisturbed way in the real situation under consideration. It is the presence and operation of the identified causes in reality that, under the right circumstances, allow the idealized model to approximate the behavior of that reality. Empirical evidence may allow us to calibrate the degree of approximation. A “non-causal idealized model” is an idealized model that is not causal – it does not attempt to capture causes or the effects of causes that operate in reality. It is not apparent how a non-causal idealized model approximates the behavior of real, non-ideal situations. On occasion a model may regularly and accurately predict the behavior of a real system, although the causes that underpin such behavior have not been identified. Such was the case with the early models of lasers – Cartwright’s account tells how much importance the early laser scientists attached to finding the causes. Such an idealized model may be causal even though the causes are unknown.
3. Non-Causal Idealized Models in Economics Many idealized models used in economics are non-causal. Such idealized models are generally identified by restrictive antecedent clauses which are true of nothing actual. An example of such a restrictive antecedent clause occurs in the assumption of perfect knowledge that is used most commonly in relation to consumers or producers to underpin the achievement of certain maximizing behavior. The assumption is of course false of all actual consumers or producers; it is indeed true of nothing actual. It partially defines an idealized model – a model in which behavior is simpler and more predictable than in reality. Friedman’s (1953) essay “The Methodology of Positive Economics” still dominates the methodology of economics despite its apparent shortcomings (Friedman 1953). Nagel suggests that the important sense in which Friedman defends “unrealistic assumptions” is that they are restrictive antecedent clauses (Nagel 1963, pp. 217-18). Nagel’s analysis highlights an ambiguity underlying Friedman’s paper concerning the role of assumptions in idealized models: 1. The assumptions are merely a device for stating the conclusion so that it is only the conclusion which is descriptive of reality. In this case the assumptions and the idealized model are of little interest because they cannot support in any
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way the validity of the conclusion which must stand or fall in accordance with available empirical evidence. Nagel’s example of such an assumption is “firms behave as if they were seeking rationally to maximize returns” (1963, p. 215). The assumption concerns the behavior of firms but does not require that they do actually rationally seek to maximize returns – merely that they behave as if this were the case. 2. The assumptions are understood as dealing with “pure cases” and the model is then descriptive of the pure case. The assumptions are then restrictive antecedent clauses. Nagel comments: “laws of nature formulated with reference to pure cases are not useless. On the contrary, a law so formulated states how phenomena are related when they are unaffected by numerous factors whose influence may never be completely eliminable but whose effects generally vary in magnitude with differences in attendant circumstances under which the phenomena recur. Accordingly, discrepancies between what is asserted for pure cases and what actually happens can be attributed to factors not mentioned in the law” (1963, pp. 215-16). Nagel labels idealized models “pure cases,” and suggests that the restrictive antecedent clauses that define them succeed by eliminating extraneous causes not dealt with by the law (1963, p. 216). The simple idealized world is tractable to analysis. The antecedent clauses define idealized models that are clearly noncausal. The key question is how behavior in such an idealized model relates to the behavior of systems in the real world. Behavior in the idealized model is derived using deductive analysis that appeals to the simplifying assumptions – the restrictive antecedent clauses. In practice, an implicit assumption is made but never stated in economics that the derived behavior pictured in the idealized model does approximate the behavior of systems in reality – this is here termed the “Approximate Inference Assumption” and is discussed below. Consider, for instance, the idealized model of perfect competition. The assumptions are normally stated broadly as follows (McCormick et al. 1983, p. 348): 1. Producers aim to maximize their profits and consumers are interested in maximizing their utility. 2. There are a large number of actual and potential buyers and sellers. 3. All actual and potential buyers and sellers have perfect knowledge of all existing opportunities to buy and sell. 4. Although tastes differ, buyers are generally indifferent among all units of the commodity offered for sale. 5. Factors of production are perfectly mobile.
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6. Productive processes are perfectly divisible; that is, constant returns to scale prevail. 7. Only pure private goods are bought and sold. Conclusions are typically derived by economists concerning behavior within such conditions over both the short run and the long run. The structure is causally complex. The short run/long run distinctions are not easy to explicate, so that it is far from clear, even in principle, that the behavior pictured in the idealized model could be produced in reality. How close is the behavior pictured in the model to the behavior of a given real economy? It is not clear how a user of this non-causal idealized model could begin to answer this question. The idealized model of perfect competition is a causally complex structure which, if the economists are right, allows certain functional relationships (in Russell’s (1913) sense) that are the effects of the behavior of firms, to be exhibited within the ideal circumstances prescribed by the assumptions. It is the contention of this paper that such an idealized model has very limited use in predicting the behavior of real economies.
4. The “Approximate Inference Assumption” The Approximate Inference Assumption (AIA) states that if a situation is “close” in some sense to the one captured by an idealized model then it may be inferred that the behavior in that situation is approximately that pictured in the idealized model. For a causal idealized model, the presence of the causes modeled in the real situation provides some basis for supposing that under the right circumstances such an approximation may hold. In the case of non-causal idealized models, the AIA is unsound. Chaos theory leads us to expect that in many situations the AIA is incorrect. Small changes to the boundary conditions of a model can lead to major changes in the behavior of the system. There are thus serious theoretic problems concerning the applicability of the AIA. Nevertheless Gibbard and Varian comment: It is almost always preposterous to suppose that the assumptions of the applied model are exactly true . . . The prevailing view is that when an investigator applies a model to a situation he hypothesizes that the assumptions of the applied model are close enough to the truth for his purposes (1978, pp. 668-9).
On this view of the behavior of economists, which seems to me to be correct, economists do indeed rely upon the AIA even in the case of non-causal idealized models.
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5. Mathematical Economics Mathematical economics requires highly idealized models of reality. Within the mathematical model, results are derived and these are deemed to be descriptive of reality. In order to apply the results of the mathematical model to reality, the AIA is usually required. A particularly good example is Arrow and Debreu’s proof of the existence of a general equilibrium within an economy (Debreu 1959). The proof rests on modeling the economy as a multi-dimensional vector space in which certain sets of points are assumed to be compact – a quality which only in the loosest sense could be deemed to be descriptive of reality. This idealization of an economy is non-causal. Once the nature of the relationship between the mathematical model and reality is brought into question, and the problems with the AIA accepted, it becomes clear that the proof of the existence of an equilibrium within an economy is simply an artifact of the mathematical model, and does not demonstrate the existence of a corresponding counterpart in reality.
6. The Black and Scholes Argument The Black and Scholes (hereafter ‘B&S’) paper on option pricing is a first-class example in its economic field – mathematical in style and almost universally accepted (Black and Scholes 1973). For this reason it is also a good example of economics that, for its practical application and in order to claim empirical content, rests wholly upon the AIA to make inferences from a non-causal idealized model to reality. This paper uses the B&S argument to illustrate the use of the AIA and to give an example of its failure. B&S make the following assumptions: (a) The short-term interest rate is known and is constant through time. (b) The stock price follows a random walk in continuous time with a variance rate proportional to the square root of the stock price. Thus the distribution of the stock price at the end of any finite interval is lognormal. The variance rate of return on the stock is constant. (c) The stock pays no dividends or other distributions. (d) The option is “European,” that is, it can only be exercised at maturity. (e) There are no transaction costs in buying or selling the stock or the option. (f) It is possible to borrow any fraction of the price of a security to buy it or to hold it at the short-term interest rate. (g) There are no penalties for short selling. A seller who does not own a security will simply accept the price of the security from a buyer, and
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will agree to settle with the buyer on some future date by paying him an amount equal to the price of the security on that date. (a), (e), (f) and (g) are false. (c) is generally false. (d) is false if the option is American. In the case of (b) a far weaker assumption, namely that the price of the stock is a continuous function of time, is false. These assumptions function as restrictive antecedent clauses that define a non-causal idealized model. Using these assumptions B&S derive a solution to the option-pricing problem. By the end of their paper it is clear that the authors believe the solution in the idealized model situation is applicable to real options. It is rather surprising and worthy of note that many followers of B&S have not only employed, implicitly, the AIA but appear to have used a stronger assumption – a “precise inference assumption” – to the effect that the idealized solution is precise in real situations. Cox and Rubenstein for instance write a section of their leading textbook on option pricing under the title “An Exact Option Pricing Formula” (1985, pp. 165-252). B&S themselves conclude that: the expected return on the stock does not appear in the equation. The option value as a function of the stock price is independent of the expected return on the stock (1973, p. 644).
The failure of the expected return on the stock to appear as a parameter of the value in the option is a direct result of the powerful assumptions that B&S employ for defining their idealized model. They have not succeeded in showing that in real situations the expected return on the stock is not a parameter in the value of an option. This logically incorrect conclusion demonstrates their use of the AIA. (This is the equivalent of the conclusion that walking uphill is as quick as walking downhill in the Narrow Island analogy below.) Many economists have sought to demonstrate the relevance of the B&S solution to real options by showing that similar results hold under different (usually claimed to be weaker) assumptions than those used for the B&S idealized model. Beenstock’s attempt in “The Robustness of the Black-Scholes Option Pricing Model” (1982) is typical. Unfortunately, these “relaxations” of the assumptions merely tell us what would happen in ideal circumstances and do little to bridge the gap to the real world. Beenstock’s first conclusion is that “[o]ption prices are sensitive to the stochastic processes that determine underlying stock prices . . . Relaxation of these assumptions can produce large percentage changes in option prices” (1982, p. 40). The B&S solution is not necessarily a good approximation even in the carefully controlled idealized situations where all except one of their assumptions are held constant. The AIA simply does not work. A more tangible practical example of the failure of the AIA arises when the stock price movement is discontinuous. Discontinuities arise in a wide range of
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practical situations, but perhaps most markedly in relation to bids. A situation arose recently where one morning a major stake in a top 100 company changed hands. The purchaser made known its intention to make a statement concerning its intentions at 1pm. Expert analysts considered there to be a significant possibility of a bid – probabilities in the 10% to 50% range were typical assessments. In the event of a bid, the stock price would rise by some 20% or more. In the event of no bid, the stock price would drop some 10%. For a slightly in-the-money, short-dated call option, cash receipt at expiry would almost certainly be zero if no bid were received, and close to 20%-odd of the stock price per underlying share if a bid were forthcoming. Under any practical method of valuation, the value of the option must be close to the probability of a bid times 20%-odd of the stock price. The B&S solution simply does not work in this situation. (This breakdown of the B&S solution is the equivalent of the breakdown of Professor White’s solution for villages on opposite coasts at broader parts of Narrow Island (see below). The assumption that stock price moves are continuous is a good one most of the time, but is totally wrong here, just as Professor White’s assumption that the island is a line breaks down for the corresponding case.) Practicing options experts recognize the shortcomings of B&S and will commonly adjust their results for the non-lognormality of the stock price distribution since by an ad hoc increase to the stock price volatility estimate, empirical evidence shows that most real stock price distributions have higher kurtosis than the lognormal distribution. But B&S provides no basis for such adjustments. The key question is “If a real situation is close to the B&S assumptions, how close is it to the B&S conclusion?” The major complaint about the B&S derivation is that it does not allow an answer to this question. Their precise solution to the idealized case tells us nothing about real situations. In the case of the imminent bid announcement, B&S breaks down entirely. What characteristics of the real situation will ensure the B&S solution “works” sufficiently well? The B&S approach provides no answer.
7. The Narrow Island Analogy In the Southern Seas, some way to the east and south of Zanzibar is a thin strip of land that modern visitors call “Narrow Island.” An indigenous people inhabit the island whose customs derive from beyond the mists of time. At the northern end of the island is a hill cut at its midpoint by a high cliff which crashes vertically into the sea. On the headland above the cliff, which to local people is a sacred site, a shrine has been erected. It is the custom of the island that all able-bodied adults walk to the shrine to pay their respects every seventh day.
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Despite its primitive condition the island possesses the secret of accurate time-keeping using instruments that visitors recognize as simple clocks. In addition to a traditional name, each village has a “numeric name,” which is the length of time it takes to walk to the shrine, pay due respects and return to the village. The island being of a fair length, the numeric names stretch into the thousands. Many years ago one of the first visitors to the island from Europe was a traveler the islanders called Professor White. Modern opinion has it that White was an economist. What is known is that at the time of his visit the local people were wrestling with the problem of establishing how long it took to walk between villages on the island. The argument of Professor White is recorded as follows: The problem as it stands is a little intractable. Let us make some assumptions. Suppose that the island is a straight line. Suppose the speed of walking is uniform. Then the time taken to walk between two villages is half the absolute difference between their numeric names.
The islanders were delighted with this solution and more delighted still when they found how well it worked in practice. It was noted with considerable interest that the time taken to walk between two villages is independent of the height difference between them. As the island is quite hilly this astonishing result was considered an important discovery. Stories tell that so great was the islanders’ enthusiasm for their new solution that they attempted to share it with some of their neighboring islands. To this day there is no confirmation of the dreadful fate which is said to have befallen an envoy to Broad Island, inhabited by an altogether more fearsome people, who were apparently disappointed with the Narrow’s solution. Although the Narrow Islanders have used their solution happily for many years, more recently doubts have begun to emerge. In some parts of Narrow, where the island is slightly broader, reports suggest that the time between villages on opposite coasts is greater than Professor White’s solution would suggest. Others who live near the hills quite frankly doubt that the time taken to walk from the bottom of the hill to the top is the same as the time taken to walk from the top to the bottom. It is a tradition amongst the islanders that land is passed to sons upon their marriage. Upon the marriage of a grandson the grandfather moves to a sacred village near the middle of the island which is situated in the lee of a large stone known as the McCarthy. The McCarthy Stoners report that Professor White’s solution suggests it is quicker to walk to villages further south than it is to walk to villages that appear to be their immediate neighbors. The island’s Establishment continues to point out that Professor White’s solution gives “the time to walk between two villages,” so that the time taken on
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any particular journey – resting as it does on a particular person in particular climactic conditions – is hardly adequate contrary evidence. Those who would talk of average times are considered to be wide of the mark. Whilst few islanders seriously doubt the veracity of the theory, it is reported that many have taken to making ad hoc adjustments to the official solution, a practice that is difficult to condone. Last year a visitor to the island was impolite enough to question the logic of Professor White’s solution itself. His main points were as follows: 1. The “time taken to walk between two villages” is not well defined. A workable definition might be “the average time taken to walk between the two villages in daylight hours, by able-bodied men between the ages of eighteen and forty, traveling at a comfortable pace, without rest stops, during normal climatic conditions, e.g., excluding unduly wet or windy weather.” 2. Both of the assumptions are incorrect. The conclusion is not always approximately correct. 3. A more robust solution which should provide answers that are approximately correct for all pairs of villages is to regress the average times as proposed in (1) against the two principal causal factors underlying journey times – horizontal distance and height of climb, positive or negative. If a linear equation does not provide a sufficiently good fit, a higher order polynomial might be used. To the Narrow Islanders such talk was incomprehensible.
8. A Robust Solution to the Option Pricing Problem The Narrow Island analogy shows how the use of a non-causal idealized model breaks down. It may represent a good approximation most of the time, but on occasion it is no approximation at all. Moreover, the model itself provides no clues as to when it is, and when it is not, applicable. We have this knowledge (if at all) from a consideration of broader factors; it would seem these must include causal factors. A causal idealized model always provides a good approximation whenever it captures enough of the causes sufficiently accurately, and the causes modeled operate in reality in a sufficiently undisturbed way. Often our knowledge of the situation will allow us to judge whether this is likely to be the case. The visitor’s solution to the Narrow Island problem is correct; it is a robust causal solution. A similar solution exists for the option pricing problem.
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In the absence of any generally accepted definition of investment value, we may choose as a robust measure the expected value of receipts using a discount rate appropriate to the net liabilities. The causal parameters of value are those which affect the stock price at expiry. These may be categorized as known and unknown causes. Known causes: 1. Expected growth of stock price. Unless the dividend yield is unusually high, growth in stock price is part of the anticipated investment return. 2. Bifurcating event. To the extent that the market is efficient (all causes known to any market participant are reflected in the stock price, say), the probability density function (pdf) that describes the stock price at expiry should be evenly distributed about the central expectation. A bifurcating event induces a double-humped pdf. 3. Market inefficiencies. If we have insight into a stock which differs from that of other market participants then we may on occasion anticipate a movement in the market price of the stock during the period to expiry. Unknown causes: John Stuart Mill referred to “disturbing causes,” causes that do not appear explicitly within the model (1967, pp. 330-31). Such unknown causes may be allowed for by choosing a pdf that allows for a range of outcomes. It is usual to use a lognormal distribution for stock prices, but empirical evidence suggests that the chosen distribution should have higher kurtosis than this. A pdf may be chosen that makes allowance for all the causes, both known and unknown, and the discounted expected value calculated to provide a robust approximate measure of value. Sensitivity to changing assumptions may be checked.
9. Causal Idealized Models in Economics In the physical sciences real working systems can sometimes be constructed that arrange for causes to operate in just the right way to sustain the prescribed behavior of the system. Pendula, lasers and car engines are examples. Whilst the systems are working, aspects of their behavior may be described by functional relationships (again, in Russell’s (1913) sense) between variables. The design of the system ensures consistency, repeatability and reversibility. Real economies are not so neat; they have a complex causal structure, and are more akin to machines with many handles, each of which is turned continually and independently. The state of the machine is continually changing and evolving as the handles are turned. The effect of turning a single handle is
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not in general consistent, repeatable or reversible. Simple functional relationships between variables are at best approximate. Simple mathematical models do not capture such a complicated process, but may on occasion approximate part of the process for some duration. Economists do on occasion use causal idealized models. Examples are equilibrium models where causes are identified that tend to push the economic system back towards equilibrium. One such model equates money supply with money demand. Economics textbooks argue that behavioral patterns create causes that ensure equality holds “in equilibrium.” Such causal idealized models leave out the vast bulk of causes and simplify to an extreme extent. It is far from clear that such models can demonstrate any predictive success – their usefulness is at best very limited.
10. Conclusion Economists’ use of non-causal idealized models is problematic. No account can be provided in terms of the idealized model as to when the model will provide a sufficient approximation to reality. Such models do not predict reliably. Moreover, the causal complexity of economies suggests that they may be intractable to simple models, so that causal idealized models may also have very limited predictive success. John Pemberton Institute of Actuaries, London
[email protected]
REFERENCES Beenstock, M. (1982). The Robustness of the Black-Scholes Option Pricing Model. The Investment Analyst, October 1982, 30-40. Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy 82, 637-54. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Cox, J. C. and Rubinstein, M. (1985). Options Markets. Englewood Cliffs, NJ: Prentice-Hall. Debreu, G. (1959). Theory of Value: An Axiomatic Analysis of Economic Equilibrium. New York: Wiley. Friedman, M. (1953). The Methodology of Positive Economics. In: Essays in Positive Economics, pp. 637-54. Chicago: University of Chicago Press. Gibbard, A. and Varian, H. (1978). Economic Models. Journal of Philosophy 75, 664-77. McCormick, B. J., Kitchin, P. D., Marshall, G. P., Sampson, A. A., and Sedgwick, R. (1983). Introducing Economics. 3rd edition. Harmondsworth: Penguin.
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Mill, J. S. (1967). On the Definition of Political Economy. In: J. M. Robson (ed.), Collected Works, Vols. 4-5: Essays on Economics and Society, pp. 324-42. Toronto: Toronto University Press. Nagel, E. (1963). Assumptions in Economic Theory. American Economic Review: Papers and Proceedings 53, 211-19. Russell, B. (1913). On the Notion of Cause. Proceedings of the Aristotelian Society 13, 1-26.
Amos Funkenstein THE REVIVAL OF ARISTOTLE’S NATURE
1. The Problem In her recent book on Nature’s Capacities and their Measurement (1989), Nancy Cartwright argued forcefully for the recognition of “capacities” as an indispensable ingredient of causal scientific explanations. Idealizations in science assume them anyhow; abstract laws explain their causal impact; symbolic representation secures their proper formulation and formalization. So very satisfactory is the picture of the language and operation of science thus emerging that one wonders why the language of capacities, which indeed once dominated the language of science, was ever abandoned. Aristotle had based his systematic understanding of nature on potentialities (δυνάµεις) and their actualization; his terminology and perspective ruled throughout the Middle Ages, and was abandoned – at least explicitly – only in the seventeenth century. But why? The historical retrospection may also lead us towards some more systematic insights into the difficulties involved in the notion of nature’s capacities. These difficulties may not be insurmountable: and it may or may not turn out to be the case that we stand more to gain than to lose by readopting the lost idiom with due modification. With this hope in mind I shall begin a historical account which, needless to say, is highly schematized and therefore not above suspicion of bias or error.
2. Aristotle and the Aristotelian Tradition Aristotle’s language of “potentialities” and their “actualization” reflects his inability or unwillingness to view nature as uniform, homogeneous, always and everywhere “true to itself” – uniform in the sense that it is always and everywhere, “in Europe and in America,” ruled by the same laws (Newton 1687,
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 47-58. Amsterdam/New York, NY: Rodopi, 2005.
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p. 402).1 This latter view, I shall argue, eventually drove out the Aristotelian language of capacities, their realization or the lack thereof (“privation”). Indeed, Aristotle’s “nature” is rather a ladder of many “natures,” classified in orders down to the most specific nature. The “nature” of sublunar bodies was to him unlike the “nature” of celestial bodies. The former are made of a stuff which, by nature (φσύει), comes-to-be and decays; and its natural motion is “upwards” or “downwards” in a straight line – sublunar bodies are, of necessity, either light or heavy (1922, ã 2.301 a 20ff.). The latter are imperishable, and move by their nature in a perfect circle.2 Further down the ladder, we come across more particularized natures (forms) – until we reach the most specialized nature, the species specialissima. In order to secure the objectivity of his classification of nature, Aristotle commits himself to a heavy ontological, or at least a priori, assumption: namely, that a specific difference within a genus (say, rationality within mammals) can never appear in another genus (say, metals);3 at best he admits analogous formations (1912, A 4.644 a 15ff.). To this view of “natures” of diverse groups of things Aristotle’s predicatelogic was a most suitable “instrument” (organon). All scientific propositions, inasmuch as they gave account of the nature of things, should be able to be cast into the form S ε P. But what if S, a subject, actually lacks a predicate which “by nature” belongs to it? In the case of such an unrealized “capacity” Aristotle spoke of “privation” (στερήσις). So important to his scientific enterprise was this concept that he did not shy away from ranking it, together with form (ει’δός) and matter (υ‛πουείµενον), as chief “causes” or “principles” of all there is (1957, Λ 2, 1069 b 32-4; ∆ 22, 1022 b 22-1023 a 7; and cf. Wolfson 1947). But it is an ambiguous notion. Already the logicians of Megara recognized that it commits Aristotle to the strange view that a log of wood, even if it stays under water for the duration of its existence, is nonetheless “burnable” (Kneale and Kneale 1962, pp. 117-28). Worse still, while the negation of a negation, assuming the principle of excluded middle, is perfectly unequivocal, the negation of a privation is not; it either negates the proposition that S ε P or says that the proposition S ε P is a category mistake, but not both.4 ⎯⎯⎯⎯⎯⎯⎯ 1
I have elaborated this demand for homogeneity in my (1986), pp. 29, 37-9, and 63-97. The Greek “obsession with circularity” (Koyré) can be said to have ruled, unchallenged, until Kepler – even while any other astronomical presupposition, e.g., geocentricity, was debated. An exception of sorts – in very vague terms – were the atomists: cf. Cicero (1933), 1.10.24. 3 Aristotle (1958), Z 6.144 b 13ff., and (1957), Z 12, 1038 a 5-35. That Aristotle actually dropped this requirement in his biological research was argued by Furth (1988, pp. 97-8). He also joins those who maintain that Aristotle’s main objective was the complete description of species, not their hierarchical classification. On the methodological level, this principle corresponds to the demand not to apply principles of one discipline to another: Aristotle (1960), A 7.75 a 38-75 b 6. Cf. Livesey (1982), pp. 1-50, and Lloyd (1987), p. 184ff. 4 Because of this ambiguity, it could serve Maimonides’s negative theology as a way to generate divine attributes; cf. my (1986), p. 53, nn. 41 and 44. 2
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The coalescence of properties that makes a singular thing into that specific thing is its “form” – medieval schoolmen will speak of the “substantial form.” The form determines the capacities of a thing: if an essential property is missing “by accident” from that thing, we speak of a privation, as when we say that Homer was blind or Himmler inhuman. For, below the level of the infima species, what particularizes an object (down to its singular features) is matter, not form: wherefore Aristotle could never endorse Leibniz’s principle of the identity of indiscernibles. Only some unevenness in their matter explains why one cow has a birthmark on her left shoulder while her twin has none. Matter, however, can by definition not be cognited – if cognition is, as Aristotle thought, an assimilatory process of “knowing the same by the same,” an identity of the form of the mind with that of the object cognited.5 There is no direct knowledge of singulars qua singulars. Nor is it needed for the purposes of science, which always consists of knowledge of common features, of universals. Such, in broad outlines, was the meaning of “nature” in the most successful body of scientific explanations during antiquity and in the Middle Ages. Indeed, it articulated a deep-seated linguistic intuition. The Greek word φύσις, much as the Latin natura, is derived from the verb “to be born, to become” (φύω, nasci). The “nature” of a thing is the set of properties with which this thing came into the world – in contrast to acquired, “mechanical” or “accidental” properties. Milk teeth are called, in ancient Greek, “natural teeth” (φύσικοι o’δόντες). A “slave by nature” is a born slave, as against an “accidental” slave captured and sold by pirates or conquerors (Aristotle 1957, A5, 1254 b 25-32, and A6, 1255 a 3ff.). At times, custom will be called “second nature.” In short: the term “nature” was attached, in common discourse, to concrete entities. The set of properties with which something is born was its “nature.”6 Aristotle accommodated this intuition – with the important condition that such essential properties be thought of as capacities, as discernible potentialities to be actualized. Were there, in antiquity, other conceptions than Aristotle’s hierarchy of “natures,” anticipations of a more modern sense of the uniformity of nature? Indeed there were, but they remained, through the Middle Ages, vague and marginal. From its very beginning in the sixth century, Greek science sought the “causes” (αι’τία) of all things. This demand of the φυσιολόγοι reached its culmination with Parmenides, who postulated the existence of but one indivisible being (τò ‛o′ν), without differentiation or internal qualification, ⎯⎯⎯⎯⎯⎯⎯ 5
‛′µοιον ωˆ o‛µοίω see Schneider (1923). It is the basis for On the Aristotelian assumption of o Aristotle’s distinction between a “passive” intellect, which “becomes everything,” and an active intellect, which “makes everything” (πάντα γίγνεται – πάντα ποιειˆν) (1961, Γ5, 430 a 14-15). This distinction leads to later, far-reaching theories of the “active intellect.” 6 Hence also the conviction that, explaining the origin of a nation, one uncovers its nature or character: cf. Funkenstein (1981), especially pp. 57-9.
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without motion or change, negation or privation: it has, indeed, only a general “nature.” Every subsequent Greek cosmological theory had to take up the Parmenidean challenge; each of them tried to gain back something from the domain of “illusion” or “opinion” for the domain of truth. Democritus, Plato, and Aristotle, each of them in his own way, divided Parmenides’s one “being” into many – be they atoms, forms, or natures. Only the Stoics renewed the idea of the homogeneity of the cosmos, a cosmos filled with a homogeneous, continuous matter suspended in an infinite space and penetrated everywhere by one force – the πνευˆµα – which holds it together by giving it tension (τόνος) (Sambursky 1965; Lapidge 1978). The Stoic cosmos, like their ideal world-state (κοσµόλογις), was subject everywhere to the same rules (ι’σονοµία). Instead of Aristotle’s “natures” or “essential forms” they looked for forces: indeed, the very term δύναµις – Aristotle’s “potentiality” – came to mean an active, internal, actual force (Sambursky 1965, pp. 217-9; Lapidge 1978, pp. 163-5 (ποˆιον); Frede 1987, pp. 125-50). Inasmuch as an entity, a body, is saturated with πνευˆµα, it desires to preserve its existence: “omnis natura vult esse conservatrix sua.” All forces seemed to them as so many expressions of one force, which is God and nature at once – and of course also “matter”: “Cleanthes totius naturae mentis atque animo hoc nomen [dei] tribuit” (Cicero 1933, 1, 14, 37 and 4, 17, 16). Here nature is a totality. But its “capacities” are always actualized. In fact, Stoic logic, like the Megarian, did not recognize unactualized possibilities: the possible is that which happens at some time (Mates 1953, pp. 6, 36-41). Still another source for a more uniform “nature” was, in later antiquity as in the Middle Ages, the Neoplatonic conception of light as prime matter and all pervasive: “natura lucis est in omnibus” (Witelo 1908, 7.1, 8.1-4, 9.1-2; cf. also Crombie 1962, pp. 128-34). Close attention to Witelo’s wording reveals the two almost incompatible notions of “nature” at work: light is a definite body with a specific “nature” – this is the Aristotelian heritage; but it is in everything and everywhere – this is the Stoic, and sometimes Neoplatonic, sense of a homogeneous universe. A minority tradition in the Middle Ages, this view became popular, in many varieties, during the Renaissance. In their campaign against Aristotelianism, Renaissance philosophers of nature tried to revive alternative traditions – Presocratic, Stoic and Epicurean (Barker 1985; Barker and Goldstein 1984).
3. The Decline of the Aristotelian-Thomistic “Forms” While these deviant traditions were not without importance in the preparation for an alternative scheme of nature, a more serious and enduring challenge to Aristotle arose within the scholastic discourse itself in the turn from the
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thirteenth to the fourteenth centuries. Aristotle relegated the differences between singulars of the same species specialissima to matter; matter is his (and Thomas’s) “principle of individuation.” Consequently, since knowledge is always knowledge of forms (whereby the knower and the known become identical),7 and since matter is that substrate which remains when forms are abstracted, individuals (singulars) can be known only by inference. As mentioned above, Aristotle could never have endorsed Leibniz’s principle of the identity of indiscernibles (and nor could Thomas) (Funkenstein 1986, pp. 135-40, 309-10). The theological difficulties of this position were numerous. It prevented God from creating more than one separate intelligence (angel) of the same species, since separate intelligences lack matter. It made individual post-existence almost impossible to account for. It posed difficulties for the beatific vision – knowledge of individuals qua individuals without the mediation of the senses (Day 1947). For these and other reasons, the whole scholastic discourse was changed between Thomas Aquinas and William of Ockham; and much of the change must be credited to Duns Scotus, who gave up “substantial forms” for the sake of a coalescence of many common forms in every singular being down to an individual form of “haecceity.” He also postulated an immediated, “intuitive” cognition of singulars qua existents: form, not matter, particularizes every individual down to its very singularity (Tachau 1988; Hochstetter 1927; Funkenstein 1986, p. 139, n. 42). Ockham and his followers even denied the need for a “principle of individuation”: individual things exist because they do, and their intuitive cognition is the ultimate basis for simple terms (incomplexa) which build propositions (complexa), scientific or other. “Forms,” “natures,” “universals” are no more than inductive generalizations of properties. They ceased to be the backbone of the understanding of “nature” (cf. also Eco 1988, pp. 205-10, and Pererius 1592, pp. 87-8). Whatever Aristotle’s physics declared to be conceptually impossible and contrary to nature, now became a possibility from the vantage point of God’s absolute power (de potentia Dei absoluta) – as long as it did not violate the principle of non-contradiction (see Funkenstein 1986, pp. 115-52, and the literature mentioned there). If he so wished, God could make stones move habitually upwards, or make the whole universe move rectilinearly in empty space, or save humankind not by sending his son, but rather with a stone, a donkey, or a piece of wood. With their penchant for devising counterfactual worlds, the schoolmen of the fourteenth century sought to enlarge the domain of God’s omnipotence without violating any purely logical principle; they virtually introduced Leibniz’s distinction between logical and less-than-logical necessity, ⎯⎯⎯⎯⎯⎯⎯ 7
Above, n. 5.
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a distinction the ancients never made. Every order or nature was to them at best an empirical, contingent fact. How far did the new discourse really permeate the explanation of natural phenomena? A telling example of the sixteenth century shows how indeed Aristotle’s “natures,” “forms,” or Thomas’s “substantial forms” (with their natural capacities) were in fact dethroned, and turned into mere properties or forces. In his treatise on “Fallacious and Superstitious Sciences,” Benedict Pereira – whose works were read by Galileo – summed up, among other matters, the history and the état de question of discussions concerning the value of alchemy, and concluded: No philosophical reason exists, either necessary or very probable, by which it can be demonstrated that chemical accounts of making true gold are impossible (Pererius 1592, pp. 87-8).
The arguments against turning baser metals into gold that he found in the Aristotelian-Thomistic tradition (Avicenna, Averroës, Thomas, Aegidius Romanus) were all variations on the assumption that a substantial form induced by a natural agent cannot be induced artificially. Artificial gold may, they said, resemble natural gold, but it will always differ from it in some essential properties (amongst which is the therapeutic value of gold for cardiac diseases): just as a louse generated inorganically from dirt will differ in specie from a louse with respectable organic parents (Pererius 1592, pp. 75-82, esp. p. 78). Pereira discards this argument as unwarranted. The natural agent that molds other metals into gold is the sun’s heat, a property shared by fire, which can certainly be induced artificially – at least in principle. Yet Pereira, too, believed that it is, with our technical means, impossible to do so and that claims of success are fraudulent. While possible in principle, given our tools, knowledge and the fact that no case has been proven, it seems to him that it will at best be much more expensive to generate gold artificially, even should we know one day how to do so, than it is to mine it. The “forms” have visibly turned into qualities and forces – here as elsewhere in the natural philosophy of the Renaissance. Empirical evidence rather than a priori argument governs even the scholastic dispute. And the distance between the natural and the artificial seems considerably undermined. A new language of science was about to be forged. The role of fourteenth century scholastic debates in this process was largely a critical one: to purge the scientific discourse of excess ontological baggage.
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4. Galileo’s Idealizations It became, then, increasingly unfashionable to ascribe natural “capacities” or “tendencies” to specific substances in an absolute sense. Now it is worthwhile to look at the process by which they were actually dethroned, their place to be occupied by “forces” or “tendencies” common to all bodies. Seldom can the actual point of transition from medieval to classical physics be identified as clearly as in the case of Galileo. As a young professor of mathematics in Pisa he tried to account for the free fall of bodies in the following way. When a body is heaved or thrown upwards, it accumulates an “impetus.”8 It is also endowed with more or less “gravity,” depending on its specific weight. Now, as long as g
This is the language of the late medieval impetus mechanics, initiated by Olivi and Franciscus de Marchia, developed by Buridan and Oresme, held still by Dominicus de Soto. It responded to the most embarrassing question in Aristotle’s mechanics: why does a projectile continue to move cessante movente? Cf. Wolff (1978), and my (1986), pp. 164-71. 9 Galilei (1890-1909); Clavelin (1974), pp. 120ff., esp. 132-3 on the hydrostatic analogy; Drake (1978), pp. 21-32, esp. p. 28ff. on Pereira as the source from which Galileo learned the Hipparchian hypothesis.
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continue to move with uniform velocity. Now, given that uniform acceleration can be expressed in terms of uniform motion v = (v0 + vt)/2, an application of this “mean speed theorem” to the distance traveled in the time t, renders the formula for the free fall (see Funkenstein 1986, pp. 171-4 for the literature). If g be the steady increment, at any time unit, no matter how small, then (in our notation) d = g/2 + 3g/2 + 5g/2 + . . . + gt/2 = [g + (t – 1)g] t/2 = gt2/2; Galileo’s notation was geometrical. I have schematized Galileo’s reasoning to some extent, but not overly so. Without the free-fall law, he could not have found the parabolic path of a trajectory; without the latter, Newton could not have proven that the same law that governs free fall also keeps the earth in an elliptic orbit around the sun. Its importance has never been exaggerated. Two new mental habits, it seems to me, made this achievement possible, one theoretical and one practical. The theoretical habit was the willingness to accept counterfactual states as asymptotically approachable limiting cases of reality. The implicitly employed principle of inertia describes such a limiting case, and I shall return to its discussion presently. The practical bent of mind that changed since the Middle Ages was the ability to measure accelerations by means of a mechanical clock. One cannot measure accelerations with sundials or common types of sand-clocks. Galileo united the two.
5. Idealizations or Capacities These, then, were the historical circumstances in which the language of capacities was abandoned and another idiom – that of idealizations – appropriated. We should not, however, fall into the fallacy of origins: the fact that capacities were abandoned does not constitute an irrefutable argument against them. The antiAristotelian zealotry of early modern science may have blocked advantageous strategies for explaining nature. Perhaps “nature” is not homogeneous after all. Or perhaps, albeit uniform, it is inhabited with a multitude of free-floating “capacities” – not capacities of this or that particular class of objects (“natures” in the Aristotelian sense) but capacities of one and the same “nature” (in the singular). And perhaps – such, I believe, is Nancy Cartwright’s argument – idealizations (of the Galilean type) presuppose capacities anyway. The former arguments are a matter of creed; the latter is not. In her book, Nancy Cartwright quotes my statement that, for Galileo, the limiting case, even where it did not describe reality, was the constitutive element in its explanation; and argues that it is
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a glaring non sequitur. Funkenstein has been at pains to show that Galileo took the real and the ideal to be commensurable. Indeed, the section is titled ‘Galileo: Idealization as Limiting Cases.’ So now, post-Galileo, we think that there is some truth about what happens in ideal cases; we think that that truth is commensurable with what happens in real cases; and we think that we thereby can find out what happens in ideal cases. But what has that to do with explanation? We must not be misled by the ‘ideal.’ Ideal circumstances are just some circumstances among a great variety of others, with the peculiarly inconvenient characteristic that it is hard for us to figure out what happens in them. Why do we think that what happens in those circumstances will explain what happens elsewhere?
Because, she continues, [w]hen nothing else is going on, you can see what tendencies a factor has by looking at what it does . . . but only if you assume that the factor has a fixed capacity that it carries with it from situation to situation (1989, pp. 189-91).
Now, I would argue that capacities (or, in the case of Galileo, forces) depend, for their articulation, on ideal cases rather than vice versa. Cartwright would have been right if ideal cases were only an inductive extrapolation from real cases, the corroboration, so to say, of an interpretive hunch we gather from looking at a series of situations in which one or more variables (“disturbing factors”) is diminished continuously. If, however, the “ideal case” is not “just some circumstances among others” but a circumstance in which Galileo knows a priori that such-and-such is the case – say, that a body will continue its rectilinear, uniform motion – then the ideal case is nothing but an explication or articulation of what we mean when we say that a body has the “capacity” or “tendency” to so move. The other, more blurred cases, which certainly can be interpreted many ways, now are measured by the yardstick of the ideal case. This is what Galileo meant by “explaining,” and indeed Cartwright admits that [t]he fundamental idea of the Galilean method is to use what happens in special or ideal cases to explain very different kinds of things that happen in very non-ideal cases (1989, p. 191).
It seems as if Cartwright’s “capacities” and my “idealizations”10 are locked into a hermeneutical circle of sorts. To say that a body under ideal conditions will necessarily act in such-and-such way amounts, of course, to saying much more than that it has the possibility of so acting: in looking for a cause of the behavior of that body, I name it “capacity” or “force.” On the other hand, to say that a body has the capacity to act in such-and-such a way even if this capacity is never fully actualized can mean several things. If we deal with a capacity that is specific to a certain class of bodies (or even to most bodies) but is not actualized in this particular body, no limiting cases are required; it is a more or ⎯⎯⎯⎯⎯⎯⎯ 10
Meaning: ideal conditions as asymptotically approachable limiting cases.
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less legitimate inductive generalization. If, however, we mean that this capacity is never actualized under real conditions, then to say that this body has the capacity in question is to say nothing more than that, under ideal conditions, it would act in a certain way. Such is the case of “Galilean idealizations,” in which we are dealing with a capacity – if one prefers to call it so – which all bodies share albeit they never actually manifest it. The ideal conditions define the “capacity” in question. Within a uniform, homogeneous nature there is, then, no further meaning to “capacities” but “idealizations.” Yet the uniformity of nature is, in itself, only an ideal of science, an ideal that emerged, for better or worse, in the seventeenth century. Could it be that the ideal is a mistaken or misguided one? Indeed it could be the case, and, if so, then our discussion of “capacities” would take a different turn. In a nature like Aristotle’s, in which different objects (or classes of objects) have profoundly different properties, the language of “capacities” seems much more suitable, since it indicates precisely the circumstance that while, under certain (even ideal) conditions, bodies of a certain kind behave in a certain way, other bodies do not. Hadrons act on each other in a different way than leptons. Now, here we enter the realm of ideals – or visions – of science; and we are free to choose among them. Modern physicists seek to unite all four forces of nature – but the quest for a unified theory may be a hunt for the snark. Kant, who endorsed the principle of parsimony (which ultimately guides the vision of a uniform nature) – “entia praeter necessitatem non sunt multiplicanda” – balanced it with a contrary principle or regulative idea, namely “not to fear the variety of nature” (1964, B670-96).11 Amos Funkenstein was the Koret Professor of Jewish History in the Department of History at the University of California, Berkeley, and University Professor at the University of California
REFERENCES Aristotle (1912). De Partibus Animalium. Edited by W. D. Ross. Oxford: Clarendon Press. Aristotle (1922). De Caelo. Edited by J. L. Stocks. Oxford: Clarendon Press. Aristotle (1957). Metaphysica. Edited by W. Jaeger. Oxford: Clarendon Press. Aristotle (1957). Politics. Edited by W. D. Ross. Oxford: Clarendon Press.
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Kant’s account of contradictory regulative ideas which are sustained nonetheless in the “interest of reason” reminds one of the principle of complementarity – except that it operates only at the metatheoretical level, never in the interpretation of a concrete phenomenon.
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Aristotle (1958). Topics. Edited by W. D. Ross. Oxford: Clarendon Press. Aristotle (1960). Posterior Analytics. Translated by H. Tredennick. Cambridge, Mass.: Harvard University Press. Aristotle (1961). De Anima. Edited by W. D. Ross. Oxford: Clarendon Press. Barker, P. (1985). Jean Pena (1528-58) and Stoic Physics in the Sixteenth Century. The Southern Journal of Philosophy 23, Supplement, 93-107. Barker, P. and Goldstein, B. R. (1984). Is Seventeenth Century Physics Indebted to the Stoics? Centaurus 27, 148-64. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Cicero, M. T. (1933). De natura deorum. Translated by H. Rackham. London: W. Heinemann. Clavelin, M. (1974). The Natural Philosophy of Galileo: Essay on the Origins and Formation of Classical Mechanics. Translated by A. J. Pomerans. Cambridge, Mass.: The M.I.T. Press. Crombie, A. C. (1962). Robert Grosseteste and the Origins of Experimental Science, 1100-1700. Oxford: Clarendon Press. Day, S. J. (1947). Intuitive Cognition: A Key to the Significance of Later Scholastics. St. Bonaventure, N. Y.: The Franciscan Institute. Drake, S. (1978). Galileo at Work His Scientific Biography. Chicago: University of Chicago Press. Eco, U. (1988). The Aesthetics of Thomas Aquinas. Translated by H. Bredin. Cambridge, Mass.: Harvard University Press. Frede, M. (1987). Essays in Ancient Philosophy. Minneapolis: University of Minnesota Press. Funkenstein, A. (1981). Anti-Jewish Propaganda: Ancient, Medieval and Modern. The Jerusalem Quarterly 19, 56-72. Funkenstein, A. (1986). Theology and the Scientific Imagination from the Middle Ages to the Seventeenth Century. Princeton, N.J.: Princeton University Press. Furth, M. (1988). Substance, Form and Psyche: An Aristotelean Metaphysics. Cambridge: Cambridge University Press. Galilei, G. (1890-1909). Le Opere di Galileo Galilei. Edited by A. Favaro. Florence: Tip. di G. Barbèra. Hochstetter, E. (1927). Studien zur Metaphysik und Erkenntnislehre Wilhelms von Ockham. Berlin, Leipzig: W. de Gruyter. Kant, I. (1964). Kritik der reinen Vernunft. Vol. 4 of Werke. Edited by W. Weischedel. Frankfurtam-Main: Suhrkamp. Kneale, W. C. and Kneale, M. (1962). The Development of Logic. Oxford: Clarendon Press. Lapidge, M. (1978). Stoic Cosmology. In J. M. Rist (ed.), The Stoics, pp. 161-85. Berkeley: University of California Press. Livesey, S. J. (1982). Metabasis: The Interrelationship of the Sciences in Antiquity and the Middle Ages. Ph.D. dissertation, University of California, Los Angeles. Lloyd, G. E. R. (1987). The Revolutions of Wisdom: Studies in the Claims and Practice of Ancient Greek Science. Berkeley: University of California Press. Mates, B. (1953). Stoic Logic. Berkeley: University of California Press. Newton, I. (1687). Philosophiae Naturalis Principia Mathematica. London: J. Societatis Regiae ac Typis J. Streater. Pererius, B. (1592). Benedicti Pererii Valentini e Societate Iesv Aduersus fallaces & superstitiosas artes, id est, De magia, de obseruatione somniorum, & de diuinatione astrologica, libri tres. Lvgdvni : Ex officina Ivntarvm. Sambursky, S. (1965). Das physikalische Weltbild der Antike. Zürich: Artemis Verlag. Schneider, A. (1923). Der Gedanke der Erkenntnis des Gleichen durch Gleiches in antiker und patristischer Zeit. In C. Baeumker (ed.), Beiträge zur Geschichte der Philosophie des Mittelalters, Texte und Untersuchungen, Supplement 2, pp. 65-76. Münster: Aschendorff. Tachau, K. (1988). Vision and Certitude in the Age of Ockham: Optics, Epistemology, and the Foundations of Semantics, 1250-1345. Leiden, New York: E.J. Brill.
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Wallace, W. A. (1984). Galileo and His Sources: The Heritage of the Collegio Romano in Galileo’s Science. Princeton, N.J.: Princeton University Press. Witelo (1908). Liber de intelligentiis. In C. Baeumker (ed.), Witelo, ein Philosoph und Naturforscher des XIII. Jahrhunderts, 1-71. Münster: Aschendorff. Wolff, M. (1978). Geschichte der Impetustheorie: Untersuchungen zum Ursprung der klassischen Mechanik. Frankfurt-am-Main: Suhrkamp. Wolfson, H. A. (1947). Infinite and Privative Judgements in Aristotle, Averroës, and Kant. Philosophy and Phenomenological Research 7, 173-87.
James R. Griesemer THE INFORMATIONAL GENE AND THE SUBSTANTIAL BODY: ON THE GENERALIZATION OF EVOLUTIONARY THEORY BY ABSTRACTION
1. Introduction This essay is about the nature of Darwinian evolutionary theory and strategies for generalizing it. In this section I sketch the main argument. In this essay I describe some of the limitations of classical Darwinism and criticize two strategies to get around them that have been popular in the philosophical literature. Both strategies involve abstraction from the entities that Darwin talked about: organisms in populations. One strategy draws on the notion of a fixed biological hierarchy running from the level of biological molecules (like DNA and proteins) through cells, organisms, and groups on up to species or ecological communities. As a consequence, evolution is thought to operate at any level of the hierarchy whenever certain properties hold of the “units” at that level. The other strategy rejects this hierarchy, in part because it seems strange to imagine the evolutionary process “wandering” from level to level as it alters the properties of organisms and populations, creating and destroying the conditions for its operation. The second strategy constructs a different, two-level hierarchy of “interactors” and “replicators” by abstracting functional roles of organisms and their genes. The second strategy simplifies analysis of the sorts of properties deemed essential by the first, but also describes the key process of natural selection as operating at a single ontological level (when it does operate). Along with these virtuous ontological simplifications, however, the second strategy raises metaphysical problems for both strategies, suggesting that neither is on the right track. I trace these further problems to two features the strategies share. To do this, I offer a twist to Cartwright and Mendell’s (1984) view of abstraction in science which relativizes the degree of abstractness of an object to an Aristotelian theory of explanatory kinds. I focus on science as a process rather than on the
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 59-115. Amsterdam/New York, NY: Rodopi, 2005.
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structure of scientific objects and suggest that, for purposes of theory generalization, abstraction is relative to an empirical, rather than a metaphysical, background theory. Scientific background theories do roughly the same work in my view that Aristotle’s conception of four types of explanatory causes does in Cartwright and Mendell’s: things are more abstract if they have causes specified in fewer explanatory categories. Because I seek to understand abstraction as a scientific process rather than as a formal structure, our projects differ on where to seek explanatory categories: in metaphysical theories such as Aristotle’s or in empirical background theories. The two abstraction strategies for generalizing evolutionary theory both depend on an empirical background theory of biological hierarchy for explanatory categories. In addition, both strategies rely on theories of hierarchy to ground their abstractions. The first strategy assumes “the biological hierarchy” as a structural framework within which to formulate evolutionary theory as a set of functions without any justification. As a result, it is difficult to apply the generalized theory to biological entities not easily located among its a priori compositional levels. The background theory of hierarchy ought to guide us through applications of the generalized evolutionary theory to problematic cases, but only the fact, not the theory of hierarchy is specified. This lends the mistaken impression that the levels of the hierarchy are unchangeable facts of conceptual framework rather than empirical products of evolution itself, even though many major phases of evolutionary history – origins of cells, eukaryotes, sex, embryogenesis, sociality – involve the creation of new levels of organization. The second strategy assumes a well-developed, but false background theory. I will call this theory “molecular Weismannism” to distinguish it from views held by August Weismann. A central aim of the paper, in distinguishing Weismann from Weismannism, is to isolate the role in the second strategy of the twentieth-century concept of molecular information from its nineteenth-century roots in material theories of heredity. Information has been made to do too much of the explanatory work in philosophical accounts of evolutionary theory and too many of the explanatory insights of the old materialism have been lost. The problem has become acute because evolutionary theory has become hierarchical. Information provided a useful interpretive frame for working out aspects of the genetic code in the 1960s (at the dawn of the “information age”), but that was when evolution was a single-level theory about the evolution of organisms. Now, evolution is about all possible levels of biological organization. Biologists and philosophers tell nice stories about how the levels fit together, but they are more rhetoric and sketch than flesh and blood theory. The problem is how to square the information analysis at the molecular level with the belief that evolution may occur at a variety of levels: the more seriously one takes information, the more likely one is to deny that evolution happens at any level other than that of the gene. If one takes information too seriously, it
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can even come to replace the molecular concept of the gene altogether. The result is a theory that genes are evolutionary information. Hence if evolution occurs at other levels, there must be “genes” at those levels. As formal theory, this reflexive definition of the gene in terms of evolutionary theory works, but it deprives empirical science of the conceptual resources needed to look for material evidence of genes at other levels. Thus the problem of squaring information with a belief in hierarchical evolution is replaced by the problem of squaring a philosophical exposition of the formal structure of evolutionary theory with the fuller, richer resources needed for evolutionary science. Undoubtedly I place too much emphasis on information here, but it is a pressure point: something is rotten in Denmark and it is yet unclear whether the rot is a small piece or the whole cheese. Molecular Weismannism is a theory relating genes and organisms as causes and effects. It appears to be a species of pure functionalism whose theoretical entities are defined solely in terms of their evolutionary effects, as a result of the operation of the evolutionary process. It replaces Weismann’s nineteenthcentury analysis of the flow of matter (germ- and somato-plasm) with a flow of molecular information as basic to evolutionary theory. I say “appears” because contingent, material features of the traditional organizational hierarchy invoked by the first strategy are tacitly smuggled into the inferences made under the second strategy. Insofar as claims to ontological simplification due to the concept of “informational gene” rest on the purity of the functionalism, contamination by material and structural considerations casts doubt on these claims. In contrast to purists of the second strategy, I find this contamination useful and instructive. I see a return to a more materialist conception of the gene as part of an alternative strategy to formulate multi-level evolutionary theory. I argue further that molecular Weismannism misrepresents important features of the complex relationship between genes and organisms. One of the most interesting representations concerns its analysis of the “lower” level of the two-level hierarchy, the level of replicators or informational genes. The copying process by which DNA transmits genetic information is taken to be the model replication process, but consideration of the molecular biology reveals important disanalogies between gene “replication” and copying processes. The disanalogies raise doubts about the adequacy of an evolutionary theory that defines replication and replicators in terms of copying and indeed raise serious questions about the applicability of the concept of information to the evolutionary analysis of replication. A more crucial point is that the disanalogies are revealed by taking into account the very properties of biological matter (the details of how genes “code” information) that are supposed to be removed by abstraction in a successful generalization of evolutionary theory. If correct, this critique undermines the use of molecular Weismannism as a purely functionalist basis for “generalization-by-abstraction.” The criticism rests on the worry that
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the genic mechanisms that are supposed to characterize the evolutionary functions of genes may be peculiar to the genic level, and therefore ill-suited to serve as the basis for a general theory, i.e., one that describes similar functions of mechanisms operating at other levels.1 I argue that the problem is not, as the functionalists argue, that particular material bodies only contingently realize or instantiate certain biological functions and therefore are irrelevant to the general analysis of selection processes, which must rely on necessary conditions for the functions themselves. Rather, the problem is to identify certain relations that hold among the material bodies which perform the functions. Since I will argue that in biology, material as well as functional conditions are relevant to the general analysis of selection processes, some abstraction or generalization strategy other than the pure functionalism examined below seems needed. My diagnosis of the trouble is that molecular Weismannism is a poor substitute for a full theory of development relating genes and characters, genotypes and phenotypes, genomes and phenomes. In its particular idealizations and abstractions, molecular Weismannism has gotten key facts about the causal structure of development wrong. Molecular Weismannism has at its core two components that seem to make it well-suited to be a background theory: (1) a simple part-whole relation between genes and organisms, and (2) an inference from this compositional relationship to the causal structure relating genes and organisms within embryological development and also among generations. These ideas together entail some of the same facts as other, more adequate theories of development (e.g., Weismann’s own theory) but this is not a sufficient reason for adopting molecular Weismannism. The weaknesses of molecular Weismannism make it ill suited to the work it is supposed to do in generalizing evolutionary theory. Moreover, its flaws are easily discovered by following the “flow” and rearrangement of matter during reproduction. Comparison of reproduction with the abstractly characterized “flow” of information in gene replication suggests that a more adequate basis for generalizing evolutionary theory will rest with reproduction and a richer theory of development, not with the informational gene and its replication. One implication of renewed attention to the material basis of evolutionary theory after the “informational turn” in biology is the recognition that the logic of development can shed considerable light on the general analysis of evolution. Proximate and ultimate biology – Mayr’s terms to distinguish the rest of biology from evolution – can be distinguished as conceptual categories, but the ⎯⎯⎯⎯⎯⎯⎯ 1 I take it that reference to a mechanism implies reference to the matter out of which the mechanism is constructed. To take an ordinary example, to speak of a watchwork mechanism for telling time is to speak of specific (even if not specified), concrete materials arranged in such a way that under certain specifiable conditions, the mechanism is caused to operate in a specifiable way or to perform a specifiable function. Thus, mechanistic explanations are more concrete than either purely functional (no reference to matter) or purely structural (no reference to motion) explanations.
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dynamics of theory elaboration routinely require crossing the boundaries between them. In particular, it is a theory of development, not evolution, that must reveal how descent relations are different from mere cause-effect relations and why material overlap – having parts in common – between ancestors and descendants arranged in lineages is universal in biology.
2. The Generality of Darwin’s Theory of Evolution Darwin’s theory of evolution by natural selection is restricted in scope. One sense in which it is restricted is that it refers to organisms. The form that a generalized evolutionary theory should take is an outstanding conceptual problem in biology. Darwin’s theory of evolution is a theory of descent with modification. The two component processes of descent and modification operating together in populations can be invoked to explain facts of adaptation and diversity. Darwin’s achievement was to argue successfully that evolution had occurred in nature and that natural selection is an important, perhaps the most important, mechanism of modification operating within generations. Darwin’s theory is commonly characterized as an “umbrella theory,” unifying explanations of diverse biological phenomena. However, many biologists have questioned whether the theory is umbrella enough, in the mathematical form given it by population genetics, to cover phenomena from the lowest molecular to the highest taxonomic and ecological levels. The (apparently) restricted character of biological theories, as compared to the universal form of physical theories, suggests to some philosophers not only a difference but also an inadequacy of biological theories. Some apologists for evolutionary theory argue that because biology is a historical science, the restricted scope of its theories is to be expected and is appropriate. Nevertheless, one wonders whether evolutionary theory’s restrictedness is really grounded in its content, an artifact of biologists’ focus on restricted classes of concrete phenomena, or instead due to a genuine conceptual difficulty in formulating general biological theories. Darwin’s own formulation of his theory of evolution is clearly restricted in scope. It is evident that Darwin expressed his theory so as to apply to organisms, for which he frequently used the term ‘individual’: Owing to this struggle for life, any variation, however slight and from whatever cause proceeding, if it be in any degree profitable to an individual of any species, in its infinitely complex relations to other organic beings and to external nature, will tend to the preservation of that individual, and will generally be inherited by its offspring. The offspring, also, will thus have a better chance of surviving, for, of the many individuals of any species which are periodically born, but a small number can survive. I have called this principle, by which each slight variation, if useful, is
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preserved, by the term of Natural Selection, in order to mark its relation to man’s power of selection (Darwin 1859, p. 61).
Although quite central to biology, organisms constitute only one form of biological organization and manifest only some of the diverse phenomena of interest to evolutionists. Moreover, evolutionists have not come to grips with all the sorts of organismal phenomena that biologists have already described. At least three forms of restriction are evident in the above passage: 1. Darwin’s theory is a theory of evolution (primarily) by means of natural selection. It does not (adequately) cover evolution by other means, such as genetic drift or “biased” (so-called Lamarckian) inheritance. 2. Darwin’s is a theory of the evolution of organisms (in populations).2 However, it supplies no criterion for individuating organisms. Rather, Darwin presented exemplary cases of organismal evolutionary analysis in On the Origin of Species, leaving vague the intended, let alone the actual, scope of the theory. Despite the profound faith of some biologists, it is uncertain whether neo-Darwinian theory, as developed in the twentieth century to include population genetics and the conceptual apparatus of the evolutionary synthesis, fully applies to clonal organisms, plants, symbiotic protists, bacteria, and viruses. As Hull puts it, the bias of evolutionists is to treat the higher vertebrates as the paradigm organisms, despite their rarity and atypicality.3 3. Darwin’s is a theory of selection operating at the organismal level. But biology concerns many levels of organization, from molecules to organelles, to cells, to organisms, to families, groups, populations, species, higher taxa and ecological communities. Many evolutionists suspect or believe that selection may occur at many levels of organization, but it is uncertain whether Darwin’s theory applies without modification to these other levels or exactly what modifications might be needed, or even how the levels should be individuated.4 In addition, many philosophers and some biologists expect that evolutionary theory in a broad sense applies to cultural and/or conceptual change. It is controversial what form a theory of cultural or conceptual evolution should take and whether it would turn out to be a generalization of Darwinism or of some other, “non-Darwinian,” theory ⎯⎯⎯⎯⎯⎯⎯ 2
Lewontin (pers. comm.) argues that Darwin’s theory is inherently hierarchical because it explains the evolution of populations (ensembles) in terms of causes such as natural selection operating on the members. Nevertheless, this fact about evolution’s hierarchical character alone does not suffice to make the theory general. Rather, it merely divides the elements of the theory (account of causes, account of effects) into accounts at different descriptive levels. 3 Hull (1988). See also Jackson et al. (1985) and Buss (1987). 4 The fact that Darwin explored a “kin selection” explanation of the evolution of traits in sterile castes of social insects establishes neither that the scope of his theory includes all levels of organization nor that the theory adequately covers kin groups.
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(Boyd and Richerson 1985; Hull 1988; Griesemer 1988; Griesemer and Wimsatt 1989).
3. Lewontin’s Generalization-by-Abstraction One way to generalize neo-Darwinian theory is by abstraction, removing the reference to organisms to make the theory applicable to any level of organization. There are two prominent abstraction strategies in the units of selection literature. The first takes the biological hierarchy to define a set of entity types, names of which may be substituted for occurrences of ‘organism’ to produce a more general theory. There are several ways one might construe the project of generalizing evolutionary theory. One strategy involves abstraction as a process of representing objects of scientific explanation.5 An important “Platonic” conception is that abstraction is a mental process by which properties are thought of as entities distinct from the concrete objects in which they are instantiated. On an alternative, Aristotelian conception, abstraction is the mental process of subtracting certain accidental properties from concrete objects so as to regard objects in a manner closer to their essential natures. Objects so considered still have properties of actual substances, but they are regarded in isolation from accidental features, such as the material in which a particular concrete triangle is inscribed. The generalization strategy in selection theory on which I shall focus below takes certain functions (replication, interaction) to be essential to the entities that participate in selection processes and the matter that implements these functions with concrete mechanisms to be accidental contingencies of the actual history of life on Earth. The view of abstraction relevant to science that serves as a framework for this essay is a modification of the Aristotelian notion due to Cartwright and Mendell (Cartwright and Mendell 1984). They point out that the Aristotelian concept does not lead to a strict ordering of things from concrete to abstract since there is no obvious way to count properties to determine which of two entities has more of them, and hence is more concrete. They modify this conception to consider kinds of explanatory properties, following an Aristotelian model of four kinds of cause – material, efficient, formal and final – mention of which they require to count an explanation complete. Their revision leads not to an analysis of the abstract, but to a partial-ordering criterion for degrees of relative abstractness: ⎯⎯⎯⎯⎯⎯⎯ 5
Duhem (1954); Cartwright and Mendell (1984); Cartwright (1989); Darden and Cain (1988); Griesemer (1990). The last discusses the basis of abstraction as a process in the “material culture” of science rather than in a logic of the abstract.
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The four causes of Aristotle constitute a natural division of the sorts of properties that figure in explanation, and they thus provide a way of measuring the amount of explanatory information given. We can combine this with the idea of nesting to formulate a general criterion of abstractness: a) an object with explanatory factors specified is more concrete than one without explanatory features; and b) if the kinds of explanatory factors specified for one object are a subset of the kinds specified for a second, the second is more concrete than the first (Cartwright and Mendell 1984, p. 147).
In light of this view of degrees of explanatory abstraction, how might evolutionary theory be generalized? One way is to abstract from organisms by subtracting the reference to them in the statement of Darwin’s principles (or more accurately: by subtracting the reference to their form and matter). That way, the principles may be taken to range over any entities having “Darwinian” properties regardless of whether these are such as to lead us to call them organisms or even whether they are material objects at all. Abstraction is a central device for removing the reference to organisms in the two most prominent programs for generalization discussed in the “units of selection” literature.6 The first strategy stems from the work of Richard Lewontin, who characterized Darwinian evolutionary theory in terms of three principles which he claimed are severally necessary and jointly sufficient conditions for the occurrence of the process of evolution by natural selection.7 Lewontin suggested, in effect, ⎯⎯⎯⎯⎯⎯⎯ 6
It should be noted that some prefer to distinguish two problems: the “units” of selection problem and the “levels” of selection problem (see Hull (1980) and Brandon (1982)). For recent reviews of the units and levels of selection problems, see Mitchell (1987), Hull (1988), Lloyd (1988), and Brandon (1990). Hull (1988, ch. 11) gives an especially thorough review of the two programs with the issue of strategies of theory generalization clearly in mind. Lloyd (1988) gives a detailed semantic analysis in terms of abstract entity types. 7 “1. Different individuals in a population have different morphologies, physiologies, and behaviors (phenotypic variation). 2. Different phenotypes have different rates of survival and reproduction in different environments (differential fitness). 3. There is a correlation between parents and offspring in the contribution of each to future generations (fitness is heritable)” ( Lewontin 1970, p. 1). Much of the units of selection literature concerns whether these principles are necessary and sufficient, as Lewontin claimed. Wimsatt (1980, 1981) argues that Lewontin’s principles give necessary and sufficient conditions for evolution by means of natural selection to occur, but only necessary conditions for entities to act as units of selection. Wimsatt claims an additional constraint on the conditions must be made in order to distinguish entities which are units of selection from entities merely composed of units of selection. Lloyd (1988) argues that Wimsatt’s criteria require still further refinement. Sober (1981, 1984) and Brandon (1982, 1990) argue that the Lewontinian, “additivity” or “units” of selection approach fails to address the central problem of describing evolution as a causal process, but differ as to the form a causal analysis should take. Others (e.g., Sterelny and Kitcher 1988) reject this causal interpretation, arguing that the units of selection problem rests on matters of convention for representing allelic fitnesses in their appropriate genetic contexts. Although these are important problems, they are not of direct concern here. Rather, the topic at hand is the abstraction strategy used in generalization regardless of which of these views is
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that if the term ‘individual’ occurring in the statement of Darwin’s principles is replaced by a term denoting an entity at another level of organization, then the principles successfully describe an evolutionary process at that level. Hence, although Darwin stated his principles in terms of the organismal or “individual” level, they can be interpreted generally to mean “that any entities in nature that have variation, reproduction, and heritability may evolve.”8 The form of this first strategy can be characterized as “levels abstraction.” A hierarchy of biological entities of definite organizational form (structure) and matter is assumed as a partial description of the potential scope of Darwinian theory. By subtracting the explicit reference to organisms, Lewontin achieved an abstract characterization of Darwinian evolution by natural selection. The cellular level, for example, is characterized in terms of structural and material properties of cells (a lipid bilayer membrane surrounding a metabolic cytoplasm and genetic material). The specific tactic employed is subtraction of properties accidental to a given level in the hierarchy by means of substitution of terms. By successfully substituting terms for entities at another level of organization, Lewontin showed that reference to entities at any particular level is not an essential part of the theory. At least, reference to structural or material properties that locate them with respect to level of organization is not necessary. Demes, for example, unlike cells, are not bounded by physical membranes but rather by geographic, ecological, or behavioral properties and relations and yet may undergo a process of interdeme selection. Despite substantial differences among the levels, the hierarchy of significant biological entities and their compositional relations is itself taken for granted.9 The a priori hierarchy serves the same role in characterizing evolutionary explanation as Cartwright and Mendell’s a priori Aristotelian classification of kinds of explanatory factors. The hierarchy specifies a partial ordering criterion, not of the abstract, but of the compositional levels, which are “reached” from the organismal level by a process of abstraction. The hierarchy gives the relevant explanatory kinds and also shows how Darwin’s theory is restricted: it applies literally to only one kind – organisms. By abstracting from this particular kind (entities at a given organizational level) and substituting a term right. I concur with the view that Lewontin’s principles are at most necessary conditions for something’s being a unit of selection. 8 Lewontin (1970), p. 1. It may seem odd that Lewontin offers a generalization of Darwinism using the very same term, ‘individual,’ that Darwin used, but it is clear from the context that Lewontin means something much broader than ‘organism.’ 9 See Hull (1988), ch. 11, for a full critique of this tactic. It should be noted that Lloyd’s (1988, p. 70) analysis in terms of entity types does not take the traditional hierarchy for granted, but rather uses that hierarchy as an illustration of a system that satisfies her account. Other instances of partwhole or member-class relations may also satisfy her definition of units of selection. As such, her analysis defines units of selection for a family of semantically specified theories, one of which is, presumably, Lewontin’s theory.
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which ranges over all of the kinds (levels) in the hierarchy, evolutionary theory is generalized relative to the theory of the hierarchy. Since the hierarchy determines the range of the relevant explanatory kinds, an evolutionary theory which refers essentially to particular levels in the hierarchy is more concrete than one which does not. The reason an ordering criterion is desired concerns the strategy for generalizing evolutionary theory. The aim is to specify abstract entities that are supposed to play a given role in the evolutionary process. One produces a general theory by quantifying over the abstract, functional entities rather than over members of the original class of concrete instances at a given level of organization. General laws or principles will be formulated in terms of “individuals” rather than in terms of “organisms” since entities from any level of the biological hierarchy might play the role of an individual in a population, whereas the qualities of organisms will include some that are particular to organisms. Populations might serve as individuals in a meta-population, for example. Put differently, the idea is to identify those properties of organisms essential to their role in evolution and, taking those properties in abstraction, to define abstract entities (“individuals”) that satisfy that role. The ordering criterion is needed to insure that the quantified theory is sufficiently abstract to include entities at all relevant hierarchical levels within its scope. A theory referring to concrete entities such as organisms will not be adequately generalized merely by quantifying over its elements because entities higher and lower in the hierarchy are not sufficiently like organisms to count as instances of the same evolutionary kind. Populations are not super-organisms and cell components are not organs. Only a theory that is more abstract than every member of the set of theories for single levels in the hierarchy can meet the criterion. Lewontin noted that one virtue of Darwin’s formulation of his principles is that no mention is made of any specific mechanism of inheritance or specific cause of differential fitness, even though both heredity and selection must be understood as causal. Darwin’s theory is about a complex causal process, not merely a description of effects or patterns. Moreover, fitness has been widely interpreted as a property which supervenes on the physical properties of organisms, so it would have been futile for Darwin to try to supply causes of differential fitness that operate in general (Sober 1984; Rosenberg 1985). The specific means of interaction between organisms and their selective environments is less important in establishing the nature of natural selection as a process than the fact that there is interaction of a certain sort.10 Although Darwin clearly intended his theory of natural selection to describe causal powers of nature, as suggested by the explicit analogy to man’s power in the ⎯⎯⎯⎯⎯⎯⎯ 10
On the concept of selective environment, see Brandon (1990).
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passage quoted above, the theory is phenomenological, avoiding mention of particular causal mechanisms wherever possible. What Lewontin did not discuss is that while an apparently general theory can be constructed by abstraction from Darwin’s principles, neither Darwin’s theory nor standard generalizations of neo-Darwinism supply criteria for identifying entities at the various levels of organization. Nor, for that matter, do such theories tell us how to determine when the principles hold at a level, even assuming they are necessary and sufficient. Rather, these theories specify only that entities function as units of selection whenever the principles hold and they therefore carry a tacit assumption that we know how to recognize when the relevant properties hold. One might think that intuitive criteria of individuation at the organismal level could be supplied via analogy to humans, given our deeply held beliefs about our own organismhood. No one has any trouble telling where one member of our species ends and another begins (although problems about abortion and when life begins and ends should give one pause about even this). But it was precisely because entities at many levels, including the “organismal,” are not very similar to the exemplary organisms about which we have strong beliefs that doubts about generality arose in the first place.11 None of the relevant three properties Lewontin mentions – variation, reproduction, and heritability – are intuitively grasped at levels other than the organismal just in virtue of an imagined analogy with organisms. Even at the organismal level these properties can raise problems, so an argument by analogy is on weak ground indeed. Until Harper introduced the distinction between ramets and genets into plant biology, for example, it was quite unclear what, if anything, distinguished plant growth from plant reproduction. Similar problems plague evolutionary analysis of asexual and clonal organisms.12 Typically, intuition about organisms is supplemented by mathematical models in the extension of evolutionary theory to other levels. Unfortunately, not only does reliance on such models beg the question of whether the theory is adequately generalized by such models (since use of the models in theory ⎯⎯⎯⎯⎯⎯⎯ 11
Controversy and confusion over four theses provide some evidence of this difficulty: (1) that biological species are individuals (Ghiselin 1974; Hull 1975, 1980, 1988); (2) that plant stems individuate plant organisms (Harper 1977); (3) that standard evolutionary models cannot explain the origin of organismality (Buss 1987); (4) that organisms are the product of symbiogenesis (Margulis and Sagan 1986). 12 Ultimately, I think Harper’s distinction is flawed for the very same reason that the abstraction strategy described below is flawed: both rely on mechanisms that by their nature operate only at a single level in virtue of structural and material properties peculiar to entities at that level. Lewontin (pers. comm.) characterizes the flaw differently. He suggests that the Darwinian concept of a “variational theory” for ensembles of organisms may be at fault because it forces us to count individuals rather than to measure continuous quantities such as amount of matter or energy, as in certain styles of ecological research.
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generalization requires the assumption that they adequately capture the organismal properties of interest), but the models frequently turn out to violate our intuitions about the organismal level, and in such a way that the violations go unnoticed.13 Since evolutionary theory does not itself supply the relevant individuation criteria, other theories must operate in the background to support claims, for each level, about the entities and properties which make it the case that evolution by natural selection occurs at that level. For Lewontin’s strategy, the relevant background should determine the levels of the biological hierarchy and individuate entities at those levels. Whether this background is specified by any precise biological theory is open to doubt.14 It is critical to distinguish here between the formalized evolutionary theory developed by Lloyd (1988) and the quasi-formal treatment by Lewontin, because Lloyd aligns her view with that of Lewontin. Lloyd’s semantic analysis does indeed supply individuation criteria in virtue of its use of the concept of “entity types” (see note 14). This can be done because individuation criteria are supplied in the specification of model structure without requiring the ontological commitments of background theory needed to interpret the models for empirical use. Indeed, Lloyd’s empiricist stance is designed to show that it is possible to formalize evolutionary theory without making any specific ontological commitments such as Lewontin makes. Moreover, it is precisely because the treatment is formal that individuation criteria can be supplied without reference to any empirical background theory or knowledge. Lloyd’s formal approach only requires a relation of compositionality between entities at different levels for her formal individuation of entities to work. It is therefore important to distinguish between “the biological hierarchy” as employed by biologists, which requires ontological commitment to a structure with empirical content, and the abstract “conceptual” hierarchy defined by Lloyd’s formal theory. The differences between the clarity of presuppositions in ⎯⎯⎯⎯⎯⎯⎯ 13
The discussion in Wade (1978) and Wimsatt (1980) of how migrant pool models of group selection turn out to provide an analog of blending rather than Mendelian inheritance at the organismal level is a revealing example of the systematic biases inherent in the heuristic use of mathematical models for generalizing evolutionary theory, a subject Wimsatt has treated extensively. 14 When evolutionists say that one has to “know the biology” or “know the organisms” to do the evolutionary theory, they refer to a tacit body of knowledge that includes a variety of reproductive and ontogenetic mechanisms, ecological factors relevant to the generation of selective pressures, facts about population size and distribution, and a wealth of other facts that all play a role in determining whether something should count as an “entity” at a level. In a vein similar to my point here, Elliott Sober (1988) argues persuasively for a role for background theory in the confirmation of phylogenetic hypotheses. But more than this, he argues that claims that appear ontologically neutral because they appeal to a purely methodological principle of parsimony turn out to hide important empirical background theories or knowledge. Nevertheless, Sober’s argument concerns only the epistemological status of parsimony claims and of methods of phylogenetic inference. My argument is concerned with the metaphysical standing of evolutionary theories resulting from a certain strategy of theory construction, not only with the epistemology of evolutionary inferences.
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quasi-formal and formal analyses of theory structure recommends Lloyd’s formal approach. Unfortunately, formalism alone does not solve the problem of precisely how scientists’ ontological commitments are made or precisely which ones work well or badly in the project of generalizing empirical theories of evolution. Much ink has been spilled over the merits of Lewontin’s strategy, but it is not my main target. Its problem of properly abstracting functional evolutionary roles is shared by a second strategy that makes more explicit ontological commitments open to scrutiny. Insofar as strategic errors are made by practitioners of Lewontin’s strategy, I think its critics have rightly traced them to its degree of ambiguity on separable issues of units and levels of selection. In particular, claims about empirically adequate representation in mathematical models have sometimes been confounded with analysis of the structure of selection and evolution as causal processes.15 The ambiguity is resolved by making explicit the assumptions in the background theories, which specify certain aspects of the causal structure of the biological processes required for the operation of selection and evolution. It is no wonder that the units of selection controversy has been inconclusive: the controversy rests in part on biological assumptions, principles, and theories outside the scope of evolutionary theory proper. While Lewontin was right to consider Darwin’s phenomenological treatment of heritability and the causes of fitness differences a virtue, it does not follow that any Lewontinian generalization of Darwinism is thereby freed of dubious causal assumptions about inheritance, or about other key processes that are articulated in empirical background theories. The role of critical causal background theories is virtually unexamined in Lewontin’s program, as are the ways in which these background theories must articulate with neo-Darwinism in order to yield an empirically adequate hierarchical model of evolution.16 ⎯⎯⎯⎯⎯⎯⎯ 15
At least, proponents have not always been clear. Wimsatt (1980), for example, criticizes genic selection in ways that suggest that chunks of genome larger than single genes may be units of selection. Because of his favorable discussion of Lewontin’s (1974a) continuous chromosome model, some have interpreted Wimsatt’s argument as implying that there might be units of selection up to the limit of the entire genome. But if the genome is the largest unit, this interpretation goes, Wimsatt must have had Dawkins’s replicator hierarchy in mind rather than an interactor hierarchy, as others have supposed him to have been discussing. Brandon (1982, 1990) and Hull (1980, 1981) have argued, for example, that Wimsatt’s analysis confounds discussion of replicators and interactors. In his defense, Wimsatt (1981) gives an alternative interpretation of the “confounding” in which the two questions are taken to be intertwined in virtue of the dual role of genes as both autocatalytic and heterocatalytic. Wimsatt urges attention to the latter function of genes and an analysis of the hierarchy of levels in terms of “generative” structures as an alternative means to disentangle the concepts (see Wimsatt 1986). Moreover, Wimsatt (1981, table 3, p. 164) clearly indicates that he includes entities at levels higher than the genome. 16 This is not an accident: genetics as a discipline made it a virtue in the first half of the twentieth century to isolate questions of hereditary transmission from those of embryological development. These now separate domains must be put back together to interpret the relevant background
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4. Dawkins-Hull Generalization-by-Abstraction A second abstraction strategy for generalizing neo-Darwinism makes a fundamental ontological shift. It replaces the traditional biological hierarchy as a framework within which to formulate the theory. This strategy abstracts certain functional roles of entities (and their components) from a description of the evolutionary process at the levels of organisms and genes. The abstract entities thus characterized support an ontology of biological individuals and classes, leaving open the empirical question of whether entities at the levels of the traditional biological hierarchy serve as units of selection. The second strategy for generalization-by-abstraction draws on some insights of Lewontin’s school, particularly in its attention to the role of individuals in the evolutionary process.17 However, it takes explicit notice of the problems inherent in assuming the traditional biological hierarchy and of the need to specify relevant background theories for a full explanation of the evolutionary process. That is, while the Lewontinian program is concerned primarily with the epistemology of evolutionary analysis, formulated within the ontological frame of the assumed biological hierarchy, the second program is concerned directly with the metaphysics of evolution and the formulation of an ontology that facilitates generalization. The first strategy abstracts from the level in the biological hierarchy at which significant entities occur; the second strategy abstracts from kinds of explanatory properties of significant entities at the canonical hierarchical levels of neo-Darwinian explanation. In particular, the second strategy analyzes the causal mechanisms through which genes and organisms play significant roles in the process of evolution by natural selection and subtracts kinds of explanatory factors which appear to rest on features peculiar to genes and organisms. Such features tend to be associated with the particular material from which genes and organisms are constructed, e.g., the particular molecular mechanism by which DNA replicates, or the mechanisms by which sexual or asexual organisms reproduce. The strategy is to abstract from the matter and structure of the concrete mechanisms of genes and organisms to yield a theory specified solely
assumptions. Nevertheless, there is irony here since Lewontin (1974a, 1974b) has given one of the most penetrating critiques of acausal approaches, drawing a firm distinction between analysis of variance and analysis of causes. But the causal role of Mendelian principles which Lewontin champions, as opposed to the phenomenological, acausal analysis in terms of quantitative genetic principles, does not address the core problem of causal analysis of evolution: Mendelism is only part of the required causal story of heredity/development. 17 Hull (1980, 1981, 1988) argues that a coherent theory of evolution will require that the entities which are units of selection or of evolution be individuals of a certain historical sort. He points out that on this view “group selection” is incoherent, but that at least some of the entities biologists refer to as “groups” actually function as evolutionary individuals.
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in terms of functions. The evolutionary process is regarded as having two components, genetic replication and selective interaction, and these are defined for any entities performing those functions. Since there may be distinct mechanisms for entities at genic, organismal, and other levels that satisfy the sort of causal structure required for evolution by natural selection to occur, the varying properties cannot be essential to the process. Such aspects are inessential to the roles of entities as relevant units in the evolutionary process. Thus generalization (over the class of mechanisms and levels) is achieved by abstraction from the accidental properties of mechanisms at the gene and organism levels. The first strategy relies on an a priori biological hierarchy, one that might be implied by unacknowledged background theories describing embryological part-whole relations for lower levels and by theories of population dynamics or ecological community assembly for higher levels. The second strategy relies on a single acknowledged background theory, Weismannism, which purports to specify the causal relations between genes and organisms germane to their evolutionary roles.18 Richard Dawkins, in several pioneering works, developed an approach to generalizing evolutionary theory by focusing on what he took to be distinct evolutionary roles of genes and organisms. He radicalized the units of selection controversy in 1976, arguing that only genes can be significant units of selection.19 The Selfish Gene (1976) went a long way toward focusing the theoretical and philosophical issues by consciously taking G. C. Williams’s conclusions of a decade earlier to extremes. Williams had argued vigorously against group selection, concluding that in most cases, adaptations could be explained at the level of organisms (Williams 1966). Dawkins developed the view that adaptation could best be explained at the level of the individual gene. In The Extended Phenotype (1982a), he again focused issues by drawing attention to the distinction between the bookkeeping conventions for representing evolutionary change in models and the causal process of selection in nature.20 Critics discerned enough of a shift in this attention to conventions to ⎯⎯⎯⎯⎯⎯⎯ 18
As I will argue below, there are several versions of Weismannism, only one of which expresses the views of Weismann himself, which must be distinguished in order to press the objections I make to the second abstraction strategy (see also Griesemer and Wimsatt (1989)). The version operative in the second strategy, “molecular Weismannism,” rests as much on the “central dogma” of molecular genetics with its emphasis on the flow of genetic information (Crick 1958, 1970; cf. Watson, et al., 1987) as it does on anything Weismann said about the material basis of heredity. See also Maynard Smith (1975). 19 Dawkins (1976, 1978, 1982a, 1982b). For present purposes I will set to one side Dawkins’s claim that there can be cultural units of selection, “memes,” as well as biological units. Since I am concerned here with the form of the generalization strategy, consideration of non-biological entities would complicate but not add to my analysis. 20 See Wimsatt (1980) for the analysis of the bookkeeping argument and a criticism.
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claim Dawkins had softened his position and even that he was becoming pluralistic. It nevertheless seems to me that Dawkins’s widely noted sea change concerns only his perspective on bookkeeping conventions; his conclusions about the causal process were as radical in 1982 as they were in 1976. The main idea is that genes pass on their relevant structure – the nucleotide sequences that code genetic information – to copies in the process of DNA replication. Organisms serve as vehicles, in which the genes ride, whose differential survival and reproduction biases the distribution of gene copies of different structural types in subsequent generations. Genes, in the form of copies, exhibit the properties of “longevity, fecundity, and fidelity.” According to Dawkins, Evolution results from the differential survival of replicators. Genes are replicators; organisms and groups of organisms are not replicators, they are vehicles in which replicators travel about. Vehicle selection is the process by which some vehicles are more successful than other vehicles in ensuring the survival of their replicators (Dawkins 1982b, p. 162 of 1984 reprint).
In 1978, Dawkins defined “replicator” as follows: We may define a replicator as any entity in the universe which interacts with its world, including other replicators, in such a way that copies of itself are made. A corollary of the definition is that at least some of these copies, in their turn, serve as replicators, so that a replicator is, at least potentially, an ancestor of an indefinitely long line of identical descendant replicators (Dawkins 1978, p. 67, as quoted in Hull 1981, p. 33).
Dawkins thus distinguishes replicators and vehicles in terms of a role in evolution the former play that the latter do not. The evolutionary role of genes is to bear information that can be passed on in replication. The role of organisms is to act as agents of propagation, but since some are better than others, they serve to make the replication of the genes they carry differential. Genes only indirectly cause the biasing of their representation in future generations through their role in the construction of organisms. The structure of organisms is only indirectly transmitted to future generations through its role in perpetuating the genes that caused the construction of the organism. The propagation of information by transmission of structure and selective bias are the two main functions of entities in the evolutionary process. The phenomena of segregation and recombination during mitosis and meiosis cause genes occurring together in the same chromosome or cell sometimes to be separated from one another. Dawkins, like Williams before him, recognized that the structure of the genetic material of an organism as a whole, its genome, is unlikely to survive intact even for one generation, let alone through the many generations required for significant evolutionary adaptation. Therefore, not only do traits of organisms (components of pheno-
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type) not get transmitted directly from parent to offspring, but the material complexes of genes that collectively determine such traits do not get transmitted as intact collectives either. To acknowledge this fact, Williams redefined the gene in functional terms as “that which segregates and recombines with appreciable frequency,” i.e., as the maximal chunks of genetic material that survive the segregation and recombination processes (Williams 1966, p. 24). Segregation entails that the maximal chunk will typically be smaller than the genome as a whole. Recombination entails that the maximal chunk will typically be smaller than a single chromosome. Recombination can separate parts of coding sequences, so the maximal chunks may even be smaller than (coding) genes. Since the material substance of even single whole genes cannot be relevant to evolution, Dawkins concludes that it is the informational state, rather than the substance, of the gene that is relevant. More significantly, as Hull emphasizes, Williams also provided a more specialized, functional definition of “evolutionary genes” in terms of their role in the selection process directly: “In evolutionary theory, a gene could be defined as any hereditary information for which there is a favorable or unfavorable selection bias equal to several or many times its rate of endogenous change.”21 This definition implies that evolutionary genes are information and that they only exist at those times when the conditions mentioned in the definition hold. The main significance of this definition is to detach the concept of gene that is relevant to evolutionary theory from any basis in the material and structural properties of molecular genes and to attach it to the process of selection. (There cannot, for example, be such genes undergoing evolution by drift since by definition they could not meet the conditions.) While it is certainly the case that such properties are relevant to explaining how genes can function as hereditary information, Williams’s definition allows evolutionary theory to refer to anything which functions in that way without requiring that it have the material or structural properties of molecular genes. Evolutionary genes are an abstraction to pure function; they are information-bearing states. The simplification of the generalized evolutionary theory built by Dawkins and Hull upon the foundation of evolutionary genes clarifies the ontology of the theory, but it has a price: instead of selection wandering from level to level in the organizational hierarchy, evolutionary genes wander in and out of existence as the selective and genetic environments change. Further implications of this definition will be explored in the next section. The death of the (multicellular) body each generation implies that neither organisms nor their genomes persist long enough to be the beneficiaries of adaptation. Socrates’s nose died with Socrates, but the genes which caused his ⎯⎯⎯⎯⎯⎯⎯ 21
Williams (1966), p. 25. Cf. Hull (1988), ch. 11. Wimsatt (1981) explores this functional definition through an analysis of “segregation analogues” for entities at higher levels of organization.
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nose to be distinctive may be with us still through their persistence in the form of copies organized into a genic lineage. And persistence is quite different in character for acellular organisms (those consisting of a single cell); when a cell divides, all the parts of the parent organism persist but the parent does not. The background theory to the strategy is that the specific material nature and structure of the substances that carry genetic information is inessential to the analysis of something’s functioning as genetic material. Williams, Dawkins, and Hull abstract from mechanism to produce their various theories of the evolutionary gene or replicator. Our problem, then, is to analyze the notion of persistence in the form of copies, which underlies these concepts. As Hull reminds us, material genes no more persist in populations than do material organisms (see especially Hull 1980, 1981, 1988). In order to distinguish that which persists from that which does not, Williams and Dawkins define genes in abstract, functional terms: the “information” coded in genes that persists in the form of copies – tokens with similar structure due to descent – is what matters in evolution, not the persistence of any given items of matter. The structure of a gene persists, has a material embodiment or avatar, just as long as one or more of its copies exists. Dawkins thus argues that the definitive answer to the question – what are adaptations for the good of? – is genes. Adaptations must be for the benefit of genes, not organisms, because genes are the only biological entities with sufficient longevity, fecundity, and fidelity to reap the benefits of evolution.22 Dawkins’s challenge is to make this seem more than a hollow victory since his genes are abstract entities and it is not clear what it means for an abstraction to receive a benefit. We may speak, Dawkins concludes, of selection as a causal process operating on organisms, but since they cannot be the beneficiaries of the evolutionary process, such talk is vicarious when it comes to explaining adaptations. Wimsatt points out that Dawkins’s argument is fallacious, turning on an equivocation between, say, Socrates as an individual and Socrates as a member of the class of instantiations of a phenotype: “Socrates’ phenotoken was killed by the hemlock, but his phenotype may well live on.” Wimsatt continues, If evolution had to depend upon the passing on of gene-tokens, it could not have happened. Genotokens and phenotokens are not inherited, but genotypes and phenotypes may be! Many of the remarks of modern evolutionists on the relative significance of genotype and phenotype for evolution are wrong as a result of the failure to make this distinction. In particular, if the phenotype can itself be inherited or passed on, it need not be regarded merely as a means of passing on its genes or genotype (Wimsatt 1981, n. 2; emphasis in original).
To avoid Dawkins’s fallacy, Hull focuses on functional rather than structural differences between the evolutionary roles of genes and organisms. ⎯⎯⎯⎯⎯⎯⎯ 22
For an excellent critique of Dawkins’s analysis of evolutionary benefit, see Lloyd (2001).
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Hull is careful to avoid too close a reliance on the concept of copying because of his view that genes and organisms, qua material tokens, suffer the same fate. He agrees with Williams and Dawkins when he argues that “The natural selection of phenotypes cannot in itself produce cumulative change because phenotypes are extremely temporary manifestations.” (Williams, quoted in Hull 1980, p. 320). But he also argues that the same point applies to genes, which after all are parts of the body, and that this is the reason that structure rather than substance is the key to generalizing the gene concept. Hull rejects Dawkins’s abstraction of the gene as an informational sequence in favor of abstraction of the evolutionary function of the gene when he writes, Neither genes nor organisms are preserved or increased in frequency. The phenotypic characteristics of organisms are extremely temporary manifestations – almost as temporary as the “phenotypic” characteristics of genes. As substantial entities, all replicators come into existence and pass away. Only their structure persists, and that is all that is needed for them to function as replicators (Hull 1980, p. 320; emphasis added).
Hull is careful not to refer to copying here, but his last point is still not warranted by the preceding claims. It is simply not true that only the structure of replicators persists, however gene structure is interpreted (see section 5). Some of their parts also persist, and it is precisely because DNA replication involves the splitting up of a replicator into parts that are incorporated into new replicators, rather than copying, that replicators are relevant to the evolutionary process. It does not matter that a given part does not persist indefinitely. Persistence into the next generation (molecular, organismal, or whatever) is all that is required to make material overlap a property of the evolutionary process. Evolution is a material process, not a relation among abstractions in which biologically structured matter is accidental. When the type-token confusion is cleared up, the issue is seen to turn on whether there are differences in the causal processes by which genes and organisms “pass on their type.” Of course, Wimsatt’s argument is not right either: genotokens and phenotokens are inherited, but they are not the same tokens as the ones the parent inherited from its parents. The role of these tokens has been severely obscured by the obsession of transmission and molecular geneticists with analogies to the concept of information. One must clearly distinguish between heredity (a relation), heritability (a capacity), and inheritance (a process) in order to see the elision in Wimsatt’s critique that is shared by Dawkins’s and Hull’s analyses. It may be reasonable to talk about hereditary information, since heredity is a relation. But it does not follow from the fact that this relation holds that types (rather than tokens) are “passed on” in the process of inheritance. To reason this way is to get the causal order of things backwards: things – tokens – are passed on in inheritance and types (whether genotypes or phenotypes) thereby exhibit the heredity relation.
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By identifying distinct evolutionary roles for genes and organisms, Dawkins is able to reformulate the description of evolution so as to leave open the empirical question of which entities serve those roles. As a matter of empirical fact, however, Dawkins thinks that genes are the only likely biological replicators. To emphasize that entities other than DNA might in principle serve the evolutionary role of genes and that entities other than organisms might serve the evolutionary role of individuals, Dawkins substitutes the more abstract terms “replicators” and “vehicles” respectively (Dawkins 1978). Replicators, according to Dawkins, are things of which copies are made; active replicators influence the probability that they will be copied, usually but not necessarily through the vehicles in which they ride; passive replicators have no such influence, although they may make vehicles; germ-line replicators are the potential ancestors of indefinitely long lineages of replicators. Active, germ-line replicators are the evolutionarily significant replicators (Dawkins 1982a, pp. 82-83). It would probably be better to say that “the replicated” are things of which copies are made or that do pass on their structure and reserve “replicator” for those things of which copies can be made or which can pass on their structure. Replicative success should not be part of what it means to be a replicator, although Hull (1988) insists that merely having the potential or capacity to replicate is not what it means to be a replicator either.23 Because Hull accepts a purely functional definition of the evolutionary gene, material bodies such as pieces of DNA can be evolutionary genes when and only when they function as evolutionary genes. Thus, entities which are not functioning in a process at a given time in a certain way, but merely have the capacity to function in that way at some other time cannot count as genes (at the given time), hence evolutionary genes wander in and out of existence, as I claimed above. This is again a problem of distinguishing heredity, heritability, and inheritance: Hull resists the idea that replicatorhood can be interpreted as a capacity, since capacities can remain unfulfilled: to be a replicator is to go through the process of inheritance. Dawkins’s expressive language of replicators and vehicles captures the partwhole relation that exists between physical genes and organisms and at the same time indicates that organisms are not the relevant subjects when it comes to evolutionary theory.24 But it is problematic language because these terms lead ⎯⎯⎯⎯⎯⎯⎯ 23
I shall not dispute Hull’s point here because, although I think his insistence poses significant problems for his process ontology, he considers this to be a terminological issue upon which very little turns (Hull, pers. comm.). 24 Grene (1989, p. 68) points out that Dawkins chose the terms “replicator” and “vehicle” to differentiate the primary role of genes in evolution from the derivative role of their bearers. Brandon (1985, p. 84) concurs and finds this emphasis sufficient to prefer Hull’s terminology. Dawkins’s language serves his rhetorical purpose well, which is to persuade biologists that the question of replicator persistence (rather than vehicle survival) is the central question of evolutionary biology. The language reflects the imagery of Dawkins’s earlier book, The Selfish Gene (1976), in which
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us to search for the physical entities that correspond to them, even though Dawkins’s theory is an abstract one of pure function and process. What matters in replication, as Hull glosses Dawkins, is “retention of structure through descent.” Dawkins’s fidelity is copying-fidelity and longevity is longevity-inthe-form-of-copies: “neither material identity nor extensive material overlap is necessary for copying-fidelity . . .” (Hull 1981, p. 31). While material overlap is not necessary for an entity to satisfy the conditions of replicatorhood, I claim that material overlap is a necessary condition for a system to count as biological, and thus that all cases of biological lineages of replicators include material overlap as a property. Just how extensive the overlap must be depends on how the concept of information is analyzed. I think it is more substantial than Hull and Dawkins suggest because genetic information does not “reside” in the material genes but in the relation between genes and cytoplasm, between signals and coding system. My complaint with Dawkins’s theory is not that it fails to clarify functional roles in the evolutionary process – it does. But it does not provide resources to identify empirically the physical avatars of his functional entities. We know that the informational genes are tied to matter and structure, but if evolutionary theory – to be general enough to cover cultural and conceptual change – must be devoid of all reference to concrete mechanism, it cannot follow from the theory, for example, that genes are inside organisms or are even parts of organisms, as Dawkins’s language suggests. Strictly, only the correlations between replicator and vehicle due to causal connections of a completely unspecified sort can be implied by such a theory. Striving to get matter and specific structure out of the theory in order to make it apply to immaterial realms may thus leave it bankrupt as an account of causal connection for the material, biological cases. Hull clarified the distinction between replicators and vehicles by noting that Dawkins mixed together two notions of interaction. Interaction with the world in such a way that replication of copies of replicators is differential is a causal power distinct from the interaction involved in copy-making per se. DNA influences the former mode of interaction, albeit somewhat indirectly, via its “heterocatalytic” functions of coding for the sequence of amino acids in proteins and regulating the temporal and spatial expression of coding genes in the developing organism. Proteins play vital roles in the metabolism and structure of the cellular vehicles that in turn interact with the outside world. Since DNA molecules are inside organisms, when an organism’s interactions with the external world cause its chances of survival and reproduction to be different from those of other types of organisms, the probability that the DNA molecule’s genes are depicted as homunculi riding around in lumbering organismal robots. Hull’s term “interactor” is silent on the relative importance of the two kinds of functionally characterized abstract entities and Hull clearly emphasizes that both functions are logically required for evolution to occur.
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information can be passed on is likewise affected. However, as I suggested in the previous paragraph, this cannot be a deduction from the theory of the informational gene, but must come from background theory. The interaction involved in copy-making itself, of one DNA molecule with the various chemical entities needed for replication, is the “autocatalytic” function of DNA. This mode of interaction involves only the most immediate cellular environment. Thus, Hull introduced the term ‘interactor’ to indicate the evolutionary function served by Dawkins’s vehicles: replicators – entities that pass on their structure directly in replication; interactors – entities that produce differential replication by means of directly interacting as cohesive wholes with their environment (Hull 1981, p. 33. Cf. Hull 1980).
For Hull, it is an open empirical question what entities serve either of these evolutionary roles and whether a given entity may serve both. Also, on Hull’s analysis, the notions of directness in replication and directness in environmental interaction explicate the causal difference between replicators and interactors, since interactors may pass on their structure, but only indirectly, and replicators (genes at least) may interact with their “external” environment, but only indirectly.25 There is one substantial point of disagreement between Dawkins and Hull which has to do with their respective copying and directness criteria. Dawkins supposes that, although replication is not a perfect process, evolutionary benefit is conferred on a replicator only to the extent that its copies are identical in structure: sequence identity rather than material boundaries serves as the criterion of individuation for evolutionary genes. Hull, in contrast, finds this requirement to be a stumbling block for the distinction between the evolutionary roles of replicators and interactors. Hull does not share Dawkins’s intuition that there is a necessary difference in evolutionary kind between genes and organisms: Hull’s definitions of replicator and interactor in terms of two distinct modes of interaction suggests that they differ only by degrees of relative directness in their participation in the two modes (Brandon and Burian 1984, p. 89). Hull writes, ⎯⎯⎯⎯⎯⎯⎯ 25
Bibliographic caution is required in interpreting Hull’s view. Hull’s 1980 paper was reprinted in Hull (1989), but not verbatim. Hull (1980) and Hull (1981) include “directness” as a defining property of replicators and interactors. This language was dropped from Hull (1988). Hull (1989) preserves the modified 1988 analysis rather than the exact text of the 1980 paper reprinted. Thus, despite the publication dates of the various essays, Hull consistently used the “directness” as a criterion in conjunction with passing on structure in the early 1980s and dropped it from the definitions in the late 1980s. I argue below that the reason Hull dropped directness is that it is a contingent property of the particular material mechanisms by which DNA and organisms operate and therefore he did not consider it to be a proper part of the general analysis of selection processes.
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Both replicators and interactors exhibit structure; the difference between them concerns the directness of transmission. Genes pass on their structure in about as direct a fashion as can occur in the material world. But entities more inclusive than genes possess structure and can pass it on largely intact. . . . We part company most noticeably in cases of sexual reproduction between genetically heterogeneous organisms. Dawkins would argue that only those segments of the genetic material that remained undisturbed can count as replicators, while I see no reason not to consider the organisms themselves replicators if the parents and offspring are sufficiently similar to each other. Genes tend to be the entities that pass on their structure most directly, while they interact with ever more global environments with decreasing directness. Other, more inclusive entities interact directly with their environments but tend to pass on their structure, if at all, more and more indirectly (Hull 1981, p. 34).
Hull’s abstraction problem differs slightly from Dawkins’s because of his emphasis on replicator function rather than on replicator structure, that is, on direct transmission of structure rather than on the nature of copies. Hull’s turn away from copying in the early 1980s has remarkable and subtle ramifications. His return to it in the late 1980s is equally remarkable. He writes, In my definition, a replicator need only pass on its structure largely intact. Thus entities more inclusive than genomes might be able to function as replicators. As I argue later, they seldom if ever do. The relevant factor is not retention of structure but the directness of transmission. Replicators replicate themselves directly but interact with increasingly inclusive environments only indirectly. Interactors interact with their effective environments directly but usually replicate themselves only indirectly (Hull 1980, p. 319. For criticism, see Wimsatt 1981, n. 4).
This seems intuitive enough if we hold to standard idealizations about “typical” genes and phenotypes. Replicators seem to replicate directly because there aren’t any things intervening between them and the copies they make. DNA strands directly contact others through hydrogen bonds. What could be more direct? Interactors seem to interact directly because there aren’t any events intervening between the selection and the change in phenotype distribution. There is nothing between the teeth of the lion (agent of selection) and the diseased zebra it brings down, nor between the bringing down and the change in distribution of zebra characteristics. The difficulty is that Hull never explains what counts as transmission, so the analysis of directness remains unaddressed. Indeed, since transmission is an aspect of mechanism, Hull has removed all the resources to deal with it from his theory. Dawkins’s copying metaphor, though flawed, permitted a simple mechanistic interpretation of transmission: there is physico-chemical contact between elements of the original (template) and the copy (daughter strand) via hydrogen bonding and enzyme-mediated ligation and, as a result, the daughter strand takes on a certain structure.
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One might think that directness could be made precise by interpreting it as the absence of any intervening entities in the causal sequence from original to copy: A causes B directly if and only if A causes B and there is no C intermediate in the causal chain from A to B. Then perhaps A causes B relatively directly (compared to D’s causing E) if there are fewer intermediaries between A and B than there are between D and E. But the fact that DNA strands resemble the complements to their templates rather than their templates means that a given sequence is transmitted from one strand to another via an intermediary entity and a series of intervening causal events involving a substantial amount of cellular machinery. If there is anything between a cause and its effect, then we have to know how to count such things in order to define relative directness. Since there is an infinity of causal intermediaries between any two timeseparated events related as cause and effect, we have the same level of difficulty in counting events that Cartwright and Mendell had in counting properties. Thus DNA copying may or may not be direct relative to some other molecular processes; we do not know how to measure the difference. It may even be indirect compared to organismal reproduction if certain assumptions of Weismannism are false. Relative directness is an acceptable intuitive distinction between replicators and interactors so long as there appears to be an obvious asymmetry. If it is obvious that every interactor reproduction is less direct than every replicator replication, then perhaps a precise criterion of relative directness is unnecessary. But if this be challenged, why shouldn’t Dawkins and Hull accept the indirect route by which parent and offspring vehicles resemble one another as copying, and hence accept that vehicles or interactors will usually be replicators?26 In order to deny that template intermediaries violate a condition of sufficient relative directness, either physico-chemical contact must be rejected as the interpretation of transmission or else the notion of structure must be so loose that a strand and its complement can be said to have the same structure or at least that one structure can be said to be “preserved” in a different structure. Either way, some appeal to mechanism is required. The copying metaphor, due to its unrigorous functionalism, at least had the virtue of supporting a straightforward interpretation of direct transmission. Hull’s more rigorous analysis requires that we be able to analyze (or at least to order) degrees of relative directness. While this seems possible in principle in the case of genes and organisms, it is not very workable in practice because we have been denied access, on general principle, to an adequate specification of causal structure. It ⎯⎯⎯⎯⎯⎯⎯ It is important to note that this is not the same as Hull’s claim that it is possible for one and the same entity type in the traditional biological hierarchy to be both replicator and interactor, e.g., paramecia that reproduce by dividing their entire body in two. My claim is that because of the problems in the concept of directness, the view should lead Hull to think that properties of interactors will be sufficient to count them as replicators too, thus defeating the distinction.
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seems even less workable for hierarchical evolutionary theory because we know even less about causal structure at other levels of organization. The directness of DNA replication seems to work as well as it does as a paradigm because the sequence similarity of ancestor and descendant nucleic acids is produced by a nearly universal chemical mechanism. The features of the mechanism are supposed to supply the interpretation of directness and transmission. But since descent, not sequence similarity, is the basis of Hull’s view, it is not clear what should serve instead of the chemical mechanism to support an interpretation of direct transmission. Directness of transmission cannot do the work of the copying metaphor without some further analysis: a definition of “replication” is conspicuously lacking in Hull’s analysis. “Replication” will function as a primitive term in Hull’s system until it is given a description that is independent of evolutionary considerations. Hull’s theory is either radically incomplete, leaving its generality open to doubt, or else it is thrown upon the mercy of Dawkins’s analysis of copying, which has substantial problems of its own. These problems arise because there is as yet no clear and distinct notion of the molecular gene which can resolve claims about sequences when they function as evolutionary genes. We have only the claim that the passing on of structure is relevant to the role of replicator, not any suggestion about the range of mechanisms of structure transmissions that count as hereditary information. Despite the distinction between the several concepts of the gene, the “informational turn” is integral to them all, and because of it they are not easily explicated independently of one another.27 It is harmless enough to talk about sequence “copying” as the consequence of replication in the standard molecular genetic context, but that leaves the structure of the replication process intended to serve in the general theory unaccounted for. As Hull notes, it is critical that Dawkins’s notion of copying identify copying as a process involving descent relations and not mere similarity.28 But the foregoing remarks are designed to undermine the impression that simple appeals to what happens to DNA can legitimately serve as the foundation for the causal interpretation of the evolutionary process of replication in abstraction from any particularly structured matter. One cannot have the ontological simplification of pure, abstract functionalism and also appeal to concrete mechanisms whenever it suits. Moreover, even if the copying metaphor did account for relationships among sequences, it would not explicate the relationship between replication and reproduction that I claim is needed to generalize evolutionary theory. We know, for example, in a rough way what is involved in claiming that groups of ⎯⎯⎯⎯⎯⎯⎯ 27 28
For a philosophical analysis of these different senses of “gene,” see Kitcher (1982). See especially the treatment in Hull (1988), ch. 11.
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organisms reproduce; we do not know what it means for them to replicate unless that comes to the same thing as reproduction. Copying does not adequately specify the material conditions of life processes: DNA replication and reproduction are flows of matter, not just of information. I think that abstraction from matter capable of reproduction supplies a faulty base for generalizing evolutionary theory. Indeed, it is a wonder how transmission of information could be understood as an explication of replication as an ordinary causal process when the carriers of information are functionally defined, abstract objects. If DNA replication were fully conservative rather than semi-conservative, then copying would have served as a more adequate analysis of replication, since no transfer of parts from original to copy would have been involved and information would be the only thing left to track from generation to generation.29 But then replication would clearly not be analogous to reproduction and, if I am right that reproduction is the proper basis for evolutionary generalization, that would have made replication an even weaker basis. Hull’s analysis in terms of directness fails to break completely with the traditional hierarchy in so far as it explicates the concept of directness in terms of compositional levels. A gene (lower compositional level) inside a cell (higher compositional level) interacts indirectly with the environment outside the cell, but relatively directly with the DNA molecules for which it serves as a template in replication (same compositional level). Likewise, phenotypic traits of organisms (higher level) are passed to offspring only indirectly through the activities of the genes inside (lower level). Dawkins’s use of the term “vehicle” appears to commit him even more strongly to acceptance of the traditional hierarchy than does Hull’s more neutral term “interactor.” But the commonalities between their analyses undermine the claims of both Hull and Dawkins to be elaborating an alternative conceptual scheme to Lewontin’s. Thus, the directness criterion seems to violate the aim of Hull’s approach to generalization by abstraction. In the late 1980s, Hull modified his analysis of replicators and interactors, dropping directness as the degree-property distinguishing the two roles and emphasizing instead the degree of intactness of structure through the respective ⎯⎯⎯⎯⎯⎯⎯ 29
I haven’t yet mentioned viruses with single-stranded RNA genetic material; copying would seem an apt description of them since no transfer of parts occurs. (The production of cDNA which incorporates into the host genome and then serves as a template for the production of new viral RNAs acts as a filter for the original RNA material.) However, since all cellular life is DNA-based, I am more inclined to think that RNA viruses should be treated as a special case of copying which is neither replication nor reproduction, rather than that they are (the only) clear cases which satisfy Dawkins’s analysis. This view does not entail mechanism- or level-specific assumptions and so does not put the project of generalizing evolutionary theory at risk.
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causal processes. This is a partial return to a concept of copying. Degree of intactness preserved through replication is only contingently related to degree of directness via the mechanisms that happen to cause replication. Indeed, it might be interpreted as just a weaker similarity criterion than Dawkins’s copying criterion, depending on how one understands the relevant notion of structure. I quote Hull’s new analysis here in full: Dawkins’s (1976) replacement of Williams’s (1966) evolutionary gene with “replicator” is an improvement, both because it avoids the confusion of Mendelian and molecular genes with evolutionary genes and because it does not assume the resolution of certain empirical questions about the levels at which selection can occur in biological evolution; but it too carries with it opportunities for misunderstanding. Among these is the confusion of replication with what I term “interaction” and in turn the confusion of these two processes with selection. Thus, in an effort to reduce conceptual confusion, I suggest the following definitions: replicator – an entity that passes on its structure largely intact in successive replications. interactor – an entity that interacts as a cohesive whole with its environment in such a way that this interaction causes replication to be differential. With the aid of these two technical terms, selection can be characterized succinctly as follows: selection – a process in which the differential extinction and proliferation of interactors cause the differential perpetuation of the relevant replicators. Replicators and interactors are the entities that function in selection processes. Some general term is also needed for the entities that result from successive replications: lineage – an entity that persists indefinitely through time either in the same or an altered state as a result of replication (Hull 1988, pp. 408-409).
Only the structure of genes need be transmitted in an ancestor-descendant sequence for genes to function as replicators. Hull’s further analysis suggests a new ontology consisting of historical individuals – replicators, interactors and lineages – and classes of individuals, the higher taxa and sets of individuals defined in terms of traits in common. Replicators and interactors are arranged into a two-level functional hierarchy. Reference to organisms in evolutionary theory is removed and a new ontology is constructed which appears to disregard the traditional biological hierarchy. Whether entities of the traditional hierarchy serve as replicators and/or interactors is still left as an empirical question, as in Dawkins’s analysis. But in Hull’s revised definitions, replicators and interactors are no longer contrasted in terms of directness. (Compare his definitions quoted on p. 73, above.) On the new analysis, they are only linked by the definition of ‘selection,’ where reference is made to the differential perpetuation of the relevant replicators as a
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function of selective interaction. (One might think they are linked by the definition of ‘interactor’ because of the reference to replication, but this process is undefined in Hull’s system.) This leaves open the possibility of some link other than the compositional arrangement of the organizational hierarchy, but at the same time it leaves unclear what counts as relevant transmission of structure. By returning to copying, Hull must face Dawkins’s problem that the theory has no resources to specify the relevance relation between replicators and interactors other than bare cause-effect. The particulars of this relation in biology come from theories of development, including gene expression; they are not supplied by the theory of the informational gene. The directness criterion clearly focused attention on those aspects of DNA and organisms which count as relevant transmission, although it provided no analysis of transmission. Hull is very clear about his generalization strategy, but steering between Scylla and Charybdis is tricky. The following passage suggests that he decided the directness criterion tied his concept of replicator too closely to the material nature of the DNA mechanism: In this chapter I adopt a different strategy [than Lewontin’s]. I define the entities that function in the evolutionary process in terms of the process itself, without referring to any particular level of organization. Any entities that turn out to have the relevant characteristics belong to the same evolutionary kind. Entities that perform the same function in the evolutionary process are treated as being the same, regardless of the level of organization they happen to exhibit. Generalizations about the evolutionary process are then couched in terms of these kinds. The result is increased simplicity and coherence. . . . the benefits [of this strategy] are worth the price [in damage to common sense]. One benefit is that, once properly reformulated, evolutionary theory applies equally to all sorts of organisms: prokaryotes and eukaryotes, sexual and asexual organisms, plants and animals alike. A second benefit is that the analysis of selection processes I present is sufficiently general so as to apply to sociocultural change as well (Hull 1988, p. 402).
Rather than analyze directness, Hull shifts back to copying to correct a tacit dependency on the traditional organizational hierarchy, in the sense that directness is a contingent property of the way molecular genes replicate. While it is true that directness is contingent, it is nevertheless a very important property: the whole domain of biological systems (as opposed to merely physico-chemical systems on the one hand and human social and psychological systems on the other) can be described as the domain of lineages formed by descent relations. A central, and universal, fact about biological descent is that it includes the material overlap of the entities that form biological lineages. By expunging the directness condition in his later analysis, Hull has left unclear what distinguishes biological lineages and descent relations from any other sort of cause-effect change and causal relation. Hull’s general analysis of selection
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processes leaves us without the tools to analyze the empirical differences among selective systems along with their similarities. While there is no necessity in material overlap, nor any necessity in the degree of relative directness with which one DNA molecule gives rise to another, directness of a qualitative sort does follow from the material overlap property of biological lineages (and as I will argue in the next section, it also follows that organismal reproduction, which also produces lineages with material overlap, is direct). Thus I think Hull was mistaken to turn away from his earlier analysis. Rather than reintroduce copying (in the sense of transmission of structure), which is all we have in the vacuum left by the repeal of directness, Hull should instead have rejected pure functionalism in favor of some explicit handling of the facts of mechanism. This is the idea of what an empirical background theory is intended to do. Hull’s rejection of extensive material overlap as a condition on the evolutionary process only reveals the conventionality of the biological domain within the domain of physical systems, not the irrelevance of material overlap to evolution. The historical traditions and conventions by which some physical systems have been singled out as biological systems are arbitrary choices with respect to the broadened domain of generalized evolutionary theory. The attempt to produce a general analysis of selection processes may therefore require that the artificial domain of biology be scrapped. It may seem appropriate to Hull to do so, since his goal is an analysis general enough to include sociocultural evolution, but it is not necessarily the wisest course of action to ignore a universal property of descent mechanisms just because current theory suggests it is contingent. Unfortunately, Hull’s modification in terms of intactness of structure through replication is not entirely successful in removing other difficulties either. While he has eliminated a dependency on the traditional organizational hierarchy, Hull has not removed a dependency on Weismannism, which functions as the background theory that plays the a priori ontological role in the Dawkins-Hull strategy that the traditional hierarchy did for the Lewontin strategy.
5. Copying, Information and the Dawkins-Hull Program The concept of transmitting information in the form of copies is central to the analysis of replicators, but the metaphysical assumptions behind it are inadequate for an understanding of genes made of DNA, which “replicates” semi-conservatively, and are worse still as a basis for generalizing evolutionary theory. The notion of copying is central to Dawkins’s and Hull’s argument. Because DNA strands serve as templates for the construction of new strands from free
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nucleic acids, some mutational changes of nucleotides in a strand are reliably repeated in subsequent strand formation, just as a photocopier reliably repeats the marks due to lint on the photocopying glass or on its lint-ridden copies. However, copying fails as an analysis of DNA replication, and the aspect it fails to capture – the relation between the material overlap of parts between parent and offspring and the transmission of heritable information – is precisely what makes replication part of a biological process. Dawkins identifies replication with copying. Likewise, Hull analyzes replication as a copying process in order to generalize selection theory beyond biology. But there are important aspects of mechanism and properties of specific biological materials still left in his analysis of copying in the form of inferences about the transmission of genetic information and in assumptions about the nature of copying. Ultimately, I claim, there are ineliminable facts about biological mechanisms operating in evolutionary theory, and a generalization which eliminates all reference to matter must either be false or else merely shift the explanatory and predictive burdens to background theories. Dawkins’s conception of the gene as abstract or “informational,” i.e., as the sequence property or state instantiated in all of a material gene’s “copies,” leads him to treat replication as if it were a copying process and copying as any process which produces similarities among objects with respect to their information content. Dawkins’s appeal to the analogy of photocopying has the effect of shifting attention away from, or “black-boxing,” the mechanism by which copying occurs. Instead, Dawkins focuses on the copy relation manifest in the mere fact that an original goes in at one place and a copy, resembling the original in relevant respects and to a relevant degree, comes out at another (Dawkins 1982a, p. 83). Hull’s earlier focus on the degree of directness of the mechanism rather than on the degree of resemblance of the copy is irrelevant to Dawkins’s analysis because directness is a feature of mechanism, which is black-boxed. But surely not every process in which output objects resemble input objects counts as copying and the output objects as copies. Nor must every copy resemble its original in a given, or even the same, respect. These are notorious facts about the resemblance relation. Hull’s concern is that Dawkins does not emphasize sufficiently the genealogical nature of copying. Genealogy is part of a process that happens inside Dawkins’s black box. In biology, replication is a process in which similarities result from descent and descent relations are not merely cause-effect relations. Descent enters Dawkins’s picture only in the weak sense that some process is causally responsible for the similarity: entities whose similarities are not traceable to a common cause cannot be copies. However, mere causality cannot yield a sufficient analysis of descent relations or of the semi-conservative replication of DNA double helices, which involves the destruction of one double helix molecule in the creation of two molecules with the same or similar
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sequences. Copies are not, in general, things made out of the things of which they are copies. Rather, copies are things which resemble originals because a physical process induced a relevantly similar or common pattern in numerically distinct materials. The word “copy” nicely trades in ambiguities – between noun and verb, relation and process. If the ambiguity is allowed to stand, it will appear that the theory of replicators avoids reference to matter and mechanism when in fact it does not. To succeed it must detach the copy relation from the copy process and refer only to the former. Otherwise, a further analysis is required to justify the theory’s ontological pretenses. The unsolved logical problem is twofold: is descent a subrelation of the copy relation and are all descent processes copy processes? I think the answer to these questions cannot be found unless an analysis of reproduction is attempted. In copying, “genealogical” relationship does not include material overlap: the original is part of neither the material nor efficient cause of the copy. Thus copying captures a weaker, more abstract notion of resemblance due to causeeffect relationship rather than the stronger, more concrete notion of resemblance due to descent with material overlap, which obtains in biological cases. Think of cases of artistic copying: an artist sits before a picture in a museum and paints another picture which resembles the one on the wall. We may speak as though the picture on the wall “gave rise to” or is an “ancestor” of the one on the easel, but no material part of the one on the wall is a part of the one on the easel and the artist, not the picture on the wall, is the efficient cause. In contrast, new double helices of DNA are not made from materials that are entirely numerically distinct form old double helices, and DNA is (part of) the efficient cause of DNA. One might say that the relation of original to copy holds of evolutionary genes, derivatively, whenever material genes function as evolutionary genes, but the copying process is not the causal process that causes the copy relation to hold among evolutionary genes: functioning entails process and consideration of formal causes alone cannot explain process. Descent does the work in replication that intention does for artistic or human acts of copying. To mix up relation and process in this way is to invite confusion. Because we ourselves act with intention, it is all too easy to fill in the black box with mechanism while claiming to consider only functions. In a sense, the last remnant of materialism infecting Dawkins’s and Hull’s abstract theories is the notion that DNA “carries” heritable information. It is this information which is supposedly “copied” in the process of replication. But I think they have paid insufficient attention to the concept of information or to the way in which it is carried. A proper understanding of heritable information requires detailed consideration of the matter out of which replicators are made as well as of the mechanisms by which information is “transmitted.” From this it does not follow that there
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cannot be a pure function abstraction of the Dawkins-Hull sort leading to a generalization of evolutionary theory. But it does imply that the resulting generalized theory cannot tell us much about empirical cases. The mechanistic analysis of the properties that give matter the capacity to carry heritable information and the relation between this information and the material causes of descent relations form the core of empirical analysis of evolution by natural selection. Evolutionary theory may be clarified, but empirical practice is obscured. In science, that is too high a price to pay for ontological simplification. Double helices of DNA instantiate two sequences, one for each strand, so it is unclear what claims about the gene sequence (or the heritable information) are supposed to mean if we consider only the relations between DNA molecules. It won’t do to take as a convention that the sequence is that of the “sense” strand that codes for a polypeptide, rather than of the “nonsense” strand, because in some cases complementing strands or their parts are both “sense” strands and have different senses. And, sensibility cannot be determined by the syntax of the DNA alone; it depends on further relations between DNA and other chemical kinds. Moreover, some regulatory “genes” do not code for polypeptide products at all, nor do all the nucleotides of (eukaryotic) structural genes code: introns are important functional parts of genes that do not make “sense”; are they parts of the relevant active germ-line replicator when such a material gene is functioning as an evolutionary gene/replicator or not? We do not know what the genetic information is because what it is for is development, which lacks a proper theory. We have only fragments that run in the background of evolutionary theory. The linear sequence of amino acids in proteins is not a language that DNA “speaks” in order to communicate (Stent 1977). Rather, it is another code. The genetic code is just that, a code. In knowing a code we do not thereby know what information, if any, is transmitted by means of it, nor can we know that any particular usage of it is a transmission of information. From codes we can only calculate the quantity of information, not its content. To claim that events in molecular biology are transmissions of information, we have to analyze communication – far beyond the minimal sense that engineers have given it in the formal theory of communication – and not just coding relations. Some single strands of DNA do not exhibit material overlap with parental strands and therefore might count as copies. But since it is plausible to assume that a process including material overlap is more direct than one without it, DNA strands result from physical processes that are not maximally direct. Therefore, a quantitative analysis of degrees of causal directness is required to interpret the significance of copying as a function of directness, as Hull tried to do in his earlier analysis. Indeed, in order to assess the relative degree of directness of replication of any two entities, many facts about mechanism must
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be considered. Depending on how such facts are described, it may not even turn out that DNA is replicated relatively more directly than organisms are reproduced, despite Hull’s and Dawkins’s strong intuitions that this must be the case. The problem of description in the case of DNA is that the structure of a DNA strand is not copied by the process of strand synthesis from the template. The new DNA strand is highly similar in sequence to the strand complementary to the template, not to the strand which serves as the template. Indeed, a strand and its complement never have a single nucleotide in common at any given location (except in special cases such as palindromes and highly repetitive sequences). Because the causal interactions which produce the new strand are not interactions with the complementing strand it comes to resemble, these interactions do not constitute copying. If we count as the copying process the entire complex sequence of events, black-boxed by Dawkins, involving dozens of enzymes, magnesium ions, free nucleotide-triphosphates, and so forth leading from one strand to a complement-of-a-complement strand having the same nucleotide sequence, then there will be problems interpreting this causal process as measurably more direct than, and hence as distinguishable from, the allegedly indirect way in which interactors (such as organisms, on Dawkins’s analysis) might be taken to cause their own replication. An objection might be raised in light of the fact that DNA replication is only contingently semi-conservative. Since it might have been fully conservative – yielding the parent double helix and an offspring double helix rather than two hybrids with one parent – and one offspring-strand each, my objection is to a mere contingent fact about mechanism which is nicely avoided by the DawkinsHull abstraction to pure function. There would nevertheless be a flow of information from parent double helix to offspring double helix. Therefore, the semi-conservative nature of actual DNA replication, with its material overlap, is irrelevant. Worse still, it can be claimed that processes we commonly call copying processes do indeed involve material overlap, such as in letterpress printing or mimeographing, where ink is laid on an original and then a sheet of paper is pressed against the original and ink is physically transferred from original to copy. Insofar as the ink counts as first a part of the original and then a part of the copy, such processes satisfy material overlap.30 I have three points to make in reply to these objections. First, semiconservative DNA replication is not the only problem of material overlap to arise for the copying view; another concerns the more fundamental functionalist move in interpreting the evolutionary gene as information. I argue that there must still be material overlap for evolutionary genes to exist, but (below the level of organisms) the material overlap must be in the chemical machinery of ⎯⎯⎯⎯⎯⎯⎯ 30
These objections have been raised by Paul Teller and Eörs Szathmáry independently and I thank them for prodding me into addressing them.
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replication which makes it the case that the DNA (or RNA) molecules transferred from parent to offspring count as bearing information. The chemical machine must move from one cell to another in order for genetic material to count as information-bearing. This involves the direct cytoplasmic transfer in cell division of the enzymes of translation – aminoacyl-tRNA synthetases – which make it the case that a sequence of nucleic acids in mRNA count as coded information at all. A simple thought experiment shows this. If an accident of metabolism were to result in all the molecules of tryptophan-aminoacyltRNA synthetase ending up in only one of two daughter cells, then the other cell could not survive. I think it is plausible to say that the reason is that in such a cellular context, the genetic material is meaningless: that cell would not have a rich enough genetic code for the DNA to carry information. This material overlap is not eliminable even in principle because without it the whole system cannot be construed as informational. Without the translation machinery or with a changed machine there is either no genetic code at all or there is a different one. In biology, the code must reside in the cell, not in a table in a molecular engineer’s handbook. This form of material overlap is not required for the flow of information in cell fusions, e.g., from sperm nucleus to pre-existing egg cell, but it is required in all cell fissions, including the flow from primordial germ cell to mature egg cell. In biology – in contrast to the formal engineering theory of information – there is only a pre-existing sender, but not a pre-existing receiver or communication channel, nor a pre-arranged “agreement” on a set of symbols that serve as a fixed alphabet. Information does not “reside” in a given “informational macro-molecule” but rather in the relation between such molecules and the molecular contexts which determine an alphabet and channel.31 In reproduction (whether of DNA molecules or of organisms), the mechanism that determines the informational context must be transferred along with the information “bearers” or signals. For information to flow, in cases like these where the material circumstances of communication do not pre-exist, matter must also flow. The analogy to engineer’s information misleads because the engineer sets up the matter – transmitter, receiver, and channel – before any information flows. The second point of reply concerns the possible worlds in which DNA replication is fully conservative. There are two ways to imagine such a world that have different implications. One way is to imagine that the new DNA strands are synthesized in the usual semi-conservative way but that, for unknown reasons, there exist enzymes which come along, unzip the hybrid daughter double helices, and reanneal the two newly synthesized strands and the two old parental ones. It is hard to imagine how the extra apparatus could be favored in evolution, but if such a system existed, it would still support my ⎯⎯⎯⎯⎯⎯⎯ 31
See Cherry (1966) for a description of the formal requirements of information theory.
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claims that DNA replication is anything but direct and that material overlap of the apparatus would still be required. There would also still exist an intermediate stage with hybrid molecules and these would exhibit material overlap with both the parental molecule and the offspring molecule, so the detour doesn’t present a counterexample. An example of the other way to imagine fully conservative replication would be to imagine a world in which each of the nucleotides stereochemically hydrogen bonded with its own kind rather than with a complementing nucleotide, as in the actual system where A usually bonds to T (or U) and G usually bonds to C. I can imagine such a counterfactual being true, but I cannot imagine all the implications if it for the rest of biology. For example, even short repetitive sequences would fold upon themselves. It is not clear that in such a world the sort of catalytic activity would occur that is now thought crucial to the evolution of genetic systems in the primitive RNA world. I do not know how to determine whether there could even exist cells and organisms of the sorts with which we are familiar in such a world, even if no laws of chemistry were changed. Therefore, it is idle to raise this fantasy world in objection to my point. The issue raised in the objection appears serious but misses the point of my argument. I agree that semi-conservative replication of DNA is contingent and that it would therefore seem to be a fact about the material mechanism from which Hull should abstract, given his program. My point, however, is that Hull requires an analysis of the concept of directness and Dawkins requires an analysis of the concept of copying in order to use them in their explications of replication. In such an analysis, they must either appeal to accidental features of DNA replication, to essential features of DNA replication, or to features of replication that DNA violates. If the third is Hull’s route, then the actual world falsifies his general analysis. If he appeals to what DNA actually does, then consideration of the facts of semi-conservative replication fail to support the concept of directness or justify use of the concept of copying. If he appeals to some “essence” of DNA replication, then it must involve some other properties of DNA replication than semi-conservation. What are these features? In his earlier writings, Hull does not tell us. In his later writings, Hull drops the requirement of directness in favor of the requirement that replicators must “pass on information largely intact via their structure.” (Hull 1991, p. 42). But no analysis of information is given. If we rely on the common wisdom about genetic information, which is an amalgam of folk linguistics and the engineering theory of communication, we arrive at new problems about the actual nucleic acid replication mechanisms, problems as that of saying where genetic information “resides,” which the generic term “copying” was originally supposed to avoid. Thus, the point is not whether Hull (and Dawkins) have the facts of molecular biology right, but rather whether their generalization strategy has succeeded in avoiding reference to any such facts. If the above arguments
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are sound, it certainly seems that they depend on such facts to explicate their core notions. The third point in reply regards the claim that processes commonly called copying processes can involve material overlap. I doubt that when sufficient attention is paid to the physical processes involved, any alleged copying process will be a counterexample. But if there is such, I contend it will be a freakish example and not at all common. If such were the case, I would, like Hull, conclude that some cases of common usage must fall by the wayside if theoretical progress is to be made. At best, such odd cases would lead to a draw: their anomaly would incline one to decide the matter by imposing a convention or not to decide it at all. One shouldn’t be distracted by the fact that a particular object is called a copy: the problem here is not with the copy relation but with copying as a process. The analogies of relation distract us from the disanalogies of process. That every copy of a newspaper, for example, carries the same information traces to a common material cause: they type in the press that is repeatedly inked and pressed onto paper. Is it really worthwhile, unless we do it merely in order to prop up the analogy, to say that the ink is part of the original so as to allow it as a case of material transfer? Moreover, the common cause structure relating newspapers as copies to an original press plate is different than that of a lineage caused by descent. Using the word “copy” to refer merely to the resemblance among things is no improvement in understanding, as Hull argued. We needn’t retain every common usage if it obscures analysis. In this case, it seems clearer to say that the ink isn’t really part of the original, but rather is a numerically distinct object which is induced to take on the pattern of the original via the impression of the type. Similarly, free nucleotides are added to the replication reaction to make a new DNA strand, but they are linked one to another to make a strand, whereas the blobs of ink are linked only to the receiving paper, not to one another. Thus letterpress or mimeograph appears to satisfy the condition of material overlap only if we accept the convention that the ink is part of the original rather than a third thing mediating between the original and the blank paper. To continue the main argument: that there are more chemical events involved in the “copying” of an organism than of a gene, and that organismal reproduction may always require gene replication, do not suffice to show that organismal reproduction is less direct than gene replication. Since gene replication and organismal reproduction are arranged hierarchically, these processes can occur in parallel and the degree of directness measured at one level may not have to count all the steps at the other level.32 To quantify ⎯⎯⎯⎯⎯⎯⎯ 32
I will discuss below the point that Weismannism seems to entail that higher-level reproduction is necessarily less direct than lower-level replication because all the steps of the latter are included within the steps of the former. My main point will be that this is true of Weismannism because that
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directness, one would have to have a quantitative theory of mediated causation capable of distinguishing these cases. Dawkins’s copying criterion and Hull’s directness criterion turn out to be odd bedfellows. Hull rejects the directness criterion in his later analysis apparently because of its dependency on mechanism. But to replace it with copying is just to ignore the features of mechanism which were so helpful, albeit illicit given the rhetoric of ontological simplification, in understanding the basic concepts of replicator and replication. The reference to information in the later analysis either reintroduces the original problem Hull found in Dawkins (deemphasis of genealogical aspects and over-emphasis of similarity relations) or it just replaces reference to one aspect of the DNA mechanism with reference to another. Hull is wary of the problems with treating genes as abstract information rather than as material bodies and with analyzing replication as copying. Directness is supposed to remedy a defect in the copying analysis of replication. That analysis, if it works at all for DNA, suggests that replication is anything but direct. Unfortunately, directness also fails as an analysis of replication unless some sense can be made out of what is known to happen to individual strands in the transmission of information, and copying is the only other candidate on the table for that job. (One senses a whiff of false dichotomy.) Thus it seems that while Hull intended directness to replace copying in the generalization, we need the latter to explicate the former. Dawkins’s treatment of replicators is exceedingly subtle in its use of the passive voice, as noted above, which may have been designed to skirt the issue of biological agency and the “homuncular” ring of his earlier statement of the gene’s eye view: replicators are things of which copies are made. Unfortunately, this formulation masks the difficult problems of understanding what sort of a process copying is: problems about whether replicators make copies of themselves – which they must if we are to be able to speak of a direct causal relation – and even problems about whether copying is a material process at all or just a relation that holds among abstractions because certain processes (like reproduction) do operate. In contrast to the Dawkins-Hull account of replication, my view is that whether or not “the” parental nucleotide sequence is instantiated in offspring is irrelevant to an analysis of reproduction. Hence, I will claim, it is irrelevant to the analysis of evolution as a process, however much this instantiation in offspring bears on evolutionary outcomes by determining the degree to which descent with modification causes resemblance among members of a lineage. In a word: one cannot produce process out of function alone. If the mechanism of
doctrine idealizes the organism in such a way that genes and organisms exist sequentially in time as well as compositionally in structure.
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DNA replication were indeed essential to reproduction in general, then Dawkins’s copying process might support a suitably general analysis of evolutionary benefit. But since this mechanism is contingent, the criteria Dawkins attributes to replicators such that they are the sole beneficiaries of evolution fail. It is not necessary that reproducers be replicators in Dawkins’s sense. Reproduction could occur by some other mechanism and the reproductive entities would nevertheless be beneficiaries in the relevant evolutionary sense. The problem with the Dawkins-Hull analysis is that it claims to abstract from mechanism but fails to do so completely. The remedy is not to be even more vigilant in the formulation of the abstraction, but to find those aspects of mechanism which are common and relevant to functional entities as evolutionary units regardless of level of organization. Material overlap is such a property of biological systems, whether it is necessarily or only contingently universal. It would be tidy if, as Hull hopes, a purely functional theory could be produced because then it would be a simple matter to extend the theory to include cultural and conceptual systems. So much the worse for tidy systembuilding. The descent relation implicit in Dawkins’s notion of copying is incorporated into Hull’s description. On Hull’s version, replication is treated as the paradigm case of a causal process of reproduction which operates at the level of DNA. But the particular mechanisms by which reproduction in any species occurs are themselves products of evolution, so an analysis of the replication process that relies on features of biologically contingent mechanisms cannot provide necessary conditions for the process as such. Biologists now argue, for example, that RNA was probably the original hereditary material rather than DNA because of the self-catalytic and synthetic capabilities of some RNAs.33 So, unless DNA replication is necessary for evolution to occur, a theory of evolution based on specific properties of the DNA mechanism isn’t guaranteed to be general. But if evolution depends necessarily on DNA, the DNA mechanism itself could not have evolved, even if it “came from” an RNA-based system. It is conceivable that an RNA-based rather than a DNA-based genetic system could have become entrenched in the history of life on earth. The near universality of the DNA mechanism may make replication a convenient metaphor for the evolutionarily significant process of reproduction, but because of its evolved character, it is a potentially misleading metaphor.34 ⎯⎯⎯⎯⎯⎯⎯ See Watson et al. (1987) and Alberts et al. (1989) for reviews. This point is analogous to Beatty’s (1982) argument that Mendel’s laws are not reducible to molecular genetics because what explains Mendel’s laws is the cellular process of normal meiosis, which is itself under genetic control. The explanation of that control will be evolutionary, and evolutionary explanations are not part of molecular genetics. Likewise, replication is a mechanism that serves the process of reproduction which in turn makes biological evolution possible. This mechanism has evolved, as can be gleaned from arguments to the effect that the first replicators
33 34
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The analysis of evolutionary theory in terms of replication subtracts the materiality of the connection between generations by treating that connection as essentially informational; even if some material connection or other also occurs, no particular type of material considerations seem relevant once the abstraction to replicators has been made. But how are we to understand the nature of this information? I suggested above that hereditary information in biological systems resides in the relation between the materials with “information bearing” structure (such as nucleic acids) and the material context which makes these structures count as information-bearing. If this reference to mechanism is not required to specify what is to count as hereditary information, then it is incumbent on Hull to show why not and to show further that the explication of hereditary information can be done in purely functional terms. An alternative view that preserves the essentially material quality of the evolutionary process might focus on what distinguishes the replication and transmission of information from reproduction. A generalization strategy that takes matter or stuff (as well as structure and function) into account through a general theory of reproduction rather than a generalization of DNA replication may do this. Such a strategy would be preferable if, as I believe, persistence of parts is a universal property of all (biological) reproduction processes but not of all replication processes, as explicated in terms of copying or directness of transmission of structure. By way of summary of this section, I will discuss the difficulties sketched above in terms of broader aspects of the generalization strategy that Hull and Dawkins pursue. The lesson to be learned is that no piecemeal modification of the criteria for replicators and interactors will resolve these difficulties. Hull’s and Dawkins’s criteria, although offered as alternatives, are fundamentally locked together. My aim is not to undercut the novelty or importance of their analysis. Rather, I aim to explore problems with the use of the Dawkins-Hull ontology for evolutionary theory generalization due to the unexamined role of the background theories that supply the properties of biological materials and mechanisms. Once the background theories that supply such ontological resources are acknowledged, however, there is no longer any principled reason for keeping them out of the foreground theory. This problem is generic to all versions of the strategy because it underlies the whole notion of generalizing theories by abstraction. The problems start with Dawkins’s and Hull’s analysis of the particular properties of nucleic acid replication mechanisms. A different understanding of these properties might lead to a strategy of generalization that does not begin
were catalytic RNAs. But the mechanisms that serve reproduction might have been otherwise, and at other levels of organization they probably are otherwise, so replication cannot be an adequate basis for analyzing reproduction (and hence evolution).
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with abstraction to pure function, devoid of reference to mechanism. The Dawkins-Hull strategy for generalization, based on abstraction of kinds of explanatory factors from genic and organismal matter, does not go far enough toward a full process ontology for evolutionary theory. The concepts central to Dawkins’s and Hull’s versions of the strategy, copying and directness respectively, are inadequate for their purposes because they do not provide the conceptual tools for a purely functionalist analysis. Instead, they tacitly draw on background theory which includes consideration of matter and mechanism. Copying and directness fail to capture important aspects of actual replication, and the retreat to “transmission of structure largely intact” just raises questions about these aspects anew. But my conclusion is stronger: even if they succeeded in expressing all pertinent facts about DNA replication their success, by making explicit the dependency of their generalization on level-specific mechanisms, would merely show that DNA replication is an insufficient basis from which to build a general evolutionary theory according to their requirement of pure functionalism. The point, vis-à-vis Dawkins, is this: if genes are defined abstractly, in terms of heritable information, instead of more concretely, in terms of the particular embodiments or “avatars” of information, then it no longer follows from the definition itself that there is a hierarchical arrangements into levels. But the hierarchical arrangement figured centrally in Dawkins’s argument that the gene is the sole unit of selection. In so far as hierarchy is used in inferences drawn by Dawkins, the concept of hierarchy must somehow be reintroduced into the theory. That is, his success would have the unintended consequence of revealing how the “generalization” from gene to replicator is contaminated by levelspecific mechanisms in which the hierarchical arrangement of DNA inside cells of organisms is extrapolated to the general concept of replicator. Dawkins reintroduces the concept of hierarchy by explicitly invoking Weismannism, which is merely to replace on background assumption with another. The point vis-à-vis Hull is that the relative directness that differentiates replicators from interactors depends on contingent facts about mechanisms. If any entity at any level of the traditional hierarchy could be either a replicator or an interactor, then there is no necessity that DNA replicate more directly than organisms. There would also be no necessity that organisms interact more directly with their environments than genes do. If genes can be interactors and organisms can be replicators, then any claim about the relative directness or indirectness of the replication and interaction of typical genes and organisms is as much an empirical assumption as is the focal level of selection. Hull preserves a notion of hierarchy by a tacit assumption of Weismannism that guides him to conclusions about the structure of transmission of hereditary information and to the conclusion that pieces of genetic material are more likely to function as replicators than organisms.
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More broadly still, the Dawkins-Hull strategy takes replication to be one of the two component processes of evolution and relies on properties of replication rather than properties of reproduction, the process which underlies all biological descent relations. Replication and reproduction are easily confounded and must be distinguished if a full account of evolutionary process is to succeed. In my view, replication turns out to be merely one contingent, albeit widespread, family of mechanisms for reproduction. Whatever else biological reproduction is, it is a process that requires material overlap between sequential elements of the lineages it creates. The underlying difficulty in achieving a pure function abstraction is most easily seen by examination of Dawkins’s and Hull’s (various) definitions of replicator. Dawkins defines replicators in terms of the notion of copy. But “copy” and “copying” are explicated only in terms of analogies to photocopying machines along with the assertion that DNA is a paradigm replicator. For Dawkins’s generalization strategy to work, the analogies must be precise and robust. Hull defines replicators in terms of the process of replication. While this has the virtue of appearing to avoid essential reference to the traditional biological hierarchy, it fails to secure generality for the resulting theory unless replication can be antecedently understood. But what is replication? Hull doesn’t define it in any of the published essays discussed thus far. If we simply appeal to the properties of DNA replication, it will remain unclear whether the identified features are essential properties of the process or only properties of the mechanism by which DNA happens to do it (or worse, perhaps only properties of the molecular level at which DNA resides, making the new ontology derivative on the old one). In a 1991 manuscript, Hull does define replication, but alas in terms of copying: In replication, certain entities replicate, transmitting the information embodied in their structure largely intact from one generation to the next. The operative terms are “transmission” and “generation.” Replication is a copying process. The information incorporated in the structure of one physical vehicle is passed on to another (Hull 1991, pp. 23-24).
But if accepted, this refinement would merely move the problem all the way back to Dawkins’s original discussion of replication in terms of copying. It raises anew the problems of understanding the concepts of information and descent in such a way that the transmission of this information involves descent. If it is a copying process, DNA replication isn’t just any copying process. Since an adequate description of the process of DNA replication depends crucially on reference to properties and relations specified by background theories (primarily in molecular biology), these theories may fail to specify the sort of evolutionarily relevant functional roles required by the Dawkins-Hull strategy. Thus, Dawkins and Hull must either produce the insights which will allow them to
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truly purge their abstraction to function of all traces of reference to matter and mechanism, or they must find a way to accommodate the facts about mechanism that still permits generalization. As I will stress below, standard characterizations of genes in terms of their information content risk inadequacy by ignoring features of development important to evolution, but this does not mean that there is no route to a general theory of evolution open to the materialist. To what seemingly more general properties of replication might one appeal that do not depend on mechanisms of DNA replication? As I have argued, mining Dawkins’s analysis of copying as a source would merely throw the problem back to the worry about the weakness of his analogies. The other source of properties I favor is conceptual analysis of the process of reproduction. But I haven’t given such an analysis, and it is an interesting fact that while biologists have devoted much effort to the description and evolutionary analysis of mechanisms of reproduction, they have not paid much attention to the concept of reproduction itself.35 One way to begin to understand what is needed is to examine the source of the analysis of replication in the Dawkins-Hull program evident in their writings: Weismannism.
6. Weismannism as a Basis for Generalization-by-Abstraction The Dawkins-Hull abstraction strategy articulates evolutionary roles in terms of causal relations specified by Weismannism in order to abstract evolutionary functional roles from organismal and genetic material, i.e., to subtract the mechanism-dependent properties of this specific material. But the version used, molecular Weismannism, contaminates the abstract causal structure with levelspecific mechanisms of the matter in which they operate. Weismannism misconstrues the role of development in specifying the causal structure Weismann envisioned. The fundamental shift away from the Lewontin strategy is to characterize the entities that function in the evolutionary process directly, without consideration of traditional hierarchical levels of organization. In order to focus on process, Hull and Dawkins rely on a background theory of causal relations between genic and organismic material that explains their capacity to function in the evolutionary roles of replicators and interactors. Once the evolutionary roles of genes and organisms are analyzed in terms of the implied causal structure, they can be abstracted from the specific material and the concrete mechanisms through which genes and organisms exercise their capacities. By quantifying ⎯⎯⎯⎯⎯⎯⎯ 35
Since I do not intend to present an analysis of reproduction here, my sweeping statements are intended only as a sketch of the difficulty. For an interesting attempt to analyze the concept of reproduction, see Bell (1982). For theoretical work that shows how important it is to develop an analysis, see Harper (1977), Jackson et al. (1985), and Buss (1987).
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over these abstract entities specified in terms of developmental and hereditary causal structure and evolutionary function, evolutionary theory is made general and devoid of reference to the traditional biological hierarchy. The critical background theory which supplies the relevant causal relations is generally known as Weismannism.36 In fact, there are at least three significantly different versions of this theory: Weismann’s own (mature) theory; a contemporary variant due to Weismann in an earlier period also held by Jäger, Nussbaum, and Wilson; and a modern molecular version attributable to Crick and Maynard Smith.37
Fig. 1. Weismannism as represented by E. B. Wilson, reproduced from Wilson (1896), p. 13, fig. 5.
The standard interpretation of Weismann’s theory is not Weismann’s own, but rather the version presented by E.B. Wilson in a famous diagram in his 1896 textbook, The Cell in Development and Inheritance (see figure 1). Wilson was apparently aware that his version expressed only some aspects of Weismann’s theory. But Wilson’s purpose was more limited than Weismann’s: to assert the non-inheritance of acquired characteristics as a consequence of the continuity of the germ-cells and discontinuity of the soma. Weismann’s mature view is subtly different: he asserted the continuity of the germ-plasm and discontinuity of the soma. Wilson’s diagram characterizes three central points about the causal structure of development and heredity that are mapped into Dawkins’s abstract ⎯⎯⎯⎯⎯⎯⎯ 36
Weismann (1892), Wilson (1896). See Churchill (1968, 1985, 1987), Maienschein (1987), Mayr (1982, 1985), and Griesemer and Wimsatt (1989) for historical details. 37 See Griesemer and Wimsatt (1989). On Weismann’s change of views from a germ-cell to a germplasm theory in the 1880s, see Churchill’s excellent (1987) article.
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treatment of replicators. First, the germinal material is potentially immortal since it may be passed from generation to generation (succession of arrows along the bottom of figure 1). Second, the somatic material, which represents the body, is shown to be transitory through the lack of arrows extending directly from generation to generation. Third, the germinal material is also causally responsible for the production of the soma (arrows from G to S in each generation), but not conversely (no arrows from S to G).
Fig. 2. The central dogma of molecular genetics, reproduced from Crick (1970), p. 561, fig. 2. Arrows represent transfers of information. Solid arrows indicate “probable” transfers and broken arrows indicate “possible” transfers. Crick’s diagram indicated how he thought things stood in 1958.
The molecular version of Weismannism is expressed in Crick’s central dogma of molecular genetics.38 It asserts an asymmetrical causal relation between nucleic acids and protein that is isomorphic to the Wilson diagram of Weismannism and supplies a rough molecular interpretation of Weismannism. DNA codes for DNA and DNA also codes for protein, but protein does not code for DNA (see figure 2). Maynard Smith drew explicit attention to the isomorphism in a diagram comparing a simplified version of Wilson’s diagram of Weismannism with a simplified version of Crick’s diagram of the central dogma (see figure 3) (Maynard Smith 1975, p. 67, fig. 8). The relative directness of DNA replication as compared to replication of the proteins (in an offspring) is evident in the causal asymmetry of the diagrams. The indirectness ⎯⎯⎯⎯⎯⎯⎯ 38
Crick (1958, p. 153) expressed the dogma in words: The Central Dogma This states that once ‘information’ has passed into protein it cannot get out again. In more detail, the transfer of information from nucleic acid to nucleic acid, or from nucleic acid to protein may be possible, but transfer from protein to protein, or from protein to nucleic acid is impossible. Information means here the precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein.
Crick (1970) expressed the dogma in a diagram (see fig. 2) which reinforced the original interpretation in light of the recent discovery of reverse transcriptase. For reviews, see Watson et al. (1987) and Alberts et al. (1989).
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of somatic replication is manifest in the fact that all of development is involved in making a new organism: complex developmental pathways are involved in the organization of a soma from the protein (and other molecular) constituents of a zygote. But this complexity is represented in the diagrams simply as the lack of a causal arrow from soma to soma. What was supposed to be a quantitative, degree property – relative directness – is mysteriously represented by a qualitative difference: whether there is or is not a causal path shown in the diagram. It is crucial to note that tracing the pathway from soma to soma involves running backward along some causal arrows in the sequence.
Fig. 3. Comparison of a simplified representation of the central dogma of molecular genetics with a simplified representation of Weismannism, from Maynard Smith (1975), p. 67, fig. 8. Reproduced by permission of Penguin Books Ltd.
Weismann’s own version and diagrams tell a different story.39 Weismann clearly held that the germ-plasm, i.e., the molecular protoplasm of the nucleus, was continuous despite the discontinuity of the germ-cells. Weismann’s famous figure 16 (see figure 4) illustrates this well: germ-cells are products of somatic differentiation that appear at some number of cell divisions characteristic for each species after a zygote begins to divide. In the example illustrated in figure 4, germ-cells (UrKeimzellen) make their first appearance in the embryo in cell generation nine. Nevertheless, Weismann theorized, the germ-plasm inside these somatic cells remained intact and continuous from cell-generation to cellgeneration (except for the part Weismann called accessory idioplasm, which ⎯⎯⎯⎯⎯⎯⎯ 39
Weismann (1892); cf. Griesemer and Wimsatt (1989). Churchill, (1987, p. 346) argues that Weismann held the germ-cell theory in his 1883 essay “On Heredity” (collected in Weismann (1889)), a view he rejected in the 1892 book.
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was responsible for the somatic differentiation of cells carrying the germ-plasm of the future germ-cells). Weismann vigorously objected to the Jäger-Nussbaum theory of germ-cell continuity as a violation of his mature views on how cell differentiation occurred in a wide variety of organisms, a distinction Wilson failed to include in his various representations of Weismannism.
Fig. 4. Weismann’s own representation of his theory of the continuity of the germ-plasm and discontinuity of the soma, showing 12 cell generations in the development of Rhabditis nigrovenosa with time extending from the bottom to the top of the diagram. Germ-cells (UrKeimzellen) appear in the cell generation marked “9.” Braces indicate different germ layers so as to correspond with preceding diagrams in the text (endoderm, “Ent”; mesoderm, “Mes”; ectoderm, “Ekt”). Reproduced from Weismann (1893), p. 196, fig. 16.
One plausible reason that Weismann’s views are not typically discussed in their entirety in the twentieth-century literature is that this complementing mosaic theory of development was discredited. This theory explained differentiation of the soma as the result of the qualitative division of germ-plasm in the somatic cells, such that terminally differentiated cells exhibited only a single remaining “genetic” determinant. While modern biologists accepted Weismann’s
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argument against the inheritance of acquired characteristics, they rejected part of his developmental theory which simultaneously explained facts of heredity and development. One critical difference between Weismann and his expositors is that Weismann would never have drawn a diagram like Wilson’s to summarize his views. The Wilson diagram really only illustrates one implication of Weismann’s unified heredity-development theory for genetics: that characteristics acquired by the soma are not inherited because there is no developmental pathway by which they could influence the germ-plasm. While Weismann’s modern expositors reject the mosaic theory of differentiation, it is wrong to conclude that only the non-inheritance of acquired characteristics follows from Weismann’s theory of the continuity of the germ-plasm. Most modern evolutionists write as though molecular Weismannism (or Wilson’s nonmolecular version) expresses the whole of Weismann’s doctrine. It is important to attend to these historical details because the version of Weismannism chosen as a background theory is crucial for understanding the uses and applicability of a generalized evolutionary theory.40 Weismannism entails the causal asymmetry that guides the replicator-interactor distinction. But Weismann’s own view includes a more complex story of development, one which leaves room for a less asymmetrical picture of the causal relations between germ-plasm and soma: a picture in which somatic differentiation causes the continuity of the germ-plasm, thus making heredity a phenomenon of development and requiring that a causal arrow extend from soma to soma in order to explain facts of heredity. The molecular version of Weismannism is the most rigid of all: its idealization of the soma, as if it were made of protein, and abstraction of the germ-plasm, as if it were merely the information of the DNA sequence, leaves no room for development at all.41 ⎯⎯⎯⎯⎯⎯⎯ 40
The aim here is not to criticize Dawkins or Hull for misreading Weismann, but rather to point out the nature and role of the assumptions they make and to suggest that evolutionary theory would be better off if Weismann were heeded rather than Weismannism. While Dawkins clearly identifies himself as a Weismannian (1982a, p. 164), it is no part of Hull’s project to reconstruct or even be faithful to Weismann’s views: historical accuracy does not typically play a role in scientific progress. 41 I am here following Cartwright’s distinction between idealization and abstraction. Simply put, idealizations involve the mental “rearrangement” of inconvenient features of an object, such as treating a plane as frictionless, before formalizing a description of it. Abstraction involves taking certain features or factors “out of context all together.” The latter “is not a matter of changing any particular features or properties, but rather of subtracting, not only the concrete circumstances but even the material in which the cause is embedded and all that follows from that” ( Cartwright 1989, §5.2, esp. p. 187). The soma is treated ideally as protein in the following sense. Although organisms are not made only of protein, the presence and arrangement of the other constituents is by and large caused (and explained) by the metabolic activity of enzymes, which are proteins. Thus it is an idealization, though a reasonable one for some purposes, to exclude from consideration the complications due to taking other molecular constituents into account. Ignoring the other
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Molecular Weismannism’s causal story of development goes like this: DNA replicates to make more DNA; then in the offspring, the DNA makes protein; then a miracle happens and the protein and a lot of other stuff gets arranged in cells causing them to differentiate and form complex tissues and organs, yielding the soma. I claim that the abstraction strategy for generalizing evolutionary theory under discussion here draws primarily on molecular Weismannism (and occasionally on the less specific Wilson version). But the success of molecular Weismannism as a theory of genes and organisms rests on level-specific mechanisms through which DNA sequences code for the “information” in protein sequences. If they are level-specific, generalization of such mechanisms will not yield a multi-level account of evolution. Development can be successfully treated as miraculous in this context because the entities are idealized and their relevant properties are taken to be information in abstraction. The problem with the abstraction for evolutionary purposes is that genes do not specify information in abstraction from their matter any more than cassette tapes specify music in abstraction from tape players.42 If different types of mechanisms are embodied at other levels due to differences in the material entities involved, then the strategy may fail to even recognize information when it is present, let alone properly analyze its transmission. If, for example, features of the “environment” of biological entities are “transmitted” and function as “genetic information,” then a rather different assemblage of matter must be followed to analyze evolution. The causal structure of Weismannism rules out this possibility a priori. Dawkins is much more explicit than Hull about the Weismannian foundation of his work, but since the replicator-interactor distinction Hull draws depends on the same causal structure as Dawkins’s replicator-vehicle distinction, I think it is fair to attribute reliance on Weismannism to both. Dawkins expressed the dependency in no uncertain terms: “the theoretical position adopted in this book is fairly describable as ‘extreme Weismannism’ . . .” (Dawkins 1982a, p. 164). It is interesting to note that Dawkins did not cite Weismann’s work in his book, nor does it seem necessary to do so: Weismannism is thoroughly infused in the thinking of biologists. To underscore the main issue, my point is not that Dawkins or Hull is guilty of misreading Weismann – they are not reading Weismann at all – but rather that they should read Weismann because his views are closer to an adequate basis for generalization-by-abstraction of evolutionary theory than the attenuated twentieth-century versions of Weismannism. The first fact of Weismannism represented in the Wilson diagram (see figure 1) underlies Dawkins’s answer to the question about what adaptations are for constituents is analogous to treating the plane as frictionless. By contrast, treating DNA sequences, i.e., genetic information, as germ-plasm involves taking the information content of a molecule out of all material context. It is not at all clear that it is reasonable to treat organisms as information. 42 For criticisms of the concept of genetic information, see Hanna (1985) and Wimsatt (1986).
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the good of. The causal continuity of the germinal material implies that it is potentially immortal, hence at least a candidate to receive the evolutionary benefit of an increasingly adapted soma. The second fact underlies Dawkins’s view that the body serves merely as a vehicle in which the evolutionarily significant entities, the replicators, ride and through which their replication is made differential (in virtue of the vehicles’ having different fitness). The discontinuity of the soma implies that it cannot be an evolutionary beneficiary because it fails to persist. The third fact governs the distinction between active and passive replicators and determines which replicators are the ones whose perpetuation is differential in virtue of a given interactor’s causal interaction with the external environment. Germ-line replicators may be active in virtue of their causal role in producing the soma and thus possibly influence the probability with which they are copied. Although Wilson’s diagram does not directly imply a part-whole relationship between germ-line and soma, this is the usual interpretation of the relationship between the germ cells and the soma. Hull’s discomfort with Dawkins’s definition of replicators in terms of copying can be interpreted in the light of what Weismannism does and does not imply. The arrows connecting elements of Wilson’s diagram are all causal, but nothing is implied about the degree of similarity required for the relevant causal relations to hold. Rather, the degree of similarity will depend on the specific mechanisms through which the materials of the germ-plasm and the soma exhibit their causal capacities by the effects of their action. Thus, Hull’s focus on directness or on intact transmission reflects only the causal structure exhibited in Wilson’s diagram of Weismannism. The most celebrated consequence of Weismannism, the non-inheritance of acquired characteristics, is entailed by the causal asymmetry underlying similarities among interactors (somata) and among replicators (germ-cells). The resemblance among successive interactors is indirect and a consequence of mediation by the germ-line. The resemblance among replicators and their copies is direct and due to the direct causal relation between them. For characteristics acquired by somatic interactors to be inherited there would have to be causal arrows from the soma back to the germ-line. Thus, bare causal roles interpreted in terms of the directness of transmission of structure or of interaction with the external environment as specified by Weismannism replace the specific similarity requirement in Hull’s original modification of Dawkins’s analysis. In Hull’s later treatment, directness is dropped as a characterization of the causal quality of the relations in favor of unvarnished reference to causation: passing on structure largely intact in the case of replicators and causal interaction in the case of interactors. These modifications insure that nothing more than is contained in the Weismannian structure is read into the evolutionary analysis. Directness thus seems to turn on features of qualitative causal structure rather than on any specific mechanisms limited to the materials
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that happen to be isomorphic to that structure at the canonical levels of genes and organisms. But why should directness or intactness of structure in transmission be essential to replicators? Continuity and cohesiveness, Hull argues, are properties of historical individuals.43 Transmission of structure largely intact appears to be a sufficient condition for preservation of these properties in the parts of a lineage (and possibly of the lineage itself). But these are properties maintained by development (or ecology in the case of higher level ecological entities like communities) within generations, and hence are contingent and subject to evolutionary change. They appear to be necessary properties of replicators only because Weismannism dictates that it is through the replicators (genes) that structure, and hence continuity and cohesiveness, are perpetuated. A different causal structure might not have the same implications; in particular, one in which there are causal arrows from soma to soma would not.44 It is important to recognize that the mere presence of a causal arrow from soma to soma does not entail the inheritance of acquired characteristics as many authors, including Dawkins and Hull, seem to conclude. Such a causal relation is clearly a necessary condition, but much more is required than that. In particular, development must be arranged in just the right way for characters acquired by the non-germinal elements to be passed on. In many types of organism, development involves passage through a single cell “bottleneck” between generations in the form of a zygote. Characters acquired by other cells that are not passed through the germ-plasm must somehow transmit such characters, or information about them, to the germ-cells giving rise to the zygote in order to be inherited. Thus it is not presence of a causal arrow from soma to soma per se which implies the inheritance of acquired characteristics, but just the right sort of causal arrow of development. Articulation of such developmental causal relations was the centerpiece of Weismann’s research. It should also be noted that on Weismann’s view, germ-cells are somatic and germ-plasm passes through the soma, so in an important sense all modifications are acquired and somatic. Weismann was willing to allow this meaning of “acquired” as long as it is clear that modifications not transmitted are distinguished from those that are (Weismann 1888). But while it is true that the evolutionary fate of modifications is a different question from the largely developmental explanation of their origin, it does not follow from this fact that ⎯⎯⎯⎯⎯⎯⎯ 43
Consider, e.g., Hull (1975) in light of his subsequent work. Wimsatt (1981) points out that one must minimally consider the trade-off between rates of replication and degree of stability to account for the transmission of structure (and hence the heritability of adaptive characters). Since different combinations of replication rates and degrees of stability can satisfy the same trade-off, there is no single degree of stability that will satisfy the condition Hull argues for. Direct causal arrows from soma to soma might change the trade-off in fundamental ways.
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the causal analysis of the former can be made independently of the latter: development figures prominently in how hereditary transmission works. To summarize, I claim that Weismannism in general and molecular Weismannism in particular endorse a picture of certain biological causal relations which serves as a background theory in the generalization-byabstraction strategy employed by Dawkins and Hull. This background theory facilitates abstraction by representing causal structure without the need for explicit reference to concrete material entities: ‘G’ and ‘S’ or ‘DNA’ and ‘P’ practically serve as the variables in a theory that quantifies over many potential material entity types that may serve evolutionary roles. But molecular Weismannism facilitates abstraction in a way that gets facts of development and inheritance wrong that are crucial for evolutionary theory. In particular it gets facts about the causal relations among somata and between germ-plasm and soma wrong. Indeed, it misidentifies them as accidental facts about hereditary transmission of information rather than as essential facts about development, which in turn explains heredity. Weismann’s view and Weismannism both entail the non-inheritance of acquired characteristics, but for different reasons. The former entails it because of specific facts about developmental mechanisms that happen to hold at the levels of genes and organisms; the latter entails it because of its abstraction of causal structure from material genes and organisms.
7. Conclusion: A Function for Background Theories in Theory Construction I have argued that molecular Weismannism functions as a crucial background theory for the Dawkins-Hull generalization-by-abstraction strategy applied to neo-Darwinian evolutionary theory. The Lewontin strategy, by contrast, relies less on an articulated background theory for its generalization than on unarticulated assumptions about the biological hierarchy. Some such background theory or assumption is needed for the project because modern evolutionary theory, while rich in its causal account of selection and its tracing of the implications of inheritance, is lacking in resources to individuate the entities that are its subject. Weismannism, or the part-whole relation implicit in standard assumptions about the biological hierarchy, provides just enough causal structure to serve the minimal requirements for generalizing evolutionary theory. Unfortunately, that structure gives a false or misleading account of evolution: it inadequately abstracts from the relevant developmental phenomena responsible for the evolutionary properties of biological entities. The remedy for this inadequacy will be dealt with elsewhere. Here my aim has been to raise some philosophical problems with the extant strategy that is most articulate in its metaphysical assumptions.
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The key to abstraction for the purpose of generalizing evolutionary theory is in adopting a background theory that identifies relevant kinds of explanatory factors. Weismannism does this by emphasizing the causal asymmetry between two sorts of biological entities, abstracting from the materials in which this asymmetry is paradigmatically instantiated. Even the part-whole relation between genes and organisms, so central to Dawkins’s metaphor of replicators and vehicles, is expunged from molecular Weismannism. Nevertheless, use of the metaphor in theory generalization requires that the mechanisms which sustain the part-whole relation between genes and organisms hold in general. In this way, mechanism-specific features of genes and organisms, which spoil the chances for adequate generalization, are tacitly built into diagrammatic representations of Weismannism or its theorem about the non-inheritance of acquired characteristics. Mechanism-specific features are needed by the strategies discussed here because an adequate generalization of evolutionary theory must somehow take development into account. The part-whole relation between genes and organisms is tacitly used in place of a theory of development because it entails some of the same facts. The absurd view that organisms can be reduced to their genes is the counterpart to this abstraction strategy. Hull concludes that “this is not your ordinary reductionism” because it fails to take all the parts and their interrelations into account (Hull, personal communication). Failure to recognize this oddity of gene reduction means that attacks on gene reductionism rarely address the root problem with the underlying assumptions common to reductionism and the abstraction strategy. By identifying kinds of explanatory factors and abstracting from some, molecular Weismannism makes generalization tractable. Biological entities at each level are quite heterogeneous, even in such critical functions as reproduction, as the mountain of empirical literature on the relatively small proportion of described taxa already attests. Studying organisms and species in their particularity is essential to understanding, and saying, what happens. Biological theorizing about such heterogeneity is, however, utterly unfamiliar to classical philosophy of science. For a biological theory to be general, it must range over the diversity we know about and the diversity we don’t know about. Abstraction from matter seems crucial in a world of prions (proteinaceous infectious particles), viruses, bacteria, cellular slime molds, plants, and animals. What matters from an evolutionary point of view is whether an entity has the capacity to function in the evolutionary process, not what it is made of. But asserting such capacities is quite different than claiming that evolutionary theory can be made general by abstraction from matter or substance. Some properties of matter qua matter are essential to evolution as a process and if these are abstracted away, the resulting generalization will be vacuous.
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The history of twentieth-century biology has conspired to obscure crucial elements of the strategy for making evolutionary theory general. As biology diversified as a science and its subdisciplines professionalized, interrelationships among phenomena studied by emerging subdisciplines were forgotten and phenomena distinctly in the domain of each separate specialty emphasized. Problems of heredity became divided into problems of genetics and problems of development. Problems of natural history became divided into problems of ecology, systematics, biogeography and paleontology. But the evolutionary process requires an integrated understanding of these problems: solutions to all of them depend on the fact that the properties of entities described in these specialties are products of evolution and on the fact that a general evolutionary theory must somehow take them all into account. This contextualization of the part of evolutionary theorizing that has to do with generalization suggests a way to broaden the view of abstraction as a scientific process. Generalization-by-abstraction involves quantifying over abstract entities. The abstract entities are constructed by a process that is welldescribed in terms of the Cartwright-Mendell partial ordering criterion of abstract objects, with the proviso that abstraction is relative to an empirical background theory that specifies explanatory kinds. Cartwright and Mendell suggest that one object is more abstract than another if the kinds of explanatory factors specified for it are a subset of those specified for the other. This criterion assumes an Aristotelian theory of kinds of explanatory factors. One unsatisfying feature of their approach, however, is the seeming arbitrariness of the explanatory theory assumed. Another theory of explanatory factors may yield a different ordering of the abstract under the criterion as described. When abstraction is used in science for purposes of theory generalization, the field of explanatory kinds is determined by adoption of a scientific background theory that operates in the way molecular Weismannism does for evolutionary theory. This view makes the ordering of abstract objects scientifically non-arbitrary, while leaving room for fundamental differences in the form of general theories which depend on background theories that order the field of explanatory kinds differently. If it is the case, for example, that there really are two units of selection questions, one about the levels of the hierarchy at which units “reside” and one about the ontic levels at which the causal process of natural selection occurs, this fact entails that the two background “theories,” the theory of the biological hierarchy and the theory of molecular Weismannism, have different implications. It is thus a matter of some interest for the sake of general evolutionary theory to understand what sorts of biological phenomena are left out of the picture by these two background theories. Getting evolutionary theory straight may thus depend as much on
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clarifying the implications of non-evolutionary theories as it does on adding further epicycles to the units of selection story itself.* James R. Griesemer Wissenschaftskolleg zu Berlin Collegium Budapest, and University of California, Davis
[email protected]
REFERENCES Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., and Watson, J. (1989). Molecular Biology of the Cell. 2nd ed. New York: Garland Publishing, Inc. Antonovics, J., Ellstrand, N., and Brandon, R. (1988). Genetic Variation and Environmental Variation: Expectations and Experiments. In: L. Gottlieb and S. Jain (eds.), Plant Evolutionary Biology, pp. 275-303. New York: Chapman and Hall. Asquith, P. and Giere, R., eds. (1981). PSA 1980. East Lansing: Philosophy of Science Association. Asquith, P. and Nickles, T., eds. (1982). PSA 1982. East Lansing: Philosophy of Science Association. Beatty, J. (1982). The Insights and Oversights of Molecular Genetics: The Place of the Evolutionary Perspective. In: Asquith and Nickles (1982), vol. 1, pp. 341-355. Bell, G. (1982). The Masterpiece of Nature. Berkeley: University of California Press. Boyd, R. and Richerson, P. (1985). Culture and the Evolutionary Process. Chicago: University of Chicago Press. Brandon, R. (1982). The Levels of Selection. In: Asquith and Nickles (1982), vol. 1, pp. 315-323. Brandon, R. (1985). Adaptation Explanations: Are Adaptations for the Good of the Replicators or Interactors? In: D. Depew and B. Weber (eds.), Evolution at a Crossroads, pp. 81-96. Cambridge, Mass.: The MIT Press. Brandon, R. (1990). Adaptation and Environment. Princeton: Princeton University Press. Brandon, R. and Burian, R., eds. (1984). Genes, Organisms, Populations: Controversies over the Units of Selection. Cambridge, Mass.: The MIT Press. Buss, L. (1987). The Evolution of Individuality. Princeton: Princeton University Press. Cartwright, N. (1989). Nature’s Capacities and their Measurement. New York: Oxford University Press. Cartwright, N. and Mendell, H. (1984). What Makes Physics’ Objects Abstract? In: J. Cushing, C. Delaney, and G. Gutting (eds.), Science and Reality: Recent Work in the Philosophy of Science, pp. 134-152. Notre Dame: University of Notre Dame Press. Cherry, C. (1966). On Human Communication: A Review, A Survey, and A Criticism. 2nd ed. Cambridge, Mass.: The MIT Press.
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I wish to thank Robert Brandon, Dick Burian, Leo Buss, Marjorie Grene, Lorraine Heisler, David Hull, Evelyn Fox Keller, Dick Lewontin, Lisa Lloyd, Sandy Mitchell, Eörs Szathmáry, Bill Wimsatt and Jeff Workman for helpful comments on previous versions of the manuscript. Lisa Lloyd helped clarify important features of her formal analysis of evolutionary theory. JaRue Manning, Rob Page, Bruce Riska, Brad Shaffer and Michael Wedin provided helpful discussion. I also wish to thank Stuart Kauffman and the Santa Fe Institute for their invitation to participate in the Foundations of Development and Evolution Conference in 1989 and the Wissenschaftskolleg zu Berlin for a fellowship in 1992-93. This essay is dedicated to Bruce Riska.
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Lloyd, E. (1988). The Structure and Confirmation of Evolutionary Theory. New York: Greenwood Press. Lloyd, E. (2001). Different Questions: Levels and Units of Selection. In: R. S. Singh, C. B. Krimbas, D. Paul, and J. Beatty (eds.), Thinking about Evolution: Historical, Philosophical and Political Perspectives. Cambridge: Cambridge University Press. Margulis, L. and Sagan, D. (1986). Origins of Sex, Three Billion Years of Genetic Recombination. New Haven, Conn.: Yale University Press. Maienschein, J. (1987). Heredity/Development in the United States, circa 1900. History and Philosophy of the Life Sciences 9, 79-93. Maynard Smith, J. (1975). The Theory of Evolution. 3rd ed. Middlesex: Penguin. Mayr, E. (1982). The Growth of Biological Thought. Cambridge, Mass.: Belknap-Harvard Press. Mayr, E. (1985). Weismann and Evolution. Journal of the History of Biology 18, 295-329. Mendel, G. (1865). Experiments in Plant Hybridization. Reprinted by P. Mangelsdorf, 1965. Cambridge, Mass.: Harvard University Press. Mitchell, S. (1987). Competing Units of Selection? A Case of Symbiosis. Philosophy of Science 54, 351-367. Rosenberg, A. (1985). The Structure of Biological Science. New York: Cambridge University Press. Ruse, M., ed. (1989). What the Philosophy of Biology Is: Essays Dedicated to David Hull. Boston: Kluwer Academic Publishers. Sapp, J. (1987). Beyond the Gene. New York: Oxford University Press. Sober, E. (1981). Holism, Individualism, and the Units of Selection. In: Asquith and Giere (1981), vol. 2, pp. 93-121. Sober, E. (1984). The Nature of Selection. Cambridge, Mass.: The MIT Press. Sober, E. (1988). Reconstructing the Past: Parsimony, Evolution, and Inference. Cambridge, Mass.: The MIT Press. Stent, G. S. (1977). Explicit and Implicit Semantic Content of the Genetic Information. In: R. Butts and J. Hintikka (eds.), Foundational Problems in the Special Sciences, pp. 121-149. Dordrecht: D. Reidel. Sterelny, K. and Kitcher, P. (1988). The Return of the Gene. Journal of Philosophy 85, 339-361. Wade, M. (1978). A Critical Review of the Models of Group Selection. Quarterly Review of Biology 53, 101-114. Watson, J., Hopkins, N., Roberts, J., Steitz, J., and Weiner, A. (1987). Molecular Biology of the Gene. 4th ed. Menlo Park: Benjamin/Cummings Publ. Co. Weismann, A. (1888). On the Supposed Botanical Proofs of the Inheritance of Acquired Characters. Reprinted in: Weismann, (1889), p. 419ff. Weismann, A. (1889). Essays upon Heredity and Kindred Biological Problems. Authorized translation edited by E. B. Poulton, S. Schonland, and A. E. Shipley. Oxford: Clarendon Press. Reprinted and with an introduction by J. Mazzeo, (1977). Oceanside: Dabor Science Publications. Weismann, A. (1892). Das Keimplasma: eine theorie der Vererbung. Jena: Gustav Fischer. Translated by W. N. Parker and H. Rönnfeldt (1893), under the title The Germ-Plasm: A Theory of Heredity. New York: Charles Scribner’s Sons. Williams, G. (1966). Adaptation and Natural Selection. Princeton: Princeton University Press. Wilson, E. B. (1896). The Cell in Development and Inheritance. 2nd ed.: 1900. London: Macmillan Co. Wimsatt, W. (1980). Reductionistic Research Strategies and their Biases in the Units of Selection Controversy. In T. Nickles (ed.), Scientific Discovery, Volume II: Historical and Scientific Case Studies, pp. 213-259. Dordrecht: D. Reidel. Wimsatt, W. (1981). Units of Selection and the Structure of the Multi-Level Genome. In: Asquith and Giere (1981), vol. 2, 122-183.
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Nancy J. Nersessian ABSTRACTION VIA GENERIC MODELING IN CONCEPT FORMATION IN SCIENCE
1. Introduction Analogies have played a significant role in many instances of concept formation in the sciences. In my own analysis of Faraday’s and Maxwell’s use of analogies in formulating concepts of electric and magnetic actions as field processes, I characterized the process as one of abstraction through increasing constraint satisfaction and hypothesized that it might play a role more widely in science (Nersessian 1988, 1992). What I want to explore here is the role generic modeling plays in conceptual innovation; specifically, in James Clerk Maxwell’s construction of a mathematical representation of his concept of the electromagnetic field as a state of a mechanical aether. What I mean by “generic modeling” is the process of constructing a model that represents features common to a class of phenomena. Abstraction via generic modeling is a strategy that is commonly employed in deriving equations in physics problems. Ronald Giere’s (1988) analysis of how the linear oscillator is presented in science textbooks provides a good example. In modeling a problem about a pendulum by means of a spring, the scientist understands the spring model as generic, that is, as representing the class of simple harmonic oscillators of which the pendulum is a member. Studies of expert physicists’ problem-solving practices carried out by cognitive psychologists reveal the same strategy of finding a generic model from which to abstract the mathematical relationships preliminary to solving the problem (see, e.g., Chi et al. 1981; Clement 1989). Thus, while the Maxwell case is exceptional in its complexity and creativity, examining it stands to provide us with insights about more common usage. My own procedure is to attempt to move from specific case studies to a more general analysis by integrating conclusions from these with those from cognitive studies of like practices. Although I will not discuss that part of my analysis here, my thoughts on generic modeling have been developing in conjunction with ongoing research with several cognitive In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 117-143. Amsterdam/New York, NY: Rodopi, 2005.
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scientists on mental modeling in creating scientific understanding. In that and other analyses, I have identified a reasoning process I call “constructive modeling,” one that employs both analogical and visual modeling as well as thought experimentation (mental simulation) to create source models where no direct analogy exists. I refer interested readers to that work (Nersessian 1995; Nersessian, Griffith and Goel 1996). In what follows we examine a case of concept formation. Thus, we address what Nancy Cartwright (1989, p. 3) has identified as one of the two central traditional empiricist questions: Where do we get our scientific concepts? Unlike earlier empiricist approaches, I believe that to answer the question we need to examine the processes through which concepts emerge and are articulated. One dimension of articulating a quantitative concept is representing its mathematical structure. Cartwright’s analysis addresses the other empiricist question: How should we judge claims to empirical knowledge? That abstraction is of fundamental importance to answering both these questions underscores the need to understand what abstraction is and how it is accomplished. It also shows that the two questions are interrelated. Cartwright’s analysis provides insights and raises questions about abstraction, generalization, specialization, and idealization that will be addressed with respect to our question in the later sections of the paper.
2. Maxwell’s Mathematization of the Field Concept Although Maxwell formulated the mathematical representation of his electromagnetic field concept over the course of three papers, we will focus on the second (Maxwell 1861-2). It is in this paper that he first derived the field equations. That is, he met his goal of providing a unified representation of the transmission of electric and magnetic actions and calculated the velocity of their propagation. He achieved this by transforming the problem of analyzing the production and transmission of electromagnetic forces into that of analyzing potential stresses and strains in a continuum-mechanical medium. So, examining his procedures will shed light on the role existing representations play in the construction of new – and sometimes radically different – representations. Continuum mechanics was the obvious source domain on which to model his electromagnetic aether. There were two forms of analysis of forces available at the time Maxwell was working. The motions of bodies, such as projectiles and planets, were analyzed by means of forces acting at a distance. In attempting to bring electromagnetic forces into the province of Newtonian mechanics, Ampère and others had constructed a mathematical representation for them as actions at a distance. Continuous-action phenomena, such as fluid flow, heat, and elasticity, had all recently been given dynamical analyses
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consistent with Newtonian mechanics. The initial presumption behind these analyses was that underlying action-at-a-distance forces in the medium at the micro-level are responsible for the macro-level phenomena. However, continuum-mechanical analyses are carried out at the macro-level, with transmission of force treated as continuous. Maxwell, following Michael Faraday, conceived of electromagnetic actions as continuous transmissions. Unlike Faraday, he believed these to be transmitted through a Newtonian aether, similar to the light aether. William Thomson, Maxwell’s mentor and friend, had constructed mathematical representations for electrostatics on analogy with Fourier’s equations for heat, and representations for magnetism on analogy with equations of fluid flow. Thomson also had conducted geometrical analyses of the aether conceived as an elastic medium under stress. Maxwell’s first paper (1855-6) provided a kinematical analysis of magnetic lines of force as representing the intensity and direction of the force at a point in space on analogy with the flow of an imaginary, incompressible fluid through a fine tube of variable section. In the second paper his goal was a unified representation of how electric and magnetic forces are produced and transmitted through investigating possible mechanisms by which tensions and motion in a continuum-mechanical medium could produce the observed phenomena. In this analysis Maxwell, again following Faraday, assumed a field theory of currents and charges. On this view, current and charges are the result of stresses in the medium and not the sources of fields, as we now understand them to be. In the first paper, Maxwell had called his method of analysis “physical analogy.” It is a method “which allows the mind at every step to lay hold of a clear physical conception, without being committed to any theory founded on the physical science from which the conception is borrowed” (Maxwell 1855-6, p. 156). I will be arguing that the method of “physical analogy” employs generic modeling. In the first paper, Maxwell took a fluid-dynamical system as his analogical source and made certain idealizing assumptions, such as that the fluid is incompressible. He then treated processes in the fluid generically, e.g., as “flow,” rather than “fluid flow,” and abstracted mathematical relationships into which the electromagnetic variables could be substituted. In the second paper, he used continuum mechanics and machine mechanics as source domains, together with constraints from electromagnetism, to construct an imaginary mechanical system. The generic mechanical relationships within the imaginary system served as the basis from which he abstracted a mathematical structure of sufficient generality that it could represent causal processes in the electromagnetic medium without requiring knowledge of specific causal mechanisms.1 ⎯⎯⎯⎯⎯⎯⎯ 1
Our discussion will follow Maxwell’s presentation in the 1861-2 paper. As I have argued (1984a, b; 1992), the extant historical records support my supposition that Maxwell’s construction of the mathematical representation followed a course comparable to that which he presented to the scientific community.
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Maxwell began the 1861-2 paper by discussing general features of stress in a medium. Stress results from action and reaction of the contiguous parts of a medium and “consists in general of pressures or tensions different in different directions at the same point in the medium” (p. 454).2 The force is a pressure along the axis of greatest pressure and a tension along the axis of least pressure. As explicit constraints on stresses that could account for magnetism, Maxwell considered: (1) a tension in the direction of the lines of force, because in both attraction and repulsion the object is drawn in the direction of the resultant of the lines of force and (2) a pressure greater in the equatorial than in the axial direction, because of the lateral repulsion of the lines of force. These constraints derive from observations of the behavior of iron filings around and between magnetic sources and Faraday’s interpretation of these. a)
Fig. 1
b)
a) Actual pattern of lines of force surrounding a bar magnet (Faraday 1839-55, vol. 3, plate IV). b) Faraday’s schematic representation of the lines of force surrounding a bar magnet (Faraday 1839-55, vol. 1, plate I).
Figure 1a displays patterns of iron filings that are produced by magnets and Figure 1b is Faraday’s schematic representation of these. Faraday interpreted the attractions and repulsions of the lines of force as showing the directions of magnetic force, the “quantity” of magnetic force (summed across the lines, and so related to the density of lines in a region) and the “intensity” of magnetic force (tension along the lines). Maxwell’s first paper on electromagnetism (1855-6) provided a mathematical formulation for the notions of “quantity” and “intensity” as “flux” and “flow,” respectively. Flux is sometimes a vector quantity, flow is always a vector. The configuration of the lines in a given situation is a function of the magnetic force and the permeability of the medium. ⎯⎯⎯⎯⎯⎯⎯ 2
Throughout the remainder of section 2 all references will be to (Maxwell, 1861-2) unless otherwise specified. References to that work will involve only page numbers and, where appropriate, equation numbers.
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Maxwell argued that a fluid medium with a hydrostatic pressure symmetrical around the axis and a tension along the axis is consistent with Faraday’s constraints on the lines of force. A mechanical explanation of the excess pressure in the equatorial direction that “most readily occurs to the mind” (p. 455) is that of centrifugal force of vortices in the medium, with axes parallel to the lines of force. The centrifugal force of a vortex would cause it to expand equatorially and to contract longitudinally, thus representing the lateral expansion and longitudinal contraction of the lines of force. Each vortex is dipolar, i.e., it rotates in opposite directions at its extremities. Maxwell set the direction of rotation of a vortex by the constraint that it rotate so as to produce lines of force in the same direction as those about a current. So, if one looks toward the north pole of the magnet along a line of force, the vortex moves clockwise. This represents the north-south polarity of magnetism.
Fig. 2. The author’s rendering of a vortex segment from Maxwell’s description.
The geometric constraints of the lines of force are satisfied because of the shape of each vortex. A vortex is wider the farther it is from its origin, which gives the system the property that lines become farther apart as they approach their midpoints. Figure 2 is a representation of a vortex segment in motion drawn from Maxwell’s description. The vortex-fluid model is consistent with constraints that derive from Faraday’s experiments: (1) electric and magnetic forces are at right angles to each other, (2) magnetism is dipolar, and (3) the plane of polarized light passed through a diamagnetic substance is rotated by magnetic action. Maxwell first derived the equations for the stresses in the hydrodynamic model. He derived the equation for pressure difference in a medium filled with vortices placed side by side with axes parallel for the general case where the
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vortices are not circular and the angular velocity and the density are not uniform: (1) p1 – p2 = 1/4πµv2 (p. 457, equation 1); where ‘p2’ is parallel to the axes and ‘p1’ is perpendicular to the axes in any direction, ‘µ’ is the average density of the vortices, and ‘v’ is the linear velocity at the circumference of each vortex. Taking 1/4πµv2 from equation (1) to be a simple tension along the axis of stress and p1 to be a simple hydrostatic pressure in all directions, he derived an expression – what we now call the general mechanical stress tensor – for the resultant force on an element of the medium due to variation in internal stress (p. 458, equation 5):3 F = v(1/4πdiv µv) + 1/8πµ grad v2 – [µv × 1/4πcurl v] – grad p1 Given equation 5, he then constructed the analogy with the magnetic relations by mapping quantitative properties as follows. He stipulated that the quantities related to the velocity of the vortex (α = vl, β = vm, and γ = vn, with l, m, n the direction cosines of the axes of the vortices) be mapped to the components of the force acting on a unit magnetic bar pointing north. So, the magnetic intensity, which in contemporary notation is designated as ‘H’, is here related to the velocity gradient of the vortex at the surface. The quantity ‘µ’ is taken to represent the magnetic permeability, thus relating it to the mass of the medium. The quantity ‘µH’ represents the magnetic induction. Substituting the magnetic quantities, Maxwell next rewrote the first term of the mechanical stress tensor for the magnetic system as H(1/4πdiv µH) (p. 459, equation 7). He followed the same procedure of constructing a mapping between the model and the magnetic quantities and relations to rewrite all of the components of the stress tensor for magnetism. The resulting electromagnetic stress tensor represents the resultant force on an element of the magnetic medium due to its internal stress. We will not go through the details of these additional mappings, except to point out two noteworthy derivations. First, he derived an expression relating current density to the circulation of the magnetic field around the current-carrying wire, j = 1/4π curl H (p. 462, equation 9). This equation agreed with the differential form of Ampère’s law that he had derived in the earlier paper (1855-6, p. 194). The derivation given here still did not provide a mechanism connecting current and magnetism. Second, he established ⎯⎯⎯⎯⎯⎯⎯ 3
I have written this equation, which Maxwell wrote in component form, in modern vector notation and will do so throughout. The vector calculus was just being developed around the time of Maxwell’s analysis. Note the actual physical meaning of the vector operators here: the gradient is a slope along a vortex, the curl is the rotation of the fluid vortex, and the divergence is the flowing of fluid in the medium. In the Treatise of 1873, Maxwell reformulated his electromagnetic theory in terms of the theory of quaternions, a form of vector calculus developed by Hamilton (Maxwell, 1891). Although the fluid-mechanical model had been discarded by that time, Maxwell saw the vector calculus itself as “call[ing] upon us at every step to form a mental image of the geometrical features represented by the symbols” (1873, p. 137).
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that in the limiting case of no currents in the medium and a unified magnetic permeability, the inverse square law for magnetism could be derived. Thus, the system agreed in the limit with the action-at-a-distance law for magnetic force (pp. 464-66, equations 19-26). Thus far, then, Maxwell had been able to provide a mathematical formulation and what he called a “mechanical explanation” for magnetic induction, paramagnetism, and diamagnetism. Although the system of a medium filled with infinitesimal vortices does not correspond to any known physical system, Maxwell was able to use mathematical properties of individual vortices to derive formulas for quantitative relations with the constraints on magnetic systems discussed above. The four components of the mechanical stress tensor, as interpreted for the electromagnetic medium, are (p. 463, equations 12-14): F = H(1/4πdiv µH) + 1/8πµ (grad H2) – [µH × 1/4πcurl H] – grad p1 By component they are (1) the force acting on magnetic poles, (2) the action of magnetic induction, (3) the force of magnetic action on currents, and (4) the effect of simple pressure. The last component is required by the model – it is the pressure along the axis of a vortex – but had not yet been given an electromagnetic interpretation. Note that we call the contemporary version of this equation the “electromagnetic stress tensor” even though it is now devoid of the physical meaning of stresses and strains in a medium. The hydrodynamical model developed in Part I of the paper is the starting point for the remainder of Maxwell’s analysis. All subsequent reasoning is based on modifications of it. Before going on, it will be useful to underscore salient aspects of how the mathematical representation was constructed. 2.1.1. Summary In Part I the mathematical representation of various magnetic phenomena derives from the vortex-fluid model. The model was constructed by first selecting the domain of continuum mechanics as an analogical source domain and constructing a preliminary model consistent with the magnetic constraints. These constraints are the geometrical configurations of the lines of force and Faraday’s interpretation of them as resulting from lateral repulsion and longitudinal attraction. Maxwell hypothesized that the attractive and repulsive forces are stresses in a mechanical aether. Given this hypothesis, one can assume that relationships that hold in the domain of continuum mechanics will hold in the domain of electromagnetism. The magnetic constraints specify a configuration of forces in the medium and this configuration, in turn, is readily explained as resulting from the centrifugal forces of vortices in the medium with axes parallel to the lines of force. So, the vortex motion supplies a causal process that is capable of producing the configuration of the lines of force and the stresses in and among them. We can contrast this result with his analysis of
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the magnetic forces on current. In Part I he had not yet specified a causal process in the aether connecting electricity and magnetism, and so claimed not to have provided a mechanical explanation for their interaction. Thus, it seems that Maxwell thought that establishing a mathematical law connecting them does not, in itself, provide an explanation. The mathematical expressions for the magnetic phenomena are derived by substitution from the mathematical formula for the stresses in the vortex-fluid model. That model is not a system that exists in nature: it is idealized and it is generic. One way in which it is idealized will become the focus of the next stage of analysis: the friction between adjacent vortices is ignored. The model is generic in that it satisfies constraints that apply to the types of entities and processes that can be considered as constituting either domain. The model represents the class of phenomena in each domain that are capable of producing specific configurations of stresses. More will be said about generic models after developing Maxwell’s complete analysis. 2.2. The Electromagnetic Model The physical implausibility of the hydrodynamic model led Maxwell to a means of representing the causal relationships between magnetism and electricity. He began Part II by stating that his purpose was to inquire into the connection between the magnetic vortices and current. He also stated that he wanted to make a distinction between this analysis and that in Part I. He believed there was sufficient reason to support the physical hypothesis of vortices in the electromagnetic medium. That is, he thought it plausible that there actually is vortex motion in the aether. He made no such claims for the entities and mechanisms introduced in Part II. Indeed, he stressed that while they are mechanically “conceivable” it is highly implausible that they are actual entities and mechanisms in the aether responsible for electromagnetic phenomena. They simply provide a means for representing the causal relations between current electricity and magnetism in mechanical terms. He admitted a serious problem with the vortex model: he “found great difficulty in conceiving of the existence of vortices in a medium, side by side, revolving in the same direction” (p. 468). Figure 3a represents a cross section of the vortex model. To begin with, at the places of contact among vortices there will be friction and, thus, jamming. Further, since they are all going in the same direction, at points of contact they would be going in opposite directions. So, in the case where they are revolving at the same rate, the whole mechanism should stop. Maxwell noted that in machine mechanics this kind of problem is solved by the introduction of “idle wheels.” On this basis he proposed to enhance his imaginary model by supposing that “a layer of particles, acting as idle wheels is interposed between each vortex and the next” (p. 468). He stipulated that the particles would revolve in place without slipping or touching in a direction
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opposite to the vortices. This is consistent with the constraint that the lines of force around a magnetic source can exist for an indefinite period of time, so there can be no loss of energy in the model. He also stipulated that there should be no slipping between the interior and exterior layers of the vortices, making the angular velocity constant. This constraint simplified calculations and would be altered in Part III.
Fig. 3a. The author’s schematic representation of a cross-section of the preliminary analogical model described by Maxwell.
The model is now a hybrid constructed from two source domains: fluid dynamics and machine mechanics. In ordinary mechanisms, idle wheels rotate in place. This allowed representation of the situation in a dielectric, or insulating, medium. To represent a current, though, they need to be capable of translational motion in a conducting body. Maxwell noted that mechanisms such as the “Siemens governor for steam-engines” have such idle wheels. Throughout Part II, he provided analogies with machinery as interpretations of the relationships he had derived between the idle wheel particles and the fluid vortices. His procedure was to derive the equations using the model, map the results to the electromagnetic case assuming the established correlations, and then reinterpret the results in terms of plausible machine mechanisms. The constraints governing the relationships between electric currents and magnetism are modeled by the relationships between the vortices and the idle wheels, conceived as small spherical particles surrounding the vortices. Figure 3b (next page) is Maxwell’s own rendering of the model. The major constraints are that (1) a steady current produces magnetic lines of force around it, (2) commencement or cessation of a current produces a current, of opposite orientation, in a nearby conducting wire, and (3) motion of a conductor across the magnetic lines of force induces a current in it. The analysis began by deriving the equations for the translational motion of the particles in the imaginary system. There is a tangential pressure between the surfaces of spherical particles and the surfaces of the vortices, treated as
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approximating rigid pseudospheres. Maxwell noted that the equation he derived for the average flux density of the particles as a function of the circumferential velocity of the vortices, p = 1/2 ρ curl v (p. 471, equation 33) is of the same form as the equation relating current density and magnetic field intensity, j = 1\4π curl H (p. 462, equation 9). This is the form of Ampère's law for closed circuits he had derived in Part I. All that was required to make the equations identical was to set ‘ρ’, the quantity of particles on a unit of surface, equal to 1/2π. He concluded that “[i]t appears therefore, according to our hypothesis, an electric current is represented by the transference of the moveable particles interposed between the neighboring vortices” (p. 471). That is, the flux density of the particles represents the electric current density.
Fig. 3b. Maxwell’s representation of the fully constructed “physical analogy” (Maxwell 1861-2, plate VIII).
We can see how the imaginary system provides a mechanical interpretation for the first constraint. Current is represented by translational motion of the particles. In a conductor the particles are free to move, but in a dielectric (which the aetherial medium is assumed to be) the particles can only rotate in place. In a nonhomogeneous field, different vortices would have different velocities and the particles would experience translational motion. They would experience resistance and waste energy by generating heat, as is consistent with current. A continuous flow of particles would thus be needed to maintain the configuration of the magnetic lines of force about a current. The causal relationship between a
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steady current and magnetic lines of force is captured in the following way. When an electromotive force, such as from a battery, acts on the particles in a conductor it pushes them and starts them rolling. The tangential pressure between them and the vortices sets the neighboring vortices in motion in opposite directions on opposite sides – thus capturing polarity of magnetism – and this motion is transmitted throughout the medium. The mathematical expression (equation 33) connects current with the rotating torque the vortices exert on the particles. Maxwell went on to show that this equation is consistent with the equations he had derived in Part I for the distribution and configuration of the magnetic lines of force around a steady current (p. 464, equations 15-16). Maxwell derived the laws of electromagnetic induction in two parts because each case is different mechanically. The first constraint in the case of electromagnetic induction ((2) above) can be reformulated as: a changing (nonhomogeneous) magnetic field induces a current in a conductor. The analysis began with finding the electromotive force on a stationary conductor produced by a changing magnetic field. This first case corresponds, for example, to induction by switching current off and on in a conducting loop and having a current produced in a nearby conducting loop. A changing magnetic field would induce a current in the model as follows. A decrease or increase in the current will cause a corresponding change in velocity in the adjacent vortices. This row of vortices will have a different velocity from the next adjacent row. The difference will cause the particles surrounding those vortices to speed up or slow down, which motion will in turn be communicated to the next row of vortices and so on until the second conducting wire is reached. The particles in that wire will be set in translational motion by the differential electromotive force between the vortices, thus inducing a current oriented in a direction opposite to that of the initial current, which agrees with the experimental results. The neighboring vortices will then be set in motion in the same direction and the resistance in the medium will ultimately cause the translational motion to stop, i.e., the particles will only rotate in place and there will be no induced current. Maxwell’s diagram (figure 3b) illustrates this mechanism. The diagram shows a cross section of the medium. The vortex cross sections are represented by hexagons rather than circles, presumably to provide a better representation of how the particles are packed around the vortices. The accompanying text (p. 477) tells the reader how to animate the drawing for the case of electromagnetic induction by the action of an electromotive force of the kind he had been considering. The mechanism for communicating rotational velocity in the medium accounts for the induction of currents by the starting and stopping of a primary current. In deriving the mathematical relationships, Maxwell used considerations about the energy of the vortices. The mathematics is too complex to include in detail here. The general procedure he followed was to derive the equations for
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the imaginary system on its electromagnetic interpretation. In outline form, we know from Part I that magnetic permeability is represented by the average density (mass) of vortices and the intensity of magnetic force is represented by the velocity of a vortex at its surface with orientation in the direction of the axis of the vortex. So, the kinetic energy (mass × velocity2) of the vortices is proportional to the energy of the magnetic field, i.e., µH2. By the constraint of action and reaction, the force exerted on the particles by the vortices must be equal and opposite to the force on the vortices by the particles. The energy put into the vortices per second by the particles is the reactive force times the vortex velocity. Next Maxwell found the relationship between the change in vortex velocity and the force exerted on the particles. This derivation made use of the formula he had just derived for the energy density of the vortices, thus expressing change in energy in terms of change in magnetic force. Combining the two formulae gives an expression relating the change in magnetic force to the product of the forces acting on the particles and the vortex velocity, – curl E = µ ∂H/∂t (p. 475, equation 54). To solve this equation for the electromotive force, he connected it to an expression he had derived in the 1857 paper for the state of stress in the medium related to electromagnetic induction. Faraday had called this state the “electrotonic state” and Maxwell had derived a mathematical expression for it relating the lines of force to the curl of what he later called the “vector potential” (designated by ‘A’ here): curl A = µH (p. 476, equation 55). This maneuver enabled him to derive an expression for the electromotive force in terms of the variation of the electrotonic state, E = ∂A/∂t. It also enabled him to provide a mechanical interpretation of the electrotonic state, which was one of the goals of this paper. On his interpretation, the electromotive force is modeled by the pressure on the axle of a wheel in a machine when the velocity of the driving wheel is increased or decreased. The equation for the electrotonic state is of the form ‘mass × velocity,’ which is an expression for momentum. So he identified the electrotonic state with the impulse that would jar a machine into starting or cause it to stop suddenly; i.e., to the reduced momentum at a point. In the machine, you would calculate the force arising from the variation of motion at a point from the time derivative of the reduced momentum; which is what had just been established for the electromotive force as derived from the electrotonic state. Continuing, Maxwell derived the equations for the second case, that in which a current is induced by motion of a conductor across the lines of force (constraint (3) above). Here he used considerations about the changing form and position of the fluid medium. Briefly, the portion of the medium in the direction of the motion of a conducting wire becomes compressed, causing the vortices to elongate and speed up. Behind the wire the vortices will contract back into place and decrease in velocity. The net force will push the particles inside the
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conductor, producing a current, provided there is a circuit connecting the ends of the wire. The form of the equation for the electromotive force in a moving body, E = v × µH – ∂A/∂t – gradψ (p. 482, equation 77), shows clearly its correspondence to the parts of the imaginary model. The first component corresponds to the effect of the motion of the body through the field, i.e., the “cutting” of the lines Faraday had described is now represented by a continuous measure. The second component corresponds to the time derivative of the electrotonic state, i.e., the “cutting” in virtue of the variation of the field itself due to changes in position or intensity of the magnets or currents. The third component does not have a clear mechanical interpretation. Maxwell interpreted it as the “electric tension” at each point in space. How to conceive of electrostatic tension is the subject of Part III. By the end of Part II, Maxwell had given mathematical expression to some electromagnetic phenomena in terms of actions in a mechanical medium and had shown the resulting model to be coherent and consistent with known phenomena. He stressed that the idle wheel mechanism was not to be considered “a mode of connexion existing in nature” (p. 486). Rather it is “a mode of connexion which is mechanically conceivable and easily investigated, and it serves to bring out the actual mechanical connexions between the known electro-magnetic phenomena” (p. 486). His analysis thus far still had not shown that action in a medium is essential for transmitting electromagnetic forces. For this he would have to show that there is a necessary time delay in the transmission of the action and be able to calculate the velocity of the transmission in the medium. He concluded in the summary of his results that he had at least shown the “mathematical coherence” of the hypothesis that electromagnetic phenomena are due to rotational motion in an aetherial medium. The paper had not yet provided a unified theory of electric and magnetic actions because static electricity was not yet incorporated into the analysis. Thus, all Maxwell claimed was that the “imaginary system” gives “mathematical coherence, and a comparison, so far satisfactory, between its necessary results and known facts” (p. 488). 2.2.1. Summary In Part II the mathematical representation of the relationships between current and magnetism is derived from a model that is a hybrid of machine mechanics and fluid dynamics. The idle wheel mechanism is introduced from a constraint deriving from the vortex fluid model: if the vortices are rotating side by side, there is friction where they come into contact. Specific idealizations about the relationships among the particles – that there is no slipping and they do not touch when rotating in place – are dictated by the constraint that no energy is lost in the field surrounding a constant magnetic source. On translation, however, the particles must experience resistance so that energy is lost and heat
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created, as in current electricity. The vortices are treated as rigid to simplify calculations. The forces between the vortices and the particles that would produce rotational and translational motion fitting the requisite constraints were examined. The equation for translational motion has, on interpretation of a constant factor, the same form as the equation Maxwell had derived earlier for the relationship between a closed current and magnetism. This leads to an identification of the translational motion of the particles with current and allows examination of other known relations between current and magnetism. The cases of electromagnetic induction produced by a changing magnetic field and produced by motion of a conductor across the magnetic lines of force were treated separately because, given the model, they are different mechanical phenomena. The idle wheel mechanism is a highly implausible mode of connection for a fluid-mechanical system. However, the relational structures among the forces producing stresses in the medium do correspond to those among forces between current electricity and magnetism. There are causal processes in machines that are capable of producing the kinds of forces examined in the model. For example, the “pressure on the axle of a wheel” under specified conditions and the “reduced momentum” of a machine are phenomena that belong to classes of mechanical systems that are capable of producing the stresses Maxwell associated with, respectively, the electromotive force and the electrotonic state in a mechanical electromagnetic medium. The point is that in the idle wheelvortex model they are treated as generic processes. 2.3. The Electrostatic Model Representing static electricity by means of further modifications to the imaginary system enabled Maxwell to calculate the time delay in transmission. That Part III was published eight months after the previous installment indicates that Maxwell did not see how to modify the model at the time of its publication. Given the correspondence between the flux density of the particles and current, a natural extension of the model would have been to identify excess accumulation of the particles as charge. But the equations he had derived were only applicable to closed circuits, which do not allow accumulation of particles. Resolving the problem of how to represent static charge in terms of the model led Maxwell to modify Ampère’s law to include open currents and to provide a means by which to calculate the transverse propagation of motion in the model. The analysis in Part III has caused interpreters of Maxwell much puzzlement. This is primarily because his sign conventions are not what is now – and what Maxwell later took to be – customary. He also made fortuitous errors, in sign and in the equation for transmission of transverse effects in the medium. These problems have led many commentators to argue that the imaginary model
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played little role in Maxwell’s analysis; with one, Duhem (1914), going so far as to charge Maxwell with falsifying his results and with cooking up the model after he had derived the equations by formal means. Nersessian (1984a, 1984b) has argued that, properly understood, the model, taken together with Maxwell’s previous work on elasticity, provides the basis for the all the errors except one that can easily be interpreted as a substitution error. As in Part II, the analogical model was modified in Part III by considering its plausibility as a mechanical system. In Part II, the system contains cells of rotating fluid separated by particles very small in comparison to them. There he considered the transmission of rotation from one cell to another via the tangential action between the surface of the vortices and the particles. To simplify calculations he had assumed the vortices to be rigid. But in order for the rotation to be transmitted from the exterior to the interior parts of the cells, the cell material must be elastic. He noted that the light aether – considered at this point as possibly a different aetherial medium – is assumed to have elasticity, so the assumption that the electromagnetic medium has elasticity is equally as plausible. Conceiving the molecular vortices as spherical blobs of elastic material would also give them the right configuration on rotation, satisfying the geometrical constraints of Part I for magnetism. He began by noting the constraint that the “electric tension” associated with a charged body is the same, experimentally, whether produced from static or current electricity. If there is a difference in tension in a body, it will produce either current or static charge, depending on whether the substance is a conductor or insulator. He likened a conductor to a “porous membrane which opposes more or less resistance to the passage of a fluid” (p. 490) and a dielectric to an elastic membrane which does not allow passage of a fluid, but “transmits the pressure of the fluid on one side to that on the other” (p. 491). Although Maxwell did not immediately link his discussion of the different manifestations of electric tension to the hybrid model of Part II, it is clear that the model figures throughout the discussion. This is made explicit in the calculations immediately following the general discussion. I note this because the notion of “displacement current” introduced before these calculations cannot properly be understood without the model. In the process of electrostatic induction, electricity can be viewed as “displaced” within a molecule of a dielectric, so that one side becomes positive and the other negative, but does not pass from molecule to molecule. Maxwell likened this displacement to a current in that change in displacement is similar to “the commencement of a current” (p. 491). That is, in the imaginary model the idle wheel particles experience a slight translational motion in electrostatic induction. The mathematical expression relating the electromotive force and the displacement is: E = – 4πk2D, where ‘E’ is the electromotive force (electric field), ‘k’ the coefficient for the specific dielectric, and ‘D’ is the displacement
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(p. 491). The amount of current due to displacement is jdisp = ∂D/∂t. The equation relating the electromotive force and the displacement has the displacement in the direction opposite from that which is customary now and in Maxwell’s later work. The orientation given here can be accounted for if we keep in mind that an elastic restoring force is opposite in orientation to the impressed force. The analogy between a dielectric and an elastic membrane is sufficient to account for the sign “error.” Maxwell himself stressed that the relations expressed by the above formula are independent of a specific theory about the actual internal mechanisms of a dielectric. However, without the imaginary system, there is no basis on which to call the motion a “current.” It is translational motion of the particles that constitutes current. Thus, in its initial derivation, the “displacement current” is modeled on a mechanical process. We can see this in the following way. Recall the difference Maxwell specified between conductors and dielectrics when he first introduced the idle wheel particles. In a conductor, they are free to move from vortex to vortex. In a dielectric, they can only rotate in place. In electrostatic induction, the particles are urged forward by the elastic distortion of the vortices, but since they are not free to flow, they react back on the vortices with a force to restore their position. This motion is similar to the “commencement of a current.” But, their motion “does not amount to a current, because when it has attained a certain value it remains constant” (p. 491). That is, the particles do not actually move out of place by translational motion as in conduction. The system reaches a certain level of stress and remains there. “Charge” is the excess of tension in the dielectric medium. Without the model, “current” loses its physical meaning, which is what bothered so many of the readers of the Treatise, where the mechanical model is abandoned, having served its purpose. That situation is comparable to our continued use of “stress tensor” when there is no medium in which there could be stresses. Propositions XII and XIII provide the calculations for the elastic forces. In these calculations the vortices are treated as spherical for simplicity. Proposition XII determines the conditions of equilibrium for the vortices subject to normal and tangential forces. Proposition XIII shows how to derive the relationship between the electromotive force and the electric displacement, E = – 4πk2D (p. 495, equation 105) using the mapping with the imaginary system. What can quite readily be interpreted as a substitution error in equation 104 (p. 495) makes things turn out right. That is, the restoring force and the electromotive force have opposite orientation as in the opening discussion. The equation for Ampère’s law (equation 9) was now in need of correction “for the effect due to elasticity in the medium” (p. 496). That is, since the blobs are elastic and since in a conductor the particles are free to move, the current produced by the medium (i.e., net flow of particles per unit area) must include a factor for their motion due to elasticity, j = 1/4π curl H – ∂E/∂t (p. 496,
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equation 112). This equation is used in conjunction with the equation of continuity for charge, which links current and charge, to derive an expression linking charge and the electric field, e = 1/4πk2 div E (p. 497, equation 115). This expression is what we now call Coulomb’s law. “Charge” is here a region of elastic distortion in the medium. Maxwell then derived the forces acting between charged bodies using energy considerations and showed this expression to be an inverse square law and, thus, consistent with the action-at-a-distance formulation of Coulomb’s law as modified by Faraday to account for the inductive capacitance of the dielectric. The form of Maxwell’s modified equation for current (equation 112) again demonstrates his field conception of current and its relationship to the imaginary system: total current equals magnetic intensity from rotation minus the electromotive force from elastic distortion. The electromotive force has orientation opposite to the rotation of the vortices, so the “displacement current” actually opens the closed circuit of equation 9. Our contemporary expression is equivalent, but written in a form that makes the current plus the electric field the source of the magnetic field. Maxwell’s form of the expression clearly derives from the imaginary mechanical system. Now that the vortices are assumed to be elastic, the total flux density of the particles arises from the rotation of the vortices combined with the effect on the particles from elastic distortion of the vortices. The rotation of the vortices creates a translation of particles in a conductor in the same direction. The motion of the particles causes an elastic distortion of the vortices. The elastic distortion of the vortices, in turn, produces a reactive force on the particles, i.e., a restoring force in the opposite direction. Thus, the current is the translational motion minus the restoring force. Maxwell proceeded to derive an equation establishing the relationship between the electrodynamic and electrostatic forces due to charge and obtained the value for the constant relating them using the experimental value determined by Weber and Kohlraush. This constant has the dimensions of millimeters per second, i.e., it is a velocity, because the electrodynamic forces are due to the motion of charges, while electrostatic forces are not. He was now in a position to calculate the velocity of propagation of displacement in the imaginary medium. Since all displacement is tangential, he needed to find only the transverse velocity of propagation for the medium. From the general theory of elasticity, the square of the velocity of transverse propagation in an elastic medium is the ratio of its elasticity to its density. Thus, the velocity in the elastic vortex medium is v = (m/ρ)1/2 (p. 499, equation 132), where ‘m’ is the coefficient of transverse elasticity (shear modulus) and ‘ρ’ is the density of the vortices. Maxwell had derived this formula for the general case in an earlier analysis (1854) of elastic solids and most likely assumed the ‘m’ to be the same as in this case (Nersessian 1984b). However, on the model under consideration here, the ‘m’ should be divided by 2, as Duhem (1902) first pointed out. Duhem
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used this error to reinforce his contention that the model was cooked up after the derivations of the field equations and had played no role in their genesis. My explanation is that Maxwell simply appropriated the formula from the earlier paper in which it is correct. This lack of concern for multiplicative factors is consistent with thinking about the model in generic terms. Referring back to Part I, ‘ρ’ is the average density of the vortices (mass) and ‘µ’ is the magnetic permeability. Substituting these into equation 132 and noting that µ = 1 in air or a vacuum, he derived the result that the velocity is equal to the ratio between electrodynamic and electrostatic units. He then noted that, on converting this number to English units, it is nearly the same value as the velocity of light. Maxwell’s conclusion here is significant. In his words, “we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena” (italics in the original, p. 500). That is, Maxwell believed that the close agreement between the velocities was more than coincidental. However, he did “avoid the inference” until his next paper, where he derived the now standard wave equation for electromagnetic phenomena and concluded that light itself is an electromagnetic phenomenon. We can interpret Maxwell’s reticence at this point as arising because the value of the transverse velocity in the electromagnetic medium was determined from the presuppositions of the idle wheelvortex model. There were no grounds to assume vortex motion in the light aether. Note also that he did not claim that light is an electromagnetic phenomenon here, only the possible identity of the media of transmission. On the nineteenth-century view, light is a transverse wave in an elastic aether. This was not the same kind of mechanism as that provided for propagating electric and magnetic actions on the model. Maxwell ended the analysis of Part III by showing how to calculate the electric capacity of a Leyden jar using his analysis of electrostatic force. Part IV applied the whole analysis to the rotation of the plane of polarized light by magnetism and established that the direction of rotation depends on the angular momentum of the molecular vortices. It also predicted a relationship between the refractive index of light and the dielectric constant. 2.3.1. Summary In Part III the equations for electrostatic induction are derived from the hybrid mechanical system of Part II, by endowing the vortices with the mechanical property of elasticity. This modification again arises from considering the constraints of the model that were ignored in the earlier analyses. In order for the tangential motion of the particles on the vortices to be transmitted to their interior, they must be elastic. Elasticity of the vortices is also consistent with the geometrical constraints of Part I. Maxwell re-enforced endowing the electromagnetic medium with this property by noting that the luminiferous medium
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needs also to possess elasticity on the wave theory of light. This relatively simple enhancement of the model enabled Maxwell to represent electrostatic induction and open currents mathematically and to calculate the amount of delay in transmission of electromagnetic actions. The forms of the equations for the displacement current and for the modified version of the equation for current both derive from the modification to the hybrid mechanical model. When a force is applied to an elastic medium, the reaction force is of opposite orientation. This led Maxwell to make the electromotive force and the displacement due to elasticity have opposite orientation. In a dielectric, where the particles are not free to translate, the excess tension represents charge. In a conductor, a factor needs to be added to the expression for current to account for the displacement of the particles due to the elasticity of the vortices. Once the medium has elasticity, a time delay in transmission of electromagnetic actions is necessary. Because the forces between the vortices and the particles are tangential, only the transverse velocity of propagation in the medium need be calculated. Although its value is nearly that of light, Maxwell only speculated that the two aethers might in fact be one. He did not claim that light actually might be an electromagnetic phenomenon. On my analysis, the most likely explanation for his refusing to make this claim is that the vortex mechanism and wave propagation do not belong to the same class of mechanisms. In his next paper he made the identification of light as an electromagnetic phenomenon by treating the electromagnetic medium even more generically as simply a “connected system.” I will say more about this in what follows.
3. Abstraction: Idealization and Generic Modeling As we have seen, in constructing a quantitative electromagnetic field concept, Maxwell fashioned a series of generic models by integrating constraints drawn from the domains of electromagnetism, fluid mechanics, machine mechanics, and elastic media. This synthesis produced generic models from which he abstracted mathematical structures common to the domains. I want first to clarify the terms I am using by looking at a simpler example taken from Polya (1954). The kind of abstraction process Polya calls “generalization” in mathematics is what I am calling “generic modeling.” I think it is necessary to distinguish the two to contrast the process we have been examining with that of “generalization” in logic. The examples Polya gives are those of abstracting from an equilateral triangle to a triangle-in-general and from it to a polygon-ingeneral (figure 4, next page). Loss of specificity is the central aspect of this kind
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of abstraction process. The abstracted geometrical figures are taken to be what I have been calling “generic.” The generic triangle represents those features that all kinds of triangles have in common. The loss in specificity in this case is of the equality of the lengths of the sides and of the degrees of the angles. By contrast, logical generalization from one equilateral triangle to all equilateral triangles does not involve loss of specificity of these essential features. In the case of the generic polygon, there is an additional loss of specificity of the number of sides and the number of angles of the figure. In her recent book, Nancy Cartwright (1989) claims that abstraction is central to modern science. As I said at the outset, this claim is reinforced here by recognizing its major role in at least some kinds of conceptual innovation. She is also correct in pointing out that while idealization and abstraction are not the same processes, they tend to be conflated in philosophical discussions. She distinguishes between them by holding that idealization involves “changing” features or properties, while abstraction involves “subtracting” them (Cartwright 1989, p. 187). She argues that in idealizing we may extrapolate a feature to the limit, but we still need to say something about it as a relevant factor. This contrasts with abstracting, where we eliminate features. For example, to idealize from the triangle on the paper to the triangle as a mathematical object we would not eliminate the feature of width from the lines, but extrapolate it to zero. To abstract from a material triangle to a mathematical one we would eliminate all features but shape.
Fig. 4. Abstraction via generic modeling
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Although this may be more a matter of emphasis than disagreement with her, I find the contrast between changing features and eliminating them not the most salient for capturing the kind of abstraction we have been examining. First, rather than making a distinction between abstraction and idealization, I prefer to say that there are various abstraction processes. Idealization is one; eliminating features, another; and generic modeling, yet another. The main feature of the process we have been considering can best be characterized as a loss of specificity.4 That is why I have called it generic modeling. In the simple example from Polya, the generic triangle has lost the specificity of the individual angles and sides. However, angles and sides have not been eliminated as features of triangles. In the Maxwell case, abstraction takes place through generic modeling of the salient properties, relationships, and processes. One key feature of Maxwell’s generic mechanical models is that they have lost the specificity of the mechanisms creating the stresses. A concrete mechanism is supplied, but it is meant to represent generic processes. Thus, in the analysis of electromagnetic induction, e.g., causal structure is maintained but not specific causal mechanisms. The idle wheel-vortex mechanism is not the cause of electromagnetic induction; it represents the causal structure of that process. When we reason about a generic triangle we often draw a concrete representation or imagine one in our mind, but from our reasoning context we understand it as being without specificity of angles and sides. That is, we know from the context that the interpretation of the concrete figure is as generic. Thus, the same concrete representation can be generic or specific depending on the context. While supplying concrete mechanisms, we know from the context that Maxwell is considering them generically. That is, these mechanisms are treated in the way that the spring is treated generically when it is taken to represent the class of simple harmonic oscillators. On Maxwell’s analysis, the causal structure is to be viewed as separated from the specific physical systems by means of which it has been made concrete. This is what I take to be the essence of what Maxwell is saying in his own methodological reflections on “physical analogy.” In employing the method of physical analogy, generic mechanisms are represented by concrete mechanisms to assist in the reasoning process. They present the mind with an embodied form to reason about and with, but from the context the reasoner knows not to adopt any specific physical hypothesis belonging to the domain that is the source of the analogy. The goal is to explore the consequences of a partial isomorphism between the laws of two physical domains. But, this exploration needs to be carried out at a level of generality sufficient to encompass both domains. Thus, the models derived from the “physical analogies” are to be regarded generically. ⎯⎯⎯⎯⎯⎯⎯ 4 While I will not discuss the details here, generic modeling has much in common with what Darden and Cain (1989) call “generalizing theories by abstraction.” See also Griesemer (this volume).
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I said earlier that my divergence from Cartwright’s account is more a matter of emphasis than disagreement. Talking about Maxwell’s generic models as representing causal structure apart from any specific causal mechanisms comes close to what she says about “capacities.” This is because her question of what abstract laws say about reality, and my question of how they are formulated in the first place, are related significantly. The discussion of Maxwell’s formulation of the abstract laws of the electromagnetic field in the next section extrapolates from her analysis to encompass the latter question.
4. Mathematization and Generic Modeling Alexandre Koyré called the process of expressing physical relationships in mathematical form, which has been integral to the sciences since the Scientific Revolution of the sixteenth and seventeenth centuries, “mathematization.” Koyré held that idealization is the essence of the mathematization process. This is seen most clearly in his account of the mathematization of the concept of inertia as carried out by Galileo, Descartes, and Newton. What mathematization involved was, according to Koyré, “the explanation of that which exists by reference to that which does not exist, which never exists, by reference even to that which never could exist” (Koyré 1978). That is, inertial motion, as represented by Newton’s laws, does not occur in nature. The laws of motion apply to ideal entities (point masses), moving and interacting in a frictionless, geometrical space. Idealization is achieved through extrapolation of physical features to the limiting case, which can only be carried out in the mind. The quotation from Koyré provides an example of conflating abstraction and idealization. Although an idealized model is “that which does not exist,” as many commentators on the “Galilean method” have pointed out, part of what was worked out during the Scientific Revolution was just how the ideal can be commensurate with the real. Idealization is needed to reduce and simplify phenomena to a form to which mathematics can be applied. Contingent factors influencing the nature of the motion of real projectiles obscure what is common to all forms of motion. According to the law of inertia, this common feature is the tendency, left unimpeded, to continue in a straight line. The projectile’s actual motion is too “complicated and messy” to express in mathematical relationships (Cartwright 1989, p. 187). Instead, we create an ideal model where there are no accidental factors, such as the mass of the object and the density of the medium. The ideal model can be transformed into a real system by adding back the density or the friction or the mass. So, in some sense, idealized models approximate realistic systems. The generic model, on the other hand, “never could exist”; that is, it could never be transformed into a real system. It represents what is common among
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the members of classes of physical systems. Both idealization and generic modeling play a role in mathematization. But generic modeling plays a more significant role than idealization; for the mathematical representation expresses what is common to many systems. Newton’s inverse-square law of gravitation abstracts what the motion of a projectile and a planet have in common. The inverse-square-law model served as a generic model of action-at-a-distance forces for those who tried to bring all forces into the scope of Newtonian mechanics. Also, as we saw in the Maxwell case, a model can remain generic even when it is, in fact, made less ideal. In this case, at different stages of the analysis friction and elasticity are added to the model. Additionally, as we saw, the generic model need not even pretend to be realistic. Maxwell’s idle wheelvortex mechanism is highly implausible as a real fluid-dynamical system. However, it does not need to be realistic since what it represents is a relational structure. Cartwright claims “the point of constructing an ideal model is to establish an abstract law” but that abstraction is “extrapolation beyond” the ideal model (Cartwright 1989, p. 187). This extrapolation leads, e.g., with the laws of a laser, to the situation that “the physics principles somehow abstract from all the different manifestations . . . to provide a general description that is in some sense common to all, although not literally true of any” (Cartwright 1989, p. 211). Since her focus is on how the abstract laws relate to real systems rather than on how they are constructed, she does not say how the additional extrapolation leading to the laws takes place. I would add that in many cases the extrapolation occurs through treating the ideal model as generic. As we have seen, Maxwell first formulated the mathematical representation – the abstract laws – of the electromagnetic field by abstracting from the models what continuum-mechanical systems, certain machine mechanisms, and electromagnetic systems have in common. In their mathematical treatment, these common dynamical properties and relationships are separated from the specific systems by means of which they had been made concrete. Once he had abstracted these properties and relationships, he was in a position to reconstruct the mathematical representation using generalized dynamics, which is what he did in the next paper. That analysis assumes only that the electromagnetic medium is a “connected system,” possessing elasticity and thus having energy. The electromagnetic medium is treated as “a complicated mechanism capable of a vast variety of motion, but at the same time so connected that the motion of one part depends, according to definite relations, on the motion of other parts, these motions being communicated by forces arising from the relative displacement of the connected parts, in virtue of their elasticity” (Maxwell 1864, p. 533). But the real physical mechanisms through which the motion is communicated remain unknown.
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The assumptions of the general dynamical analysis are minimal. Maxwell endowed the electromagnetic connected system with features on analogy with the medium that was thought to transmit light and radiant heat. These features are density and a finite velocity of transmission of actions. Recall from the 1861-2 paper that he thought it highly plausible that they were the same medium. In fact, by moving to the level of generality of a connected system, he derived the result that electromagnetic phenomena propagate as waves, and thus was able to identify light as an electromagnetic phenomenon. This unification goes beyond the suggestion in the earlier paper that the two media might be one. The connected system needs to be elastic to provide for the time delay. Elastic systems can receive and store energy. The energy of such a system has two forms: “energy of motion,” or kinetic energy, and “energy of tension,” or potential energy. To apply the formalism of generalized dynamics to the system we need to know how to represent its potential and kinetic energy. Maxwell identified kinetic energy with magnetic polarization and potential energy with electric polarization. We can see in what way the earlier analysis showed him how to do this. Schematically, in the earlier analysis kinetic energy is associated with the rotation of vortices, which considered generically becomes rotation, which in the later analysis is just motion in the medium associated with magnetic effects. Potential energy is associated with elastic tension between the vortices and the particles, which, generically, becomes elastic stress, which here is elastic tension due to electrostatic effects. As Mary Hesse (1974) noted in her analysis of Maxwell’s “logic of analogy,” his analysis in the third paper relies on interchangeability of properties in different contexts, which she called “generic identification” of the properties of different systems (Hesse 1974, p. 266). For example, interchanging the mechanical and electromagnetic energy assumes that all forms of energy are the same. We saw this to be the case in the second paper as well, e.g., where the electromagnetic stress tensor is obtained from the mechanical stress tensor. But as we have seen, both analyses also rely on generic identification of relational structures.5 For example, in reformulating the equations, he identified the electromagnetic momentum with the reduced momentum of the system. In the earlier analysis, the reduced momentum of the idle wheel-vortex mechanism is associated with the relational structure between the magnetic lines of force and current electricity that Faraday called the “electrotonic state” – here called the “electromagnetic momentum” by Maxwell – associated with the state of the medium in the vicinity of currents. Additionally, the reformulation in the third paper makes the assumption that the relational structures of generalized dynamics hold in each domain. ⎯⎯⎯⎯⎯⎯⎯ 5
This reinforces Sellars’s (1965) criticism of Hesse that to create novelty in analogical reasoning requires mapping relational structures, not simply predicates. For an analysis of their dispute and of Sellars’s views on conceptual change, see Brown (1986).
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In the 1861-2 paper, Maxwell had said that the causal mechanisms he considered provided “mechanical explanations” of the phenomena. In the 1864 paper, he said that the mechanical analogies should be viewed as “merely illustrative, not as explanatory” (1864, p. 564), and in the Treatise, that the problem of “determining the mechanism required to establish a certain species of connexion . . . admits of an infinite number of mechanisms” (1891, p. 470). As we have seen, the “mechanical explanations” of the earlier analysis are themselves generic in nature. They only specify the kinds of mechanical processes that could produce the stresses under examination. They provide no means for picking out which processes actually do produce the stresses. In a later discussion of generalized dynamics, Maxwell likened the situation to that in which the bellringers in the belfry can see only the ropes, but not the mechanism that rings the bell (1890b, pp. 783-4). The first formulation treated the mechanical models as representing classes of physical systems with common properties and relationships. After that, Maxwell simply treated the properties and relationships in the abstract and – in all subsequent formulations – replaced the supposition of a continuum-mechanical medium with the mere supposition of a connected system and proceeded as a bellringer. This move is at the heart of the disagreement with Thomson, who never did accept Maxwell’s representation. Maxwell’s own position was that the situation was not any worse than that with Newton’s law of gravitation, since that, too, had been formulated without any knowledge of causal mechanisms. What we know, but Maxwell did not, is that many different kinds of dynamical systems can be formulated in generalized dynamics. Electrodynamical systems are not the same kind of dynamical system as Newtonian systems. What he abstracted through the generic modeling process is a representation of the general dynamical properties and relationships for electromagnetism. The abstract laws, when applied to the class of electromagnetic systems, yield the laws of a dynamical system that is non-mechanical; that is, one that cannot be mapped back onto the mechanical domains used in their construction.
5. Conclusion The history of science is full of examples of the formation of new concepts by analogy. I think the notion of abstraction via generic modeling can shed light on many of these cases. A major puzzle that lies at the heart of conceptual innovation is how genuinely novel representations can be constructed from existing ones. Clearly more is involved than simply transferring representations from one domain to another. Abstraction via generic modeling provides one answer to the puzzle. In mathematizing the field concept of electromagnetic forces, Maxwell formulated the laws of a non-Newtonian dynamical system for
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the first time. As we saw, he constructed this novel representation by integrating constraints from the source domains and from electromagnetism into generic models and formulating the quantitative relationships among the entities and processes in these.* Nancy J. Nersessian School of Literature, Communication, and Culture and College of Computing Georgia Institute of Technology
[email protected]
REFERENCES Brown, H. (1986). Sellars, Concepts, and Conceptual Change. Synthese 68, 275-307. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Chi, M. T. H., Feltovich, P. J., and Glaser, R. (1981). Categorization and Representation of Physics Problems by Experts and Novices. Cognitive Science 5,121-52. Clement, J. (1989). Learning via Model Construction and Criticism. In: G. Glover, R. Ronning, and C. Reynolds (eds.), Handbook of Creativity: Assessment, Theory, and Research, pp. 341-81. New York: Plenum. Darden, L. and Cain, J. A. (1989). Selection Type Theories. Philosophy of Science 56,106-129. Duhem, P. (1902). Les Théories Électriques de J. Clerk Maxwell. Etude Historique et Critique. Paris: A. Hermann & Cie. Duhem, P. (1914). The Aim and Structure of Physical Theory. New York: Atheneum, 1962. Faraday, M. (1839-55). Experimental Researches in Electricity. Reprinted, New York: Dover, 1965. Giere, R. N. (1988). Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press. Hesse, M. (1974). Maxwell’s Logic of Analogy. In: The Structure of Scientific Inference, pp. 259-282. Berkeley: University of California Press. Koyré, A. (1978). Galileo Studies. Atlantic Highlands, NJ: Humanities Press. Maxwell, J. C. (1854). On the Equilibrium of Elastic Solids. In: Maxwell (1890a), vol. 1, pp. 30-74. Maxwell, J. C. (1855-6). On Faraday’s Lines of Force. In: Maxwell (1890a), vol. 1, pp. 155-229. Maxwell, J. C. (1861-2). On Physical Lines of Force. In: Maxwell (1890a), vol. 1, pp. 451-513. Maxwell, J. C. (1864). A Dynamical Theory of the Electromagnetic Field. In: Maxwell (1890a), vol. 1, pp. 526-97. Maxwell, J. C. (1873). Quarternions. Nature 9, 137-38. Maxwell, J. C. (1890a). The Scientific Papers of J. C. Maxwell. Edited by W. D. Niven. Cambridge: Cambridge University Press. Reprinted, New York: Dover, 1952. Maxwell, J. C. (1890b). Thomson and Tait’s Natural Philosophy. In: Maxwell (1890a), vol. 2, pp. 776-85. Maxwell, J. C. (1891). A Treatise on Electricity and Magnetism. 3rd ed. (1st ed. 1873). Oxford: Clarendon Press. Reprinted, New York: Dover, 1954. Nersessian, N. J. (1984a). Faraday to Einstein: Constructing Meaning in Scientific Theories. Dordrecht: Martinus Nijhoff.
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My analysis has profited from extensive discussions with James Greeno. I acknowledge and appreciate the support of NSF Scholars Awards DIR 8821442 and DIR 9111779 in conducting this research.
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Nersessian, N. J. (1984b). Aether/Or: The Creation of Scientific Concepts. Studies in the History and Philosophy of Science 15, 175-218. Nersessian, N. J. (1988). Reasoning from Imagery and Analogy in Scientific Concept Formation. In: A. Fine and J. Leplin (eds.), PSA 1988, vol. 1, pp. 41-48. East Lansing, MI: Philosophy of Science Association. Nersessian, N. J. (1992). How Do Scientists Think? In: R. Giere (ed.), Cognitive Models of Science, Minnesota Studies in the Philosophy of Science XV, pp. 3-44. Minnesota: University of Minnesota Press. Nersessian, N. J. (1995). Should Physicists Preach What They Practice? Constructive Modeling in Doing and Learning Physics. Science & Education 4, 203-226. Nersessian, N. J., Griffith, T., and Goel, A. (1996). Constructive Modeling in Scientific Discovery. Cognitive Science Technical Report, Georgia Institute of Technology. Polya, G. (1954). Induction and Analogy in Mathematics. Vol. 1. Princeton: Princeton University Press. Sellars, W. (1965). Scientific Realism or Irenic Instrumentalism. In: R. Cohen and M. Wartofsky (eds.), Boston Studies in the Philosophy of Science, vol. 2, pp. 171-204. Dordrecht: D. Reidel.
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Margaret Morrison APPROXIMATING THE REAL: THE ROLE OF IDEALIZATIONS IN PHYSICAL THEORY
1. Introduction Throughout history as well as in contemporary science and philosophy there has been an ongoing debate about the role, status and nature of models. In 1906 Pierre Duhem wrote that the use of mechanical models “has not brought to the progress of physics the rich contribution boasted for it.” (Duhem 1977, p. 99. Hereafter ‘A&S’). Moreover, “the share of the booty it has poured into the bulk of our knowledge seems quite meager when we compare it with the opulent conquests of abstract theories.” (A&S, p. 99). The target of his criticism is the use of mechanical models by British field theorists as well as their apparent disregard for logical coherence in their use of symbolic algebras.1 When compared with the more formal approach of Continental physicists the result is a disruption of the unity and logical order of the theory itself. Implicit in Duhem’s preference for the abstract method is the assumption that nature is itself ordered and since it is the goal of theories to classify and systematize phenomena, ideals like logical coherence should be adhered to. In British methodology the fact that the same law can be represented by different models is a testimony to the power of the imagination over reason. In contrast, the emphasis on rational systematization by the French is touted as superior to visualizable approaches that dominate the process of model building. Modern theory construction involves a process that utilizes abstract methods as well as visualization in building models that represent physical systems; an approach resembling that used by British field theorists. We frequently refer to abstract formal systems as models that provide a way of setting a theory in a mathematical framework; gauge theory, for example, is a model for elementary particle physics insofar as it provides a mathematical structure for describing the interactions specified by the electroweak theory. ⎯⎯⎯⎯⎯⎯⎯ 1
See A&S, pp. 69-86 as well as Duhem (1902), pp. 221-225.
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 145-172. Amsterdam/New York, NY: Rodopi, 2005.
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Other approaches to modeling involve the more straightforward idealizations like frictionless planes and the billiard ball model of gases. As our physics has become more complicated, modeling has involved an increasing amount of mathematical abstraction as well as qualitative assumptions so far removed from known physical systems that they are unhelpful in providing a concrete conception of the phenomena; in fact some of the historical literature suggests that the models associated with the early quantum theory were criticized because they were unable to provide visualizable accounts of the behavior of quantum systems (see Miller 1985). In attempting to overcome the problem associated with the use of abstract mathematics Maxwell combined the analytical dynamics of Lagrange with mechanical concepts and images to produce a formal account of electromagnetism that enabled one to retain a physical conception of the phenomena. Some aspects of this physical representation were considered heuristic while other parts were thought to involve, at best, physical possibilities. Nevertheless, both played a substantive role in the development of electromagnetism despite their non-realist construal, a feature which prompted severe criticism from Lord Kelvin, who saw Maxwell’s theory as nothing more than an abstract account having little contact with reality. My goal in the paper is to explore the processes of abstraction and model building both from a contemporary and an historical perspective. Some of the issues I want to address concern the ways in which abstraction assists in theory construction and development and whether there is anything theoretically significant about the degree of abstraction that is present in our models of reality. Duhem sees abstraction as a necessary feature of physics since it is only by making our laws and theories general enough to account for a variety of phenomena that we can achieve any degree of certainty. As Nancy Cartwright has argued however, this severely limits the view that our theories can be both accurate and certain (Cartwright 1983). The significant question seems to be the extent to which we can represent reality using the techniques involving abstraction and idealization while remaining loyal to realist intuitions. The typical realist response in addressing the issue of abstraction in physical models is to claim that the gap between the model and the world, created by the abstract nature of the model, can be closed simply by adding back the appropriate parameters to the model. For example, we can add the force of friction to the model of a frictionless plane thereby making the model a more realistic and accurate picture of the world. And, to the extent that we can continue adding parameters to a model, the model becomes an even better representation of the world. Because this process has been successful the abstract nature of models creates no problems for realism. I want to challenge the realist characterization outlined above by claiming that this picture fails to capture many of the important features of modeling in
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physics; consequently it gives a rather abstract model of what that practice entails. I argue that the addition of parameters to a model can be accounted for without assuming a realist framework. In fact, the traditional realistic vs. heuristic distinction used to classify models presents, in most cases, a false dichotomy since the requisite characteristics necessary for assigning a model to the realist category are frequently indiscernible. As a result this distinction needs to be recast in order to provide a more accurate account of how models function in theory construction and application. I conclude by isolating two levels at which idealization operates in science, each of which has different implications for the connection between models and reality. The historical portion of the paper shows the affinities between the current debate about models and the issues raised by Kelvin and Duhem concerning Maxwellian electrodynamics. By tracing the various stages in the development of Maxwell’s theory one can clearly illustrate how models, analogies and abstract mathematical techniques function in the articulation of a fully developed theory. Interestingly enough, Maxwell’s rather sophisticated methodological techniques closely resemble modern approaches to theory construction.
2. Models, Idealizations and Abstraction 2.1. The Gap between Theory and Reality Duhem characterizes scientific laws and concepts as abstract symbols that represent concrete cases in some loose sense; but the correspondence is never one of faithful representation. Because the precision of abstract mathematical formulae is not found in nature we cannot view physical/mathematical laws as true or false; instead they are understood as symbolic relations. The symbols that stand for particular things are brought together in a relation expressed as a law, with the law itself serving as a symbol of the relations among various phenomena or properties.2 These symbolic terms connected by the law represent some aspect of reality in a more or less precise or detailed manner. It is the job of a theory to classify these laws in a rational, systematic order.3 One of the ⎯⎯⎯⎯⎯⎯⎯ 2
For example Boyle’s law, PV = RT, relates the various properties of a gas, including pressure, volume, temperature and the universal gas constant. 3 The reason that Duhem reacts so strongly to Maxwell’s mathematical representation of electromagnetism is that he sees the English as using different sorts of symbolic algebras and failing to differentiate the algebra from the theory itself. In contrast, a Continental physicist’s theory is essentially a logical system uniting hypotheses through rigorous deductions to their consequences, which are then compared with experimental laws. Algebra plays a purely auxiliary role facilitating calculations that lead from hypotheses to consequences. The calculations can always be replaced by a strict logical progression of hypotheses and consequently each symbol corresponds to a property
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implications of Duhem’s view of theories as classification systems is that they fail to provide an explanation of the laws they contain. Explanations “strip reality of the appearances covering it” (A&S, p. 7), while experimental laws deal only with sensible appearances “taken in an abstract form” (A&S, p. 7). The question of whether, and to what extent, our laws mirror an underlying reality transcends the realm of physics, entering the domain of metaphysics. Hence in order to guarantee the autonomy of physics one must recognize its limitations. Nevertheless, the more complete the theory becomes, the more we suspect that the logical order it exhibits reflects an underlying natural order. Although this conviction cannot be proven, we are at the same time “powerless to rid our reason of it” (A&S, pp. 26-7). One of the most important features of Duhem’s account is that the symbolic relationship is not reducible to the modern language of approximate truth. When we are able to manipulate the symbolic relationships in a way that allows us to capture more features of a particular phenomenon, we are not, according to Duhem, converging on some true description or law governing that specific case. A symbol by its very nature is neither true nor false since its worth is determined by its usefulness (A&S, p. 172). In some cases we may want exceedingly accurate results thereby requiring laws that involve more complicated parameters. A simple example is the use of Boyle’s law in one context and van der Waals’s in another; the latter takes account of the intermolecular attractive and repulsive forces, yielding more accurate results for high temperatures and low pressures. Duhem sees this use of laws in practical contexts as evidence for the relativity of laws rather than an indication of their approximate truth. His respect for classical truth and logic rules out a redefinition of truth as something that admits of degrees (A&S, pp. l68, 171). Approximation embodies an idea like “reliable within certain limits for certain purposes.” Consequently, a law of physics that is eventually superseded by more accurate ones, such as the law of universal gravitation (superseded by general relativity), is not shown to be false; nor would it be correct to say that Boyle’s law is false for the physicist who wants a more accurate description of the behavior of noble gases – the term simply doesn’t apply. The approximation suffices in one case and not in the other. Initially this plurality in the use of laws seems at odds with Duhem’s emphasis on logical coherence. However, because theories are classification systems we are able to sanction the use of different schemes provided we do not mix them together or attempt to use various methods within the framework of the same theory. If theories were understood as explanations of the true nature of material systems then such diversity would be unacceptable. It is because Duhem sees British field theorists as guilty of using different models for the
that can be physically measured. This correspondence was not to be found in Maxwell’s electromagnetism. Cf. A&S, ch.4.
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same phenomena and having a realist view of theories that he takes issue with their methodological practices (A&S, pp. 79-82, 101). Duhem’s other arguments against the truth or falsity of physical laws concern the case of underdetermination that facilitates the application of a potentially infinite number of symbolic representations for each concrete fact, thereby ruling out a unique correspondence between one particular law and a real system. In addition, constant refinement of instruments leads to a continual adjustment of laws, a process that continues indefinitely. Hence, by its very nature, physics and the provisional character of its abstract laws can claim to be nothing more than an approximation.4 The more complicated the law becomes the greater its approximation, yet it is only by retaining their approximative nature that physical laws can function as laws at all. Generality and abstraction are built in to the very nature of exact sciences like physics. The mathematical symbol forged by theory applies to reality as armor to the body of a knight clad in iron: the more complicated the armor, the more supple will the rigid metal seem to be; the multiplication of the pieces that are overlaid like shells assures more perfect contact between the steel and the limbs it protects; but no matter how numerous the fragments composing it, the armor will never be exactly wedded to the human body being modeled (A&S, p. 175).
Realist accounts of idealization willingly accept abstraction and approximation as a fundamental feature of physical theory and simply recast Duhem’s argument as one that involves a practical problem of calculation, rather than one that prevents us from characterizing our models or laws as realistic (or approximately true) descriptions of reality. In other words, because all scientific laws are idealizations or abstractions, the problem becomes one of supplementing laws and theories with parameters necessary for better and consequently more accurate representations of reality. Constant revision is seen as evidence for convergence toward a law that will capture more of the essential features of the phenomena in question. The challenge of bridging the gap between idealized models, abstract laws and the reality they represent requires that we be able to say something about ⎯⎯⎯⎯⎯⎯⎯ 4
Unlike geometry which progresses by adding new indisputable truths to a fixed body of knowledge, and unlike the laws of common sense which are themselves fixed (expressing very general and unrestricted judgements), the laws of physics face constant revision and the prospect of being overturned. The symbols that the laws relate are too simple to represent reality completely. For example, when we describe the sun and its motion using physical laws we replace the irregularities of its surface with a geometrically perfect sphere. Consequently the precision of the law cannot be mirrored by reality. The common sense law stating that the sun rises each day in the east, climbs in the sky and sets in the west has a degree of certainty that is fixed and immediate and relatively easy to calculate. The corresponding physical law that provides the formulas that furnish the coordinates of the sun’s center at each instant acquires a minuteness of detail that is achieved only by sacrificing the fixed and absolute certainty of common sense. Cf. A&S, pp. 165-179.
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how it is that these models, laws and theories facilitate the production of scientific knowledge. To do that one must first determine whether the problem of abstraction in Duhem’s sense is simply one of calculation and filling in appropriate parameters. 2.2. Closing the Gap Ernan McMullin (McMullin 1985) suggests that one can retain a significant number of our realist intuitions by properly identifying exactly how idealization operates in the physical sciences. His target is the view characterized by Duhem and endorsed by Cartwright that techniques of idealization, although permissible as explanatory tools, are not truth-producing.5 McMullin’s discussion of the debate between Salviati and Simplicio highlights an interesting feature of the way in which mathematics bears on physical phenomena. Mathematical idealization involves impediments or practical difficulties in the application of mathematical relations to real systems. However, the assumption behind the process is that the impediments can be allowed for by calculating their effects and discovering whether real complex situations can be based on this idealized construct. Although the process is still used today, the mathematics of modern physical theory has incorporated a greater physical dimension, thereby diminishing its idealized nature (McMullin 1985, p. 254). For example, the geometry of general relativity is refined to fit a system in which the space-time metric is matter-dependent, unlike the Euclidean geometry of Newtonian physics. What this indicates, suggests McMullin, is that contrary to Galileo and his contemporaries the book of nature is not written in the language of mathematics; the syntax is mathematical while the semantics is physical. McMullin concludes that mathematical idealization simply doesn’t pose a problem for either philosophy or physics. As an integral part of the natural sciences it has worked extremely well (McMullin 1985, p. 254), and insofar as it presupposes a distinction between reality and a formal structure, it is a tacit endorsement of scientific realism.6 To quote McMullin, idealization “pre⎯⎯⎯⎯⎯⎯⎯ 5
I should distinguish between Cartwright’s (1983, n. 5) version of this thesis and Duhem’s. Cartwright characterizes fundamental laws that do not accurately describe the real world as false while Duhem sees them as neither true nor false but approximate. 6 In other words, the idea of a determinate reality is implicit in the distinction. This dichotomy needn’t be seen as supporting scientific realism since the latter view encompasses the idea that the structure or theory mirrors, to a greater or lesser extent, that reality. One can be a metaphysical realist and support the distinction between theory and reality while remaining agnostic about whether the formal structure is an accurate representation of that reality. This latter view is the one advocated by van Fraassen. McMullin claims (in correspondence) that the phenomenological models popular in recent physics are not idealizations in his sense but simply constructions intended to summarize the phenomena. If this is so then one needs to provide an account of how it is possible
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supposes a world to which the scientist is attempting to fit his conceptual schemes, a world which is in some sense independent of these schemas . . . This is (it would seem) equivalent to presupposing some version or other of scientific realism” (1985, p. 254). For the argument to work it seems necessary that current techniques for mathematical idealization closely resemble those practiced by Galileo. However, idealization in modern physics often involves constructing models that may have little to do with reality. Frequently there is no simple mapping that will take us from the model to reality since in many cases the model involves highly complex structures that provide a way of arriving at the laws or equations that we want. High energy physics is a case in point. Idealization is not simply the abstraction of particular properties so as to facilitate calculation, as in the case of Galileo’s law of falling bodies where we can account for the air resistance that was ignored in the formulation of the law. Instead, many idealizing assumptions are made with no independent standard of comparison between the model and the physical system. For instance, current physics has verified that the weak and electromagnetic forces converge at high energies, but the theory only works if one introduces a highly idealized assumption about the nature of the vacuum. The model for the electroweak theory assumes the existence of Higgs particles that create a field that permeates all of space, and consequently, influences the properties of the vacuum. This Higgs field has no direction or spin and is introduced in order to preserve symmetry at high energies and to hide or break symmetry at low energies. Since the Higgs field is present even when no particles are present, it is rather like the nineteenth-century aether that was postulated as the carrier of electromagnetic energy. The difficulty, of course, is that no experimental verification of the Higgs field or its quantum equivalent, the Higgs particle, has been obtained. But it isn’t simply that there has been no verification for the Higgs particle that makes it an idealization. In other words, it is not the hypothesis claiming the existence of the particle that is an idealization, but rather the way in which it and the accompanying Higgs field is described. The idealizing assumptions about the vacuum and broken symmetries cannot be properly judged as approximations since there is no independent standard of comparison. In other words, we have no way of knowing the degree to which the properties attributed to the vacuum by the Higgs mechanism approximate its actual structure, yet the electroweak theory is considered highly confirmed. In many ways the model resembles Maxwell’s early aether model yet the difference is that, unlike the Higgs case, Maxwell intended his model to be purely heuristic with no direct connection to a real physical system, even though it enabled him to deduce the initial formulation of his field equations. The
to differentiate these from the models that supposedly provide a realistic representation of the phenomena.
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following quote from Gell-Mann suggests that this kind of heuristic use of models may in fact be common in modern theory; but as a methodological device it does little to bolster the connection between the process of idealization and an underlying presupposition about the relationship between models and reality that is characteristic of scientific realism and the debate between Simplicio and Salviati. We construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable algebraic expressions that hold in the model, postulate their validity and then throw away the model (Cf. GellMann and Ne’eman 1964, p. 198).
Although McMullin’s discussion may account for the more straightforward problem of idealization, a deeper problem arises in the context of modern theory. In addition to the complex mathematical abstraction, physical concepts like that of the Higgs field are not only highly idealized but their degree of departure from real physical systems often cannot be determined due to a lack of information. In these situations the question of how models relate to reality takes on an entirely new dimension. McMullin does discuss complex cases of idealization as instances of what he refers to as “construct idealization,” a process that involves a simplification of the conceptual representation of an object. This is a more specific type of mathematical idealization and is utilized in the development of models as opposed to the formulation of laws. The process operates in a way that resembles Cartwright’s use of abstraction; features that are known to be relevant are simply omitted (or simplified) in order to obtain a result.7 When this is done by simplifying properties already known to exist, as in the case where Newton assumed the sun to be at rest in order to derive Kepler’s laws, we have an example of formal idealization. When a model leaves much of the material structure of the phenomena unspecified we have an instance of material ⎯⎯⎯⎯⎯⎯⎯ 7
Cartwright distinguishes between abstraction and idealization, claiming that modern science works by abstraction and that the process is multi-dimensional. When we formulate laws we often begin with a real system or object and either rearrange specific properties in order to facilitate calculation or ignore small perturbations. For example, we know that the law governing the lever is specified for cases involving homogenous and perfectly rigid rods, even though these are not realizable in practice. Similarly in the case of Galileo’s law for free fall, we typically ignore the perturbations caused by air resistance or friction. In both cases, all relevant features of the situation are represented and the deviations from the ideal case can supposedly be accounted for. According to Cartwright, this differs significantly from the process of abstraction where we subtract not only small perturbations from concrete cases but often ignore highly relevant information as well. To use one of her examples, if we have an idealized model of how an helium-neon laser works, the information contained in the model will include a description of the lasing material and the specific laws that govern that particular kind of laser. We can ignore these details and move to a higher level of abstraction when we formulate a law that applies to all lasers; a law which states that the basic operating mechanism of the laser involves an inverted population of atoms. See Cartwright (1989).
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idealization. The distinguishing feature is the way the properties are added back in order to make the model more realistic. Most accounts of idealization, including McMullin’s and Laymon’s (Laymon 1982), assume that the process of adding back properties or calculating the effects of simplification involves a cumulative aspect that results in the model gradually becoming a more realistic representation of the phenomena. The difficulty with this view, as a philosophical reconstruction, is that it greatly simplifies the process of model building, thereby giving us an idealized model of scientific practice. The two most important concerns that these accounts overlook are that the growth of models occurs usually by the proliferation of structures rather than by a cumulative process, and secondly, changes in the qualitative or conceptual understanding often accompany slight changes in a model or idealization. Consequently, there is no stable structure to which parameters can be added to increase the model’s predictive and explanatory power. Without this kind of stability no degree of inductive support can be assigned to the model since the addition of each new parameter results in either the construction of a new model or the addition of new assumptions that are incompatible with the previous structure. In either case there is no constancy or uniqueness of a theoretical picture. Consider the following cases. McMullin describes the derivation of the ideal gas law as an example of formal idealization. The law is formulated using the assumption that the molecular constituents of a gas are perfectly elastic spheres that exert no forces and have a negligible volume relative to that occupied by the gas. This law holds for normal ranges of temperatures and pressures and predicts only a continuous monotonic change in the system’s properties. As a result, it is unable to explain a change from an homogeneous to an heterogeneous system, such as the appearance of liquid droplets in a gas. Technically it is inappropriate in accounting for phase transitions – the changes from a solid to a liquid to a gas. When this law is amended to take account of the finite size of the molecules and intermolecular forces, the result is the van der Waals law, which describes “real” as opposed to “ideal” gases and is valid at high temperatures. If we are to assume that the van der Waals law builds on the ideal gas law to give a better and more realistic approximation then it is important to consider the qualitative assumptions appropriate to each case. The van der Waals approach assumes that the gas pressure has its “ideal” value in the bulk of the gas and that the molecules suffer a loss of energy and momentum as they escape from the bulk and collide with the walls of the container.8 This too is an idealizing assumption which is further changed by yet another law, the Dieterici ⎯⎯⎯⎯⎯⎯⎯ 8
What this means is that in the bulk of the gas the molecules behave as though they were in a gas without attractive force so that the effective pressure is the same as for an ideal gas. Cf. Tabor (1985), ch. 5.
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equation, which states that the temperature of the gas is everywhere constant, even near the walls of the container. This law entails a reduction in the mean density by assuming that the density at the wall is less. As a result the Boltzmann distribution for total energy applies to the molecules striking the walls as well as those in the bulk, thereby contradicting the model provided by the van der Waals equation. The Dieterici equation gives a more accurate result for heavier complex gases, but like the van der Waals equation it cannot accommodate data near the critical point.9 In addition to this inconsistency the van der Waals equation has a fundamental theoretical difficulty; it leads to negative compressibility for some values of thermodynamic variables. This result contradicts the well-established van Hove theorem which states that an accurate statistical calculation can lead only to non-negative compressibility. The difficulty that arises when attempting to describe the development of these gas laws as an “adding back” of realistic assumptions is that in each case there are fundamental differences in the way the molecular system is described. Rather than accumulating properties in one basic structure, we have a number of mutually inconsistent ways of representing the system in each case. If we merely changed the properties of the ideal gas in order to accommodate the van der Waals law, a case could be made that the inconsistency only occurred between the ideal and the real case; but the problem is more significant. The socalled real system represented by the van der Waals approach is not a unique description, since it conflicts with other non-ideal cases like the Dieterici equation. The two models make different assumptions about how the molecular system is constituted. Instead of a refinement of one basic molecular model, we have a number of different models that are suitable for different purposes. The billiard ball model is used for deriving the ideal gas law, the weakly attracting rigid sphere model for the van der Waals law, and a model representing molecules as point centers of inverse power repulsion is used for facilitating transport equations. The fact that this situation arises in one of our better developed and highly confirmed theories suggests that the problem is not one that is peculiar to newly proposed theories and phenomena. In fact nuclear physics exhibits the same pattern as the kinetic theory. There exist a number of contradictory nuclear models each of which postulates a different structure for the atomic nucleus. According to the liquid drop model, nucleons are expected to move very rapidly within the nucleus and produce frequent collisions, similar to the molecules in a drop of liquid. Despite its success there are many experimental results that this model cannot account for (Cf. Gitterman and Halpern 1981). Moreover, the model ignores the fact that, ⎯⎯⎯⎯⎯⎯⎯ 9
PV = RT represents the ideal gas law, but in the van der Waals case two terms, a and b, are added to represent intermolecular forces yielding a new law, P + (a/V2) (V–b) = RT. The Dieterici equation adds yet another term, P(V–b) = RT exp(–a /VRT). Again, see Tabor (1985), ch. 5.
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like electrons, nucleons in rapid motion have spin 1/2, and therefore obey the Fermi-Dirac statistics and are subject to the Pauli exclusion principle. Again it isn’t possible to simply reintroduce these conditions (even partially) into the original model. Instead an alternative, the shell model, was proposed which would incorporate the spin statistics and account for the anomalous experimental data. In this model, each nucleon has an independent motion. Although the new model is superior to the drop model and can accommodate many nuclear data, it cannot account for the total energy of the nuclei or nuclear fission, phenomena for which the liquid drop model was initially proposed. Still other experimental results are explained using what is termed the compound nucleus model, while another possibility is the optical model which accounts for some of the observed neutron scattering. In all of these cases the departure from reality must be addressed from within the context of each different model, since each presents a different description of the phenomena. For calculations where the departure is seemingly irrelevant a simple model is used, and when a more complex account is required the process of adding back parameters takes place within the domain of an entirely different model or set of idealized circumstances. McMullin argues that the technique of “de-idealizing,” which serves to ground the model as the basis for a continuing research program, works only if the original model idealizes the real structure of the object. But, because we often have many models and the real structure of the object is often too complicated to manipulate or is simply unknown, the claim is perhaps better understood as one that characterizes successful de-idealization as evidence for some degree of approximation to the real structure of the object. But even this seems an overly optimistic, if not inaccurate way of representing the modeling process in modern physics. The inductive support that might normally be gained through successful predictions, provided that the properties of the model were added in a cumulative way to a stable structure, is simply not present. Because each model is different the inductive base is not strengthened in a systematic way. McMullin does claim that if processes of self-correction and imaginative extension of a model are suggested by the structure of the model itself, then the processes are not ad hoc, and we can have a reasonable belief that the model gives a relatively good fit with the real system (1985, p. 264). However, the sense in which modifications to nuclear models were suggested by the original model of the atomic nucleus is somewhat remote, since the only claim that remained constant was the fact that the nucleus consisted of protons and neutrons. The linkages tracing the complex models we use today to their origins in the Rutherford model are certainly less than perspicuous.10 A similar story can be told in the case of van der Waals’s ⎯⎯⎯⎯⎯⎯⎯ 10
Also, if the process was cumulative, the shell model would surely be able to account for the phenomena associated with the liquid drop model, which is not the case.
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law and its relationship to the kinetic theory. Historical work by Martin Klein11 and others has shown that the van der Waals equation did not even qualify as a deduction from the kinetic theory. In fact, its explanations of the gas-liquid transition in terms of intermolecular forces was not really an application of statistical mechanics. Nevertheless, no one would suggest that the law is somehow ad hoc. The very nature of theory construction is such that one expects extensions and refinements to models and idealized laws to be motivated in part by experimental findings, as well as by theoretical considerations that are both internal and external to the model. The difficulty of ad hoc postulations arises when mathematical refinements, intended to establish a physical result, cannot be physically explained using any available model, as in the case of renormalization of mass in quantum electrodynamics. In some cases, like the example of the frictionless plane, correcting the model presupposes that we know the degree of departure from the real system or what parameters have been omitted. In this sense all of science involves idealization, since every model or law contains what Michael Redhead has called “computational gaps” (Redhead 1980). This poses a philosophical problem only if we fail to recognize that our theories are only correct within a certain margin of error rather than in some sense of absolute correspondence, and where the acceptable degree of approximation is determined within the practice itself. However, what the examples above alluded to was a more problematic notion of idealization, one which creates difficulties that are motivated not only by philosophical worries about correspondence, but by theoretical concerns that arise within the scientific context. These cases involve computational gaps that are not merely practical problems about calculation but create more serious problems for theorists, as well as for traditional realist interpretations of scientific practice. The examples discussed above are such that it is difficult to determine the degree to which the model represents the real system, since little can be determined about the actual structure of the system due to a lack of direct information and the number of conflicting models. Consequently, the only indicator of the model’s success is its predictive power rather than its isomorphism with reality. Laymon also uses the van der Waals equation as an example of how the kinetic theory can acquire increased confirmation. He claims that the fact that added parameters (which make the model of a gas more realistic) result in more accurate predictions lends credence to the kinetic theory (Laymon 1985). As I mentioned above, the problem with this view is that the van der Waals law itself contradicts other features of the kinetic theory and disagrees with experimental results near the critical point. In addition there are several different ways of ⎯⎯⎯⎯⎯⎯⎯ 11
See Klein (1974), as well as the appendix of Morrison (1990). My account draws on the work of Klein.
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calculating the parameter b, the intermolecular force, each of which makes different assumptions about how the force operates. A recent textbook in gas theory refers to these methods as providing good, but not correct numerical results (Cf. Tabor 1985, p. 122). Although there are accurate predictions for some ranges of phenomena, it occurs at the expense of others.12 Although we may not be able to determine whether our models present an accurate picture of physical systems, we are able to some extent to carry out the process McMullin refers to as “de-idealizing”; adding parameters that facilitate a more concrete representation of the phenomena. What I want to suggest is a redefinition of what this process entails. Instead of seeing the van der Waals law as a realistic interpretation of molecular structure we should think of it as providing a more concrete representation; one that represents a physically possible state. When thinking in terms of realistic models there is a tendency to assume that one is approximating the true nature of the properties or phenomena under investigation, a claim which, in cases where there are a variety of inconsistent models or incomplete information, cannot be reasonably upheld. A concrete representation can be successfully used as an idealization without implying that the structure is approximating the true nature of the physical system.13 For example, the ideal gas law refers to a system that is not physically realizable insofar as molecules are not infinitesimal, while the van der Waals law involves properties (the finite size of molecules) ascribable to real physical systems even though they may be contradicted by other gas laws like the Dieterici equation. Of course, concrete representations will be more realistic insofar as they refer to physically realizable possibilities, but this characterization does not involve the problems that accompany the realist construal of models discussed above. What we are left with then is two kinds of idealization that operate in physics. The first, which I will call “computational idealization,” involves the straightforward sort of approximation used in cases like the rigid rod or frictionless plane, where we know how to account for perturbations and can calculate the degree of departure between the real and ideal cases. The second kind, predictive idealization, typically involves a variety of different ways of ⎯⎯⎯⎯⎯⎯⎯ 12
One would perhaps be able to make a case that the evidence accounted for by the van der Waals law confirmed the kinetic theory if the law could be deduced from the theory, or even if the additional parameters, a and b, were suggested by the theory. But, of course, neither is the case. 13 This difference between realistic and concrete models becomes important in Kelvin’s work, which I discuss below. Sometimes it is the case that certain metaphors function as a way of turning abstract theoretical notions into concrete representations, as was the case with the clock metaphor in the seventeenth century. As Larry Laudan has pointed out, it was this metaphor that solidified the notion that the physical world operated as a mechanical system ( Laudan 1981). Another example is the case of elliptical orbits, which became concrete for Newton, but were considered abstract by Kepler.
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idealizing the phenomena in question, each of which is used for different purposes, so that as a result we are unable to determine the degree of approximation between the real system and the idealized model. In the computational case we know how a perfectly rigid rod ought to behave, and when we formulate the law of the lever we know the degree of departure from the ideal or theoretical construct that is exemplified by the real system. It is important to note, however, that when we calculate the degree of departure we do so for a specific property that we are measuring, be it friction, rigidity, etc. We don’t have anything like a complete model or perfect information about the real system, since this would involve not only an account of macroscopic properties, but also micro properties. Hence to model the real system would also require a variety of different structures; Newtonian as well as quantum mechanical models. We do have direct access to some features of the real system, and consequently, we are able to calculate approximations in a relatively straightforward way. But because this can only be done in a limited sense, it fails to provide an inductive base for judgements about the accuracy of more complex models.14 Contrast this with the predictive case and the example of the different gas laws. Here the theory does not present an idealized system that can account for the behavior of gases in particular contexts. Instead several different idealizations are proposed from within the overall framework of the kinetic theory, each of which gives fairly accurate predictions for a specific group of phenomena, but fails to provide confirmation about a unique molecular structure that is determinable using the kinetic theory. In most cases of predictive idealization, we are uncertain about the correspondence between our model and the structure of the system in question, while other instances may involve the postulation of a structure that we know to be false, yet we use it for achieving predictive power. Both the ideal gas law and the model of the electron as a point particle fit in this latter category; and in both cases further modeling prevents us from closing the computational gap due to lack of information about the real system. The case of the electron is especially interesting since relativistic electrodynamics requires that we treat the particle as a point mass. This results in the electron having an infinite self-energy, a theoretical difficulty that is accounted for through the use of a mathematical technique called renormalization, the physical significance of which has come under debate. Given that the degree of approximation involved in using models and idealizations cannot often be determined, something needs to be said about how the heuristic use of models contributes to the process of theory construction. It is ⎯⎯⎯⎯⎯⎯⎯ 14
I would like to thank Carl Hoefer for calling my attention to this point, and forcing me to rethink some of the difficulties that arise even with computational idealization.
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often the case that in describing the role of models a distinction is made between those that are “merely heuristic” and those which are presumed to have some truth component or represent reality in an accurate way. Implicit in this distinction is usually a view that heuristic models serve as placeholders until a more “realistic” model can be developed. However, this kind of dichotomy misrepresents and undermines to some extent the way heuristic models function in theory construction and confirmation. Instead of valuing models as supposedly accurate representations of reality, we need to draw attention to the heuristic role played by all models in establishing empirical laws and theories. The recognition of the heuristic component in model building and theory construction serves to minimize the division between different kinds of models. This, of course, does not preclude distinguishing between those models we know to be false and those about which we are uncertain. The point is simply that given the nature of modeling and our relative inability in many cases to independently determine whether models are in fact accurate representations of reality, the distinction between supposedly “realistic” models and those that are “merely” heuristic can be successfully made only in cases where we knowingly use fictional representations. Of course these fictional representations can be either concrete, like Maxwell’s aether model, or ideal, like the case of a point particle. As I stressed above, concrete models represent an object or system that is physically realizable; it may be possible but in fact not actual, or alternatively, it may be a candidate for reality in the form of an hypothesis. In order to illustrate the importance of heuristic models I want to discuss the development of Maxwell’s electromagnetic theory, which provides an interesting account of how it is possible to move from a mathematical analogy to a fictional model to a more abstract dynamical theory. Not only does it illustrate the importance of idealized constructs and mathematical representations as heuristic mechanisms, but it shows how they play a substantive role in theory construction and development. The criticisms of Maxwell’s theory by Duhem and Kelvin, which centered on the way he used idealization and models, bear a significant similarity to modern debates on the subject.
3. Models and Reality in Maxwell’s Electromagnetic Theory In the various stages of development that led to the version of field theory presented in the Treatise on Electricity and Magnetism (Maxwell 1873; hereafter ‘TEM’), Maxwell relied on a variety of methodological tools that included a fictional model of the aether in addition to a variety of physical analogies. Although the model was recognized by Maxwell as fictitious it nevertheless played an important role in developing both mathematical and
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physical ideas that were crucial to the formulation and conceptual understanding of field theory. The evolution of electromagnetism illustrates a process of theory construction that has, to a great extent, remained unchanged in modern science. In 1856 Maxwell attempted a representation of Faraday’s electromagnetic theory in what he called a mathematically precise yet visualizable form (Maxwell 1856; hereafter ‘FL’). The method involved both mathematical and “physical analogies” that were based on Kelvin’s 1842 analogy between electrostatics and heat flow (FL, p. 156). Maxwell’s analogy was between stationary fields and the motion of an incompressible fluid that flowed through tubes with the lines of force represented by the tubes. Using the formal equivalence between the equations of heat flow and action at a distance, Maxwell substituted the flow of the ideal fluid for the distant action. Although the pressure in the tubes varied inversely as the distance from the source, the crucial difference was that the energy of the system was in the tubes rather than being transmitted at a distance. The direction of the tubes indicated the direction of the fluid in the way that the lines of force indicated the direction and intensity of a current. Both the tubes and the lines of force satisfied the same partial differential equations. Maxwell went on to extend the hydrodynamic analogy to include electrostatics, current electricity and magnetism. The purpose of the analogy was to illustrate the mathematical similarity of the laws, and although the fluid was a purely fictional entity it provided a visual representation of this new field theoretic approach to electromagnetism. What Maxwell’s analogy did was furnish a physical “conception” for Faraday’s lines of force; a conception that involved a fictional representation, yet provided a mathematical account of electromagnetic phenomena. This method of physical analogy, as Maxwell referred to it, marked the beginning of what he saw as progressive stages of development in theory construction. Physical analogy was intended as a middle ground between a purely mathematical formula and a physical hypothesis. The former causes us to lose sight of the phenomena to be explained, while the latter clouds our perception by imposing theoretical assumptions that restrict our ability to evaluate alternatives. By contrast, the method of physical analogy allows us to grasp a clear physical conception without full blown commitment to a particular physical theory, while at the same time preventing us from being drawn away from the subject under investigation by the pursuit of “analytical subtleties.” (FL, p. 156). So, in a physical analogy we have a partial similarity between the laws of one science and those of another. The hydrodynamic analogy was specifically intended as a way of gaining some precision in the mathematical representation of the laws of electromagnetism and assisting others in the systematization and interpretation of their results. It was important as a visual representation because it enabled one to see electromagnetic phenomena in a new way. Until then action at a distance accounts had dominated, and as a
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result, the idea that these phenomena could be conceptualized in another way was indeed novel, but highly suspect. Although the analogy did provide a model (in some sense), it was merely a descriptive account of the distribution of the lines in space with no mechanism for understanding the forces of attraction and repulsion between magnetic poles. This physical treatment was developed further in a paper written by Maxwell in 1861-2, entitled “On Physical Lines of Force” (Maxwell 1861-2; hereafter ‘PL’). The goal was to find an account of the physical behavior of magnetic lines that could give rise to magnetic forces. Prior to this Kelvin had construed the Faraday effect (the rotation of the plane of polarized light by magnets) as the result of the rotation of molecular vortices in a fluid aether. Maxwell used this idea to develop an account of the magnetic field that involved the rotation of the aether around lines of force. The paper also offered an account of the forces that caused the motion of the medium (or aether) and the occurrence of electric currents. This required an explanation of how the vortices could rotate in the same direction; the problem which led Maxwell to the development of his famous mechanical aether model. The model involved a vortex motion that resulted from a layer of rolling particles called idle wheels that were interspersed between the vortices. Electromotive force was then explained in terms of the forces exerted by the vortices on the particles between them. Although Maxwell was successful in developing the mathematics required for his model, he was insistent that the representation be considered provisional and temporary. The conception of a particle having its motion connected with that of a vortex by perfect rolling contact may appear somewhat awkward. I do not bring it forward as a connection existing in nature, or even as one which I would willingly assent to as an electrical hypothesis. It is, however, a mode of connexion which is mechanically conceivable, and easily investigated . . . I would venture to say that anyone who understands the provisional and temporary character of this hypothesis, will find himself rather helped than hindered by it in his search after the true interpretation of the phenomena (PL, p. 486).
In fact, Maxwell called this representation an imitation of electromagnetic phenomena by an “imaginary system of molecular vortices” (PL, p. 486). The difficulty with the model was that Maxwell was unable to extend it to electrostatics, a problem that led him to propose a rather different model in part three of the paper. Instead of the hydrodynamic model consisting of a fluid cellular structure containing vortices and idle wheels, he developed an elastic solid model made up of spherical cells endowed with elasticity. The cells were separated by electrical particles whose action on the cells would cause a kind of distortion. Hence the effect of an electromotive force was to distort the cells by a change in position of the electrical particles. This gave rise to an elastic force which set off a chain reaction throughout the entire structure. Maxwell saw the
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distortion of the cells as a displacement of electricity within each molecule. Understood literally, displacement meant that the elements of the dielectric had changed position. This action on the dielectric also produced a state of polarization, and because displacement involved the motion of electricity, Maxwell argued that it should be treated as a current. It was the equation describing displacement, which expressed the relation between polarization and force, that Maxwell used to calculate the aether’s elasticity; the crucial step that led to the identification of the optical and electromagnetic aethers.15 Once this assumption about elasticity had been made, Maxwell then used the analogy with the luminiferous aether in support of his conclusion. The undulatory theory of light requires us to admit this kind of elasticity in the luminiferous medium in order to account for transverse vibrations. We need not then be surprised if the magneto-electric medium possesses the same property (PL, p. 492).
Although Maxwell succeeded in showing that the velocity of transverse vibrations travelling through the electromagnetic aether was equivalent to the velocity of light, the model raised several difficulties that needed to be addressed before the theory could be presented in what was considered by Maxwell to be an acceptable form. The model used in PL was intended to have heuristic value as a way of assisting speculation about electromagnetic phenomena that were the result of the action of a medium rather than at a distance. The idea was to draw attention to the mechanical consequences of the model, while providing some way of visualizing how such phenomena could be produced. But, not only was there no experimental evidence for the existence of electromagnetic waves, there was no independent support for the vortex hypothesis or the displacement current. All of the experimental evidence was consistent with Ampere’s original law (which Maxwell had modified subsequent to his postulation of the displacement current) and, moreover, displacement was given an ambiguous interpretation functioning as both an equation of elasticity and an electrical equation.16 Because of this dual interpretation the equation served as a bridge between the electrical and mechanical parts of the model. Despite these difficulties, Maxwell had in place the beginnings of what would later become a fully articulated field theory. Using his fictional aether model he was able to derive the electromagnetic wave equations and now, in a manner reminiscent of Gell-Mann’s remark, he would essentially abandon the ⎯⎯⎯⎯⎯⎯⎯ 15
R = 4πE2h, where h = displacement, R = electromotive force, and E = coefficient of rigidity, which depended on the nature of the dielectric. The amount of displacement depended on the nature of the body and the electromotive force. 16 R was interpreted as an electromotive force in the direction of displacement and as an elastic restoring force in the opposite direction. E was considered an electric constant and elastic coefficient while h was interpreted as a charge per unit area and a linear displacement.
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model and attempt to derive the field equations with the aid of experimental facts and general dynamical principles. Before discussing the later formulations of electromagnetism it is important to isolate the differences between what Maxwell considered a “theory” and the kind of model he put forth in PL. Although the method Maxwell used was that of “physical analogy,” it did not involve a physical identification of properties or phenomena in the two systems. Instead it was simply taken to mean that two branches of science had the same mathematical form, as in the case of heat flow and electrostatics. A subspecies of physical analogy is what Maxwell called “dynamical analogy,” where again both analogues have the same mathematical form, but one is concerned with the motion and configuration of material systems. An example is Maxwell’s analogy between electrostatics and the motion of an incompressible fluid, where the latter is concerned with fluid flow from sources to sinks. The extension of these dynamical analogies to a more substantive interpretation constituted a “dynamical explanation,” where the properties of one system were literally identified with the properties of the other. When one is able to provide this kind of identification then the account of the material system can be understood as a “physical hypothesis.” The hypothesis must meet other conditions if it is to be considered legitimate; namely, independent existence for the entities it postulates and consistency with dynamical principles like conservation, both of which I will mention below. But first, the most important issue in distinguishing between Maxwell’s early use of models and analogies and his later work is the transition from dynamical analogy to dynamical theory.17 It is obvious from the discussion above that none of the analogies used in FL or PL would constitute an explanation, since most of the references were to fictional phenomena or properties introduced for heuristic purposes. However, when Maxwell moves on to write “A Dynamical Theory of the Electromagnetic Field” (Maxwell 1865; hereafter ‘DT’) there is also nothing in this work that would qualify as an explanation. The latter involved a specific characterization of a physical system, whereas Maxwell’s “theory” made no specific assumptions about the aether or electromagnetic medium. Instead the conclusions reached in DT were supposedly deduced from experimental facts with the aid of general dynamical principles about matter in motion; principles characterized by the abstract dynamics of Lagrange.18 This method allowed Maxwell to treat the field variables as generalized mechanical variables interpreted within the context of the Lagrangian formalism which contained terms corresponding only to observable variables. As a result, there were no assumptions about hidden mechanisms or causes that could be used to explain the behavior of material ⎯⎯⎯⎯⎯⎯⎯ 17 18
For a discussion of Maxwell’s account of dynamical explanation and theory see (Maxwell 1876). Cf. DT, p. 564.
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systems. Because of the generality of the Lagrangian formalism and its avoidance of specific hypotheses, one could attain a degree of certainty unavailable in more concrete formulations of physical theory.19 Because there is no way of determining what actual connections obtain between unobservables, and because a variety of physical possibilities can be postulated to account for such connections, the proper question is not – what phenomena will result from the hypothesis that the system is of a certain specified kind? But what is the most general specification of a material system consistent with the condition that the motions of those parts of the system which we can observe are what we find them to be (Maxwell 1879, p. 781; hereafter ‘T&T’).
Although Maxwell used this abstract approach, unlike Duhem, he remained committed to visualization and to the fact that one needs some concrete “conception” of the phenomena being examined. The use of mechanical images like electric momentum and elasticity was to be understood as illustrative, rather than as explanatory, and their role was to “direct the mind of the reader to mechanical phenomena which will assist him in understanding the electrical ones” (DT, p. 564).20 The only term that was given a substantive interpretation by Maxwell was the “energy” of the field. The method of constructing a dynamical theory was extended in the Treatise on Electricity and Magnetism. The goal of this work was to examine the consequences of the assumption that the phenomena of the electric current are those of a moving system, the motion being communicated from one part of the system to another by forces, the nature and laws of which we do not yet even attempt to define, because we can eliminate these forces from the equations of motion by the method given by Lagrange for any connected system (TEM, vol. II, sec. 552).
Although the connections between motions of the medium and specific variables were eliminated from the equations (the variables being independent of any particular form of these connections) Maxwell once again appealed to mechanical ideas in the conceptual development of the theory. In the chapter devoted to the Faraday effect he reintroduced molecular vortices as a possible way of explaining magneto-optic rotation. Although the vortices were not merely imaginary constructions, their status was not that of a physical hypothesis either. Maxwell claimed that we had “good evidence for the opinion that some phenomenon of rotation is going on in the magnetic field and that this rotation is performed by a number of very small portions of matter” (PL, ⎯⎯⎯⎯⎯⎯⎯ 19
Here we find Maxwell in agreement with the methodological principle enunciated by Duhem, that there is a trade-off between accuracy and certainty. 20 For a discussion of the difference between an explanation and a theory, see Maxwell’s example of the belfry in T&T, p. 783.
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p. 470). The problem was that the vortex hypothesis failed to satisfy the criterion of independent existence, a necessary condition for all physical hypotheses (TEM, vol. II, sec. 831). Vortices were proposed initially as an explanatory tool, from which one could then derive the desired consequences; because they lacked direct experimental evidence, Maxwell concluded that there was no independent way to verify their existence. Consequently, if they were to play any substantive role in the “dynamical theory” Maxwell would be guilty of subscribing to the same methods for which he criticized the French molecularists; a species of what we now refer to as hypothetico-deductivism (Maxwell 1876, p. 309). Maxwell had a specific justification for introducing mechanical ideas or concepts into his dynamical field theory. As I mentioned above, he stressed the importance of providing a physical image or interpretation of the phenomena, even if that image was nothing more than a fictional illustration that was consistent with mechanical principles. From these visual images one could develop mathematical representations that might assist in the formulation of physical laws. Although the specifics of Maxwell’s mechanical model were absent from the later work, aspects of his mechanical analogies remained. In fact, Maxwell’s insistence that energy be interpreted literally involved a commitment to the claim that “all energy is mechanical energy” (DT, p. 564). This emphasis is also echoed in the Treatise (TEM, vol. II, sec. 550), and in a lecture to the Chemical Society, where he connects the use of dynamical analogy and mechanical concepts: When a physical phenomenon can be completely described as a change in the configuration and motion of a material system, the dynamical explanation of that phenomenon is said to be complete. We cannot conceive any further explanation to be either necessary, desirable or possible, for as soon as we know what is meant by the words configuration, motion, mass and force, we see that the ideas which they present are so elementary that they cannot be explained by means of anything else (Maxwell, n.d.(a), p. 418).
Until we have achieved this level of understanding we must rely on a physical “conception” of the phenomena – constructive images that grew out of analogies and were necessary for a physical representation of material systems. Although there are an infinite number of possible ways the phenomena can be represented, in order to be acceptable each must be what Maxwell terms a “consistent representation”; in other words, consistent with fundamental principles like conservation of energy and with established experimental facts.21 ⎯⎯⎯⎯⎯⎯⎯ 21
As Maxwell remarks at the end of the Treatise (TEM, vol. II, sec. 831): The attempt which I then made to imagine a working model of this mechanism must be taken for no more than it really is, a demonstration that a mechanism may be imagined that is capable of producing a connexion mechanically equivalent to the actual connexion of the parts of the
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When using the method of physical analogy Maxwell was always quick to caution against extending analogies beyond the realm of mathematical laws. The method was intended to yield a knowledge of relations, rather than an identification of physical structures or essences. In other words, Maxwell’s use of analogy is significantly different from what is normally referred to as argument from analogy, where we attempt to infer the existence of particular microphenomena or properties from their apparent analogy with their macro counterparts, or where we attempt to use the analogy as the basis for an inductive inference.22 The resemblance between mathematical laws was useful in the development of further mathematical ideas, and in FL, Maxwell showed how the formal equivalence between the equations of heat flow and action at a distance could be used to present electromagnetic phenomena from two different yet mathematically equivalent points of view. Although physical ideas were prominent there was no attempt to consider them as hypotheses, yet their heuristic value added to both the qualitative and quantitative aspects of the analogy. Although one could obtain “a system of truth founded strictly on observation” if physical ideas were deleted from the analogies, the result would be “deficient in both the vividness of its conceptions and the fertility of its method” (FL, p. 156). According to Maxwell the method for recognizing real analogies rested on experimental identification. If two apparently distinct properties of different systems are interchangeable in appropriately different physical contexts they can be considered the same property.23 But, in order to have this kind of substitutability, there must be independent evidence for both analogues. So, although Maxwell could identify the optical and electromagnetic aethers, given the equal velocities for wave transmission, there was only an inferential basis for the existence of the medium. As a result the analogy could not provide the foundation for a substantive physical theory. The entire process of theory construction was one that, for Maxwell, involved a variety of methods, each of which contributed in an essential way to the development of electromagnetism. Physical analogies were used in the development of a mechanical model that eventually led to the formulation of the field equations. While the end product – a dynamical field theory – was independent of hidden assumptions, it did rely on physical ideas whose heuristic electromagnetic field. The problem of determining the mechanism required to establish a given species of connexion between the motions of the parts of a system always admits of an infinite number of solutions. Of these, some may be more clumsy or more complex than others, but all must satisfy the conditions of mechanism in general. 22 For more on Maxwell’s distrust of this method see his criticisms of Newton’s analogy of nature in an article entitled “Atom” (n.d. (b)). 23 This is a species of what Mary Hesse has called substantial identification, which occurs when the same entity is found to be involved in apparently different systems.
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value was not considered “mere” by Maxwell. Their value was not measured by their degree of truth but they nevertheless played a constitutive role in the advancement of science. The process is summed up quite nicely in Maxwell’s address to the Mathematical and Physical sections of the British Association. The figure of speech or of thought by which we transfer the language and ideas of a familiar science to one with which we are less acquainted may be called Scientific Metaphor. Thus, the words velocity, momentum, force, etc., have acquired certain precise meanings in elementary Dynamics. They are also employed in the Dynamics of a Connected System in a sense, which, though perfectly analogous to the elementary sense, is wider and more general. These generalized forms of elementary ideas may be called metaphorical terms in the sense in which every abstract term is metaphorical. The characteristic of a truly scientific system of metaphors is that each term in its metaphorical use retains all the formal relations to the other terms of the system which it had in its original use. The method is then truly scientific – that is, not only a legitimate product of science but capable of generating science in its turn. There are certain electrical phenomena again which are connected together by relations of the same form as those which connect dynamical phenomena. To apply to these the phrases of dynamics with proper distinctions and provisional reservations is an example of a metaphor of a bolder kind; but it is a legitimate metaphor if it conveys a true idea of the electrical relations to those who have already been trained in dynamics (Maxwell 1870, p. 227; italics added).
Dynamical theories that emphasize knowledge of relations, rather than things, contain the highest degree of certainty attainable in science. In summary, then, the conceptual models of electromagnetism led to the development of new relations among various phenomena that had been previously unexplored. This, in turn, led to the formulation of new quantitative laws that were shown to bear a resemblance to laws in other domains. Consequently, a model whose departure from the truth was indeterminable as well as one that functioned as a purely fictional representation played a significant role in the development of empirical laws. All of Maxwell’s physical analogies and models facilitated visual representations of the phenomena, even though many failed to qualify as physical possibilities in the sense that the molecular model issuing from van der Waals’s law does. Maxwell considered them as fictional representations, except in the case of the vortex hypothesis, which was considered only as a candidate for realistic status. The fictional models in this case were concrete in the sense that they utilized legitimate mechanical systems (unlike molecular systems that postulate point masses), yet they were fictional in that Maxwell did not assume that these concrete systems represented the structure of the field in any way.
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4. Models and Practice Although Maxwell’s theory exemplified the importance of heuristic representations, it was not without its critics on this point. Both Duhem and Kelvin objected to Maxwell’s rather liberal use of mechanical images and the apparent inconsistencies in his theory, as well as what Kelvin took to be his failure to develop a mechanical model for his field-theoretic account of electromagnetism. In addition, the theoretical difficulties that plagued the theory (specifically, the lack of experimental evidence for the displacement current) were thought to indicate a disregard for the empirical foundations considered fundamental to theory construction. Maxwell’s emphasis on presenting a visualizable account of the phenomena was insufficient for Kelvin, who insisted that models be tactile structures that could be manipulated manually, thereby allowing one to know the particular system or phenomenon as a “real” thing. In their recent biography, Crosbie Smith and Norton Wise describe how Kelvin differentiates between tactile and visual experience gained through the senses and mental constructions or images; the former being far more efficient and trustworthy. Although both Maxwell and Kelvin made extensive use of analogies, it was of primary importance to Kelvin that he convince people of the reality of the aether using his elastic solid vortex model (see Smith and Wise 1989, p. 465). Kelvin saw Maxwell’s emphasis on abstract dynamics, supplemented by mechanical images, as a form of nihilism, concerned with words and symbols rather than reality. The problems with displacement served only to bolster the criticism. As long as Kelvin could construct a workable model of a particular phenomenon or system (as in the case of the aether), he construed it as having definite contact with reality, a contact that enabled one to view the manipulation of the model as equivalent to experimental evidence. A dynamical model provided a “rigorous analysis,” operating not only as an aid to discovery but as a mechanism for the production of new phenomena, rather than simply a representation of existing ones (Smith and Wise 1989, pp. 486-7, 468-9). Even though Kelvin shared Maxwell’s demand for visualization, he demanded that any model fulfilling this demand also serve an explanatory function; a role Maxwell saw as reserved for a fully justified hypothesis. Duhem’s criticisms were directed generally toward Maxwell’s use of models and the role they played in theory construction. The main objection seemed to be the lack of a realistic attitude toward the models as well as the fact that often more than one was used to represent the same phenomenon. The emphasis on realism refers to the apparent lack of concern for developing models that could be mapped directly onto measurable properties, and although the English physicists recognized this limitation in their approach, Duhem saw it as a definite flaw in the method, since there was no attempt to bring order to a group
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of disparate models. For Duhem, this use of models was undesirable at the level of qualitative representation and was simply intolerable in the context of algebraic theories where systematic order was the sine qua non. As we saw earlier, Duhem himself was not concerned with providing an explanation of empirical laws, since this would involve an illegitimate appeal to metaphysics. Instead the goal was to furnish a realistic account of physics that was based on empirical data and methods that remained faithful to the limitations of mathematical and experimental science, while providing some degree of unity and order upon which our theories must be built. Consequently, one could admit a plurality of laws, provided they were united at some level in a classification scheme. In contrast, the British failed to distinguish between theory and the variety of models that they used, giving the appearance of underlying disorder at every level. There is an important sense in which Duhem’s criticisms of his British counterparts mask some of the similarities that existed between them. Maxwell clearly was concerned with securing an experimental foundation for electromagnetism and paid particular attention to what he saw as the limits of scientific theorizing. Like Duhem, he emphasized the distinction between the laws of physical science and an underlying reality that has no place in theory construction (see Morrison 1992). Kelvin, although somewhat more zealous in his attitudes toward realism, was similarly concerned with providing an experimental basis for hypotheses like the vortex aether, and intended the manipulation of mechanical models as a way of achieving this goal. Although Duhem’s dissatisfaction with the inherent disorder in British physics is certainly well-founded, ironically it has been the proliferation of inconsistent models, laws and the lack of strict deduction that has produced the successful science we have today.
5. Conclusion I have attempted to illustrate how in nineteenth and twentieth-century physics the role of models and idealizations, as both heuristic devices and as representations of reality, has come under debate. It has been a common practice in philosophical literature to distinguish between physical models that are “merely” heuristic and those that have the nobler task of representing reality in a supposedly accurate way. The focus of the debate about realism has centered on developing ways of articulating exactly how these models retain a degree of abstraction while bearing on reality in some significant way. Successful attempts to enhance the realistic character of the models are often seen as evidence that the physical system has essentially the same structure as the model itself. However, in both the historical and contemporary discussions above, it is
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apparent that the successful use of models does not involve refinements to a unique idealized representation of some phenomenon or group of properties, but rather a proliferation of structures, each of which is used for different purposes. Indeed in many cases we do not have the requisite information to determine the degree of approximation that the model bears to the real system. For example, most if not all of the work done in high energy physics since the mid-seventies has been based on the quark model of the atom. Out of this model grew an extensive account of the elementary structure of matter, a highly sophisticated and predictively successful theory called quantum chromodynamics. Although the models of this theory are highly detailed there has been no experimental verification that fractionally charged particles (quarks) even exist. As a result there is no way to determine the accuracy of the model aside from its predictive power. But this is not simply a problem for cutting-edge research. In other words, my argument is not that the Galilean account of models fails to take account of recent work in high energy physics. Rather, it is that the Galilean picture cannot even accommodate well-entrenched cases in nuclear physics and the kinetic theory. These relatively simple systems cannot be modeled by simply adding parameters to a basic theoretical structure. With each addition comes a change in the fundamental assumptions about the nature of the system. What this suggests is that in situations other than straightforward cases like pendulums and rigid rods, we have idealizations that are different in kind from what McMullin has characterized. Given that many models cannot be evaluated on their ability to provide realistic representations, we need to focus less on the distinction between “heuristic” and “realistic” models, and instead, emphasize the way in which models function in the development of laws and theories. This is especially true given the character of mathematical physics and the emphasis on approximation, which increasingly eludes successful calculation. Because all models function in an heuristic way the distinction serves only to separate features of models which cannot always be isolated in practice. The post-seventeenth-century problem of approximation and idealization is not only a philosophical problem but, as one to be countered by sophisticated calculations and the addition of parameters, it is also a difficulty that exists within scientific practice. We must be mindful, however, that the theories we typically hold up as paradigms of successful science, theories which we claim are realistic representations of physical systems, are those that require a proliferation of models at the level of application. What this indicates is that the question of whether a model corresponds accurately to reality must be recast in
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a way that is more appropriate to the way in which models actually function within the practice that we, as philosophers, are trying to model.* Margaret Morrison Department of Philosophy University of Toronto
[email protected]
REFERENCES Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon Press. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Duhem, P. (1902). Les theories electriques de J. Clerk Maxwell: Etude historique et critique. Paris: Hermann. Duhem, P. (1977). The Aim and Structure of Physical Theory. New York: Atheneum Press. Gell-Mann, M. and Ne’eman, Y. (1964). The Eightfold Way. New York: W. A. Benjamin. Gitterman, M. and Halpern, V. (1981). Qualitative Analysis of Physical Problems. New York: Academic Press. Klein, M. (1974). Historical Origins of van der Waals’ Equation. Physica 73, 28-47. Laudan, L. (1981). Science and Hypothesis: Historical Essays on Scientific Methodology. Dordrecht: D. Reidel. Laymon, R. (1982). Scientific Realism and the Hierarchical Counterfactual Path from Data to Theory. In: P. D. Asquith and T. Nickles (eds.), PSA 1982: Proceedings of the 1982 Biennial Meeting of the Philosophy of Science Association, pp. 107-121. East Lansing, MI: Philosophy of Science Association. Laymon, R. (1985). Idealizations and the Testing of Theories by Experimentation. In: P. Achinstein and O. Hannaway (eds.), Observation, Experiment and Hypothesis in Modern Physical Science, pp.147-174. Cambridge, MA: MIT Press. Maxwell, J. C. (1856). On Faraday’s Lines of Force. Reprinted in: Niven (1965), vol. I, pp. 155229. Maxwell, J. C. (1861-2). On Physical Lines of Force. Reprinted in: Niven (1965), vol. I, pp. 451-513. Maxwell, J. C. (1865). A Dynamical Theory of the Electromagnetic Field. Reprinted in: Niven (1965), vol. I, pp. 526-597. Maxwell, J. C. (1870). Address to the Mathematical and Physical Sections of the British Association. Reprinted in: Niven (1965), vol. II, pp. 215-229. Maxwell, J. C. (1873). A Treatise on Electricity and Magnetism. Oxford: Clarendon Press. 3rd ed. of 1891 (Oxford: Clarendon Press) reprinted by Dover, New York, 1954. All references are to the Dover edition. Maxwell, J. C. (1876). On the Proof of the Equations of Motion of a Connected System. Reprinted in: Niven (1965), vol. II, pp. 308-9. Maxwell, J. C. (1879). Thomson and Tait’s Natural Philosophy. Reprinted in: Niven (1965), vol. II, pp. 776-785.
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Thanks for helpful conversations to Mauricio Suárez, Mathias Frisch, Nancy Cartwright, Paul Teller, R.I.G. Hughes, Paddy Blanchette, Paolo Mancosu, Dorit Ganson, and Peter McInerney.
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Maxwell, J. C. (N.d.(a)). On the Dynamical Evidence of the Molecular Constitution of Bodies. Reprinted in: Niven (1965), vol. II, pp. 418-438. Maxwell, J. C. (N.d.(b)). Atom. Reprinted in: Niven (1965), vol. II, pp. 445-484. Niven, W. D., ed. (1965). The Scientific Papers of James Clerk Maxwell. 2 vols. New York: Dover. McMullin, E. (1985). Galilean Idealization. Studies in History and Philosophy of Science 16, 247-273. Miller, A. I. (1985). Imagery and Scientific Thought. Bristol: Adam-Hilger. Morrison, M. (1990). Reduction, Unification and Realism. British Journal for the Philosophy of Science 41, 305-332. Morrison, M. (1992). A Study in Theory Unification: The Case of Maxwell’s Electromagnetic Theory. Studies in History and Philosophy of Science 23, 103-145. Redhead, M. (1980). Models in Physics. British Journal for the Philosophy of Science 31, 145-163. Smith, C. and Wise, M. N. (1989). Energy and Empire. Cambridge: Cambridge University Press. Tabor, M. (1985). Gases, Liquids and Solids. Cambridge: Cambridge University Press.
Martin R. Jones IDEALIZATION AND ABSTRACTION: A FRAMEWORK
When, in the theoretical practice of science, we put forward theories, construct models, and write down laws, whether we are doing microeconomics, population genetics, or cosmology, we often seem to be describing, picturing, or making claims about systems which bear only a distant relation to the systems we actually encounter in the world around us. What is more, we often take ourselves to be doing just that. Consider, for example, the following methodological declaration by Noam Chomsky, from a passage which appears at the very beginning of his seminal Aspects of the Theory of Syntax: Linguistic theory is concerned primarily with an ideal speaker-listener, in a completely homogeneous speech-community, who knows its language perfectly and is unaffected by such grammatically irrelevant conditions as memory limitations, distractions, shifts of attention and interest, and errors (random or characteristic) in applying his knowledge of the language in actual performance. This seems to me to have been the position of the founders of modern general linguistics, and no cogent reason for modifying it has been offered (Chomsky 1965, pp. 3-4).
Chomsky is quite explicit about the chances of encountering such an ideal speaker-listener: We . . . make a fundamental distinction between competence (the speaker-hearer’s knowledge of his language) and performance (the actual use of language in concrete situations). Only under the idealization set forth . . . is performance a direct reflection of competence. In actual fact, it obviously could not directly reflect competence. A record of natural speech will show numerous false starts, deviations from the rules, changes of plan in mid-course, and so on. (Chomsky 1965, p. 4)
Similar remarks can be found in Section 1.4 of Robert A. Granger’s engineering text Fluid Mechanics, a section entitled “Fundamental Idealizations,” and they are so apposite, and so explicit, that I will quote them in full:
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 173-217. Amsterdam/New York, NY: Rodopi, 2005.
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Theoretical fluid mechanics is an attempt to predict the behavior of real fluid motions by solving boundary value problems of either appropriate partial differential equations or integral equations . . . In deriving the well-set boundary value equations, we postulate certain boundary and “inner” conditions which inevitably dictate the final form of the solution. With such a set of equations, we can solve few problems. Analytic solutions are impossible, numerical solutions are inappropriate, and nothing appears to work. Only the simplest fluid flow problems can be solved. Therefore, we introduce idealizations into the problems. We might assume that the fluid is independent of time, reasoning that the disturbances are of secondary importance. We could assume that the fluid is ideal [i.e., has zero viscosity], when in fact no known fluid is ideal. But because the viscosity may be small, much smaller than, say, for water, the idealization will yield solutions that are acceptable. What else might we assume? The possibilities are endless. For example, we could assume the flow is (a) symmetric, (b) incompressible, (c) not rotating, (d) one-dimensional, (e) continuous, (f) isothermal, (g) isobaric, (h) adiabatic, (i) reversible, (j) homogeneous, etc. The flow of course, may be none of these, for all are idealizations (Granger 1995, p. 17).
Both Chomsky and Granger are drawing attention to specific ways in which the real systems in their respective domains of inquiry are knowingly and systematically misrepresented: no real speaker-listener is unaffected by memory limitations, and no real fluid has zero viscosity or is, strictly speaking, incompressible. Representations also omit features of the systems under study without thereby misrepresenting them, of course: any real speaker-listener has a specific height and weight, and real fluids are particular colors. Putting these two points somewhat colorfully, we might say that when, in the various sciences, we theorize about a certain class of systems, we habitually lie about some aspects of the systems in question, and entirely neglect to mention others. I intend to take this distinction between misrepresentation and mere omission as fundamental, and to suggest that we organize our terminology around it. On the regimentation of usage I am thus proposing, the term ‘idealization’ applies, first and foremost, to specific respects in which a given representation misrepresents, whereas the term ‘abstraction’ applies to mere omissions.1, 2 One of my two primary aims in this paper is to develop this way ⎯⎯⎯⎯⎯⎯⎯ 1
The examples of omissions just given may make abstractions in this sense seem relatively uninteresting; the discussion of abstraction and relevance, in section 2 below, will help to dispel that impression. 2 Nancy Cartwright carves things up somewhat similarly in Nature’s Capacities and their Measurement. One important difference, however, is that Cartwright seems to build into the notion of abstraction she employs at least two features that I do not wish to build into mine: (i) that it is causal factors which we are focussing on when we “subtract” various other features of the situation, and (ii) that the “material in which the cause is embedded” is subtracted when we formulate an abstract law. Cartwright also claims that in the case of laws which are abstract in her sense, “it makes no sense to talk about the departure of the . . . law from truth;” this is not something that will necessarily be true of laws which are abstract in the sense I hope to characterize below. Note also
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of distinguishing between idealization and abstraction further; the second is to provide some characterization of the precise forms each can take in various sorts of scientific representation. These aims go hand in hand, and I will pursue them together. The overall intention is to provide an account of certain areas of the conceptual terrain, and some recommendations about how best to navigate it.3 My starting point, then, is the suggestion that we should take idealization to require the assertion of a falsehood, and take abstraction to involve the omission of a truth.4 In the next section I will be qualifying, extending, and elaborating upon this proposal for regimenting the terminology. Several immediate points of clarification are called for, however. First, not all misrepresentations can properly be called idealizations; nor, perhaps, are all omissions abstractions. What more is involved in either case will be considered later (in section 2). Secondly, the sort of omission I have in mind (a “mere omission”) is such that the category of idealizations and the category of abstractions are mutually exclusive (although happily not exhaustive). If a model of a particular fluid flow represents the flow as irrotational when it is not, we can in one sense correctly say that the model omits the rotation involved in the flow. However, such a model omits a certain feature of the real system in a way which involves misrepresenting how things stand in that respect; on the proposal I am putting forward, however, abstractions involve omission without misrepresentation. Omission in this restricted sense is, so to speak, a matter of complete silence. It follows straightforwardly that, with respect to a particular feature of a certain
that in the passages in which Cartwright characterizes her notions of idealization and abstraction, respectively, she speaks for the most part (although not exclusively) of idealized models and abstract laws. I should thus emphasize that on the proposal I wish to offer, idealizations and abstractions each appear plentifully both in models and in laws (Cartwright 1989, pp. 187-8). 3 There is by now a considerable body of work on idealization and abstraction in the philosophical literature; indeed, a significant part of that literature is represented in the series containing this volume (including much important work which has been done in continental Europe). It is no part of my ambition in this paper to provide a comprehensive discussion of the range of approaches which have been developed by various authors. Rather, my aim is to develop one specific proposal and show that some useful work can be done with it. (For an introduction to some of the European literature, see, for example, Leszek Nowak’s “The Idealizational Approach to Science: A Survey” (1992).) 4 The distinction I have in mind thus loosely parallels the medieval legal distinction between suggestio falsi and suppressio veri, except that the phrase “suggestion of a falsehood” is rather euphemistic in the case of many idealizations, and that furthermore, at least on a good day, no one is deceived by scientific idealizations and abstractions. (I am indebted to Alan Code for some useful information concerning the medieval terms.) On that note, it is worth emphasizing that idealization need not involve the assertion of a falsehood on our part – it is enough for a model to contain an idealization that it misrepresent the world in some respect. We can use idealized models without believing the untruths they speak.
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real system, a given representation can contain an idealization, or an abstraction, or neither, but it cannot contain both.5 Thirdly, it is important to be clear on the intended force of the proposal at hand. I am not hoping to capture the essence of scientific or philosophical usage in toto, for the simple reason that there is no single common usage of the terms in question. My proposal conflicts straightforwardly with the usage of some authors; indeed, both of the phenomena I have in mind have been referred to by each of the labels in question.6 Nonetheless, this proposed way of regimenting the terms does capture a philosophically important distinction between two different sorts of features scientific representations typically have (a distinction that has been recognized and employed by many authors), and it does mesh with the usage of some philosophers and, I would claim, with much ordinary scientific usage. To make a fourth and final point of clarification regarding the basic proposal, let me group misrepresentations and mere omissions together under the heading ‘RI’s’ (for “representational imperfections,” which is uncomfortably loaded in its connotations – but then this is merely a temporary device). What I wish to emphasize is that in proposing that we regard one particular semantic distinction amongst RI’s as fundamental (the distinction between misrepresentations and mere omissions), I do not mean to deny the importance of various other ways in which we might distinguish amongst them. There are certainly significant epistemological lines to be drawn: between RI’s which we know to be RI’s and those we do not; between RI’s where we know the truth of the matter and those where we do not; and between RI’s whose effects we can ⎯⎯⎯⎯⎯⎯⎯ 5
That is not to say, of course, that a given representation cannot idealize some features of a system and abstract away from others. 6 See, for example, Ernan McMullin’s “Galilean Idealization” (1985), an important contribution to the discussion of this topic. Whilst recognizing that “[t]he term, ‘idealization,’ itself is a rather loose one,” McMullin opts for taking it to “signify a deliberate simplifying of something complicated . . . with a view to achieving at least a partial understanding of that thing.” He then adds: “[Idealization] may involve a distortion of the original or it can simply mean a leaving aside of some components in a complex in order to focus the better on the remaining ones” (p. 248). In my terms, then, McMullin uses the label ‘idealization’ for both idealization and abstraction. Interestingly, however, on the next page, in characterizing what he calls “mathematical idealization,” of which omission is the primary characteristic, McMullin shows a momentary preference for the other term: “Aristotle . . ., of course, separate[d] mathematics quite sharply from physics, partly on the basis of the degree of abstraction (or idealization) characteristic of each . . . [M]athematics abstracts . . . from qualitative accidents and change. A physics that borrows its principles from mathematics is thus inevitably incomplete as physics, because it has left aside the qualitative richness of Nature. But it is not on that account distortive, as far as it goes” (p. 249, my emphasis). McMullin’s “mathematical idealization” would by my lights clearly be classed as a form of abstraction, rather than idealization. (One might, on the other hand, read McMullin’s distinction between “formal” and “material” idealization (pp. 258-9) as similar to my distinction between idealization and abstraction, in spirit at least. See n. 35.)
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predict and those whose effects we cannot, for example. We might also distinguish amongst RI’s with respect to the source of our knowledge concerning them – at the most coarse-grained level, for example, with respect to whether the source is theory or experiment. Alternatively, we might find it useful to draw distinctions along lines which reflect the causal relevance of the features which we have either misrepresented or distorted. Each of these distinctions will be important and useful in some philosophical contexts, as will yet others, and some of them have been given positions of central importance in other approaches to these issues. Indeed, we will return to some of the distinctions I have just mentioned at various points later in this essay. My claim, however, is that tying the terms “idealization” and “abstraction” to the semantic distinction between misrepresentation and omission provides a good starting point if one wishes to construct a larger framework which illuminates the various ways we think about imperfection in scientific representation, and which enables us to articulate certain ideas in greater detail. Just such a framework will be developed in the remainder of the paper. We need to begin by thinking about the sorts of things which contain abstractions and idealizations. Models, laws, and theories perhaps come first to mind, but we might add explanations, predictions, calculations, graphs, and diagrams to the list. (No doubt we could go on.) In what follows, I will focus largely on the first two sorts of item, models and laws. The hope is that if we can say what it means for models and laws, respectively, to involve idealizations, and what it means for them to involve abstractions, then much of the rest will follow. Scientific explanations and predictions will, at least in many cases, involve idealizations or abstractions just because they employ laws, models, or theories which do, and the same can be said for calculations performed in the service of other ends.7 I will take it that graphs and diagrams are implicitly covered in my discussion of models, for they are either models themselves, or, perhaps, means of presenting models. That leaves only theories. The relation between laws, models, and theories has been a much-debated issue in the philosophy of science for at least the last thirty years or so. The older, “syntactic” view typically regarded theories as deductively closed sets of sentences in a formal language, or at least as rationally reconstructable along such lines; the language itself was often regarded as only partially interpreted. Some especially important sentences, or (on some views) all the sentences which make up the theory, are then taken to state its
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Consider, for example, calculations performed to check the internal consistency of a theory, or to check the equivalence of what are intended to be two formulations of the same theory. (Of course, I do not wish to suggest that all explanations or all predictions involve calculation.)
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laws.8 The newer “semantic” view, on the other hand, is usually characterized as holding that theories are collections of models.9 The only stand I wish to take on these issues is, in the current climate, quite a minimal one, and it is that theories tend to involve both laws and models as important components.10 If that is right, then in characterizing the ways in which both abstractions and idealizations can occur in laws and models, we can hope to gain a considerable purchase on the ways in which they occur in scientific theories. The structure of the rest of this paper is thus as follows: I discuss idealization and abstraction in models in sections 1-4. I begin by focussing on models of particular systems, and offer a more precise account of the basic distinction I have drawn as it applies in that setting (section 1). I then consider what else we might have in mind when we speak of idealization and of abstraction, in addition to misrepresentation and mere omission respectively (section 2). I go on to extend the account to models of kinds of systems (section 3), and to talk of degrees of idealization and abstraction in models, and talk of idealization and abstraction as processes (section 4). Then, in sections 5-9, I turn to laws. After a few necessary preliminaries (section 5), I distinguish three different ways in which idealization can occur in laws and our employment of them (sections 6-8), and close by saying a few brief words about abstraction in laws (section 9).
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This view is still quite often called the “Received View,” even though the label is, by now, highly anachronistic. For a statement of the syntactic view, see Carnap (1970); for well-known critiques, see Suppe (1972) and (1974a), and Putnam (1979). 9 This slogan can be rather misleading, however. See Jones (forthcoming a) for further discussion. The semantic view is presented and developed in different ways in: Suppes (1957, ch. 12), (1960), (1967), (1974); van Fraassen (1970), (1972), (1980, ch. 3), (1987), (1989, ch. 9); Suppe (1967), (1974a), (1989); and Giere (1988). 10 Although proponents of the semantic view typically wish to draw our attention towards models, and away from such relatively linguistic items as laws (or law statements), they are certainly not aiming to eliminate the latter notion. Frederick Suppe, one of the earliest and most well-known proponents of the semantic view, devotes a considerable part of his extended treatise on theory structure, The Semantic Conception of Theories and Scientific Realism, to providing an account of various types of law; indeed, the work contains more explicit discussion of the nature of laws than of the nature of models (Suppe 1989). (Suppe’s aim is to give an account of laws which avoids tying them too closely to sentences in any particular language.) Even van Fraassen’s extended attack on laws in his Laws and Symmetry (1989) is primarily directed at a number of philosophical theses about laws and the role they play in science and epistemology; he does not deny that Ohm’s law, Boyle’s law, the Hardy-Weinberg law, or Schrödinger’s equation play some sort of important role in the theoretical practice of their various sciences, and in the theories with which they are associated.
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1. Models: The Basic Distinction Before we attempt to say more about what it means to talk about idealization and abstraction in models, it will be useful, particularly in the current philosophical climate, to say something about models themselves. The term ‘model’ is used in a wide variety of ways in the philosophy of science, and in science itself. Distinguishing the notions which go by that name and relating them to one another, although crucial for some philosophical purposes, is a lengthy and complex matter. Fortunately, it is not something we need to accomplish in any detail here; a few broad outlines will suffice.11 On some uses of the term, a model is a model of a set of sentences, in the sense that it makes the sentences in the set true,12 often by providing them with an interpretation on which they turn out true. On other uses, a model is a model of an object, system, event, or process, in the sense that it represents, or is used to represent that object, system, event, or process as having certain features, behaving in certain ways, and so on.13 (For the sake of brevity, I will hereafter speak simply of systems and features.) It is only models in the latter sense which will concern us here; for our purposes, a model is, first and foremost, a representation.14 One can go on to distinguish at least three notions of model as representation in the philosophy of science and in the sciences themselves, the differences lying in the kind of object which does the representing in question: a mathematical structure, such as a vector space with a trajectory running through it (i.e., a function mapping points in some interval on the real line, representing times, to elements of the vector space, representing states of the modeled system); a set of propositions; or a physical object, such as an engineer’s scale model of a bridge, or an electrical circuit used to represent the behavior of an acoustical system.15 These differences, however, are at least initially unimpor⎯⎯⎯⎯⎯⎯⎯ 11
For a taxonomy of some of the central notions of model abroad in the philosophy of science, a discussion of the suitability of the various notions to certain tasks, a critique of the semantic view (at least in some of its incarnations), and a case for taking a somewhat different view of theory structure, as well as references to the relevant literature, see Jones (forthcoming a); see also Jones (forthcoming b). 12 Or true-in-the-model, in certain logical contexts. See Jones (forthcoming a); and thanks to Charles Chihara for drawing my attention to this point. 13 See Frisch (1998) and Jones (forthcoming a) for further discussion of the distinction between models as truth-makers and models as representations. 14 In principle, of course, one and the same object might serve as a model in both senses. If and when this does occur, then we will be focussing on the object’s role as representation, rather than its role as truth-maker. (Something like this situation arises in the version of the semantic view van Fraassen presented in “On the Extension of Beth’s Semantics of Physical Theories” (1970), in which the state space for a given system plays a role in the formal semantics for the language of the theory. As I understand that approach, however, it would be an oversimplification to say that one and the same object functions as both representation and truth-maker.) 15 For more on these three notions of model as representation, see Jones (forthcoming a).
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tant from our present point of view. We can make a start on the job of clarifying the notions of abstraction and idealization simply by thinking of a model as something which represents a given system as having various features. In fact, this is insufficiently general, for in addition to models of particular systems, such as models of the 1989 Loma Prieta earthquake or the Big Bang, there are also models of kinds of systems, such as Bohr’s model of the hydrogen atom or a classical model of electromagnetic radiation in vacuo.16 The strategy I will adopt, however, is as follows: I will take as basic the notion of a specific idealization contained in a model of a particular system (i.e., an aspect of the model which idealizes the system in some specific respect), and the parallel notion of a specific abstraction present in a model of a particular system. After spending some time providing an account of these two notions (in this section and the next), it will then be a relatively quick matter to extend the account into certain neighboring areas: talk about a model of a kind idealizing and abstracting in specific respects (in section 3); the classification of a model as idealized, highly idealized, or an idealization, or as abstract, highly abstract, or an abstraction; comparative judgements about the extent to which various models idealize a given system, or kind of system, both in a given respect and overall, and about the degree of abstractness of various models; and talk about idealization and abstraction as component processes in scientific theorizing (in section 4).17 Let us begin, then, by considering a simple example of the use of a model to represent a particular system. Suppose that on some particular afternoon a certain cannon has been wheeled onto an open plain and fired. In the attempt to predict where the cannonball will land, or perhaps to explain why it lands where it does, we might construct a model of the system along the following lines.18 We assume that the ⎯⎯⎯⎯⎯⎯⎯ 16
We also sometimes speak of using one and the same model to represent different particular systems, or even different kinds of system, on different occasions. It is worth noting that it is easier to make sense of such talk when the model in question is an abstract mathematical structure or a concrete physical object that when it is a set of propositions. 17 To say that this will be a quick matter should not to be taken to suggest that there will be no open questions by the time we are done. 18 The example dates back to Niccolò Tartaglia’s Nova Scientia of 1537, the first two books of which are translated in Drake and Drabkin (1969), but the modeling of the situation presented here is, of course, far more modern, and typical of treatments to be found in contemporary introductorylevel textbooks in classical mechanics. Tartaglia, incidentally, rather charmingly distanced himself from the choice of example in the later Quesiti (1546): “I . . . have never made any profession of or delighted in shooting of any kind – artillery, arquebus, mortar, or pistol – and never intend to shoot” (Drake and Drabkin 1969, p. 98). The opening of the Nova Scientia, in which Tartaglia describes the history of his work in a letter of dedication to the Duke of Urbino, contains an expression of more emphatic, if somewhat partisan feelings on the matter: “[O]ne day I fell to thinking it a blameworthy thing, to be condemned – cruel and deserving of no small punishment by God – to study and improve such a damnable exercise, destroyer of the human species, and especially of
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path of the cannonball is contained entirely within a plane perpendicular to the ground, and we choose a pair of Cartesian axes to coordinatize this plane in such a way that the x-axis lies along the ground, and the y-axis points vertically upwards. The axes are also chosen so that the cannon is situated at the origin, and so that the cannonball, when fired, moves in such a way that its x-coordinate increases. The cannonball has an initial velocity of v when fired, and is, at that initial moment, moving at an angle α to the x-axis: y
v
α 0
x
After it has been fired from the cannon, we suppose that the cannonball moves under the sole influence of gravity, which exerts a force vertically downwards with a magnitude of mg (the mass of the cannonball, m, multiplied by a certain constant, g = 9.8 m/s2) throughout the motion. Thus we have: Fy = –mg
(1)
for the force in the y direction, and Fx = 0
(2)
for the force in the x direction. Newton’s second law of motion gives us Fy = m
d2y dt2
(3)
d2x dt2
(4)
and Fx = m
Christians in their continual wars. For which reasons . . . not only did I wholly put off the study of such matters and turn to other studies, but I also destroyed and burned all my calculations and writings that bore on this subject” (Drake and Drabkin 1969, p. 68).
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so we get d2y = –g dt2
(5)
d2x =0 dt2
(6)
and
Given specific values of v and α, it is then a matter of simple integration to calculate the time of flight of the cannonball, the distance from the cannon at which it will land, the maximum height it will reach, and other features of its trajectory. And it is not much more difficult to show that, according to this model, the range of the cannon is maximized for a given v when α = 45°.19 The sort of model I have just presented contains a number of idealizations, in the sense I am attempting to characterize.20 According to the model, for example, the gravitational force due to the Earth has the same magnitude and direction at all points on the cannonball’s trajectory, whereas in fact both the magnitude and the direction of that force will vary. According to the model, only the Earth exerts a gravitational force on the cannonball, whereas in fact the moon, the sun, and every other massive body in the universe interacts gravitationally with it. What is more, the model says that the only force acting on the projectile is gravitational, whereas in reality the cannonball is subject to air resistance, the influence of breezes, and even forces due to the photons which impinge upon it. And, as a final example, note that as the x-axis lies along the ground (which is putatively flat), the cannonball does not really begin the untrammeled part of its journey at the origin (i.e., at the point (0, 0)), simply because the mouth of the cannon is at a certain height above the ground. Here we have, then, a number of discrepancies between the way the model (or sort of model) in question represents the modeled system as being, and the way the system really is. It is perfectly in keeping with at least some standard usage to call each of those ways in which the model misrepresents the system an idealization, and in each case there is some property the system has which the ⎯⎯⎯⎯⎯⎯⎯ 19
A result which Tartaglia also achieved, and for which he cites experimental evidence – see Drake and Drabkin (1969), pp. 64-5. 20 If we are thinking of a model as a state space with a trajectory running through it, then no specific model of the cannonball’s trajectory has been presented – for that, we would need to choose a state space from amongst the various spaces adequate to the job, and specify values of v, α, and m. In the “set of propositions” sense, on the other hand, a particular model has been specified; a more detailed propositional model could simply contain additional propositions concerning the values of the various parameters.
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model represents it as not having (and, correlatively, some property the system does not have which the model represents it as having). On the regulative proposal I am making, it is correct to talk of idealization with respect to a model of a particular system only when such a state of affairs obtains. To put the rule schematically: If the model represents a system as having the properties φ1, φ2, . . ., φn, . . ., and lacking the properties ψ1, ψ2, . . ., ψn, . . .,21 then a given aspect of the picture of the system presented by the model is an idealization only when that aspect of the picture represents the system as having some φi which it does not in fact have, and/or as lacking some ψi which in fact it has.22 There are two things I want to note about this proposal before we go on to formulate a similar proposal concerning abstraction. First, it is important to bear in mind that what matters, according to the proposed necessary condition on being an idealization, is whether, in the relevant respect, the model represents the system as being the way it is; the issue is not whether the model represents the system as being the way we take it to be, nor even the way we take it to be when we are speaking as strictly as we can manage. This makes it acceptable to speak of discovering that some assumption made by some model is an idealization, or even of discovering that something we had formerly taken for an idealization is not one (a less likely turn of events, admittedly), and of doing so simply by discovering something new about a certain system. I take it that this comports with much standard usage of the term ‘idealization,’ and the fact that it does so is a point in favor of the proposal. If, however, it should be decided that some standard usage makes agreement with our Sunday best beliefs the crucial thing, and disregards the question of how the system actually is, or if it should be deemed useful to employ the term in such a way for some philosophical purposes, it will be an easy matter to introduce a distinction between senses of the term, and some device to make it clear which sense is intended on a given occasion. In this essay, though, calling some aspect of a model an idealization will imply that that aspect distorts the truth of the matter, but will not imply any conflict with the way we take things to be, even if such conflict is often present. Secondly, it is not clear, and I do not mean to be supposing, that there will be only one way, or even a best way, to individuate the idealizations present in some particular case. For example, the model we have just considered represents the gravitational force of the Earth on the cannonball as constant in both ⎯⎯⎯⎯⎯⎯⎯ 21
The labeling system used here should not be taken too seriously; in particular, I would not wish to assume that either the properties the model represents the system as having, or those it represents the system as lacking, form a countable set. 22 This may require some modification if we wish to allow for the possibility that it might be indeterminate, in some non-epistemic way or other, whether a given system has a given property, as perhaps some idealizations might then involve a model’s ascription of a property to a system, for example, when in fact it is objectively indeterminate whether that system has that property.
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direction and magnitude throughout the region in which the cannonball moves, whereas in fact there will be variation in both respects. Is that one idealization, or two? Or an uncountably infinite number, one (or two) for each spatial point at which the model misrepresents the Earth’s gravitational field? There would seem to be little prospect of settling upon a non-arbitrary answer to such questions, and that fact will become important later, when we need to account for talk of degrees of idealization in models.23 Note, however, that we have here no objection to the coherence of the proposal itself, nothing to prevent us from saying: This model’s representing the system as being φi (or as not being ψi) counts as an idealization only if the system is not in fact φi (or is ψi). Returning now to our model of the flight of the cannonball, we can treat of abstraction in a manner quite parallel to that in which we have just treated of idealization. There are innumerable features of the modeled system which the model omits, without thereby misrepresenting or distorting the system: no mention is made of the composition of the cannonball, of its internal structure, of its color or temperature, of the composition of the ground over which the cannonball flies, of the mechanism by which an initial velocity is imported to the ball, or of the country in which the firing takes place. The model is simply silent in all these respects. And according to the regulative recommendation I wish to put forward, we should say that a model of a particular system involves an abstraction in a particular respect only when it omits some feature of the modeled system without representing the system as lacking that feature.24 The two points just made about my proposal concerning the use of the term ‘idealization’ apply here, too, mutatis mutandis. First, that is, the specified necessary condition for the presence of an abstraction concerns the relationship between the model and the actual features of the modeled system, not the relationship between the model and the features we take the system to have – although, as with idealization, it would be simple enough to recognize another sense of the term “abstraction” in which it is the latter relationship which is crucial. Second, individuating and counting abstractions would seem necessarily to be a somewhat arbitrary process. Again, this will be important later, when we come to deal with degrees of abstractness (in section 4), but it presents no obstacle to coherently formulating the condition I have just laid out.
⎯⎯⎯⎯⎯⎯⎯ 23
See section 4. Talk of a model’s “involving an abstraction” is somewhat artificial, but it facilitates a more finegrained discussion of the various ways in which the model as a whole is abstract, or “is an abstraction”; such phrasing also emphasizes the parallels and the contrasts with idealization. Perhaps a more familiar way of capturing essentially the same phenomenon is to speak of various respects in which a given model “abstracts away from” features of the modeled system.
24
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The proposals I have just put forward provide only partial guides, for each lays down only a single necessary condition on correct application of the relevant term: misrepresentation for “idealization,” and omission without misrepresentation for “abstraction.” We must thus now turn to the twin questions of what more it takes for a misrepresentation to count as an idealization, and what more it takes (if anything) for an omission to count as an abstraction. As we do so, however, the purpose of my remarks becomes a different one; let me take a moment to explain how. So far, my intention has been to delineate two simple proposals for regimentation of what is currently a confusing tangle of conflicting usages. As I noted earlier, these proposals come into direct conflict with the way some have used the relevant terms; nonetheless, they are quite continuous with the usages of others. We might then hope (and I do) that the proposals in question can also be read as successfully capturing part of the meanings of the terms “idealization” and “abstraction” on those usages with which they are continuous. With that hope in mind, we may then be tempted to fall into familiar philosophical habits, and start looking for full accounts of the existing meanings of the terms on those usages by searching for additional individually necessary conditions on correct application, never ceasing until we have a set of conditions which are jointly sufficient. This is not, however, what I intend to do.25 Instead, my primary aim is simply to identify some factors which are often present when we speak of idealization and abstraction, and which perhaps have something to do with our speaking that way on those occasions when they are present. (Each factor I will mention, incidentally, has also seemed important to at least one other person in their discussion of idealization and abstraction.) No claim is being made that the presence of any of these factors is a necessary condition on the presence of an idealization (or, later, abstraction), nor that their joint presence is a sufficient condition for the same; I leave open, in other words, the possibility that the concepts of idealization and abstraction I am focussing on here are “cluster concepts” of some sort, or perhaps entirely irreducible concepts which are nonetheless importantly connected in some way to the concepts I am about to mention. Whatever the exact semantic structure of
⎯⎯⎯⎯⎯⎯⎯ 25
The reader should not be misled by the fact that at one point I will consider whether the presence of a certain factor might constitute a further substantive necessary condition on abstraction, and will, at another, ask whether the presence of a certain combination of factors is a sufficient condition for idealization. In both cases I draw a negative conclusion, and my intention, apart from that of generally illuminating the conceptual landscape, is if anything to cast doubt on the project of finding a complete set of individually necessary and jointly sufficient conditions, rather than to engage in it.
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things, my hope is that the following discussion (of section 2) will lend greater clarity to our thinking about idealization and abstraction.26, 27
2. Going Further It is clear that as far as much standard usage is concerned, not just any misrepresentation on the part of a model of a particular system counts as an idealization. One sort of case which makes this clear is that in which the model as a whole is substantially off-target. Consider some specific episode of combustion and a model of the process according to which the burning object releases phlogiston into the air. The model represents the piece of wood, say, as initially containing phlogiston; this is certainly a misrepresentation, but just as certainly it would not ordinarily be called an idealization. This suggests that perhaps a misrepresentation has to approximate the truth, or appear as part of a model which captures the approximate truth overall, or at least appear as part of a model which gets the basic ontology of the modeled system (i.e., its constituents and central features) right in order to count as an idealization, as opposed to being a useful fiction, say, or an outright mistake. Whether any of these conditions are or should be made necessary conditions on being an idealization is, as I have said, a question I will leave open (although I suspect that the answer is no); but notice that even the conjunction of them, taken in combination with the condition that misrepresentation must be taking place, does not make up a sufficient condition for something’s being an idealization. To see this, imagine a classical electrodynamical model I might construct of the flight of an electron though a simple, homogeneous magnetic field, one which gets things almost exactly right except that the mass it attributes to the electron is slightly off – 9.108 × 10–31 kg instead of 9.107 × 10–31 kg, say. Here we surely have both misrepresentation and approximate truth in all of the above senses, but it would again seem odd, from the point of view of standard usages, to call the model’s attribution of a mass of 9.108 × 10–31 kg to the electron an idealization.28 ⎯⎯⎯⎯⎯⎯⎯ 26
I am also not making further recommendations for regimentation in the next section. Should further explicit regimentation be deemed philosophically valuable, on the other hand, I would hope that the following discussion identifies some of the leading candidates for the post of additional necessary condition. 27 Remember that at this point we are still restricting our focus to talk of idealization and abstraction in models of particular systems, and in specific respects. Other ways of talking about idealization and abstraction in models will be covered in sections 3 and 4. 28 That is, odd to call it an idealization in virtue of those features (misrepresentation with approximate truth) alone. See n. 30.
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I will mention just two further features which many idealizations in models of particular systems seem to have, in addition to that of misrepresenting the modeled system in some particular respect. First, as is often noted, idealizations typically make for a simpler model than we would otherwise have on our hands, and they are often introduced for precisely that reason.29 It is usually presumed that pragmatic concerns drive such maneuvers: the desire to get started, to make a decent prediction relatively quickly rather than a perfect prediction in the distant future or no prediction at all, for example. With simplicity, it is expected, will come tractability. And in the background lies the hope that, should the initial results achieved with the simpler model seem promising, a less idealized and more predictively accurate cousin of the original can be constructed later on, albeit at the cost of greater complexity.30 As a distinct issue from simplification, many idealizations can also be said to misrepresent relevant features of the modeled system. But relevant to what, and how? Here again pragmatic concerns come to the fore.31 We often have some specific purpose in mind when we construct a model of a particular system: to explain or make predictions about certain aspects of the behavior of the system, say. (Of course, there may be an ulterior motive driving the pursuit of those goals, such as the confirmation or refutation of a theory.) And that specific purpose might then single out a set of “relevant features” of the system: those which are explanatorily or predictively relevant to these aspects of the behavior of the system. Furthermore, depending on one’s views about explanation or prediction, one might ultimately take causal relevance, say, or statistical relevance to be the crucial thing.32 In any case, perhaps we are more likely to call a model’s misrepresentation of a system in a given respect an idealization when the misrepresented feature (or features) of the system is (or are) taken to be relevant, in the appropriate manner, to those aspects of the behavior of the system which we were primarily concerned to predict or explain when we ⎯⎯⎯⎯⎯⎯⎯ 29
As we saw above (n. 6), Ernan McMullin puts simplification at the heart of his initial characterization of the notion of idealization (which, as he understands it, incorporates both idealization and abstraction in my senses). Incidentally, it may well be possible to usefully distinguish different kinds of simplicity – mathematical simplicity versus some sort of conceptual simplicity, say, or versus structural simplicity of the system as modeled – but I will not pause to attempt such a thing here. 30 Thus perhaps the misattribution of a certain mass to an electron, mentioned as an example in the preceding paragraph, might count as an idealization after all if it makes for a model which is somehow simpler, or simpler to use, than it would be otherwise, say by making certain calculations easier (perhaps via some convenient canceling out which it makes possible). 31 By ‘pragmatic’ here, I simply mean “having to do with the purposes for which we have constructed the model in question.” One such purpose may be explanation, but no commitment to what is known as a “pragmatic theory of explanation” is implied. 32 And of course one might believe those sorts of relevance to be intimately related in one way or another.
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constructed the model. (Certainly we are more likely to want to draw attention to misrepresentations of features which we take to be relevant to the behavior in which we are especially interested.) And, independently of whether that is so, it might prove fruitful in certain contexts to regiment our terminology in such a way that idealizations necessarily misrepresent relevant features.33, 34 We turn now from idealization to abstraction, and ask what more there is to abstraction than omission. Having just discussed three important things which some, and perhaps many idealizations do – approximating the truth, contributing to simplicity, and misrepresenting relevant features of the modeled system – it is natural to wonder whether there is a parallel story to be told about abstractions. The first and quite trivial point in this regard is that clearly there is no sense in which an abstraction can approximate the truth, nor any interesting sense in which it can fail to, simply because when a model contains an abstraction with respect to some particular property, it is entirely silent on the matter of whether the system it models has the property or lacks it; nor is it obvious (to me, anyway) that there is any other closely related job which abstractions can do. Might a contribution to overall simplicity be a crucial condition on an omission’s being an abstraction, or at any rate on being an interesting abstraction? Well, simplification would seem to be an automatic consequence of omission, in that, of two models of a given system, the one which omits mention of a certain feature of the system will thereby be the simpler model, ceteris paribus. Thus, although it might be true that abstraction always contributes to simplification, it would be of no help to say that an omission counts as an abstraction only if it contributes to the simplicity of the model – all omissions do. Still, it is worth noting that abstractions always contribute to simplicity, as this is no doubt one of the reasons we employ them.
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Note that if we do think of idealizations as involving the distortion of relevant features, and if relevance is elaborated along the lines I have sketched here, then which features of a given model are correctly called idealizations might vary with the pragmatic context of use of the model – what is and is not an idealization, in other words, may depend in part upon what we are at a given moment hoping to predict, or explain. On the other hand, it may be that certain elements of the model misrepresent features of the system which count as relevant for most of our typical purposes, in which case we may classify those elements of the model as idealizations without any particular context in mind. 34 On the account Nancy Cartwright offers (1989, chapter 5; see esp. p. 187 and pp. 190-1), both simplification and relevance play a crucial role. According to Cartwright, the point of constructing an idealized model (that is, a model containing a number of idealizations) is to single out the causal capacities of one particular factor in a given situation, and such a model does that by representing all other potentially causally relevant factors as absent. In doing so, the model typically both simplifies the causal structure of the situation, and misrepresents how things stand with respect to a number of causally relevant features of the system in question (by representing such features as absent when they are present).
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With regard to the role of relevance, matters are perhaps a little less straightforward. Both Nancy Cartwright and Ernan McMullin seem committed to the claim that models will contain abstractions (in my sense) only with respect to features which we deem irrelevant, for they each suggest that in constructing a model we will always include some assumption about the presence or absence of any feature of the modeled system which we deem relevant to the behavior we seek to explain or predict (Cartwright 1989, p. 187 and McMullin 1985, pp. 258-64, esp. p. 258).35 This seems plausible enough, especially if we are sufficiently liberal on the question of what assumptions a given model should be taken to include. For example, in constructing a model of the cannonball firing discussed above, we might not expressly postulate the absence of air resistance, but we might nonetheless be said to have constructed a model in which it is assumed that there is no air resistance, simply because it is Earth’s gravitational force on the cannonball which we feed into Newton’s second law, a law which relates mass and acceleration to the total force on the body. Note, however, that there are still two reasons for saying that models can abstract away from relevant features of the modeled system. First, even to the extent that Cartwright and McMullin are correct, there may be relevant features of the system which we mistakenly deem irrelevant, and abstract away from when constructing our model. Secondly, models sometimes seem to abstract away from features which we in fact deem relevant, but to make some distinct idealizing assumption which “screens off” the presence or absence of the relevant feature.36 This latter point is nicely illustrated by a case McMullin discusses, in fact. To derive the ideal gas law for some specific body of gas using the kinetic theory of gases, we construct a model of the gas according to which the molecules making it up are perfectly elastic spheres which exert no attractive forces upon one another (1985, p. 259). As McMullin emphasizes (p. 258), such ⎯⎯⎯⎯⎯⎯⎯ 35
McMullin distinguishes between two central sorts of idealization (which, the reader will recall, encompasses both idealization and abstraction in my sense of those terms) in models, calling them “formal” and “material” idealization, respectively (1985, pp. 258-64). Formal idealizations deal with relevant features of the modeled system, and material idealizations with irrelevant ones. Although McMullin does sometimes write of formal idealizations which “omit” features of the modeled system, this always seems to mean “omit by representing as absent,” and so in context to imply misrepresentation, as opposed to meaning “omit by not mentioning,” which is the sort of omission that abstraction in my sense must involve. It is McMullin’s material idealization, dealing as it does only with features which are deemed irrelevant, which involves omission in the sense I have made crucial. (More carefully we might say “not deemed relevant,” as in some cases the feature is one we have not conceived of at the time the model is constructed – consider McMullin’s own example of electron spin, discussed on pp. 263-4). 36 I am using the term ‘screens off’ in a general figurative sense here, and not in its technical probabilistic sense.
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a “billiard ball” model of the gas makes no mention of the internal structure of the molecules. Yet that internal structure is surely relevant to predicting the way in which the pressure, volume, and temperature of the gas will covary, for it is the internal arrangement of the parts of the molecules and of the atoms which make them up that gives rise to the attractive intermolecular van der Waals forces, and once those forces are taken into consideration, a different equation relating pressure, volume, and temperature results. In the original model, the possibility that such relevant features of the modeled system have been ignored is “covered,” so to speak, by the idealization that there are no attractive intermolecular forces; nonetheless, it seems accurate to say that the model omits mention of a feature of the modeled system – namely, the structure of its molecular components – which is relevant to the behavior with which the model is concerned. Thus models do sometimes abstract away from relevant features of the systems they model; and when they do so, that is an important fact about them. If we wished to stress the importance of relevance, we might choose to stipulate that abstraction should only be spoken of when what is omitted is a relevant feature of the system. We might then want to consider a related idea suggested by (although not explicitly contained in) the work of Cartwright and Mendell (1984) and Griesemer (this volume), that an abstraction properly so-called should always involve the omission of a feature of the modeled system which is of one explanatory kind or another.37 Alternatively, we could take the more generous line that although there is nothing more to abstraction per se than omission (omission without misrepresentation, that is), the omission must be of a relevant feature, in the sense indicated above, if it is to be an interesting or important abstraction. I shall not, however, try to weigh the relative merits of these two approaches here, nor even try to determine whether there is anything at stake in the choice between them. ⎯⎯⎯⎯⎯⎯⎯ 37
See also Cartwright (1989, pp. 212-24). For Cartwright and Mendell the taxonomy of explanatory kinds is derived from Aristotle’s four-fold taxonomy of causes; for Griesemer it is provided by background scientific theories. These authors have a different quarry in mind than I do at this point: rather than trying to say when a feature of a model counts as an abstraction, or what it means to say that a model abstracts away from the concrete situation in this or that respect, they are concerned to provide a way of ordering models, theories, and the like with regard to their overall degree of abstractness. Note that there is, nonetheless, an internal tension in Cartwright’s views here: if a representation is more abstract when it specifies features of fewer explanatory kinds, then if there are to be representations of different degrees of abstractness, there will have to be representations which abstract away from features of some explanatory kind, and so from features which are at least explanatorily relevant. This would then seem to cast into doubt the claim that “a model must say something, albeit something idealizing, about all the factors which are relevant” (p. 187). But perhaps not all features which are of some explanatory kind or other count as explanatorily relevant in a given situation, or perhaps Cartwright has a different sort of relevance in mind, one which is not too tightly connected to explanatory relevance.
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This, then, concludes my delineation of the two notions I am taking as basic: the notion of a model of a particular system idealizing (or containing an idealization of) the system in a given respect, and the notion of a model of a particular system abstracting away from (or involving an abstraction with regard to) some specific feature of the system. In the next two sections, I hope to show how we can extend the account developed thus far to other, related ways of talking about idealization and abstraction in models, and so illuminate them.
3. Models of Kinds It is not too difficult to see how we might extend the ideas discussed above to the case of a model which is, or is on some occasion functioning as, a model of a kind of system, rather than a particular system. The model will represent things of kind Κ, the κ’s (neutrons, carbon atoms, cells, free-market economies, ecosystems . . . ), as each having properties φ1, φ2, . . ., φn, . . ., and as failing to have properties ψ1, ψ2, . . ., ψn, . . .; it will also omit any mention of a very large number of properties χ1, χ2, . . ., χn, . . .. In the spirit of the regulative proposals described above, then, we can adopt the rule that the model should be said to contain an idealization in representing the κ’s as having φi only if some κ’s fail to have φi, and that the model should be said to contain an idealization in representing the κ’s as failing to have ψi only if some of the κ’s have ψi.38 Similarly, we can stipulate that a model of a kind Κ should be said to contain an abstraction with respect to the property χi (of which it makes no mention) only if some κ’s have χi.39 In addition to imposing this bit of regimentation, we then add that idealizations often approximate the truth about those κ’s they misrepresent (or at least most of them), that idealizations can contribute to the degree of simplicity the model enjoys, and that idealizations and abstractions are at their most interesting when they distort the truth about, or (respectively) omit mention of features ⎯⎯⎯⎯⎯⎯⎯ 38 Note that ‘some κ’s’ can strictly be read as meaning “at least one κ”; it is just that if the model misrepresents only one κ in the relevant respect, then we are likely to regard the model as idealizing the κ’s only very slightly. See the account of talk of degrees of idealization in section 4. 39 In some cases we speak of a model’s abstracting away from a quantity (understood as a determinable), such as the electric dipole moment of the molecules in a gas, or a qualitative determinable, such as the color of a cannonball. A model of a kind Κ should then be said to contain an abstraction with respect to a certain determinable (qualitative or quantitative) when it makes no mention of that determinable (nor any of the corresponding determinate properties), but some of the κ’s have one determinate property or other from the set of determinate properties corresponding to the determinable. (Typically, I suppose, if one of the κ’s possesses a determinate property from the set corresponding to the determinable, then they all will, but there may be exceptions to this.) A similar point applies to the notion of abstraction in a model of particular system.
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which are relevant, in some specified sense, to the behavior we are concerned to study. It is perhaps also interesting to note that idealizations in models of kinds sometimes ascribe a property, φi, to the κ’s which is in one sense or another a limiting case of some range of properties actually instantiated by the various κ’s. (For example, φi might be the property of experiencing zero air resistance, in a model of pendula.)40
4. Degrees of Idealization and Abstraction Until now, whether dealing with models of kinds or models of particular systems, we have been focussing on uses of the term ‘idealization’ and ‘abstraction’ on which idealizations and abstractions are tied to particular features of systems, the particular features they misrepresent or omit to mention, respectively. But models themselves are sometimes said to be idealizations, or (more commonly) to be idealized, without any further reference to specific respects; one model can be said to be more idealized than another; and the term ‘idealization’ can also be used to denote a process which occurs as part of scientific work. The same holds, mutatis mutandis, for the terms ‘abstraction’ and ‘abstract.’ Can we employ the account given above of the first sort of locution as the basis of an account of the others? I will consider this question first with respect to the various sorts of talk of idealization; the case of abstraction is parallel up to a point, but there is an important difference, and I will describe that difference after dealing with idealization. On some occasions, when we say that a model M is an idealization, or is idealized, we mean just that it contains one or more idealizations in the sense discussed above (in sections 1 and 2); and talk of idealization as a process or activity may simply denote the process or activity of constructing an idealized model in this simple sense. An account of such talk can thus be derived straightforwardly from the initial account of idealizations as aspects of models. Matters become significantly more complex, however, when in calling M an idealized model we mean to say, not just that it contains at least one ⎯⎯⎯⎯⎯⎯⎯ 40
One difficulty for this approach to understanding talk of idealization and abstraction in models of kinds is that it clearly cannot be extended straightforwardly to talk of idealization and abstraction in models of uninstantiated kinds, relying as it does on there being some κ’s to have, or fail to have, one or another property. Perhaps when a model of an uninstantiated kind (such as a relativistic model of some particular kind of universe very unlike our own) is said to contain an idealization or an abstraction, it is implicitly being thought of as a highly idealized model of an actual kind or particular (such as the actual universe). Or perhaps we might appeal to modal facts about what properties κ’s would have were there any. (This latter approach seems more promising than the former when dealing, say, with a model of some sort of molecule which does not occur naturally and which we have never synthesized.) These are topics for further investigation.
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idealization, but that it is highly idealized, or when we explicitly say just that; when we say that M is a more, or less, idealized model than some other model; when we speak of a process or activity of idealization and mean the process or activity of constructing a series (two-membered, in the trivial case) of increasingly idealized models; or when we speak of “de-idealization” or “correction,” and mean the converse process of constructing a series of increasingly less idealized models. (A term often used to describe the parallel activity of constructing less and less abstract models is “concretization.”41 We also speak of one model’s being more “realistic” than another, and it seems to me that this can mean that the more realistic model is less idealized, or that it is less abstract, or both.) What these ways of talking have in common, obviously, is that implicitly or explicitly, they all express judgements (often comparative judgements) about the degrees of idealization various models exhibit. In making such judgements, I want to suggest, we are typically taking into account a number of different factors. Consider first a model, M, of a particular system. The natural approach here is to regard the question “How idealized a model is M?” as made up of two component questions: (i) How many idealizations does M contain? (ii) How much of an idealization is each of the idealizations which M contains? The answer to the original question, about the overall degree of idealization M enjoys, can then be arrived at by taking a sort of weighted sum over all the particular idealizations M contains, in which attaching a heavy weighting to a particular idealization amounts to claiming that that idealization idealizes the modeled system to a significant degree, and so on.42 This little account of the overall extent to which a model of a particular system is idealized begs a question, however, because it assumes that we already have a well-defined way of talking about the degree to which a particular idealization, contained within the model, idealizes the system in question.43 So how is this latter quantity measured? It seems to me that all we mean to do when we talk about the degree to which model M idealizes system S by representing it as having property φi (as when we exclaim, for example, ⎯⎯⎯⎯⎯⎯⎯ 41
Juan Gris’s description of the relationship between his work and Cézanne’s provides a nice parallel to the discussion of abstraction and concretization as converse processes of model construction in science: “I try to make concrete that which is abstract . . . Cézanne turns a bottle into a cylinder, but I make a bottle – a particular bottle – out of a cylinder” (quoted in the entry on Gris in Chilvers (1990)). 42 This talk of weighted sums is not to be taken too seriously: I do not mean to suggest that in making judgements about the degree of idealization a model enjoys we employ some precise algorithm, nor that we are always, or even usually able to attach precise strengths to the various idealizations the model contains, nor even that we are interested in doing so. 43 The account begs another question, too – about how we are to count idealizations. This difficulty was foreshadowed in section 1 (see the text containing n. 23), and I will return to consider it at the end of this section.
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“That’s a huge idealization!”) is to single out the degree to which M misrepresents, or distorts the truth about S in representing it as being φi. This claim may seem unenlightening, but the point of it is to be found in what it denies. To see this, recall that we discussed three things idealizations sometimes do, in addition to simply misrepresenting the way the system is: approximating the truth, simplifying the model, and misrepresenting a feature of the system which is relevant to explaining or predicting its behavior, say (or relevant in some other way which is determined by the aims we have in constructing the model). The point then is that although simplification and relevance both come in degrees, at least some of the time, I am denying that when we size up the degree to which a particular idealization idealizes, degrees of simplification or relevance are any part of it. (Sometimes small idealizations can simplify greatly, and sometimes they can misrepresent highly relevant features.44) All that matters, when we evaluate the degree of a particular idealization, is how far from the truth it is for M to represent S as φi. This does mean, on the other hand, that when an idealization approximates the truth, the degree to which it does so does bear on the question of how much the idealization idealizes, for clearly a higher degree of approximation means a lower degree of distortion or misrepresentation, and vice versa.45 A certain nervousness may arise at this point about the notion of degrees of misrepresentation or distortion, provoked perhaps by the apparent link to the notion of approximate truth, a notion with a troubled history in the philosophy of science.46 In this case, however, it seems to me that the failure of ⎯⎯⎯⎯⎯⎯⎯ 44
Not that these claims are strictly incompatible with the idea that degrees of simplification and of relevance are part of what we are evaluating when we evaluate the degree to which a particular idealization idealizes: we might be taking a weighted sum of the degree of distortion, the degree of simplification, and the degree of relevance, and simply weighting the degree of distortion significantly more heavily than either of the other two factors. Nonetheless, it seems to me as a matter of linguistic intuition that that is not how we do it, and the alternative picture I am sketching accounts for the facts stated in parentheses in the text far more straightforwardly. 45 This does not necessarily mean that the question of the degree of misrepresentation and that of the degree of approximate truth involved in an idealization are interchangeable; whether they are depends on how we understand the notion of approximate truth. Crudely put, the telling question in this regard is: Does a representation have to be approximately true to have any degree of approximate truth? To put the point slightly less crudely: If we understand the notion of approximate truth in such a way that it is possible for partial truths to lack any degree of approximate truth (sc., partial truths which are sufficiently close to being complete falsehoods), then we may want to countenance degrees of distortion which distinguish between representations all of which have the same degree of approximate truth, namely, zero. If, on the other hand, any partial truth, no matter how partial, is to have some degree of approximate truth, then perhaps degrees of misrepresentation and degrees of approximate truth may be regarded as interdefinable. 46 See, for example, Niiniluoto (1998). Teller (2001) argues that Giere’s version of the semantic view (1988, ch. 3), with its emphasis on similarity as the crucial relation between representation and represented, helps us to see clearly a way of resolving some standard worries about approximate
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philosophical attempts to provide a precise account of the notion of approximate truth cannot mean that there is no coherent notion by that name, nor that we cannot meaningfully speak of the degree of misrepresentation or distortion present in a given aspect of a given model. There is clearly sense (and, indeed, truth) in saying that a model which represents a certain smooth metal ball rolling down a certain icy slope as experiencing no frictional force approximates the truth, if in fact there is just a small amount of friction present. We can just as clearly compare degrees of misrepresentation in specific respects, in at least some cases: we can draw such a comparison, for example, between the model of a cannonball firing presented above (in section 1) with a model of that same event which takes into account gravitational forces on the cannonball due to the moon. And comparing degrees of idealization in specific respects in models of distinct systems can also be a quite straightforward matter: If we were to fire a cannonball on an open plain on the moon, and model the system along the same lines as those sketched earlier, taking into account only gravitational forces on the projectile due to the body on which the episode occurred, then we could straightforwardly say that the resulting model would misrepresent the gravitational forces acting on the cannonball to a greater degree than that to which our original model idealizes the gravitational forces acting on its cannonball, as the moon model would be laying aside the Earth’s gravitational influence on the projectile whose motion it represents, and this is in a simple quantitative sense a greater distortion than the one in which the Earth model indulges when it eliminates the moon’s influence on the earthbound cannonball.47 In the cases just described, a precise quantitative measure of degrees of distortion in specific respects can simply be read off from the precise measures of the quantities modeled (namely, frictional and gravitational forces).48 Meaningful talk of degrees of distortion also seems intuitively possible in some truth. (And note that Giere himself claims that focussing on a relation of similarity allows us to circumvent various standard philosophical difficulties centering on the notion of truth, difficulties which have been taken to pose particular problems for the scientific realist (1988, pp. 81-2 and p. 93).) See Jones (forthcoming b) for criticisms of Giere’s approach, and Teller’s paper for a response. See also Giere’s paper in the present volume for more on models, theory structure, and realism. 47 I am assuming here that this difference is not compensated for by other differences in the gravitational forces ignored by the two models, differences which will be due to relatively small differences in the distances of various heavenly bodies from the Earth and from the moon. In any case, the judicious placement of a black hole can provide us with a more clear-cut example, if one is needed. 48 This talk of idealizing in respects and to degrees echoes Ronald Giere’s language in his (1988), ch. 3. According to the view of theory structure he presents there, a “theoretical hypothesis” makes claims about the respects in and degrees to which a certain model is similar to a particular system, or type of system, and, roughly speaking, we might say that there is an inverse relation between degree of similarity and degree of idealization. Again, for criticisms of Giere’s notion of model and his talk of similarity, see Jones (forthcoming b).
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cases where we have no ready way of measuring with any exactness the feature of the system misrepresented in the model: returning to our early example from Chomsky, some speakers have more limited memories, and are more easily distracted than others.49 This is not to say that fine-grained discriminations can always be made, however – often attempts to compare degrees of idealization in specific respects will lead only to a partial ordering, and not due to some limitation in our powers of discernment. And, more importantly, I should emphasize that in recognizing talk of degrees of misrepresentation, of distortion, and of truth as legitimate in general, I am not assuming that such talk is always meaningful. Perhaps in some cases it simply does not make sense to ask how close to the truth ‘S is φ’ is, or how great a misrepresentation it is. On the account given here, this simply implies that it will not be possible to talk about the degree of idealization involved in this aspect of the model. The account offered, such as it is, is intended only as account of the content of such judgements when they can be made.50 We are now in a position to outline an understanding of talk of degrees of idealization in models of kinds. At the lowest level of resolution, the natural approach is exactly parallel to the one we adopted for models of particular systems: We break the question “How idealized a model is M?” down into the two questions (i) “How many idealizations does M contain?” and (ii) “How much of an idealization is each of the idealizations which M contains?”, and find the answer to the original question by taking a sort of weighted sum over the various particular idealizations contained in M, bigger weights being assigned to bigger (particular) idealizations. The difference in this case, however, lies with the fact that question (ii) can itself then be divided in two. We begin by classifying M’s ascription of φi to the κ’s (systems of the kind Κ) as an idealization just in case there is at least one κ which lacks φi. Then for each particular idealization M contains we must ask (iia) “What fraction of the κ’s does M idealize in this respect?”; in addition, for each κ it idealizes, we must then ask (iib) “To what degree does M idealize κj by representing it as being φi?” (quite possibly receiving different answers for different κ’s). Thus, to put it another way, when dealing with models of kinds, the answer to question (ii) is itself arrived at by taking, for each idealization the model contains, a weighted sum over all the κ’s which that idealization idealizes, bigger weights corresponding to greater degrees of idealization in the sense discussed above ⎯⎯⎯⎯⎯⎯⎯ 49
This is not to say that precise measures of, say, memory capacity could not be constructed – indeed, psychologists have constructed such measures. The conceptual point is made, however, as soon as we recognize that those of us who have at our disposal no such precise measures can clearly make judgements of degree on these scores nonetheless, and thus could judge one given model to be a more idealized model of a certain speaker than another, at least in one of these particular respects. 50 Note that nothing I have said prevents the picturing of S as φ from counting as an idealization simpliciter in such a case.
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(i.e., greater degrees of misrepresentation or distortion), and then dividing by the total number of κ’s (to get a fraction).51 Putting it more intuitively, we can say that the degree to which a particular idealization idealizes the kind is a combination of two factors, namely, what fraction of things of that kind it idealizes, and how much it idealizes the ones it idealizes.52 Extending what I have been calling “the natural approach” to talk of degrees of abstraction (or abstractness) results in a considerably simpler story than the one I have just told about degrees of idealization, and for two reasons. First, there is no question of evaluating the degree to which a model omits a given feature of a given system, and so no parallel to the talk of degrees of misrepresentation or distortion we employed in the case of idealization. This fact then seems to preclude talk of the degree to which a model abstracts away from a feature of a particular system. Second, in the case of a model of a kind, it would seem that if a model abstracts away from a given feature possessed by one system of that kind, then it abstracts away from that feature, or from other determinates of the same determinable, for every system of the kind. So, taking color as our example of a determinable, if a model of pendula abstracts away from the redness of this pendulum, then it will abstract away from the redness, or blueness, or greenness, as the case may be, of any other pendulum. And counting the fact that a model abstracts away from the redness of red pendula and the fact that it abstracts away from the greenness of green pendula as two separate abstractions would seem to be double counting. The point might be put by saying that, when counting abstractions, we should count the number of determinables the determinates of which a given model abstracts away from. And a model cannot abstract from the determinates of a certain determinable in the case of some systems but not in the case of others. Thus there is no analogue, when interpreting talk of degrees of abstraction with respect to a model of a kind, to counting the number of systems of that kind which the model idealizes in some given respect. Given these two points, then, in the case of abstraction the natural approach thus reduces to the idea that to ask about degrees of abstraction is just to ask how many abstractions the model contains, both in the case of a model of a particular system and in the case of models of kinds. An intuitively appealing way of making sense of talk about overall degrees of idealization and abstraction in models readily suggests itself, then. And given such an account, we seem to be in a position to make equally good sense of the various sorts of talk about idealization and abstraction listed at the beginning of ⎯⎯⎯⎯⎯⎯⎯ 51
Again, this mathematical talk should not be taken too literally; see n. 42. There may be a difficulty here with the idea that what is relevant is the make-up of the class of actual κ’s. Intuitively, the worry would be that the actual κ’s may not be representative of the kind, especially if by ‘actual κ’s’ we mean the κ’s existing at some particular time. For some preliminary thoughts on a related problem, see n. 40. 52
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this section. Unfortunately, however, there is a serious problem which threatens to undermine all this. It is a problem which has its roots in something we noted on first introducing the idea of a model’s idealizing or abstracting away from the features of a system in some particular respect (in section 1), namely, that there is typically no way of individuating the idealizations and abstractions contained in a model which is obviously to be preferred. There is thus, in general, no straightforward way of saying how many idealizations a given model contains, nor how many abstractions. Consequently, given the details of the approach to judgements of overall degrees of idealization and abstraction outlined in this section, it becomes quite unclear how such judgements could ever be nonarbitrary. Yet (and this is the other horn of our dilemma), if judgements concerning overall degrees of idealization and abstraction are not understood to be, in part, judgements about the sheer numbers of idealizations and abstractions various models contain, it is not clear how they are to be understood. Admittedly, there may be ways around this difficulty with regards to comparative judgements in certain special circumstances. In certain cases it may be clear that, however we count the number of idealizations (or abstractions) in each of two models, M and M', those contained in M are a proper subset of those contained in M'. (M' might have been obtained from M by means of a single modification, or vice versa.) There is perhaps some hope that adjacent members of the series of models alluded to in talk of idealization and correction as processes (or of similar talk of abstraction and concretization) will be related in this way. In such cases, at any rate, we clearly can make sense of comparative judgements of degree of idealization (or abstraction) in a way which is entirely parasitic on our basic account of what it is for a model to contain an idealization (or abstraction) in a specific respect. If it is true, however, that some of our talk about idealization and abstraction presupposes an ability to make coherent judgements of degree (some of them comparative) in cases where this simple “proper subset” relation does not hold, then we have an unresolved problem on our hands. As mentioned above, Cartwright and Mendell (1984) propose an account of the content of judgements of degrees of abstractness which relies on a taxonomy of explanatory kinds akin to Aristotle’s, and Griesemer (this volume) advocates an importantly modified version of their account.53 It is thus interesting to investigate whether either of those accounts succeeds, and whether such an approach can be extended to the case of idealization. It is worth noting, in any case, that Cartwright and Mendell’s and Griesemer’s accounts, when applied to
⎯⎯⎯⎯⎯⎯⎯ 53
Again, see also Cartwright (1989), pp. 212-224.
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models, rely on the prior notion of an abstraction as a particular feature of a model.54
5. Laws: Preliminaries So much for the discussion of how we should understand talk of idealization and abstraction as it applies to models, and how we might usefully regiment such talk. It is now time to think about laws. The notion of law is itself hardly an unproblematic one, of course. Debates about the logical form of law statements, the precise role of laws in theories, the objectivity of lawhood, and the very possibility of drawing a principled distinction between laws and accidental generalizations, so-called, are as unresolved as they are familiar. Despite the existence of radical disagreements over such matters, however, few would dissent from the rough formula that statements intended to express scientific laws, at least for the most part, take the form55 φ’s are χ’s.
(N)
(where ‘N’ is for ‘nomological’). The claim I intend to make here concerning statements of law is quite minimal. It leaves open, for example, the question of whether the logical form of such statements is adequately captured by sentences of first-order predicate calculus of the ‘(∀x)(φx → χx)’ variety,56 whether they instead assert that a certain pair of universals, φ-ness and χ-ness, stand in a relation of necessitation to one another,57 or whether they should be understood primarily as making a claim about the capacities φ’s have in virtue of being φ’s.58 I also do not assume that English statements of the form All φ’s are χ’s provide accurate paraphrases of statements of form (N), or even that the law statement ‘φ’s are χ’s’ entails a claim which has the logical form ‘(∀x)(φx → χx).’ One might, for example, regard some or all law statements of form (N) as accurately paraphrased by statements of the form ⎯⎯⎯⎯⎯⎯⎯ 54
Although not in those words. Cartwright, for example (1989, p. 220), writes of those features which are and are not “specified.” 55 Or some closely related form, such as ‘φ’s are followed by χ’s,’ ‘φ’s have χ,’ etc. (where ‘φ’ and ‘χ’ are doing multiple duty as stand-ins for various parts of English). For the purposes of brevity, I will take ‘φ’s are χ’s’ to be canonical. ‘φ’ and ‘χ,’ of course, can stand for pieces of scientific English which are syntactically far more unwieldy than the Greek letters themselves (and the use of standard examples concerning black ravens and white swans) might suggest. 56 At least for the most part – see the discussions of the “contrapositives objection” in sections 7 and 8. 57 See Dretske (1977), Tooley (1977), and Armstrong (1983). 58 See Cartwright (1989), esp. chapter 5, for such a view.
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φ’s tend to be χ’s, reading this paraphrase in such a way that it entails ‘Most φ’s are χ’s,’ or ‘Many φ’s are χ’s,’ but not ‘All φ’s are χ’s.’ Or one might take a law statement of form (N) to be more accurately paraphrased by a statement of the form All φ’s, in virtue of being φ’s, have the capacity to (be) χ, the truth of which is, I take it, quite compatible with there being no φ’s which are χ, even if there are φ’s.59 Attributing form (N) to law statements is thus intended to commit us to very little; nonetheless, it provides us with a sufficient foothold to allow us to make some substantive claims about idealization and abstraction in laws, whilst at the same time allowing us to remain neutral on the standard philosophical issues just mentioned.60 Before outlining the remainder of what I have to say about laws it will be helpful if we first fix a piece of terminology: I will say that the law that φ’s are χ’s, or a law statement (which may or may not express a genuine law) of the form ‘φ’s are χ’s’ applies to a given system just in case the system is a φ.61 The discussion of idealization and abstraction in laws, then, will proceed as follows: I will begin by devoting some time to distinguishing and characterizing three different sorts of law-related idealization. First there are statements which are of form (N) which we treat as statements of law for some purposes, and which may apply to a large number of systems, but which are actually false, and false in a way which makes the statements themselves idealizations. For convenience, I will say that such statements express “quasi-laws.” Secondly, there are genuine laws typical employment of which nonetheless involves idealization; here the idealization is required in order that we may regard the law ⎯⎯⎯⎯⎯⎯⎯ 59
I emphasize these last two readings with Cartwright (1989) in mind. In her terms (inspired by Mill), the former reading provides us with a “tendency law,” the latter with a “law about tendencies” (p. 178). See also chapter 5, section 5 of her book. Some might say that a statement cannot express a “genuine” law, or a law in some especially important sense, if it does not entail the corresponding ‘(∀x)(φx → χx)’ statement. If that is so, however, then we may need to reckon with the possibility that the statements which we typically classify as expressions of law in actual scientific practice do not express “genuine” laws, or laws in the especially important sense. Be that as it may, we are concerned here with understanding talk of idealization and abstraction as it applies to actual scientific practice, and the things we classify as laws whilst engaged in that practice. 60 Note that if there are laws which do not take form (N), then what I have to say may not cover them. On the other hand, it seems to me that it would be a relatively straightforward matter to extend the following account beyond the domain of laws to general scientific claims of all sorts, provided only that they have the right sort of form. 61 There is a certain worry one might have here about whether the notion of application thus defined is well-formed in the case of laws (rather than law statements). For a discussion of that point, see the discussion which closes section 7 below.
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as applying. I will refer to such laws as “idealized laws.” And thirdly, there are genuine laws which only truly apply to systems which are ideal in some sense; these are the “ideal laws.”62 The distinction between the second and third sorts of law-related idealization may be especially unclear at this point, but things will become clearer below.63 My elaboration of the various distinctions will rely very centrally on that fundamental notion an account of which provided the starting point for the account of idealization in models given in sections 1 and 2 – that is, the notion of idealizing a particular system in some specific respect. Briefly, the idea is (in part) that when a law statement of the form ‘φ’s are χ’s’ expresses a quasi-law, then representing the systems we are dealing with as χ’s is an idealization in at least some cases, whereas when it expresses either an idealized law or an ideal law, our use of the law requires us in many, most, or all cases to indulge the idealization that various systems are φ’s.64 Following all of this, I will then provide a relatively quick account of abstraction in laws, one which builds in a simple way on the account of abstraction in models presented above.
6. Quasi-Laws Unfortunately, the precise articulation of the notion of a quasi-law which best captures the intuitive idea will depend on the account of law statements to which one subscribes. If a statement of form (N) is taken to be, or to entail a statement of the form ‘(∀x)(φx → χx),’ then given that being a quasi-law is a matter of its being an idealization to represent the φ’s as χ’s, it will be a necessary condition on some statement’s being a quasi-law that not all φ’s are χ’s. This necessary condition must be replaced by a stronger one if an alternative account of laws is adopted: If the emphasis is on tendency laws, which say only that most or many φ’s are χ’s, then we have a quasi-law only when it is not the case that most or many φ’s are χ’s; and if a law statement of form (N) is to be paraphrased as ‘All φ’s have the capacity to χ,’ then for the statement to express a quasi-law it must be the case that some φ’s do not have the capacity to χ. In each case, it follows that the statement expressing a quasilaw is false, and that is a crucial part of the notion I am attempting to characterize.65 For ease of exposition in other parts of this discussion, however, ⎯⎯⎯⎯⎯⎯⎯ 62
For brevity’s sake, I will also apply these labels to the statements which express such laws, whenever doing so will produce no confusion. 63 It may help to bear in mind that the categories of idealized law and of ideal law are (at least) overlapping. Again, see below. 64 Although it will turn out that this is only contingently true of ideal laws. 65 The list of sample necessary conditions is included because it is not quite enough to say “Law statement L must be false to express a quasi-law”; L must be false for the right reasons, so to speak.
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and without meaning to prejudice the issue, I will assume hereafter that we have adopted an account of laws on which a law does entail the corresponding ‘(∀x)(φx → χx)’ statement. I think it will be clear how to modify the following remarks in order to accommodate views on which this entailment does not hold. A necessary condition, then, for a statement of form (N) to express a quasilaw, given the assumption I have just made, is that some φ’s are not χ’s (regardless of what we believe in that regard).66 Another is that, at least for some purposes, we treat the statement as a law, citing it in explanations, employing it to make predictions, using it to support counterfactuals, and so on. Even together these conditions are clearly not sufficient, however, if being a quasi-law is to involve idealization in some way: some statements of form (N) which at one time or another we have treated as expressing laws for various purposes (and which we have perhaps taken to express actual laws) have simply been false, without being or involving idealizations, and without it being appropriate to say that we were idealizing in treating the statements in question as expressing laws. So what else is involved in something’s being a quasi-law? Recalling the discussion of idealization in models, we can immediately identify three important features a quasi-law may have. One is approximation: ‘φ’s are χ’s’ might be approximately true. Another is simplicity: ‘φ’s are χ’s’ might be a simplification of the truth about φ’s. And finally there is relevance: saying that φ’s are χ’s might misrepresent features of the non-χ φ’s which are relevant in one or more ways to the purposes we have in mind when employing
If, for example, law statements should be understood as claiming to express relations of necessitation between universals, then it is not enough for no such relation of necessitation to hold between the universals in question – it may still be accidentally true that all the φ’s are in fact χ’s, in which case I see no reason to speak of idealization (as opposed to error of another kind). The crucial feature of a quasi-law I am trying to get at might be rather imperfectly put this way: If L is a quasilaw, then the “extensional content” of L must be false. And for an illustration of what I mean by this imprecise use of the phrase ‘extensional content,’ I must then refer the reader back to the list of sample necessary conditions provided in the text. 66 A difficulty arises here in the case in which there are no φ’s, as intuitively it seems that a statement of the form ‘φ’s are χ’s’ might still be treated as a law in some circumstances, and might nonetheless be an idealization in something like the way I am trying to characterize. (Note that this is reminiscent of some problems we encountered in understanding talk of idealization with respect to models of uninstantiated kinds.) Perhaps we might attempt to address this difficulty by invoking counterfactuals, and making it a necessary condition on such a statement’s being a quasi-law that if there were φ’s, not all of them would be χ’s. It is easy to discover problems with at least the initial statement of this solution, however; whether those problems could be overcome, or whether the original difficulty can be dealt with in some other way, will be left as a question for further exploration.
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the quasi-law as though it were a genuine law.67 Given this, we can settle on the following characterization of the notion of a quasi-law: L, a statement of form ‘φ’s are χ’s’, is (or expresses) a quasi-law if and only if (i) L is treated as a law for some purposes, but (ii) some of the φ’s are such that it is an idealization to represent those φ’s as χ’s.
It follows, of course, from condition (ii) and my account of particular idealizations in specific respects (in sections 1 and 2) that some of the φ’s are not χ’s if L states a quasi-law, and thus that statements of quasi-laws are false, and (so) do not express laws.68 To illustrate the notion of a quasi-law, consider as a simple example the law of gravitational free fall. A typical statement of this (so-called) law might run as follows: Near the surface of the Earth, a falling body accelerates at a constant rate of 9.8 m/s2. In terms of our schema, then, ‘φ’ is ‘system falling near the surface of the Earth,’ and ‘χ’ is ‘system accelerating at a constant rate of 9.8 m/s2.’ Now it is not true that all systems falling near the surface of the Earth accelerate constantly at 9.8 m/s2. For one thing, there are feathers, leaves, and scraps of paper (like Neurath’s thousand mark note69) whose fall is influenced by the passing breezes in such a way that their acceleration is often very different from the value cited in the law. Suppose we find some way to modify the law so as to exclude such bodies from consideration, and so as to restrict attention to objects such as bricks, hammers, cannonballs, and people, objects which, relatively speaking, are only marginally affected by non-gravitational forces.70 I will suppose that this restriction can be effected in some principled manner, and indicate it by letting ‘φ’ stand for ‘system falling freely near the surface of the Earth.’71 ⎯⎯⎯⎯⎯⎯⎯ 67
This, however, seems virtually guaranteed, and to the extent that it is, relevance so elaborated seems ill suited to be an independent criterion of quasi-lawhood. Perhaps instead we might focus on the distinct question of whether representing the non−χ φ’s as χ’s misrepresents them in a way which is relevant to our purposes – whether, for example, this misrepresentation makes a difference to the predictions we are interested in making. The distinction here is between merely misrepresenting relevant features, and misrepresenting relevant features in a way that makes a (relevant) difference. 68 My intentions here are quite parallel to my intentions in the discussion of section 2, as described at the very end of section 1. Although I do provide a pair of individually necessary and jointly sufficient conditions for correct application of the label “quasi-law”, so that there is a surface-level difference, the second of those conditions employs the notion of a particular idealization in a specific respect, a central notion for which I have not tried to give necessary and sufficient conditions. 69 See, e.g., Hempel (1969), p. 173. 70 As will become clear, restricting the law in this way is a step towards the production of an idealized law (as opposed to a quasi-law). See especially the last paragraph of section 8. 71 In the present context, then, the phrase ‘free fall’ is not intended to imply the complete absence of non-gravitational forces such as air resistance, but merely their relative negligibility. (Note, on the
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Even with this modification, however, it is not the case that all φ’s are χ’s. The problem is not that the number 9.8 is not exactly right, but that there is no right number. The acceleration of a freely falling body varies from place to place, and in two ways: at a given latitude, it decreases with the height of the body above the ground, and for a given height, it increases with latitude.72 Thus the statement that all freely falling bodies near the surface of the Earth accelerate at a constant rate of 9.8 m/s2 is straightforwardly false.73 Despite its falsity, we often treat the statement in question as though it expresses a genuine law when providing explanations, making predictions, designing equipment, and so on. In doing so, we are idealizing, and the statement itself can properly be said to be an idealization. This, then, is an example of what I am calling a quasi-law. And it is interesting to note that each of the other three factors mentioned above seem to be present: the statement is a simplification of the truth of the matter, it is an approximation to that truth, and the features of the systems in question which are misrepresented will certainly be relevant features in the contexts in which we treat the statement as expressing a law. As with models, we can coherently talk about the degree of idealization involved in a given quasi-law, and presumably that is a product of two factors: the degree of idealization (that is, degree of distortion) involved in saying, of each non-χ φ, that it is a χ, and the ratio of non-χ’s to χ’s amongst the φ’s.74
7. Idealized Laws With a quasi-law, misrepresentation is involved at each of three different levels: in treating particular φ’s as χ’s when applying the law to them; in making the general claim that φ’s are χ’s; and in the distinct claim that it is a law that φ’s are χ’s.75 Given especially the presence of the second kind of misrepresentation, other hand, that even if the complete absence of any force other than the Earth’s gravitational pull were required for free fall, everything I say in the next paragraph would still be true.) The hope is also, of course, that we have been able to arrive at a statement which is at least somewhat plausible without having to define the notion of free fall in such a way that we end up with a trivial truth. 72 The first sort of variation is a straightforward consequence of Newton’s Law of Universal Gravitational Attraction, which we can treat as a genuine law for the present purposes of illustration (!); the second is due to fact that the Earth is oblate rather than spherical. (For some data on this latter point, see Cohen 1985, p. 175.) 73 Remember that for expository purposes I am assuming that such ‘φ’s are χ’s’ statements should be read as entailing the corresponding ‘(∀x) (φx → χx)’ claims. 74 Or, to use the mathematical metaphor introduced earlier, we can say that the degree of idealization enjoyed by the quasi-law can be calculated by taking a weighted sum over the non-χ φ’s, with the weights representing the degree of idealization involved in representing the corresponding φ’s as χ’s, and then (to get a ratio) dividing by the total number of φ’s (χ and non-χ). 75 To see that these are distinct claims, we need only allow that it possible for the claim that φ’s are χ’s to be true whilst the claim that it is a law that φ’s are χ’s is false.
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the general formula that idealization involves misrepresentation carries over quite straightforwardly from the case of models to the case of quasi-laws – a quasi-law says something false, and so misrepresents the world. When it comes to what I want to call “idealized laws,” however, misrepresentation is involved only in a somewhat more indirect way. The idea here is that, while the statement which expresses an idealized law is perfectly true (and while it is true to say that it expresses a law), there is typically misrepresentation involved in the employment of the law, in that we often bring it to bear upon systems which are not φ’s. When we know that we are idealizing, then, the difference between quasi-laws and idealized laws corresponds to the difference between two distinct sorts of pretence: we pretend that quasi-laws are laws, whereas we pretend that idealized laws apply more often than they do.76 To illustrate the notion of the idealized law, consider the law of inertia, which states that a body subject to no net force undergoes no acceleration, and which we will suppose to be a genuine law. The law of inertia is clearly a law which rarely, if ever, finds a foothold in the world, just because few, if any bodies have ever been subject to zero net force.77 Nonetheless, we sometimes employ the law as though it applied to various actual bodies, regarding it as a good approximation for various purposes to treat those bodies as suffering no net force. And in so applying the law, we either implicitly or explicitly misrepresent the systems to which we apply it. I will take an indirect approach to the task of making the notion of an idealized law more precise, by first asking what it might mean to say that there is idealization involved in a single instance of our employing a statement L, of the form ‘φ’s are χ’s,’ with respect to some system S (thus focussing on what it means to idealize in using a law, rather than on what it means to say that a law itself is idealized). One possibility is that part of what is meant is that although S is a φ, it is not really a χ; another is simply that L is not true, or is not a law, regardless of the particular properties of S; but in any of these cases L at best expresses a quasi-law.78 Another possibility, however, is that L expresses a genuine law, but that S is not really a φ (and thus that we are implicitly or explicitly misrepresenting S by employing L with regard to it). Clearly that is not enough to make it appropriate to say that we are idealizing when we employ L in our treatment of S – sometimes we are simply flat wrong. Talk of idealization comes to seem more fitting if, in addition to its being the case that S is not a φ, it is also true that (i) S is approximately a φ, that (ii) it is a ⎯⎯⎯⎯⎯⎯⎯ To put it another way, with an idealized law we pretend that there are more φ’s than there are. It might be objected that the law finds footholds aplenty if only we write it in the contrapositive form “All accelerating bodies are subject to a net force,” for a multitude of accelerating bodies surrounds us. I will return to consider this potential objection at the end of this section. 78 Given again my assumption, made for purely expository purposes, that ‘φ’s are χ’s’ should be taken to entail ‘(∀x)(φx → χx).’ 76 77
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simplification of the truth about S to say that it is a φ, and/or that (iii) in describing S as a φ we are misrepresenting certain relevant features of the system (where relevance is then to be understood in one of the ways discussed earlier). More generally, if L is a genuine law, but it is an idealization to regard S as a φ – or, to put it another way, it is an idealization to regard L as applying to S – then we are idealizing by using L in our dealings with system S. Given this, my suggestion is simply that we classify a law as idealized just in case we are typically forced to idealize in the way just described in employing the law, for the reason that true φ’s are relatively rare. Summing up, then:79 ‘φ’s are χ’s’ is, or expresses, an idealized law if and only if (i) it is a genuine law that φ’s are χ’s, but (ii) φ’s are relatively rare, and so (iii) our employment of the law typically involves treating various non-φ systems as φ’s even though it is an idealization to do so.
Thus if the φ’s are plentiful, then we will not regard the law that φ’s are χ’s as an idealized law, but note that it is still entirely possible that we will sometimes idealize in using the law, by employing it with regard to non-φ systems and idealizing them in doing so. As with models and quasi-laws, it makes sense to speak of the degree of idealization exhibited by an idealized law – there can be highly idealized laws and laws which are only somewhat idealized. One obvious way in which this arises is via the phrase ‘relatively rare’ (and the connected quantifier ‘typically’). The rarer the φ’s, the more idealized the law. But note that the degree of rarity of the φ’s cannot alone account for all the ways in which one law may be more idealized than another. Fortunately, however, idealizations (of particular systems, in specific respects) also come in degrees, and so how idealized an idealized law is will be a matter both of how rare the φ’s are, and of how much of an idealization is involved when we treat various non-φ’s as φ’s in our employment of the law. Suppose, for example, that there is not now, never has been, and never will be an “untrammeled” body, that is, one subject to no net force. It follows that untrammeled bodies and perfectly spherical untrammeled bodies are equally rare; yet intuitively we might be tempted to classify a law governing perfectly spherical untrammeled bodies as more idealized than a law which concerns all untrammeled bodies regardless of shape. The relative degrees of approximation, simplification, and distortion of relevant features involved in the employment of the two laws might account for that temptation, and make it a respectable one. One aspect of the definition of idealized law which perhaps calls for a little further comment is the notion of rarity invoked in the second necessary ⎯⎯⎯⎯⎯⎯⎯ 79 The same remarks apply to this definition of the notion of an idealized law as I made with respect to the definition of the notion of a quasi-law – see n. 68.
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condition on being an idealized law, and how not to understand it. Specifically, rarity cannot here be tied to absolute number in the most straightforward way. Suppose that a certain kind of stellar event occurs once every billion years, on average, but that we are fortunate enough to avoid a Big Crunch, so that the universe lives on indefinitely into the future. In that case, there will eventually be a very large number of events of the kind in question; yet such events will surely still count as rare occasions. Instead, it seems to me that to understand rarity in this sense, we need to see the law statement in question as embedded in a wider context – as part of a theory, or as a representation employed in the context of a particular sort of theorizing. We can then draw on the notion of a domain of inquiry, a class containing just those systems which the theory is a theory of, or which the theorizing is about. The φ’s then count as rare when a sufficiently small proportion of systems in the relevant domain of inquiry are φ’s. To take a relatively extreme example, the bodies subject to a net force of zero are clearly a very small proportion of the class of all bodies, and it is for that reason that the second necessary condition on being an idealized law is satisfied for the law of inertia.80 Given this way of understanding rarity, let me lay aside a potential objection which strikes me as misguided. The objection I have in mind is that the notions of “proportion” and of “sufficient smallness” on which the explication depend are unacceptably vague.81 Such a complaint could be handled in a two-pronged way. If all that is sought is an account of the way in which we classify some laws as idealized, then some vagueness in the terms of the account is not obviously a bad thing – after all, there is plausibly some vagueness inherent in the classificatory practice itself. If, on the other hand, it should seem desirable to construct a notion of idealized law which is considerably more precise for some philosophical purpose or other, then understanding the proposal at hand in this ⎯⎯⎯⎯⎯⎯⎯ Note that whether the φ’s are rare will in many cases be a contingent matter – not merely logically or metaphysically contingent, but physically or nomologically contingent. This strikes me as an advantage of the account I am offering, for it seems to me that in at least some cases when we say that a law is idealized, we are (and take ourselves to be) uttering a (physically) contingent truth. (Had the world been full of φ’s, as it might have been, such-and-such a law would not have counted as idealized; our use of the law constitutes an idealization only relative to the details of the particular world in which we employ it.) If there are cases, however, of idealized laws which do not seem to possess their status only contingently, then my hope would be that they qualify in virtue of there being sorts of rarity which are not physically contingent. Incidentally, reflection on the notion of a quasi-law makes it immediately clear that whether L expresses a quasi-law is also contingent, but that, the presumed physical contingency of our theoretical practices being what they are aside, quasi-lawhood is only a metaphysically, and not a nomologically contingent matter – it is trivially true that whether L expresses a law or not depends on what the laws are. 81 What is more, the domain of inquiry may well have vague boundaries. 80
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way certainly leaves room for such a development; perhaps the relevant notion of proportion might be cashed out in measure-theoretic terms, for example.82 It is also worth noting that the notion of an idealized law I have outlined might be, and indeed probably should be elaborated upon by taking into account the extent to which, in treating of non-φ systems by employing a “φ’s are χ’s” law, thinking of the relevant systems as χ’s also constitutes an idealization, and thus by taking into account the extent to which ‘χ’ contributes to the classification of the law as idealized, and as less or more so. Given what has come before, elaboration of that sort would be a relatively straightforward matter, and I will not enter into such embroidery here. Let us close this discussion of the notion of an idealized law by considering an objection which might be raised to the definition laid out above. The objection is this: According to the proposed definition, for “φ’s are χ’s” to state an idealized law, the φ’s – that is, systems of the type mentioned first in the candidate law statement – must be, at best, few and far between in the relevant domain of inquiry. Another way of stating the very same law, however, is simply to take the contrapositive of the initial formulation, that is, ‘Non-χ’s are non-φ’s’; and it may be that, while the φ’s are rare, the systems mentioned first in this new formulation of the law, the non-χ’s, are quite plentiful, or even ubiquitous in the relevant domain. Thus it seems that whether a given law counts as an idealized law may depend on which of two syntactically distinct but semantically equivalent ways of expressing the law we consider. And surely that is wrong; surely we are here trying to classify laws (or putative laws, in the case of quasi-laws) with an eye to types of idealization, not law statements. Indeed, the law of inertia provides a perfect example: it may be that no body has ever truly been subject to no net force, and yet a multitude of accelerating bodies (non-non-accelerating bodies, so to speak) surrounds us. So is the law of inertia an idealized law or not?83 The first point to be made in response to this objection is that it relies on an assumption about law statements which by no means all accounts of lawhood ⎯⎯⎯⎯⎯⎯⎯ Comparing the sheer cardinality of the class of φ’s with that of the class of χ’s, however, will clearly not work, for as the example of rare stellar events in a universe of infinite lifetime suggests, both sets might have the cardinality aleph-nought even when the φ’s do count as rare. The obvious problem a measure-theoretic approach would face, on the other hand, is that of locating a suitable provenance for the necessary measures. 83 Essentially the same line of thought just as readily gives rise to the claim that the definition I introduced earlier of what it is for a law or law statement to apply to a system is ill-formed with respect to laws (as opposed to law statements): The law that φ’s are χ’s is supposed to apply to S iff S is a φ; yet (this line of thought goes), the law that non-χ’s are non-φ’s is the same law, and a given S may be a non-χ but not a φ, or vice versa. (Indeed, if the law in question really is a law, then on this view any given S is bound to be one of the two!) So does the law apply to such an S or not? This is the worry I alluded to in n. 61, and the discussion which follows in the text should make it clear how I would respond to it. 82
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would regard as legitimate. Specifically, the objection assumes that when ‘φ’s are χ’s’ is a law statement, a statement of the form ‘Non-χ’s are non-φ’s’ states the same law. This is straightforwardly true if the logical form of law statements can be captured by the first-order predicate calculus in the obvious way – ‘(∀x)(φx → χx)’ and ‘(∀x)(¬χx → ¬φx)’ are indeed logically equivalent84 – and so there is a difficulty to be faced in combining accounts of law which endorse that view (such as those due to Ayer (1956) and Lewis (1983, pp. 366-7)) with the present proposals concerning the notion of an idealized law. On some other leading accounts of lawhood, however, the crucial assumption does not hold good. For example, if ‘φ’s are χ’s’ says that the universal φ-ness necessitates the universal χ-ness, then ‘Non-χ’s are non-φ’s,’ read as a law statement, would have to be understood as claiming that the universal non-χ-ness necessitates the universal non-φ-ness – a different claim, and one which at least some proponents of this view of laws would regard as not even being materially equivalent to the first (for the right choice of ‘φ’ and ‘χ’), on the grounds that there is no such universal as “non-χ-ness” or “non-φ-ness.”85 Similarly, the claim that φ’s, in virtue of being φ’s, have the capacity to χ, is clearly distinct from the claim that non-χ’s, in virtue of being non-χ’s, have the capacity to non-φ.86 Thus, the objection we are considering has no force unless we adopt the right (or wrong) account of lawhood. What if the best account of lawhood is one on which ‘φ’s are χ’s’ and ‘Nonχ’s are non-φ’s’ state the same law, however? For strategic purposes, it would be preferable if the account I am presenting here of various types idealization in laws could continue to avoid commitment to any but the most minimal assumptions about the nature of laws.87 With that goal in mind then, we could redefine the notion of an idealized law as follows: L is an idealized law if and only if (i) L is a genuine law, (ii) there is a formulation of L of the form ‘φ’s are χ’s’ such that φ’s are relatively rare, and (iii) we often employ the law in a way which involves treating various non-φ systems from the domain of inquiry as φ’s even though it is an idealization to do so.
⎯⎯⎯⎯⎯⎯⎯ 84 This is also a very familiar point, of course, as it is the observation which gives rise to the ravens paradox in confirmation theory. 85 Armstrong springs to mind here as someone who believes that there are universals, but relatively few of them. More to the point, Armstrong argues that when the predicate ‘is φ’ picks out a universal, the predicate ‘is non-φ’ typically will not. See Armstrong (1978), chapters 13 and 14. 86 See nn. 57-59 for these competing views of laws. 87 Specifically, although Ayer’s (1956) account seems deeply problematic to me (and many others), and although I am in fact inclined towards a “capacities account” of the sort Cartwright has been developing, I would rather not presuppose the falsity of what Earman calls the “Mill-RamseyLewis” or “M-R-L” view (1986, pp. 87-90), and on that view the objection involving contrapositives would indeed have teeth, just because, as noted, laws on the M-R-L view do have the logical form traditionally ascribed to them.
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This new definition retains all the central features of the initial definition, but avoids the difficulty we have been considering involving contrapositive formulations of laws. In fact, the first and second clauses on their own are sufficient to defuse the objection involving contrapositives, strictly speaking – the law of inertia would now be declared an idealized law, given this formulation, even without (iii). But (iii) is included because without it we get the wrong results: if we only ever used the law of inertia to draw the conclusion about various accelerating systems that they must be subject to net forces, say, then there would be little reason to talk of idealization. In other words, it is because we use the law in a certain way that it counts as an idealized law. But note that this is quite parallel to the case of quasi-laws: to be a quasi-law, L has to be treated as a law for some purposes. And this pragmatic dimension to the conceptual distinctions I am drawing is present even in the case of idealization in models. The account of idealization in models took as one of its fundamental building blocks the notion of idealization in a specific respect, and that has partly to do with relevance, which as characterized is clearly a pragmatic notion, and partly to do with simplicity, which is quite plausibly pragmatic, too. Despite all this, it might be argued that the new proposal still has its defects. As things stand, if the law statement ‘All accelerating bodies are subject to a net force’ does express the same law as ‘A body subject to no net force undergoes no acceleration,’ then it expresses an idealized law just because it expresses a law which, by this definition, counts as idealized (and which, in fact, turns out to be highly idealized). And that former statement thus counts as expressing a highly idealized law even though there is an abundance of non-idealizing uses of it available to us – we do, after all, use it to conclude that various accelerating bodies must be subject to some net force. If that should seem too uncomfortable a way of talking, then at the end of the day it may be best to refrain from talking of laws themselves as idealized or otherwise, and to limit ourselves instead to thinking about idealizing uses of laws. Before leaping into such a rethinking of the territory, however, it is worth remembering that these latter difficulties arise only if certain views of the nature of lawhood should turn out to be correct.
8. Ideal Laws In an attempt to capture one more way in which laws can be tied up with idealization, let me begin simply by defining the notion of an ideal law, as follows: L, of the form φ’s are χ’s, is an ideal law if and only if (i) L is a genuine law, and (ii) φ’s are ideal systems.
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The first question which comes to mind here is what it means to say that the φ’s are “ideal systems.” The basic idea is that some systems (or possible kinds of system) are ideal in the sense of being perfect, or “just right,” and that some laws then count as “ideal” just because they govern such perfect systems (or would govern such systems if there were any). But what makes perfect systems perfect? Cartwright proposes an intriguing answer to that question. In essence, she proposes that certain sorts of system count as perfect or ideal because conditions are just right for some particular capacity to reveal itself in such systems, without hindrance from any distinct factor which might otherwise interfere.88 Thus a body subject to no net force is one which will reveal the inherent, if relatively unexciting capacity every body has to just keep moving with a constant velocity.89 I find Cartwright’s proposals attractive, and will implicitly allow them to fix the sense of the phrase ‘ideal system’ in the remainder of the discussion, but it is worth bearing in mind the fact that one might wish to consider some other sense in which a system could be perfect, or ideal; the hope is then that the rest of what I have to say will carry over to other ways of being ideal. The next issue to be addressed here is the relationship between the category of ideal laws and that of idealized laws, and we can become clearer on the nature of that relationship by thinking first about the connections between being rare and being ideal. Logically speaking, these would seem to be independent features of a system (or possible kind of system). Certainly some kinds of system are both rare and ideal: consider the category of untrammeled bodies. It is just as surely true, however, that there are kinds of system which are rare without being ideal (in any obvious sense) – charged metallic spheres subject to a gravitational force of magnitude 10.378 N and a repulsive electrical force of magnitude 17.58 N pushing in directions which make an angle of 53˚ with each other, for example – and it also seems possible that the world might have been overflowing with ideal systems. Thus it is clear that the two features, being rare and being ideal, are quite separate.
⎯⎯⎯⎯⎯⎯⎯ 88
Cartwright (1989), chapter 5, esp. pp. 190-1. Ideal laws as I am characterizing them would seem to correspond to the laws which, on Cartwright’s account (and in her terms), describe what happens in a situation depicted by an idealized model. Cartwright says that a law of this sort is “a kind of ceteris paribus law: it tells what [a] factor does if circumstances are arranged in a particularly ideal way” (p. 192). I do not wish to presuppose, however (and nor, I suspect, does Cartwright), that no ideal law ever applies to an actual system; perhaps ideal conditions are sometimes realized. 89 Cartwright may prefer to classify this as a (mere) tendency rather than a capacity (1989, p. 226), but that distinction need not concern us here.
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On the other hand, it does seem to be true that in the actual world, ideal systems are rare – the two features are contingently correlated.90 Suppose for a moment that it is true to say that all ideal systems are rare. Suppose, furthermore, that all ideal laws, of the form ‘φ’s are χ’s,’ are typically employed in a way which involves treating various non-φ systems from the domain of inquiry as φ’s, even though we are idealizing those systems in doing so. Then it would follow that all ideal laws are idealized laws. The truth, of course, may not be so simple. Perhaps there are some kinds of ideal system which are relatively common. Or (more likely) perhaps there are ideal laws which we rarely or never use in the idealizing way described – simply because we never use the laws in question at all, or because the idealization involved in treating the actual non-φ systems around us as φ’s is simply too great for it ever to be useful for us ever to employ the law in our dealings with non-φ systems. Even so, it seems clear that there is considerable overlap between the categories of ideal law and idealized law. We do in fact often use ideal laws which apply (or would apply) only to some rare sort of ideal system as though they applied to various non-φ systems in the world, and idealize in so employing such laws. The law of inertia again provides us with a good example. With this in mind, we can now see that ideal laws are implicated in practices of idealization a little more loosely than either quasi-laws or idealized laws. Even if it is true that all ideal laws are in fact idealized laws, this is so only contingently. It is no part of the definition that an ideal law need ever be used in a way which involves idealizations, and this distinguishes ideal laws from both quasi-laws and idealized laws. Nonetheless, contingent though it may be, the overlap between the categories of ideal law and idealized law is there, and so de facto a full account of how idealizations arise in our use of laws must take account of the category of ideal laws.91 There is one problem to be dealt with here before leaving ideal laws behind – the worry about contrapositives again. Is the law of inertia an ideal law or not? Untrammeled bodies are plausibly to be thought of as ideal systems (at least ⎯⎯⎯⎯⎯⎯⎯ 90
And note that Cartwright’s proposals account for this fact quite straightforwardly, given the evident fact that our world is a rich and complex one in which numerous causal factors are typically at work in any given situation. 91 One might wonder why I have defined the notion of ideal law in such a way that the connection between ideal laws and idealizations is so loose. The answer is that it seems to me that we do prephilosophically recognize a category of laws which are special just because they deal with systems which are ideal in some sense; and although it is true that such laws tend to get used in ways which involves us in idealization, that is not necessarily part of what we have in mind when we label such laws “ideal laws” or “laws concerning ideal systems.” In other words, doing things this way seems to me to result in a greater degree of continuity with pre-existing usage. Incidentally, another standard locution which comes to mind when we think about idealization in laws is that of the φ’s being a “special case”; this, it seems to me, is ambiguous between the notions of being rare and being an ideal system, and so between talk of an idealized law and an ideal one.
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insofar as they are untrammeled), but an accelerating body does not thereby strike one as particularly ideal in any obvious sense. So which formulation of the law of inertia should we look to when asking whether the law is an ideal one? Given the discussion of the parallel worry at the end of the last section, it is easy enough to see what we might say here. For one thing, we might challenge the claim that the contrapositives of law statements are semantically equivalent to the law statements we started with.92 More diplomatically, we might modify the definition of the notion of an ideal law, without losing anything essential, as follows: L is an ideal law if and only if (i) L is a genuine law, (ii) there is a formulation of L of the form ‘φ’s are χ’s’ such that φ’s are ideal systems, and (iii) we often employ the law in a way which involves treating various systems as φ’s.
Although the strategy here is in many ways parallel to the strategy I outlined for dealing with the contrapositives problem in the case of the notion of an idealized law, it is important to note that the third clause of this definition is not quite the same as the third clause of the amended definition of that notion; in particular, it is not required that to be an ideal law L must be employed in such a way as to idealize non-φ systems, for it may be that whenever we employ the law in a way which involves treating various systems as φ’s, the systems in question are φ’s. As the discussion above makes clear, this is simply in keeping with the original definition of the notion of an ideal law. However, this new definition does require that we sometimes use the law, unlike the initial definition, for it is that usage which now puts an emphasis on the fact that the law can be thought of as concerning ideal systems. *
*
*
This completes my account of the specific ways in which laws and our employment of them can involve idealization. Before I turn to consider laws and abstraction very briefly, however, there are two further points worth making regarding idealization and laws. First, there is the option of introducing further categories into our scheme for classifying laws and law statements. Ideal and idealized laws must genuinely be laws, whereas quasi-laws must not. Yet perhaps there are statements of the ‘φ’s are χ’s’ form which purport to govern rare or ideal systems, and which we treat ⎯⎯⎯⎯⎯⎯⎯ 92
Note that one can deny this without denying that it follows from the law of inertia (here identified as the law that a body subject to net force does not accelerate) that all accelerating bodies are subject to a net force. If, for example, the law of inertia is understood as concerning a relation of necessitation which holds between two universals, then given the law the contrapositive will surely be true; it is just that the contrapositive will not state the law of inertia (or, most likely, any law).
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as expressions of law in at least some contexts, but which do not in fact express genuine laws.93 Some such statements might be said to express, or to be, ideal or idealized quasi-laws (‘ideal’ for ideal φ’s, ‘idealized’ for φ’s which are rare but non-ideal).94 Employment of either an idealized quasi-law or (assuming that the ideal systems in question are few and far between) an ideal quasi-law will then typically involve us in the sorry business of making both the idealization that the statement in question is true and the idealization that it applies to the system in hand.95 Second, the classificatory scheme I have laid out corresponds nicely to an important claim Cartwright makes in her 1983 book, How the Laws of Physics Lie.96 According to Cartwright, the sorts of law statement which we value most in our scientific work must generally be taken in one of two ways: as widely applicable but false, or as true but quite restricted in their scope of application. The idea is that a typical law statement of the form ‘φ’s are χ’s’ will have numerous exceptions if it is read as entailing ‘(∀x)(φx → χx),’ and so as applying to all φ’s, and that in the subsequent attempt to produce a true statement of the ‘(∀x)( . . . )’ form we will find ourselves having to add a slew of restrictive antecedent clauses, and possibly even resorting to the use of nonspecific ceteris paribus clauses (thus effectively replacing ‘φ’ with some new ‘φ*’); the end result will at best be a true generalization of very restricted applicability, one which will do very little of the work we expected our original law statement to do. Cartwright illustrates this dilemma by employing the example of Snell’s law of refraction (1983). In the terms of my account, Cartwright’s claim is that our favorite law statements must generally be taken to express either quasi-laws, or idealized (and possibly ideal) laws, so that we must either sacrifice truth or applicability. Cartwright’s main point is that if this claim is correct, it is quite devastating for covering-law models of explanation, but it is also worth reflecting on the fact that the claim raises serious problems for a wide range of accounts of confirmation in much the same way.
⎯⎯⎯⎯⎯⎯⎯ 93
And for reasons having to do with the falsehood of what I earlier called their “extensional content”; see n. 65. 94 “Some” because, in line with the preceding discussion, the conditions just specified may not be enough to make something count as an idealized (as opposed to ideal) quasi-law – for that, it needs to be the case that the quasi-law in question is typically employed in a way which idealizes non-φ systems by treating them as φ’s. 95 An example of an idealized quasi-law, in fact, is Galileo’s law of free fall, as ordinarily understood and employed (not, that is, understood in terms of the special sense of ‘free’ I introduced towards the end of section 6). 96 See especially essay 2, “The Truth Doesn’t Explain Much” (Cartwright 1983).
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9. Abstraction in Laws I wish to say relatively little about abstraction and laws. It is surely true of any law statement of the form ‘φ’s are χ’s’ that when we employ it in the treatment of a system S, describing S as being both a φ and a χ will omit mention of many features S has, without thereby misrepresenting S (that is, without representing S as lacking them). To classify L as an abstract law is thus presumably to imply that it involves, in one way or another, a lot of omission as compared to other laws. Accordingly, I propose that we understand talk of abstract laws in a way which derives from the notion of an abstract model (where an abstract model is one which omits a lot). Corresponding to any law statement of the form ‘φ’s are χ’s,’ there are two models of any given real system S, one of which simply represents S as being φ, and the other of which simply represents it as being χ. A law statement (or law, if the statement indeed expresses one) then counts as abstract if and only if, given an arbitrary S from the relevant domain of inquiry, one or both of the models in question is an abstract model of S. (Another way of putting this, perhaps, is that L counts as an abstract law just when one or both of the concepts φ-ness and χ-ness is a relatively abstract concept.) And talk of degrees of abstraction with respect to laws can then be understood in a way which derives fairly straightforwardly from our understanding of such talk with respect to models.97 Two aspects of this simple proposal concerning abstraction should be noted. First, whether a given law counts as abstract or not is determined with reference to an arbitrary system from the relevant domain of inquiry. This is simply because if a model the content of which is captured by ‘S is φ’ (say) counts as an abstract one, where S is any system from the relevant domain of inquiry, then so too will the model the content of which is captured by ‘S* is φ,’ for any other system from that domain, S*. Second, note that the proposal in no way precludes the classification of a law (or law statement) as abstract and ideal, abstract and idealized, or as abstract and a quasi-law. In particular, although it is indeed built into my own account of abstraction in models that abstraction with regard to a particular feature of real systems involves omission without misrepresentation, the misrepresentation which is prohibited is just misrepresentation of the fact that the real system or systems in question have the feature in question; nothing in the account prevents an abstract model from simultaneously misrepresenting how things stand with
⎯⎯⎯⎯⎯⎯⎯ 97
The only obvious complication being that the degree of abstractness of the law will be a product (loosely speaking) of the degree of abstractness of the two models to which it gives rise (the φ model and the χ model).
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respect to other features of systems (features other than the ones the model abstracts away from).98 The brevity and apparent simplicity of this discussion of abstraction and laws should not deceive: all the work is done by the notion of an abstract model, and as the earlier discussion of that notion made plain, providing an account of the classification of models as more or less abstract is no trivial matter. There are also a good number of difficult questions about how abstract laws function, how precisely they should be understood, and what epistemological status they have.99 The hope is, nonetheless, that the framework laid out in this paper will help us as we grapple with such questions about idealization, abstraction, and the implications of their ubiquity for our philosophical understanding of the sciences.* Martin R. Jones Department of Philosophy Oberlin College
[email protected]
REFERENCES Armstrong, D. M. (1978). A Theory of Universals. Volume II: Universals and Scientific Realism. Cambridge: Cambridge University Press. Armstrong, D. M. (1983). What is a Law of Nature? Cambridge: Cambridge University Press. Ayer, A. J. (1956). What is a Law of Nature? Revue Internationale de Philosophie 10, 144-165. Carnap, R. (1970). Theories as Partially Interpreted Formal Systems. In: B. A. Brody (ed.), Readings in the Philosophy of Science, pp. 190-199. Englewood Cliffs, NJ: Prentice-Hall. Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon Press. Cartwright, N. (1989). Nature’s Capacities and their Measurement. Oxford: Clarendon Press. Cartwright, N., and Mendell, H. (1984). What Makes Physics’ Objects Abstract? In: J. T. Cushing, C. F. Delaney and G. M. Gutting (eds.), Science and Reality, pp. 134-152. Notre Dame: University of Notre Dame Press. Chilvers, I., ed. (1990). The Concise Oxford Dictionary of Art and Artists. Oxford: Oxford University Press. Chomsky, N. (1965). Aspects of the Theory of Syntax. Cambridge, Mass.: The M.I.T. Press. Cohen, I. B. (1985). The Birth of the New Physics. Revised and updated. New York: W. W. Norton & Co.
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It is, perhaps, especially important to note that the account allows for abstract quasi-laws in the context of Cartwright’s views, for we might expect a law statement which is abstract in part because the concept of φ-ness is an abstract concept to have a wide range of application, and thus, according to Cartwright, expect it to be false. 99 Some of those questions are addressed elsewhere in this volume. See also Cartwright (1989), chapter 5, for much more on these issues. * Thanks for helpful conversations to Mauricio Suárez, Mathias Frisch, Nancy Cartwright, Paul Teller, R.I.G. Hughes, Paddy Blanchette, Paolo Mancosu, Dorit Ganson, and Peter McInerney.
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Drake, S., and Drabkin, I. E., translators and annotators (1969). Mechanics in Sixteenth-Century Italy: Selections from Tartaglia, Benedetti, Guido Ubaldo, & Galileo. Madison: The University of Wisconsin Press. Dretske, F. (1977). Laws of Nature. Philosophy of Science 44, 248-268. Earman, J. (1986). A Primer on Determinism. Dordrecht: D. Reidel. Frisch, M. (1998). Theories, Models, and Explanation. Ph.D. dissertation: University of California, Berkeley. Giere, R. N. (1988). Explaining Science: A Cognitive Approach. Chicago: The University of Chicago Press. Granger, R. A. (1995). Fluid Mechanics. New York: Dover. Hempel, C. G. (1969). Logical Positivism and the Social Sciences. In: P. Achinstein and S. F. Barker (eds.), The Legacy of Logical Positivism: Studies in the Philosophy of Science, pp. 163194. Baltimore: The Johns Hopkins Press. Jones, M. R. (forthcoming a). Models and the Semantic View. Jones, M. R. (forthcoming b). Models and Idealized Systems. Lewis, D. K. (1983). New Work for a Theory of Universals. Australasian Journal of Philosophy 61, 343-377. McMullin, E. (1985). Galilean Idealization. Studies in the History and Philosophy of Science 16, 247-73. Niiniluoto, I. (1998). Verisimilitude: The Third Period. British Journal for the Philosophy of Science 49, 1-29. Nowak, L. (1992). The Idealizational Approach to Science: A Survey. In: J. Brzeziński and L. Nowak (eds.), Idealization III: Approximation and Truth, pp. 9-63. Amsterdam: Rodopi. Putnam, H. (1979). What Theories Are Not. In: Mathematics, Matter and Method: Philosophical Papers, vol. 1, pp. 215-27. 2nd edition. Cambridge: Cambridge University Press. Suppe, F. (1967). The Meaning and Use of Models in Mathematics and the Exact Sciences. Ph.D. dissertation: University of Michigan. Suppe, F. (1972). What’s Wrong with the Received View on the Structure of Scientific Theories? Philosophy of Science 39, 1-19. Suppe, F. (1974a). The Search for Philosophic Understanding of Scientific Theories. In: Suppe (1974b), pp. 3-241. Suppe, F., ed. (1974b). The Structure of Scientific Theories. Urbana: University of Illinois Press. Suppe, F. (1989). The Semantic Conception of Theories and Scientific Realism. Urbana: University of Illinois Press. Suppes, P. (1957). Introduction to Logic. Princeton: Van Nostrand. Suppes, P. (1960). A Comparison of the Meaning and Uses of Models in Mathematics and the Empirical Sciences. Synthese 12, 287-301. Suppes, P. (1967). What is a Scientific Theory? In: S. Morgenbesser (ed.), Philosophy of Science Today, pp. 55-67. New York: Basic Books. Suppes, P. (1974). The Structure of Theories and the Analysis of Data. In: Suppe (1974b), pp. 266-283. Teller, P. (2001). Twilight of the Perfect Model Model. Erkenntnis 55, 393-415. Tooley, M. (1977). The Nature of Law. Canadian Journal of Philosophy 7, 667-698. van Fraassen, B. C. (1970). On the Extension of Beth’s Semantics of Physical Theories. Philosophy of Science 37, 325-339. van Fraassen, B. C. (1972). A Formal Approach to the Philosophy of Science. In: R. Colodny (ed.), Paradigms and Paradoxes, pp. 303-366. Pittsburgh: University of Pittsburgh Press. van Fraassen, B. C. (1980). The Scientific Image. Oxford: Clarendon Press. van Fraassen, B. C. (1987). The Semantic Approach to Scientific Theories. In: N. J. Nersessian (ed.), The Process of Science, pp. 105-124. Dordrecht: Martinus Nijhoff. van Fraassen, B. C. (1989). Laws and Symmetry. Oxford: Clarendon Press.
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David S. Nivison STANDARD TIME
The clock strikes twelve, and the local siren verifies its accuracy. I say it’s noon. But of course, when I reflect a moment, I know it isn’t. I know this, at least, unless I happen to be located on one of four lines not even marked on the map of the country, most points of which are probably uninhabited. I know it is not really noon, if by noon I mean midday, literally, when the sun is on the meridian. We used to do it that way, until we had trains, and a problem about schedules. Now we agree to a fiction, which enables the schedules to work, and each of us wears a small contraption on his wrist that automatically translates experienced temporal reality into the language of the fiction. This conventional “model” for business-day time is recent, deliberately adopted, and out in the open. Other models used to bring ordered sense into the world as we deal with it conceptually are not so recent, not deliberately adopted, and in some cases not recognized as fictions for centuries. In certain of these cases that especially interest me, the ordering schema is not thought of as a fiction at all, but continues to be thought of as ideally true, even though it comes to be seen that a few technical adjustments are needed to enable people to use the ideally true schema in dealing with the messy world they live in. We, looking back at these adjustments, sometimes can see them as halting steps in the development of what we call “science.” But sometimes they seem actually to block scientific discovery. Trying prudently to speak of something I am familiar with, and hoping to find something manageably simple, I will look at two problems in ancient Chinese calendar science. Or “science.”
I The first problem is not specifically Chinese. It must arise for any people, already in pre-historic times, if they try to organize their activities short-term to
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 219-231. Amsterdam/New York, NY: Rodopi, 2005.
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accord with the observed sequence of lunar months, but longer-term to accord with the passing of seasons and years, which depend on the sun. How many seasons in a year? In our (and China’s) latitude, four obvious ones, naturally matched with the solstices and equinoxes. (A tropical civilization might have noticed zenith crossings instead, getting different calendar concepts.) The Chinese understood the concepts before they had instruments that could determine the exact times of these events. They noticed that from winter solstice to winter solstice was more than 365 days, so they called it 366; later they saw that it is approximately 365 1/4. The solstices and equinoxes were taken (as in the ancient West) as the midpoints of the seasons; and since they are more or less equally spaced, it was assumed that the order of nature must be that they are exactly equally spaced. It was noticed that the moon moves through a band of stars, back to its original position and a little more, in a month, and the sun, which is up there too, is opposite the moon when the moon is full; so the sun must be doing the same thing, in the course of a year. A simple crude method was devised for determining the position of the sun against the (by day invisible) stellar background (one does it by mapping the zodiac – this could be done by noting constellations near successive full moons – and then noticing what stars are on the meridian before dawn and after sunset). In this way one can see that there must be four ideal points (wei) that the sun passes through as it moves around the zodiac, that mark the transitions from one season to another. Since there are 365 1/4 days in a year, one can divide the zodiac into 365 1/4 “degrees” (du, “step”), each being the distance the sun travels in a day. How many du are there from one wei to the next? The Huainanzi (ca. 130 B.C.), in its chapter on astronomy, says there are exactly 91 5/16 (chapter 3, at paragraph 12): and the system it describes implies that this must also be the exact distance between the sun’s locations at the solstices and equinoxes, and therefore (since a du is a solar day’s run) that the solstices and equinoxes divide the year temporally into fourths (approximately, resolved to whole days).1 The system in the Huainanzi divided the year into 15-day intervals, with an extra day at the beginning of each season. One more day is needed in a normal year, and it was placed at midsummer. This suggests that the Chinese were aware that the day-count from spring equinox to summer solstice is longer than a quarter of the year. (At the time of the Huainanzi it was three days longer.) They apparently recognized the inequality, but minimized it in their system. So the system is false. The Chinese, by the time they were capable of this degree of precision, must have known it was false. They didn’t care. It served their purposes well enough; it caught their idea of the order of the heavens, and so it remained ideally true. ⎯⎯⎯⎯⎯⎯⎯ 1
See Major (1993).
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What were their purposes? Back to the basic problem: how to relate the lunar calendar to the solar year. They did this (I think) as follows: (1) The moon moves around the zodiac in more than 27 days; so call it 28. Therefore, divide the zodiac (calling it 365 du) into 28 more or less equal spaces, or “lodges,” xiu, one for each night. (And forget that the moon is not always out at night.) Most will be 13 du (1 du is a sun’s day’s run). One must be 14 du. Let the xiu in which the sun is located at the winter solstice be the biggest one, and let the location of the sun at solstice be the midpoint of this xiu. The xiu had names, and rough asterism equivalents. This 14-du xiu is the one later called “Xu,” “Void,” in what we call Aquarius. (The solstice precesses, at about one du in 70 years, and the Chinese didn’t figure this out until about 400 A.D.; so this system is early: it would have been true around 2000 B.C.)2 (2) The handle of the Big Dipper is observed to point at a particular time of night, e.g., midnight, in different directions as the year progresses, its midnight pointing moving around the sky in the course of the year from left to right – clockwise, please note. So let it be the hand of a clock, created by imagining the zodiac projected on the horizon, in such a way that at winter solstice the handle’s pointing (obviously interpretable) is taken to be due north at an ideal dusk, i.e., half way from noon to midnight, and due north is made to be the middle of Xu-on-the-horizon. The relation in celestial geometry between the Dipper and the actual zodiac is always the same, of course. The point – roughly, Scorpio – to which the handle was seen as pointing in the actual zodiac was the point the sun reached at the autumn equinox; therefore that point in the horizon projection was where the handle (moving clockwise) pointed at ideal dusk at the spring equinox; so spring was “east.” (3) The moon and the sun move around the zodiac in the opposite direction (i.e., counter-clockwise, in this conception), but the moon moves much faster, the stroboscopic effect being to divide the zodiac roughly into twelfths. So let the horizon-“zodiac” be re-divided into exact twelfths. These were called chen, and were so drawn that the midpoint of the first chen was the midpoint of horizon-Xu. Thus the time-span for the handle to move from one chen to the next is a twelfth of the year, and can be thought of as a solar “month.” (Some ancient Chinese texts that have been taken to be talking about months are really talking about “months.”) A “month” is longer than a lunar month, so from time to time an extra lunar month had to be inserted, at the end of a year or earlier, to keep up the fiction that there are twelve of them. ⎯⎯⎯⎯⎯⎯⎯ 2
For reconstructions of early Chinese lunar zodiac systems, see Nivison (1989).
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(4) If one wished to do it earlier, the rule was this: If at the beginning of a lunar month the Dipper’s handle is pointing exactly at the boundary between two chen, then that lunar month is intercalary. Why? What does this mean? (5) Think now of the calendar of a normal 365-day year. It can be thought of as divided into approximate twelfths (pace whole numbers) of 30 or 31 days, and each of these again divided in two, into 15-day or 16-day periods (called (solar) weather-intervals, qi jie), which are given names, of seasonal weather conditions and natural phenomena or farmer’s activities. The first day of a solar “month” period is called a jie qi; the first day of the next 15-day or 16-day interval is called a zhong qi, or “qi-center.” (Or we can think of a qi-center as the corresponding ideal zodiac point.) The winter solstice day is the first qi-center, and there are eleven others spaced around the year, these being the middle days of their correspondingly numbered solar “months.” Now, an equivalent rule is that a regular-numbered lunar month must contain the qi-center day having that number, and if it has no qi-center day it is intercalary. The two rules are stated in the same sentence by Kong Yingda (574-648 A.D.) (Commentary to Zuo zhuan, Xiang Gong 27.6 = 12th month). Putting them together implies conceiving of the clockwise chen pointing of the Dipper’s handle as leading the sun’s corresponding counter-clockwise apparent movement around the zodiac by half a solar “month” (so if one still wants to say that the handle points due north at dusk at the winter solstice, one must suppose that the solstice had precessed to a point about 15 du short of the middle of Xu; this would have been true around 900 B.C.). Using just the qi-center rule, and the explicit concept “intercalary month” (run yue), gives this: say that the eighth month counting from the winter solstice month contains the eighth qi-center, and the next lunar month contains none; then that month is the “intercalary 8th month.” Seventeen centuries before Kong Yingda a slightly different but practically equivalent rule seems to be used. There are about 80 oracle-bone inscriptions giving day-by-day movements of the Shang royal army as it marched east to attack the “Ren Fang” in the Huai valley. All have day dates in the 60-day cycle; some have month dates; and a few have year dates, specifying the 10th-11th years of a king that the inscription style identifies as the last Shang king, Di Xin, requiring that the dates be in the first half of the – 11th century. I will select five dates in this inscription sequence that show that an intercalation has been made:3 ⎯⎯⎯⎯⎯⎯⎯ 3
See Chen (1956), pp. 301-304.
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10th year, 9th month, day 31 9th month, day 60 10th year, 10th month, day 31 11th month, day 60 10th year, 12th month, day 31 11th year, 1st month, day 34 The mean length of a lunar month is about 29 1/2 days, and classical calendar theory therefore stipulates that “long” (30-day) and “short” (29-day) months alternate, though this may not exactly correspond to astronomical fact. To make the correspondence work out in the long run, it is necessary to have an intercalary day, in the form of two 30-day months in succession, about twice in three years, amounting to less than a quarter of a day in a four-month period. But here, if there is just one “9th” month, there must be five extra days in the four months 9th through 12th, twenty times the norm; and in addition one or more months must be anomalous 31-day months. Or else the 9th month must begin with day 31, instead of day 34, 35, or 36 (since the first month of the next year must begin with day 32, 33, or 34). And then the 9th month would have to have 33 days. Therefore one of these month numbers represents two lunar cycles. The only possibility is the “9th month”; and from this and other evidence the “10th year” can be identified as 1077 B.C. (Thus the first year of Di Xin must be 1086 B.C.)4 Standard tables then show the rest of the story: If the years were beginning, Shang-style, with the post-winter-solstice month, months 8 through 12 run as follows; supplied sun locations are right ascension (approximately)5: Tung (1960)
Zhang (1987)
month
days 1st day
cycle no.
sun at
qi center
days
1st day
cycle no.
sun at
qi center
8th 9th 9th 10th 11th 12th
30 29 30 29 30 29
35 5 34 4 33 3
123 153 180 208 238 270
150 — 180 210 240 270
29 30 29 30 29 30
5 Aug 3 Sep 3 Oct 1 Nov 1 Dec 30 Dec
36 5 35 4 34 3
124 153 181 208 239 270
150 180 — 210 240 270
4 Aug 3 Sep 2 Oct 1 Nov 30 Nov 30 Dec
⎯⎯⎯⎯⎯⎯⎯ 4
Nivison (1983), pp. 501-2. (E. L. Shaughnessy contributed to this discovery.) In this table, right ascension is computed using Ahnert (1960). Ecliptic locations for the sun (and planets) can be obtained from Stahlman and Gingerich (1963). The table assumes that a qi-center day is a day when the sun reaches an ecliptic location that is a multiple of 30. 5
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The system prima facie seems to be surprisingly sophisticated: what should count as a qi-center is a day when the sun is exactly at a solstice or equinox or one twelfth of the zodiac removed therefrom. It may be, however, that the Chinese simply determined by observation the day of the autumn equinox (i.e., for us, sun at 180 degrees), and then counted off sequences of 91, 91, 92, 91 days, to get the other solsticial and equinoctial points, for working purposes. Adding 91 days to the autumn equinox date for 1077 B.C. would make the following winter solstice date two days late. Such a system seems to be required by the dating of events in the Zhou conquest era about four decades later. For example, if (as I argue) the Zhou victory over Shang was in the spring of 1040 B.C.,6 on a jiazi (1) day (the date should be April 18th), supposing the assumed winter solstice to have been two days late makes the day be the first day of the Qingming solar weather period. This seems to be what is said in the last line of Ode 236 (“Da Ming”) in the Shi jing. It also makes day wuchen (5), the date of King Cheng’s winter sacrifice at the end of the year in the “Luo Gao” chapter of the Shang shu, coincide with the eve of the winter solstice at the end of 1031 B.C. We need not suppose that the Chinese did not know that they were in error; it is more likely that their “winter solstice” date was a standard-time date. In any case, it is one of the “9th” months that lacks a qi-center – here, the equinox. As far as I am aware, the term run (“intercalary”) does not yet appear in the language. The “intercalation” rule used seems to be, simply, “the nth month must contain the nth qi-center; if a lunar month should contain the nth qi-center and does not,” then either “let the designation ‘nth month’ continue through the next lunar month” (satisfying Tung’s data), or “withhold the name ‘nth month’ until the next lunar month” (satisfying Zhang’s data). The evidence is thin. It is easy to show that such a system was not always used. (There are inscriptions that bear dates “13th month,” and even “14th month,” suggesting much sloppiness.) I have been able to show a plausible case, however, for the hypothesis that the concept of a zodiac existed, divided both into approximately equal twenty-eighths and into approximately equal twentyfourths, as early as the – 3rd millennium (Nivison 1989, pp. 203-218). And I must challenge anyone to suggest another reason why the Chinese would have done this. I have been constructing my own hypothetical model of a Chinese ideal model that would explain what evidence I have. Let me suppose that I have it right. Can I now ask, did the Chinese know that their system was not a true description of reality? It is not obvious that the question makes sense. The Chinese had a job to do, and step by step invented a system to do it, probably without thinking of it as invention. The strange entities it required, wei, chen, qi⎯⎯⎯⎯⎯⎯⎯ 6
Nivison (1983) agues that the conquest date was 1045 B.C. I have found errors in this argument. In recent conference papers and other unpublished writing I argue for 1040 B.C.
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centers, have about as much empirical reality as acupuncture points. (If I developed the set of conceptions farther, I would have to add an imaginary backward-revolving “planet.”) The system worked, on the whole probably better than our own plane and train schedules. But of course it is possible to ask whether they realized that postulated magnitudes were not always accurate. “Long” and “short” months do not succeed each other with invariable regularity. “Dusk” is usually not halfway between astronomical noon and midnight. There are those who think that “dusk” was always observed dusk, that a lunar month was supposed to begin always when it was scientifically determined (as well as possible) that the sun and moon were in conjunction, or that lunar phase terms (used in Western Zhou dates; a problem I omit) always picked out the moments in time that corresponded to their literal meaning. I do not, because it seems obvious to me that without a considerable degree of definitional simplification, the systems the Chinese were constructing to do what they needed to do would have been impossibly complicated. Did they know that they were “falsifying” reality? The evidence before me tells me that they must have. And they could hardly have dreamed these things up unless they were at least as clever as that.
II I move on to my second problem, which has more nearly the geschmack of science. This is the problem of the period of Jupiter. I have been looking at a system that did, when conscientiously applied, serve to accomplish a simple practical objective: to insert an extra lunar month in the calendar when the lunar and solar calendars got sufficiently out of line, without waiting until the end of the year. Jupiter presents a quite different problem: its movement was at one time thought to be so regular, long term, that one could base a calendar on it to give a system of absolute dating through past and future time, to keep track of the normal system of political dating (in which, e.g., 720 B.C. is the fifty-first year of King Ping of Zhou, or the third year Duke Yin of Lu, or . . .). This didn’t work. The system was amended, and the amendment didn’t work either. But both the original system and the amendment were clung to long after it must have been realized that they didn’t work. One has to ask what’s going on. Liu Xin (d. 23 A.D.) was a kind of Chinese polymath – historian, astronomer, metaphysician, cosmologist, bibliographer, and dismally unsuccessful politician (this did him in). He was perhaps the first historian anywhere to try to pin down dates of events in the remote past by recalculating astronomical phenomena referred to in old texts. One of these was a paragraph in a book called the Guoyu, “Dialogues of the States,” an anonymous “history” consisting mostly of long conversations
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between kings, dukes, ministers, etc., probably compiled in the – 4th century. The paragraph in question (“Zhou Yu” 3.7) describes certain celestial events in the 11th century B.C., and I would argue that it was based on some calculations made six centuries later, in the early – 5th century, giving data that were therefore wrong. But Liu took it at face value. This paragraph contains a rundown of the zodiac positions of Jupiter, the sun and the moon, etc., on the day when King Wu of Zhou launched his victorious campaign against the Shang kingdom. The date of this event was, and has remained, controversial. Liu attempted to settle the matter scientifically, by astronomy (getting a date that was about eighty years too early). Along with this effort, he worked out a mathematical system of positional astronomy, one that could be used to calculate the position of any planet at any time in the past. I am concerned with his rule for Jupiter. The rule makes a small improvement in a piece of general knowledge about Jupiter. The Chinese called Jupiter “sui xing,” the “year star,” because it was supposed to move, on the average, the equivalent of one zodiac space a year, completing a circuit of the sky in twelve years. Liu’s rule in effect said that Jupiter actually “jumped a space” (chao-chen) every twelve such twelve-year cycles, i.e., that it traversed 145 spaces in 144 years. Liu is to be commended for seeing that the popular view was wrong, but he was wrong himself, because the actual “jump” is about one in every seven cycles.7 I am interested in where he got his rule, and (perhaps the same question) why this wrong rule satisfied him. All I do (or can do) is to give you a possible explanation. It is the best one I can think of. Even to be aware that the popular 12-year rule was wrong, Liu, or someone before him, must have had records thought to be reliable, mentioning or implying Jupiter’s zodiac position in some identifiable year many centuries earlier. For then, simple arithmetic, together with noticing Jupiter’s current location, ought to show that the cycle could not be an exact 12 years, and ought to show at once exactly what it really is. And of course, if the record were wrong, albeit believed to be right, then one’s arithmetic would give a wrong answer. I propose that this is exactly what happened. But the record in question was one that lay buried in the tomb of King Xiang of the state of Wei from 299 B.C. until 281 A.D. So if I am right, Liu’s rule was “discovered” (shall we say) all of three centuries before Liu’s own time. Here things get controversial because the record is the so-called “Bamboo Annals,” Zhushu jinian, which many take to be a Ming Dynasty fake (of perhaps five centuries ago). It purports to be a chronicle covering about 2000 years, with exact dates of events, down to 299 B.C. Recent work, some of it by Edward Shaughnessy and some of it mine,
⎯⎯⎯⎯⎯⎯⎯ 7
For Liu Xin’s mathematics for Jupiter, see Sivin (1969), p. 16.
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proves, I think, that it is not a fake, though most of the dates in it prior to 841 B.C. are at least slightly wrong.8 This chronicle records a conjunction of the planets in the so-called “lunar lodge” Fang, about at Antares, in the 32nd year of the last Shang king, Di Xin, i.e., (according to the Annals) in 1071. Fang is the middle space in the Jupiter station Dahuo, “Great Fire,” station 11 of the twelve; one of the planets has to be Jupiter; so the Annals says that Jupiter was in Dahuo in 1071. But the real conjunction must have been the one in May 1059 B.C., when the planets clustered in Chunshou, “Quail’s Head,” which was station 7.9 This false datum must have been trusted in Wei in the late 4th century B.C. The Annals also says that the Jin state, which Wei succeeded, began in the 10th year of King Cheng of Zhou, a date converting to 1035 B.C. (in the Annals system, which dates Cheng too early) – when (since the 12-year rule works in the short run) Jupiter would also be in Dahuo. When Ying, Duke of Wei, proclaimed himself King Hui-cheng, he took the year 335, just seven centuries later, as his first year as king, according to the Annals. Further, King Huicheng’s successor King Xiang thought so highly of the Annals that it seems he had it buried with him. We read, moreover, in another part of the Guoyu (“Jin Yu” 4.1) that Jupiter was in Dahuo when Jin was first enfeoffed. (Actually Jupiter was in Dahuo in late 1032 and in 1031, not 1035.) So I infer that it was believed in high places in Wei in the late 300’s B.C. – on the basis of a text that probably was thought of as an official Jin-Wei state chronicle – that Jupiter was in Dahuo in 1035 B.C. But anyone watching the sky in the year exactly 12 × 60 years after 1035, i.e., in 315, would see that Jupiter was not in Dahuo, but was five stations farther on. Simple arithmetic would show at once that Jupiter’s cycle was not exactly 12 years. 12 × 60 is 144 × 5, and in that many years, it would seem, Jupiter had traveled 5 + (144 × 5) stations, i.e., in each 144 years it had traversed 145 stations. If this ratio, revealed by text and observation, were accepted, then King Xiang could sleep in peace: his state chronicle was accurate, and using it had enabled the scientists of the day to get their latest results. Or so I suppose. For this is exactly Liu Xin’s formula. And this is the best explanation I can think of, of where he might have gotten it. But, necessarily, indirectly: Liu was Han court bibliographer, and has left a famous catalog of the imperial library, which was the library. If there had been a copy of the Bamboo Annals above ground that he knew about, he would have listed it and would have read it; but he did not list it. So if this is his ultimate source, the rule must have been passed on among astronomers down to Liu’s time. But here there is another puzzle, ⎯⎯⎯⎯⎯⎯⎯ Nivison (1983); Shaughnessy (1986). For a text and translation of the Bamboo Annals, see Legge (1865), “Prolegomena,” pp. 105-183. (Legge usually converts year-dates in the Annals to modern calendar dates that are one year late.) 9 The actual conjunction is identified by Pankenier (1983). 8
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because every astronomer or astrologer before Liu whose beliefs are known – including pointedly Sima Qian, historian and court astrologer to Emperor Wu Di a century before Liu – says that Jupiter’s cycle is 12 years. I tentatively infer from this a deeper truth about Chinese science, that must distinguish it both from the artificiality of our modern “standard time” convention and from our modern ceteris paribus understanding of scientific laws, ideal-model-wise true, literally mendacious. It seems to me that in the ancient view of things (Chinese anyway), there was a set of ideal truths about the world, one being “Jupiter cycle, 12 years,” and another being “one year, 12 ‘months’.” These were not recognized as fictions, consciously adopted to simplify reality into something one could work with. They were naïve ordering conceptions of how the world works, that were eventually and gradually recognized to be not exactly how it works, but then kept on being cherished anyway, as somehow really capturing the underlying order of things. They did not cease to be true merely because the specialist had to use his little rules of thumb, like the 144:145 ratio, or the qi-center convention, to adjust the ideal rule to messy empirical reality. Thus one could cling to the ideal even after one saw that it didn’t work. (The simple 12-year concept persisted in a bizarre form: the twelve chen, used to count off months, were also used to count off two-hour segments of the day (the Dipper’s handle shifts its pointing clockwise in the course of the night). So a natural extension of use was to use them to count off years. The Dipper’s handle doesn’t point to the next chen in the next year; but Jupiter was thought to occupy (ideally) the next of twelve “stations” (ci) in the next year, counterclockwise; and the twelve stations were in one-one correspondence with the twelve chen, numbered in reverse order in the horizon projection of the zodiac. So an imaginary “Jupiter” was posited, as a chen-system shadow of an ideal real Jupiter, moving backwards chen-wise in an exact 12-year cycle. This concept continued to be used for centuries after it was known that the real Jupiter cycle is not 12 years.) It would follow that, usually, scientific progress lags not a little behind what could have been scientific discovery. I have probed what I take to be a case in point in my article “The Origin of the Chinese Lunar Lodge System” (1989). The Chinese appear to have worked out a lunar zodiac in the – 3rd millennium, as the basis of their calendar, locating in it the solstice and equinox points, which they thought to be eternal. After centuries, of course, it didn’t work. When this happened, instead of simply scrapping it and starting over – perhaps thereby being forced to ask themselves why they had to scrap it – they simply tinkered with it so that they could stop worrying about it, until it became something usable only by astrologers. Throughout these distortions, however, the scheme continued to be organized on a location of the winter solstice that had not been valid since about 2000 B.C. A sufficiently astute astronomer in the
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4th century B.C., if he hadn’t looked at the problem in this way, would have found that he had data in his hands that would virtually have forced on him the discovery of the precession of the equinoxes – a discovery it took the Chinese another seven centuries to make (1989, pp. 214-16). *
*
*
This is an essay in a book addressed to scientists and philosophers of science, and a very select readership even of that fraternity, one that may not include a single sinologist. Honesty requires that I admit that I have been wading in controversial waters. My work on the lunar zodiac is published (in an astronomical-archaeological, not sinological, symposium), but not generally accepted yet. My limited analysis of Liu Xin’s work is not yet published elsewhere, except as a conference presentation to a possibly uncomprehending orientalist audience. My views on the relative reliability of the Bamboo Annals would probably be scoffed at by many scholars in China (and maybe elsewhere) who consider themselves experts. Other historians of Chinese science may (at the least) question my claim that intra-year intercalation was practiced in China long before 500 B.C. You my readers should be warned. David S. Nivison Department of Philosophy Stanford University
Appendix Professor Kenichi Takashima (University of British Columbia) has called to my attention an oracle bone inscription-pair found in Shang Chengzuo, Yin qi yi cun (no. 374; copied into Shima (1977), 398.2): (1) qui you zhen ri xi/ye you shi wei nuo Divination on day quiyou (10): The sun is eclipsed at night; this is [a sign of divine] approbation. (2) qui you zhen ri xi/ye you shi fei nuo Divination on day quiyou (10): The sun is eclipsed at night; this is not [a sign of divine] approbation. The fifth graph in each line, a crescent moon, can be resolved sometimes as yue (“moon,” “month”), but here one expects xi (in later Chinese usually “evening,” but in oracle texts always “night”), or possibly ye (“night”). The inscription style, in Professor Takashima’s opinion, places it in socalled Period IV, or five periods (as sorted out by the late Tung Tso-pin), Period
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V being inscriptions that belong to the last two Shang reigns, Di Yi and Di Xin. Previous work by E. L. Shaughnessy and myself shows that the Di Xin reign began in 1086, and the Di Yi reign probably in 1105. If my “standard time” hypothesis is correct, “night” refers to the twelve hours from 6:00 p.m. to 6:00 a.m., approximately, and in all seasons, even when it is daylight for some time after 6:00 p.m. The inscription would be satisfied, then, by a solar eclipse with the following characteristics: (a) It must be on a quiyou day, no. 10 in the 60-day cycle. (b) It should be total or maximal in the area of the Shang capital at Anyang after 6:00 p.m. (c) Thus it must be dated some time after the spring equinox and some time before the autumn equinox; (d) and it must terminate at sunset about 1000 miles or less east of Anyang. (e) Finally, to be in Period IV, it must occur in some year in the half-century preceding 1105. An eclipse of this description (and the only one) would be no. 211, –1123 V 18 (18 May 1124 B.C.) in Oppolzer (1887), starting (1887, Tafel 5) in the Atlantic, west of Africa and just below the equator, at about 14 degrees west longitude, and terminating in eastern Korea, about 129 degrees east longitude, with a noon point just north of the Persian Gulf at 8 hours 32.6 minutes WT. The Julian day number is 131 1020, which is a quiyou day.10 The spring equinox in 1124 B.C. was March 31; the latitude of the untergang was about 37 degrees north. This does not give totality in or near Anyang after 6:00 p.m.; I estimate about 5:45 p.m. But this may be close enough; and well after 6:00 p.m. one would probably still notice the “bite” of the obscuring moon. Furthermore, perhaps a post-idealday’s-end eclipse totality would have been reported to the capital from further east. Two cautions are required, however. (1) It is at least imaginable that the divination was made days after the eclipse; this would invalidate the date used in my analysis. (2) As noted, the graph here translated “at night” has other readings, not only (ye or xi) “night” but also (yue) “month” or “moon.” So the meaning could be “eclipses of the sun and moon have occurred,” referring perhaps to an eclipse (at some time in the recent past) of the sun (at whatever hour), followed by an eclipse of the moon at the next syzygy (though I think this reading is unlikely). So this inscription-pair is hardly a confirmation of my “standard time” hypothesis; but it is difficult to think of any other plausible sense for the words “the sun is eclipsed at night” (ri xi/ye you shi) – if that is what the inscription ⎯⎯⎯⎯⎯⎯⎯ 10
Julian day numbers can be converted to Chinese sixty-day cycle numbers by dividing by 60, and subtracting 10 from the remainder (or from the remainder plus 60). (Julian day numbers are given in Tung (1960) and in Stahlman and Gingerich (1963).)
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says. One might try for an eclipse, even only partial, that would be seen in Anyang, perhaps at some other season, as developing before sunset or dwindling after sunrise, with an appropriate date; but I have found none. (If the inscription could be in Period II, then no. 81 (= –1175 VIII 19) in Oppolzer (1887) is almost as satisfactory as no. 211.) I am offering this problem for further study. One can see its relevance to the problem of an ideal invariant beginning point of night, in diurnal time. The dipper-dial logically requires a fixed evaluation time each day: for it is said to move exactly one du a day, and it moves through approximately equal spaces. If that fixed time happened to be before or after sunset, the location and time would have had to be deduced. The question is whether the required fixed time was conceived as an ideal “standard time” beginning of “night.”
REFERENCES Ahnert, P. (1960). Astronomisch-chronologische Tafeln für Sonne, Mond und Planeten. Leipzig: J. A. Barth. Chen, M. (1956). Yinxu buci zongshu (A comprehensive account of Shang oracle inscriptions.) Peking: Kexue Chubanshe. Legge, J. (1865). The Chinese Classics. Vol. III: The Shoo King, or Book of Historical Documents. London: Henry Frowde. Major, J. (1993). Heaven and Earth in Early Han Thought. Albany: State University of New York Press. Nivison, D. (1983). The Dates of Western Chou. Harvard Journal of Asiatic Studies 43, 481-580. Nivison, D. (1989). The Origin of the Chinese Lunar Lodge System. In: A. F. Aveni (ed.), World Archaeoastronomy, pp. 203-218. Cambridge: Cambridge University Press. Oppolzer, T. R. v. (1887). Canon der Finsternisse. Vienna: K. Gerold’s Sohn. Pankenier, D. W. (1983). Astronomical Dates in Shang and Western Zhou. Early China 7, 2-37. (Manuscript date, 1981-82). Shaughnessy, E. L. (1986). On the Authenticity of the Bamboo Annals. Harvard Journal of Asiatic Studies 46, 149-80. Shima, K. (1977). Inkyo Bokuji Sorui (A concordance of Shang oracle inscriptions). Tokyo: Kyuko Shoin. Sivin, N. (1969). Cosmos and Computation in Early Chinese Mathematical Astronomy. Leiden: E. J. Brill. Stahlman, W. D. and Gingerich, O. (1963). Solar and Planetary Longitudes for Years –2500 to +2000 by 10-Day Intervals. Madison: The University of Wisconsin Press. Tung, T.-P. (Zuobin, D.) (1960). Chronological Tables of Chinese History. Hong Kong: Hong Kong University Press. Zhang, P. (1987). Zhongquo Xian-Chin she libiao (A table of dates for Chinese pre-Chin history). Jinan: Qi-Lu Shushe.
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James Bogen and James Woodward EVADING THE IRS
I ‘IRS’ is our term for a view about theory testing originated by members and associates of the Vienna Circle. Its leading idea is that the epistemic bearing of observational evidence on a scientific theory is best understood in terms of Inferential Relations between Sentences which represent the evidence and sentences which represent hypotheses belonging to the theory. The best known versions of IRS (and the ones we concentrate on in this paper) are HypotheticoDeductive and positive instance (including bootstrapping) confirmation theories. It goes without saying that such accounts, along with the problems they generate, have exerted a dominant influence on philosophers who study the epistemology of science. We maintain that the epistemic import of observational evidence is to be understood in terms of empirical facts about particular causal connections and about the error characteristics of detection processes. These connections and characteristics are neither constituted by nor greatly illuminated by considering the formal relations between sentential structures which IRS models focus on. We argue that by taking them seriously, you too can evade the IRS. We have argued elsewhere1 that theory testing in the natural and social sciences is typically a two-stage process and that the use of observational evidence belongs primarily to the first stage. In this stage data are produced and interpreted in order to draw conclusions about what we call phenomena. This is usually a matter of considering a number of competing claims about the phenomenon under investigation and using the data to decide which of those claims is most likely to be correct. In the second stage, theoretical claims are confronted with conclusions about phenomena reached in the first stage. Some examples of data are records of temperature readings used to determine the melting point of a substance, scores on psychological tests used to investigate ⎯⎯⎯⎯⎯⎯⎯ 1
Bogen and Woodward (1988); Woodward (1989); Bogen and Woodward (1992).
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 233-267. Amsterdam/New York, NY: Rodopi, 2005.
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memory processing, bubble chamber and spark detector photographs used to detect particle interactions, drawings of prepared tissue viewed under microscopes used to determine the structure of neural systems, and the eclipse photographs Eddington, Curtis, and others used to calculate the deflection of starlight by the sun. Some examples of phenomena are the melting points calculated from the temperature readings, the widespread and regularly occurring features of memory processing investigated through the use of psychological tests, the deflection of starlight, etc. Data are effects produced by elaborate causal processes that may involve the operation of the human perceptual and cognitive systems as well as measuring and recording devices and many other sorts of natural and manufactured non-human systems. We think the epistemic importance of the human perceptual system in data production depends upon its influence on the reliability of the procedures by which the data are produced and interpreted. In this respect there is no epistemically interesting difference between human perception and any other factor which influences reliability (Bogen and Woodward 1992). The epistemic significance of data depends upon whether they possess features through which the phenomena of interest can be studied. It depends also upon whether they can be inspected and analyzed by investigators who wish to use them. The production of data meeting both of these conditions usually requires the manipulation of highly transitory and unusual combinations of causal factors which do not naturally operate together in any regular way. In many cases these causal structures are idiosyncratic to highly unusual situations many of which are highly contrived and peculiar to the laboratory. In contrast, phenomena are typically due to the uniform operation of a relatively small number of factors whose operation does not depend upon the rare and often highly artificial settings required for data production. As a result, many phenomena are capable of occurring in a variety of different natural and contrived settings (Bogen and Woodward 1988, p. 319ff.). It is phenomena rather than data that scientists typically seek to explain and predict. We believe that in most cases, scientific theories are tested directly against phenomena rather than data. For example, Einstein’s theory of general relativity was tested against a value for the deflection of starlight, rather than the photographs from which the deflection was calculated. The electro-weak theory devised by Weinberg and Salam was tested against claims about a phenomenon (the occurrence of neutral currents) rather than against the bubble chamber and spark detector data on which those claims were based. The testing of Newton’s theory of universal gravitation involved such phenomena claims as Kepler’s and Galileo’s laws rather than the data used to investigate these phenomena (e.g., descriptions of pendulum and inclined plane experiments, astronomical records of the movement of the moon, etc.). The second stage of theory testing is the confrontation of theory with phenomena.
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We will use the term ‘observation sentences’2 in connection with the sentences (also called ‘protocol sentences,’ ‘evidence sentences,’ etc.) the IRS uses to represent empirical evidence. Although details vary and controversy abounds, the IRS literature tends to associate them with reports of what individual observers perceive. As will be seen in sections IV and V below, it is often very hard to see how to construct a sentence which both represents the photographs and other non-sentential evidence scientists often use as data, and also captures what is epistemically significant about them. Nevertheless, we assume the IRS notion of an observation sentence was meant to play something like the same role as our notion of data; both notions are meant to explain the role of empirical evidence in theory testing. Accordingly, we shall speak of observation sentences as “corresponding” to data, but with the caveat (to be illustrated in section IV) that the details of this correspondence are often quite unclear. By picturing theory testing as a one-step confrontation of theory with the evidence which “observation sentences” are meant to represent, the IRS ignores the two-tiered structure just sketched. And as the bulk of this paper will be devoted to suggesting, we think the IRS picture does not provide an adequate account of real world scientific reasoning from data to phenomena. Our own view is that with regard to the investigation of phenomena, the evidential value of data is assessed in terms of general and local reliability. As we use these terms, general reliability depends upon the long-run error characteristics of repeatable processes for data production and interpretation.3 We discuss it in section VII below. Generally reliable detection procedures may fail, and generally unreliable procedures may succeed in enabling an investigator to discriminate correctly in a particular case.4 Furthermore, some procedures used in one or a very few cases are not, or cannot be repeated as ⎯⎯⎯⎯⎯⎯⎯ 2
In this we depart from the IRS literature in which the term ‘observation sentence’ is used for natural language observation reports as well as their counterparts in first order logical languages. We emphasize that we are using the term only for the latter. 3 This is roughly the notion invoked by Alvin Goldman and other reliabilists. See, e.g., Goldman (1986), chs. 4, 5, 9-15 passim. However, unlike Goldman, we think, for reasons that will emerge in section IX, that the project of investigating the reliability characteristics of most human beliefforming methods and mechanisms is unlikely to be illuminating or fruitful. Rather we apply the notion of general reliability to highly specific measurement and detection procedures, or in connection with the use of instruments for particular purposes. Such procedures and uses of instruments often have determinate error characteristics that we know how to investigate empirically, while we suspect that this is not true of many of the methods or psychological processes that underlie belief formation. 4 For example, consider a technique for staining tissue to be viewed under a light microscope which (like golgi staining) tends to produce a great many artifacts. The staining technique may nevertheless occasionally produce preparations which are free from artifacts, or whose artifacts can be easily distinguished from real cell structures. In such cases a generally unreliable microscopic technique can be locally reliable, and recognizably so.
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would be needed to establish their long-term error characteristics. Local reliability has to do with single case performances of procedures, pieces of equipment, etc. We discuss this in section VIII. We will argue that neither general nor local reliability can be assessed by considering the data all by itself without considering the processes by which it was produced and interpreted. These processes are the loci of the empirical facts upon which both the local and the general reliability – and hence, the evidential value – of data often depends. The last section of our paper argues that IRS neglects and lacks the resources needed to deal informatively with these epistemically crucial factors.5
II As compared to the best studies by historians, sociologists, and anthropologists of science, the IRS literature contains little that can be easily recognized as belonging to actual scientific practice. While IRS analyses rely heavily on a logical formalism which is known by few and used by fewer practicing scientists, the mathematical formalisms natural scientists actually rely upon do little work in the IRS literature.6 More importantly many data consist of photographs, drawings, tables of numbers, etc., which are not at all sentential in form, and scientific hypotheses are almost always set out in languages which are very different from first order logic. In contrast, the versions of IRS we consider try to account for the evidential relevance of data to theoretical claims in terms of a confirmation relation (see section III below) characterized in terms of relations between sentences in a first order language. All of this is remarkable enough to raise questions about what motivates the IRS. The following motivational sketch is intended to indicate why this program might have seemed worth pursuing, and also to show that striking discrepancies between scientific ⎯⎯⎯⎯⎯⎯⎯ 5
The relevance of causal factors in assessing evidential significance is also emphasized in Miller (1987). While we find much that is valuable and insightful in Miller’s discussion, his account diverges from ours in important respects – in particular he tends to see inductive inference generally as a species of inference to the best explanation, while we do not. The evidential relevance of datagenerating processes and the limitations of formal accounts of evidential support are also emphasized in Humphreys (1989), a discussion we have found very helpful. 6 For an excellent and forceful characterization of the disparity between the literature of science and the literature of IRS-influenced philosophy of science, see Feyerabend (1985), pp. 83-85. Although we disagree with much of what Feyerabend says elsewhere we heartily endorse his idea in this passage that much of what occupies the IRS philosophers is an artifact of their own picture of science, and in particular, that much (Feyerabend would probably say “nearly all”) research in the philosophy of science “consists in proposing ideas that fit the boundary conditions, i.e., the standards of the simple logic” chosen by the logical positivists to represent scientific reasoning (p. 85).
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practice and its IRS depiction derive non-accidentally from its basic goals and strategies. Like many of its founders and proponents, Hempel saw the IRS as an alternative to the idea that scientific theories are not or cannot be tested objectively – that “the decision as to whether a given hypothesis is acceptable in the light of a given body of evidence” rests on nothing more than a subjective “‘sense of evidence,’ or a feeling of plausibility in view of the relevant data.” This, says Hempel, is analogous to the equally noxious idea that “the validity of a mathematical proof or of a logical argument has to be judged ultimately by reference to a feeling of soundness or convincingness.” Hempel thinks both ideas rest on a confusion of rational, objective, logical factors which can actually determine whether the available evidence warrants the acceptance or rejection of a scientific hypothesis with subjective psychological factors which may influence scientific belief. To disentangle them we need purely formal criteria for confirmation of the kind deductive logic provides for the validity of deductive arguments. Such criteria would provide for “rational reconstruction[s] of the standards of scientific validation,” free from the influence of feelings of conviction, senses of evidence, or other subjective factors which vary “from person to person, and with the same person in the course of time.” And like the standards by which deductive validity is judged, “it seems reasonable to require that the criteria of empirical confirmation, besides being objective in character, should contain no reference to the specific subject matter of the hypothesis or of the evidence in question.”7 The application of this approach to a real life example of scientific reasoning from evidence to a conclusion begins with the construction of a highly idealized representation of the reasoning under consideration. Reichenbach describes this as the construction of a “logical substitute” for the “real processes” by which the scientist thinks about the evidence (Reichenbach 1938, p. 5). As he describes it, this is analogous to replacing an informal deductive argument with a formal version which omits logically irrelevant features and exhibits logical structure which was not explicit in the original version. For Hempel, it is analogous to the construction of an idealized, simplified theoretical model of a real process (Hempel 1965, p. 44). ⎯⎯⎯⎯⎯⎯⎯ 7 Hempel (1965), pp. 9-10. This is exactly what Glymour promises for his bootstrap theory. Its confirmation relations are to be “entirely structural; they have no connection to the content of the hypothesis tested, or to the meaning of the evidence sentences, or to the meaning of the theories with respect to which the tests are supposed to be carried out” (1980, pp. 374-5). The goal shared by Hempel and Glymour is closely related to Popper’s goal of providing as formal as possible a demarcation between real and pseudo science. And it bears an interesting relation to Kuhn, Feyerabend, Hanson, Shapere, Quine, and many other critics of the original positivist program. Different as their views obviously are, all of these people subscribe to some version of the idea that the IRS is the only alternative to the idea that scientific belief is not objectively constrained by evidence.
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Once a rational reconstruction of a particular argument from evidence has been produced, the next step in an IRS treatment is the application of logical standards (Hempel’s “objective criteria”) to the reconstruction. This is analogous to applying logical rules to the formalized version of an argument to explain whether (and under what interpretations) its conclusion is well supported by its premises. It is also analogous to explaining aspects of the behavior of a real system by appeal to the behavior of the items in a theoretical model. The pursuit of these analogies made it natural if not inevitable for the IRS to leave out a great deal of what seems to us to be most characteristic of real world scientific testing. Thus Reichenbach insists it is no objection to his program that its “fictive constructions” do not “correspond at every point” to the actual thought processes of working scientists (Reichenbach 1938, p. 6). We respect Reichenbach’s point: discrepancies between an idealization and a real system constitute serious objections only insofar as they defeat the purpose for which the idealization is used.8 But we think the formally defined confirmation relations of the IRS fail to correspond to the evidential relevance of data to theory in ways which render the IRS picture uninformative in many cases, and seriously misleading in others.
III The versions of IRS we will discuss are positive instance (including bootstrapping) accounts and Hypothetico-Deductive (HD) accounts of theory testing.9 Their models are populated by sentences of a first order language. As noted, observational evidence is represented by observation sentences. Theoretical claims under test are represented by what we will call ‘hypothesis sentences.’ The resources of first order logic are used to characterize a relation of evidential relevance called ‘confirmation.’ Although observational evidence is said to “confirm” hypotheses or theories, the obtaining of the confirmation relation depends upon logical relations between what we are calling observation and hypothesis sentences. Simple versions of HD depict the confirmation of the theoretical claim corresponding to a hypothesis sentence, h, by evidence ⎯⎯⎯⎯⎯⎯⎯ 8 Thus Reichenbach requires the “construction . . . [to be] bound to actual thinking by the postulate of correspondence” (1938, p. 6) and Hempel says the model should conform to actual behavior as far as it can without violating constraints imposed for the sake of attaining “simplicity, consistency, and comprehensiveness” (1965, p. 44). 9 For positive instance accounts, see “Studies in the Logic of Confirmation” in Hempel (1965), pp. 3-46. For bootstrapping accounts, see Glymour (1980). For a simple HD account see Braithwaite (1953) and Popper (1959). For more complex HD accounts see Schlesinger (1976) and Merrill (1979).
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represented by an observation sentence, o, as depending on whether (h & A) deductively entails o. Here A is a first order representation of one or more “auxiliary hypotheses,” “correspondence rules,” or “background beliefs” which belong to the same theory as the claim represented by h. The simplest positive instance versions of IRS characterize confirmation in terms of logical relations which run in exactly the opposite direction. Where evidence represented by o confirms h, o (or, in the bootstrap version, the conjunction of o and A) entails an instance of h.10 Just as entailment can hold between false as well as true sentences, confirmation can relate worthless evidence to unacceptable hypotheses as well as good evidence to correct or well justified theoretical claims. Just as the mere fact that p entails q does not tell us whether we should believe q, the mere fact that o stands in the required inferential relation to h does not tell us whether there is good reason to accept the claim h represents. So what can IRS tell us about the acceptance and rejection of theoretical claims? Let a broken arrow (--->) represent the inferential relation used to characterize confirmation. A naive HD answer to our question would be that if o ---> h, evidence which makes o true provides epistemic support for the claim represented by h or the theory to which that claim belongs and evidence which makes ~o true provides epistemic support for the rejection of the claim represented by h. A simplified positive instance answer would be that the evidence represented by o provides epistemic support for the claim represented by h if o is true and o ---> h, while evidence counts against the claim if o is true and o ---> ~h.11
IV We have emphasized that the IRS depicts confirmation as depending upon formal relations between sentences in a first order language, even though many data are photographs, drawings, etc., which are not sentences in any language, let alone a first order one. This is enough to establish that the claim that confirmation captures what is essential to evidential relevance is not trivial. In fact that claim is problematic. Hempel’s raven paradox illustrates one of its ⎯⎯⎯⎯⎯⎯⎯ 10
Different versions of HD and positive instance theories add different conditions on confirmation to meet counterexamples which concern them. For example, o may be required to have a chance of being false, to be consistent with the theory whose claims are to be tested, to be such that its denial would count against the claim it would support, etc. The details of such conditions do not affect our arguments. Thus our discussion frequently assumes these additional conditions are met so that its being the case that o ---> h is sufficient for confirmation of the claims represented by h by the evidence represented by o. 11 See the previous note. For examples of this view, see Braithwaite (1953) and Glymour (1980), ch. V.
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problems. Replacing the natural language predicate ‘is a raven’ with F, and ‘is black’ with G, let a hypothesis sentence (h1), (x) (Fx ⊃ Gx), represent the general claim (C) “All ravens are black.”12 Where a is a name, Fa & Ga is an instance of (h1). But (h1) is logically equivalent to (h2), (x)(~Gx ⊃ ~Fx). Now ~Fa & ~Ga entails ~Ga ⊃ ~Fa, an instance of (h2). Thus, ~Fa & ~Ga ---> (h2). But as Hempel observes, ~Fa & ~Ga is true when the referent of a is a red pencil (Hempel 1965, p. 15f. Cf. Glymour 1980, p. 15ff.). Therefore, assuming that evidence which confirms a claim also confirms claims which are logically equivalent to it, why shouldn’t the observation of a red pencil confirm (C)? If it does, this version of IRS allows evidence (e.g., red pencil observations) to confirm theoretical claims (like “All ravens are black”) to which it is epistemically quite irrelevant. Since the premises of a deductively valid argument cannot fail to be relevant to its conclusion, this (along with such related puzzles as Goodman’s grue riddle and Glymour’s problem of irrelevant conjunction (Glymour 1980, p. 31), points to a serious disanalogy between deductive validity and confirmation. While the deductive validity of an argument guarantees in every case that if its premises are true, then one has a compelling reason to believe its conclusion, the evidence represented by o can be epistemically irrelevant to the hypothesis represented by h even though o ---> h. The most popular response to such difficulties is to tinker with IRS by adding or modifying the formal requirements for confirmation. But close variants of the above puzzles tend to reappear in more complicated IRS models.13 We think this is symptomatic of the fact that evidential relevance depends upon features of the causal processes by which the evidence is produced and that the formal resources IRS has at its disposal are not very good at capturing or tracking these factors or the reasoning which depends upon them. This is why the tinkering doesn’t work. An equally serious problem emerges if we consider the following analogy: Just as we can’t tell whether we must accept the conclusion of a deductively valid argument unless we can decide whether its premises are true, the fact that o ---> h doesn’t give us any reason to believe a theoretical claim unless we can decide whether o is true. To see why this is a problem for the IRS consider the test Priestley and Lavoisier used to show that the gas produced by heating oxides of mercury, iron, and some other metals differ from atmospheric air.14 Anachronistically described, it depends on the fact that the gas in question was oxygen and that oxygen combines with what Priestley called “nitrous air” (nitric ⎯⎯⎯⎯⎯⎯⎯ 12
Examples featuring items which sound more theoretical than birds and colors are easily produced. For an illustration of this point in connection with Glymour’s treatment of the problem of irrelevant conjunction, see Woodward (1983). 14 This example is also discussed in Bogen and Woodward (1992). 13
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oxide) to produce water-soluble nitrous oxide. To perform the test, one combines measured amounts of nitric oxide and the gas to be tested over water in an inverted graduated tube sealed at the top. As the nitrous oxide thus produced dissolves, the total volume of gas decreases, allowing the water to rise in the tube. At fixed volumes, the more uncompounded oxygen a gas contains, the greater will be the decrease in volume of gas. The decrease is measured by watching how far the water rises. In their first experiments with this test, Priestley and Lavoisier both reported that the addition of “nitrous air” to the unknown gas released from heated red oxide of mercury decreased the volume of the latter by roughly the amount previously observed for atmospheric air. This datum could not be used to distinguish oxygen from atmospheric air. In later experiments Priestley obtained data which could be used to make the distinction. When he added three measures of “nitrous air” to two measures of the unknown gas, the volume of gas in the tube dropped to one measure. Lavoisier eventually “obtained roughly similar results” (see Conant 1957; Lavoisier 1965, pt. I, chs. 1-4). The available equipment and techniques for measuring gases, for introducing them into the graduated tube, and for measuring volumes were such as to make it impossible for either investigator to obtain accurate measures of the true decreases in volume (Priestley 1970, pp. 23-41). Therefore an IRS account which thinks of the data as putative measures of real decreases should treat observation sentences representing the data from the later as well as from the earlier experiments as false. But while unsound deductive arguments provide no epistemic support for their conclusions, the inaccurate data from Priestley’s and Lavoisier’s later experiments provide good reason to believe the phenomena claim for which they were used to argue. Alternatively, suppose the data were meant to report how things looked to Priestley and Lavoisier instead of reporting the true magnitudes of the volume decreases. If Priestley and Lavoisier were good at writing down what they saw, observation sentences representing the worthless data from the first experiments should be counted as true along with observation sentences representing the epistemically valuable data from the later experiments. But while all deductively sound arguments support their conclusions, only data from the later experiments supported the claim that the gas released from red oxide or mercury differs from atmospheric air. Here the analogy between deductive soundness and confirmation by good evidence goes lame unless the IRS has a principled way to assign true observation sentences to the inaccurate but epistemically valuable data from the later experiments, and false observation sentences to the inaccurate but epistemically worthless data from the earlier experiments. If truth values must be allocated on the basis of something other than the accuracy of the data they represent, it is far from clear how the IRS is to allocate them.
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To avoid the problem posed by Priestley’s and Lavoisier’s data the IRS must assign true observation sentences to epistemically good evidence and false ones to epistemically bad evidence. What determines whether evidence is good or bad? The following example illustrates our view that the relevance of evidence to theory and the epistemic value of the evidence depends in large part upon causal factors. If we are right about this, it is to be expected – as we will argue in sections VII and VIII – that decisions about the value of evidence depend in large part upon a sort of causal reasoning concerned with what we are calling reliability.
V Curtis and Campbell, Eddington and Cottingham (among others) produced astronomical data to test Einstein’s theory of general relativity. One of the phenomena general relativity can be used to make predictions about is the deflection of starlight due to the gravitational influence of the sun. Eddington and the others tried to produce data which would enable investigators to decide between three competing claims about this phenomenon: (N) no deflection at all, (E) deflection of the magnitude predicted by general relativity, and (NS) deflection of a different magnitude predicted by Soldner from Newtonian physics augmented by assumptions needed to apply it to the motion of light.15 (N) and (NS) would count against general relativity while (E) would count in favor of it. The data used to decide between these alternatives included photographs of stars taken in daytime during a solar eclipse, comparison photographs taken at night later in the year when the starlight which reached the photographic equipment would not pass as near to the sun, and check photographs of stars used to establish scale. To interpret the photographs, the investigators would have to establish their scale, i.e., the correspondence of radial distances between stars shown on an accurate star map to linear distances between star images on the photographs. They would have to measure differences between the positions of star images on the eclipse and the comparison photographs. They would have to calculate the deflection of starlight in seconds of arc from displacements of the star images together with the scale. At each step of the way they would have to correct for errors of different kinds from different sources (Earman and Glymour 1980, p. 59). The evidential bearing of the photographic data on Einstein’s theory is an instance of what IRS accounts of confirmation are supposed to explain. This evidential bearing depended upon two considerations: (1) the usefulness of the data in discriminating between phenomena claims (N), (NS), (E), and (2) the ⎯⎯⎯⎯⎯⎯⎯ 15 Soldner’s is roughly the same as a value predicted from an earlier theory of Einstein’s. See Pais (1982), p. 304.
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degree to which (E), the value predicted by general relativity, disagrees with predictions based on the competitor theories under consideration. (1) belongs to the first of the two stages of theory testing we mentioned in section I: the production and interpretation of data to answer a question about phenomena. (2) belongs to the second of these stages – the use of a phenomena claim to argue for or against part of a theory. With regard to the first of these considerations, evidential relevance depends upon the extent (if any) to which differences between the positions of star images on eclipse and comparison pictures are due to differences between paths of starlight due to the gravitational influence of the sun. Even if the IRS has the resources to analyze the prediction of (E) from Einstein’s theory, the relevance of the data to (E) would be another matter.16 Assuming that the sun’s gravitational field is causally relevant to differences between positions of eclipse and comparison images, the evidential value of the data depended upon a great many other factors as well. Some of these had to do with the instruments and techniques used to measure distances on the photograph. Some had to do with the resources available to the investigator for deciding whether and to what extent measured displacements of star images were due to the deflection of starlight rather than extraneous influences. As Fig. 1 indicates, one such factor was change in camera angle due to the motion of the earth. Another was parallax resulting from the distance between the geographical locations from which Eddington’s eclipse and comparison pictures were taken.17
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In the discussion which follows, we ignore the fact that the deflection values calculated from the best photographic data differed not only from (N) and (NS), but also (albeit to a lesser extent) from (E). Assuming (as we do) that the data supported general relativity, this might mean that although (E) is correct, its discrimination does not require it to be identical to the value calculated from the photographs. Alternatively, it might mean that (E) is false, but that just as inaccurate data can make it reasonable to believe a phenomenon-claim, some false phenomena claims provide epistemically good support for theoretical claims in whose testing they are employed. Deciding which if either of these alternatives is correct falls beyond the scope of this paper. But since epistemic support by inaccurate data and confirmation by false claims are major difficulties for IRS, the disparities between (E) and magnitudes calculated from the best data offer no aid and comfort to the IRS analysis. Important as they are in connection with other epistemological issues, these disparities will not affect the arguments of this paper. 17 Eddington and Cottingham took eclipse photographs from Principe, but logistical complications made it necessary for them to have comparison pictures taken from Oxford. In addition to correcting for parallax, they had to establish scale for photographs taken from two very different locations with very different equipment (Earman and Glymour 1980, pp. 73-4).
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Fig. 1. As the earth moves from its position at one time, t1, to its position at a later time, t2, the positions of the eclipse and comparison cameras change relative to the stars.
Apart from these influences, a number of factors including changes in temperature could produce mechanical effects in the photographic equipment sufficient to cause significant differences in scale (Earman and Glymour 1980). Additional complications arose from causes involved in the process of interpretation. One procedure for measuring distances between star images utilizes a low power microscope equipped with a cross hair. Having locked a photograph onto an illuminated frame, the investigator locates a star image (or part of one) against the cross hair and slowly turns a crank until the image whose distance from the first is to be measured appears against the cross hair. At each turn of the crank a gadget registers the distance traversed by the microscope in microns and fractions of microns. The distance is recorded, the photograph is removed from the frame, and the procedure is repeated with the next photograph.18 If the photographs are not oriented in the same way on the frame, image displacements will be measured incorrectly (Earman and Glymour 1980, p. 59). ⎯⎯⎯⎯⎯⎯⎯ 18
We are indebted to Alma Zook of the Pomona College physics department for showing and explaining the use of such measuring equipment to us.
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The following drawing of a star image from one of Curtis’s photographs19 illustrates effects (produced by the focus and by motions of the camera) which make this bit of data epistemically irrelevant to the testing of general relativity theory by rendering it useless in deciding between (E), (N), and (NS).
The epistemic defects of Curtis’s star image are not due to the failure of inferential connections between an observation sentence and a hypothesis sentence. Nor are they due to the falsity of an observation sentence. By the same token, the epistemic value of the best photographs was not due to the truth of observation sentences or to the obtaining of inferential connections between them and hypothesis sentences. The evidential value of the starlight data depended upon non-logical, extra-linguistic relations between non-sentential features of photographs and causes which are not sentential structures. At this point we need to say a little more about a difficulty we mentioned in section I. Observation sentences are supposed to represent evidence. But the IRS tends to associate evidence with sentences reporting observations, and even though some investigations use data of this sort, the data which supported (E) were not linguistic items of any sort, let alone sentences. They were photographs. This is not an unusual case. So many investigations depend upon nonsentential data that it would be fatal for the IRS to maintain that all scientific evidence consists of observation reports (let alone the expressions in first order logic we are calling observation sentences). What then do observation sentences represent? The most charitable answer would be that they represent whatever data are actually used as evidence, even where the data are not observation reports. But this does not tell us which observation sentences to use to represent the photographs. Thus a serious difficulty is that for theory testing which involves non-sentential evidence, the IRS provides no guidance for the construction of the required observation sentences. Lacking an account of what observation sentences the IRS would use to represent the photographs, it is hard to talk about what would decide their truth values. But we can say this much: whatever the observation sentences may be, their truth had better not depend upon how well the photographs depicted the true positions of the stars. The photographs did not purport to show (and were not used to calculate) their actual positions or the true magnitudes of distances between them. They could represent true positions of (or distances between) stars with equal accuracy only if there were no significant20 discrepancies ⎯⎯⎯⎯⎯⎯⎯ 19
From a letter from Campbell to Curtis, reproduced in Earman and Glymour (1980), p. 67. We mean measurable discrepancies not accounted for by changes in the position of the earth, differences in the location of the eclipse and comparison equipment, etc.
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between the positions of star images on the eclipse photographs and star images on the comparison photographs. But had there been no such discrepancies the photographs would have argued against (E). Thus to require both the eclipse and the comparison photographs to meet the same standard of representational accuracy would be to rule out evidence needed to support (E). Furthermore, the truth values of the observation sentences had better not be decided solely on the basis of whether the measurements of distances between their star images meet some general standard of accuracy specified independently of the particular investigation in question. In his textbook on error analysis, John Taylor points out that even though measurements can be too inaccurate to serve their purposes . . . it is not necessary that the uncertainties [i.e., levels of error] be extremely small . . . This . . . is typical of many scientific measurements, where uncertainties have to be reasonably small (perhaps a few percent of the measured value), but where extreme precision is often quite unnecessary (Taylor 1982, p. 6).
We maintain that what counts as a “reasonably small” level of error depends upon the nature of the phenomenon under investigation, the methods used to investigate it, and the alternative phenomena claims under consideration. Since these vary from case to case no single level of accuracy can distinguish between acceptable and unacceptable measurements for every case. Thus Priestley’s nitric oxide test tolerates considerably more measurement error than did the starlight bending investigations. This means that in order to decide whether or not to treat observation sentences representing Eddington’s photographs and measurements as true, the IRS epistemologist would have to know enough about local details peculiar to their production and interpretation to find out what levels of error would be acceptable. Suppose that one responds to this difficulty by stipulating that whatever observation sentences are used to represent photographs are to be called true if the photographs constitute good evidence and false if they do not. This means that the truth values of the observation sentences will depend, for example, upon whether the investigators could rule out or correct for the influences of such factors as mechanical changes in the equipment, parallax, sources of measurement error, etc., as far as necessary to allow them to discriminate correctly between (E), (N), and (NS). We submit that this stipulation is completely unilluminating. The notion of truth as applied to an observation sentence is now unconnected with any notion of representational correctness or accuracy (i.e., it is unclear what such sentences are supposed to represent or correspond to when they are true). Marking an observation sentence as true is now just a way of saying that the data associated with the sentence possess various other features that allow them to play a role in reliable discrimination. It is better to focus directly on the data and the processes that generate them and to drop the role of an observation sentence as an unnecessary intermediary.
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VI Recall that an important part of the motivation for the development of IRS was the question of what objective factors do or should determine a scientist’s decision about whether a given body of evidence warrants the acceptance of a hypothesis. We have suggested that the evidential value of data depends upon complex and multifarious causal connections between the data, the phenomenon of interest, and a host of other factors. But it does not follow from this that scientists typically do (or even can) know much about the fine details of the relevant causal mechanisms. Quite the contrary, as we have argued elsewhere, scientists can seldom if ever give, and are seldom if ever required to give, detailed, systematic causal accounts of the production of a particular bit of data or its interaction with the human perceptual system and with devices (like the measuring equipment used by the starlight investigators) involved in its interpretation.21 But even though it does not involve systematic causal explanation, we believe that a kind of causal reasoning is essential to the use of data to investigate phenomena. This reasoning focuses upon what we have called general and local reliability. The remainder of this paper discusses some features of this sort of reasoning, and argues that its objectivity does not depend upon, and is not well explained in terms of the highly general, content independent, formal criteria sought by the IRS.
VII We turn first to a more detailed characterization of what we mean by general reliability. As we have already suggested, general reliability is a matter of longrun error characteristics. A detection process is generally reliable, when used in connection with a body of data, if it has a satisfactorily high probability of outputting, under repeated use, correct discriminations among a set of competing phenomenon-claims and a satisfactorily low probability of outputting incorrect discriminations. What matters is thus that the process discriminates correctly among a set of relevant alternatives, not that it discriminates correctly among all logically possible alternatives. Whether or not a detection process is generally reliable is always an empirical matter, having to do with the causal characteristics of the detection process and its typical circumstances of use, rather than with any formal relationship between the data that figure in such a process and the phenomenon-claims for which they are evidence. The notion of general reliability thus has application in those contexts in which we can provide a non-trivial characterization of what it is to repeat a process of data ⎯⎯⎯⎯⎯⎯⎯ 21
Bogen and Woodward (1988). For an excellent illustration of this, see Hacking (1983), p. 209.
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production and interpretation (we shall call this a detection process, for brevity) and where this process possesses fairly stable, determinate error characteristics under repetition that are susceptible of empirical investigation. As we shall see in section VIII, these conditions are met in many, but by no means all the contexts in which data are used to assess claims about phenomena. Where these conditions are not met, we must assess evidential support in terms of a distinct notion of reliability, which we call local reliability. Here is an example illustrating what we have in mind by general reliability.22 Traditionally paleoanthropologists have relied on fossil evidence to infer relationships among human beings and other primates. The 1960s witnessed the emergence of an entirely distinct biochemical method for making such inferences, which involved comparing proteins and nucleic acids from living species. This method rests on the assumption that the rate of mutation in proteins is regular or clocklike; with this assumption one can infer that the greater the difference in protein structure among species, the longer the time they have been separated into distinct species. Molecular phylogeny (as such techniques came to be called) initially suggested conclusions strikingly at variance with the more traditional, generally accepted conclusions based on fossil evidence. For example, while fossil evidence suggested an early divergence between hominids and other primates, molecular techniques suggested a much later date of divergence – that hominids appeared much later than previously thought. Thus while paleoanthropologists classified the important prehistoric primate Ramapithicus as an early hominid on the basis of its fossil remains, the molecular evidence seemed to suggest that Ramapithicus could not be a hominid. Similarly, fossil and morphological data seemed to suggest that chimpanzees and gorillas were more closely related to each other than to humans, while molecular data suggested that humans and chimpanzees were more closely related. The initial reaction of most paleoanthropologists to these new claims was that the biochemical methods were unreliable, because they produced results at variance with what the fossils suggested. It was suggested that because the apparent rates of separation derived from molecular evidence were more recent than those derived from the fossil record, this showed that the molecular clock was not steady and that there had been a slow-down in the rate of change in protein structure among hominids. This debate was largely resolved in favor of the superior reliability of molecular methods. The invention of more powerful molecular techniques based on DNA hybridization, supported by convincing statistical arguments that the rate of mutation was indeed clocklike, largely corroborated the results of earlier molecular methods. The discovery of ⎯⎯⎯⎯⎯⎯⎯ 22
Details of this example are largely taken from Lewin (1987).
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additional fossil evidence undermined the hominid status of Ramapithicus and supported the claim of a late divergence between hominids and other primates. This example illustrates what we have in mind when we ask whether a measurement or detection technique is generally reliable. We can think of various methods for inferring family trees from differences in protein structure and methods for inferring such relationships from fossil evidence as distinct measurement or detection techniques. Any particular molecular method is assumed to have fairly stable, determinate error characteristics which depend upon empirical features of the method: if the method is reliable it will generally yield roughly correct conclusions about family relationship and dates of divergence; if it is unreliable it will not. Clearly the general reliability of the molecular method will depend crucially on whether it is really true that the molecular clock is regular. Similarly, the reliability of the method associated with the use of fossil evidence also depends upon a number of empirical considerations – among them the ability of human beings to detect overall patterns of similarity based on visual appearance that correlate with genetic relationships. What the partisans of fossils and of molecular methods disagree about is the reliability of the methods they favor, in just the sense of reliability as good error characteristics described above. Part of what paleoanthropologists learned as they became convinced of the superior reliability of molecular methods, was that methods based on similarity of appearance were often less reliable than they had previously thought, in part because judgements of similarity can be heavily influenced by prior expectations and can lead the investigator to think that she sees features in the fossil evidence that are simply not there.23 Issues of this sort about general reliability – about the long-run error characteristics of a technique or method under repeated applications – play a central role in many areas of scientific investigation. Whenever a new instrument or detection device is introduced, investigators will wish to know about its general reliability – whether it works in such a way as to yield correct discriminations with some reasonable probability of success, whether it can be relied upon as a source of information in some particular area of application. Thus Galileo’s contemporaries were interested not just in whether his telescopic observations of the rough and irregular surface of the moon were correct, but with the general reliability of his telescope – with whether its causal characteristics were such that it could be used to make certain kinds of discrimination in astronomical applications with some reasonable probability of correctness or with whether instead what observers seemed to see through the telescope were artifacts, produced by imperfections in the lenses or some such source. ⎯⎯⎯⎯⎯⎯⎯ 23
See especially Lewin (1987), p. 122ff.
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Similarly in many contexts in which human perceivers play an important role in science one can ask about their general reliability at various perceptual detection tasks, where this has to do with the probability or frequency with which perceivers make the relevant perceptual discriminations correctly, under repeated trials. Determinations of personal error rates in observational sciences like astronomy make use of this understanding of reliability.24 Similarly one can ask whether an automated data reduction procedure which sorts through batches of photographs selecting those which satisfy some preselected criterion is operating reliably, where this has to do with whether or not it is in fact classifying the photographs according to the indicated criterion with a low error rate. There are several general features of the above examples which are worth underscoring. Let us note to begin with that the question of whether a method, technique, or detection device and the data it produces are reliable always depends very much on the specific features of the method, technique, or instrument in question. It is these highly specific empirical facts about the general reliability of particular methods of data production and interpretation, and not the formal relationships emphasized by IRS, that are relevant to determining whether or not data are good evidence for various claims about phenomena. For example, it is the reliability characteristics of Galileo’s telescope that insure the evidential relevance of the images that it produces to the astronomical objects he wishes to detect, and it is the reliability characteristics of DNA hybridization that insure the evidential relevance of the biochemical data it produces to the reconstruction of relationships between species. How is the general reliability of an instrument or detection technique ascertained? We (and others) have discussed this issue at some length elsewhere and readers are referred to this discussion for a more detailed treatment.25 A wide variety of different kinds of considerations having to do, for example, with the observed effects of various manipulations and interventions into the detection process, with replicability, and with the use of various calibration techniques play an important role. One point that we especially wish to emphasize, and which we will make use of below, is that assessing the general reliability of an instrument or detection technique does not require that one ⎯⎯⎯⎯⎯⎯⎯ 24
For additional discussion, see Bogen and Woodward (1992). See Bogen and Woodward (1988) and Woodward (1989). Although, on our view, it is always a matter of empirical fact whether or not a detection process is generally reliable, we want to emphasize that there is rarely if ever an algorithm or mechanical procedure for deciding this. Instead it is typically the case that a variety of heterogeneous considerations are relevant, and building a case for general reliability or unreliability is a matter of building a consensus that most of these considerations, or the most compelling among them, support one conclusion rather than another. As writers like Peter Galison (1987) have emphasized, reaching such a conclusion may involve an irreducible element of judgement on the part of experimental investigators about which sources of error need to be taken seriously, about which possibilities are physically realistic, or plausible and so forth. Similar remarks apply to conclusions about local reliability. (Cf. n. 42.)
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possess a general theory that systematically explains the operation of the instrument or technique or why it is generally reliable. There are many cases in the history of science involving instruments and detection techniques that investigators reasonably believed to be generally reliable in various standard uses even though those investigators did not possess a general explanatory theory of the operation of these instruments and techniques. Thus it was reasonable of Galileo and his contemporaries to believe that his telescope was generally reliable in many of its applications, even though Galileo lacked an optical theory that explained its workings; it is reasonable to believe that the human visual system can reliably make various perceptual discriminations in specified circumstances even though our understanding of the operation of the visual system is still rudimentary; it may be reasonable to believe that a certain staining technique reliably stains certain cells and doesn’t produce artifacts even though one doesn’t understand the chemistry of the staining process, and so on. We may contrast the picture we have been advocating, according to which evidential relevance is carried by the reliability characteristics of highly specific processes of data production and interpretation, with the conception of evidential relevance which is implicit in IRS. According to that conception, the relevance of evidence to hypotheses is a matter of observation sentences standing in various highly general, structural or inferential relations to those hypotheses, relationships which, according to IRS, are exemplified in many different areas of scientific investigation. Thus the idea is that the evidential relevance of biochemical data to species relationships or the evidential relevance of the images produced by Galileo’s telescope to various astronomical hypotheses is a matter of the obtaining of some appropriate formal relationship between sentences representing these data, the hypotheses in question, and perhaps appropriate background or auxiliary assumptions. On the contrasting picture we have defended, evidential relevance is not a matter of any such formal relationship, but is instead a matter of empirical fact – a matter of there existing empirical relationships or correlations between data and phenomena which permit us to use the data to discriminate among competing claims about phenomena according to procedures that have good general error characteristics. Evidential relevance thus derives from an enormous variety of highly domainspecific facts about the error characteristics of various quite heterogeneous detection and measurement processes, rather than from the highly general, domain-independent formal relationships emphasized in IRS accounts. Our alternative conception seems to us to have several advantages that are not shared by IRS accounts. First, we have already noted that a great deal of data does not have an obvious sentential representation and that, even when such representations are available, they need not be true or exactly representationally accurate for data to play an evidential role. Our account helps to make sense of these facts. There is nothing in the notion of general reliability
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that requires that data be sentential in structure, or have a natural sentential representation, or have semantic characteristics like truth or exact representational accuracy. Data can figure in a generally reliable detection process, and features of data can be systematically correlated with the correctness or incorrectness of different claims about phenomena without the data being true or even sententially representable. For example, when a pathologist looks at an x-ray photograph and produces a diagnosis, or when a geologist looks at a rock and provides an identification of its type, all that we require, in order for these claims to be credible or evidentially well-supported, is that the relevant processes of perceptual detection and identification be generally reliable in the sense of having good error characteristics, and that we have some evidence that this is the case. It isn’t necessary that we be able to provide sentential representations of what these investigators perceive or to exhibit their conclusions as the result of the operation of general IRS-style inductive rules on sentential representations of what they see. Similarly, in the case of the Priestley/Lavoisier example, the characteristics of Priestley’s detection procedure may very well be such that it can be used to reliably discriminate between ordinary air and oxygen on the basis of volume measurements, in the sense that repeated uses of the procedure will result in correct discriminations with high probability, even though the volume measurements on which the discrimination is based are inaccurate, noisy and in fact false if taken as reports of the actual volume decrease. There is a second reason to focus on reliability in preference to IRS-style confirmation relations. According to the IRS, evidence e provides epistemic support for a theoretical claim when the observation sentence, o, which corresponds to the evidence stands in the right sort of formal relationship to the hypothesis sentence, h, which represents the theoretical claim. Our worries so far have centered around the difficulties of finding a true observation sentence o which faithfully represents the evidential significance of e, and a hypothesis sentence h which faithfully represents the content of the theoretical claim. But quite apart from these difficulties there is a perennial internal puzzle for IRS accounts. Given that within these accounts o does not, even in conjunction with background information, entail h, why should we suppose that there is any connection between o’s being true and o and h instantiating the formal relationships specified in these accounts, and h’s being true or having a high probability of truth or possessing some other feature associated with grounds for belief? For example, even if a true observation sentence representing Priestley’s data actually did entail a positive instance of a hypothesis sentence representing the claim that a certain sort of gas is not ordinary air, why would that make the latter claim belief-worthy? We think that it is very hard to see what the justification of a non-deductive IRS-style method or criterion of evidential support could possibly consist in except the provision of grounds that the
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method or criterion has good (general) reliability or error characteristics under repeated use. That is, it is hard to see why we should believe that the truth of the observation sentence o together with the fact that the relationship between o and hypothesis h satisfies the pattern recommended by, for example, hypotheticodeductivism or bootstrapping provides a reason for belief in h if it were not true that cases in which such patterns are instantiated turn out, with some reasonable probability, to be cases in which h is true, or were it not at least true that cases in which such patterns are instantiated turn out more frequently to be cases in which h is true than cases in which such patterns are not instantiated.26 However, it seems very unlikely that any of the IRS-style accounts we have considered can be given such a reliabilist justification. IRS accounts are, as we have seen, subject matter and context-independent; they are meant to supply universal criteria of evidential support. But it is all too easy to find, for any IRS account, not just hypothetical, but actual cases in which true observation sentences stand in the recommended relationship to hypothesis h and yet in which h is false: cases in which positive instances instantiate a hypothesis and yet the hypothesis is false, cases in which true observation sentences are deduced from a hypothesis and yet it is false, and so forth. Whether accepting h when it stands in the relationship to o described in one’s favorite IRS schema and o is true will lead one to accept true hypotheses some significant fraction of the time will depend entirely on the empirical details of the particular cases to which the schema in question is applied. But this is to say that the various IRS schemas we have been considering when taken as methods for forming beliefs or accepting hypotheses either have no determinate error characteristics at all when considered in the abstract (their error characteristics vary wildly, depending on the details of the particular cases to which they are applied) or at least no error characteristics that are knowable by us. Indeed, the fact that the various IRS accounts we have been considering cannot be given a satisfying reliabilist justification is tacitly conceded by their proponents, who usually do not even try to provide such a justification.27 ⎯⎯⎯⎯⎯⎯⎯ 26
For a general argument in support of this conclusion see Friedman (1979). One can think of Larry Laudan’s recent naturalizing program in philosophy of science which advocates the testing of various philosophical theses about scientific change and theory confirmation against empirical evidence provided by the history of science as (among other things) an attempt to carry out an empirical investigation of the error or reliability characteristics of the various IRS confirmation schemas (Donovan et al. 1988). We agree with Laudan that vindicating the various IRS models would require information about long-run error characteristics of the sort for which he is looking. But for reasons described in the next paragraph in the text, we are much more pessimistic than Laudan and his collaborators about the possibility of obtaining such information. 27 Typical attempts to argue for particular IRS models appeal instead to (a) alleged paradoxes, and inadequacies associated with alternative IRS approaches, (b) various supposed intuitions about evidential support, and (c) famous examples of successful science that are alleged to conform to the model in question. (Cf. Glymour 1980.) But (a) is compatible with and perhaps even supports
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By contrast, there is no corresponding problem with the notion of general reliability as applied to particular instruments or detection processes. Such instruments and processes often do have determinate error characteristics, about which we can obtain empirical evidence. Unlike the H-D method or the method associated with bootstrapping, the reliability of a telescope or a radioactive dating technique is exactly the sort of thing we know how to investigate empirically and regarding which we can obtain convincing evidence. There is no puzzle corresponding to that raised above in connection with IRS accounts about what it means to say that a dating technique has a high probability of yielding correct conclusions about the ages of certain fossils or about why, given that we have applied a reliable dating technique and have obtained a certain result, we have good prima facie grounds for believing that result. In short, it is the use of specific instruments, detection devices, measurement and observational techniques, rather than IRS-style inductive patterns, that are appropriate candidates for justification in terms of the idea of general reliability. Reflection on a reliabilist conception of justification thus reinforces our conclusion that the relevance of evidence to hypothesis is not a matter of formal, IRS-style inferential relations, but rather derives from highly specific facts about the error characteristics of various detection processes and instruments.
VIII In addition to the question of whether some type of detection process or instrument is generally reliable in the repeatable error characteristics sense described above, scientists also are interested in whether the use of the process on some particular occasion, in a particular detection task, is reliable – with whether the data produced on that particular occasion are good evidence for some phenomenon of interest. This is a matter of local reliability. While in those cases in which a detection process has repeatable error characteristics, information about its general reliability is always evidentially relevant, there are many cases in which the evidential import of data cannot be assessed just in skepticism about all IRS accounts of evidence, and with respect to (b), it is uncontroversial that intuitions about inductive support frequently lead one astray. Finally, from a reliabilist perspective (c) is quite unconvincing. Instead, what needs to be shown is that scientists systematically succeed in a variety of cases because they accept hypotheses in accord with the recommendations of the IRS account one favors. That is, what we need to know is not just that there are episodes in the history of science in which hypotheses stand in the relationship to true observation sentences described by, say, a bootstrap methodology and that these hypotheses turn out to be true or nearly so, but what the performance of a bootstrap methodology would be, on a wide variety of different kinds of evidence, in discriminating true hypotheses from false hypotheses – both what this performance is absolutely and how it compares with alternative methods one might adopt. (As we understand it, this is Glymour’s present view as well.)
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terms of general reliability. For example, even if I know that some radioactive dating technique is generally reliable when applied to fossils, this still leaves open the question of whether the date assigned to some particular fossil by the use of the technique is correct: it might be that this particular fossil is contaminated in a way that gives us mistaken data, or that the equipment I am using has misfunctioned on this particular occasion of use. That the dating process is generally reliable doesn’t preclude these possibilities. Some philosophers with a generalist turn of mind will find it tempting to try to reduce local reliability to general reliability: it will be said that if the data obtained from a particular fossil are mistaken because of the presence of a contaminant, then if that very detection process is repeated (with the contaminant present and so forth) on other occasions, it will have unfavorable error characteristics, and this is what grounds our judgement of reliability or evidential import in the particular case. As long as we take care to specify the relevant detection processes finely enough, all judgements about reliability in particular cases can be explicated in terms of the idea of repeated error characteristics. Our response is not that this is necessarily wrong, but that it is thoroughly unilluminating at least when understood as an account of how judgements of local reliability are arrived at and justified. As we shall see below, many judgements of local reliability turn on considerations that are particular or idiosyncratic to the individual case at hand. Often scientists are either unable to describe in a non-trivial way what it is to repeat the measurement or detection process that results in some particular body of data or lack (and cannot get) information about its long-run error characteristics. It is not at all clear to us that whenever a detection process is used on some particular occasion, and a judgement about its local reliability is reached on the basis of various considerations, there must be some description of the process, considerations, and judgements involved that exhibits them as repeatable. But even if this is the case, this description and the relevant error characteristics of the process when repeated often will be unknown to the individual investigator – this information is not what the investigator appeals to in reaching his judgement about local reliability or in defending his judgement. What then are the considerations which ground judgements of local reliability and how should we understand what it is that we are trying to do when we make such judgements? While the relevant considerations are, as we shall see, highly heterogeneous, we think that they very often have a common point or pattern, which we will now try to describe. Put baldly, our idea is that judgements of local reliability are a species of singular causal inference in which one tries to show that the phenomenon of interest causes the data by means of an eliminativist strategy – by ruling out other possible causes of the
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data.28 When one makes a judgement of local reliability one wants to ascertain on the basis of some body of data whether some phenomenon of interest is present or has certain features. One tries to do this by showing that the detection process and data are such that the data must have been caused by the phenomenon in question (or by a phenomenon with the features in question) – that all other relevant candidates for causes of the data can be ruled out. Since something must have caused the data, we settle on the phenomenon of interest as the only remaining possibility. For example, in the fossil dating example above, one wants to exclude (among other things) the possibility that one’s data – presumably some measure of radioactive decay rate, such as counts with a Geiger counter – were caused by (or result in part from a causal contribution due to) the presence of the contaminant. Similarly, as we have already noted, showing that some particular bubble chamber photograph was evidence for the existence of neutral currents in the CERN experiments of 1973 requires ruling out the possibility that the particular photograph might have been due instead to some alternative cause, such as a high energy neutron, that can mimic many of the effects of neutral currents. The underlying idea of this strategy is nicely described by Allan Franklin in his recent book Experiments, Right or Wrong (1990). Franklin approvingly quotes Sherlock Holmes’s remark to Watson, “How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?” and then adds, “If we can eliminate all possible sources of error and alternative explanations, then we are left with a valid experimental result” (1990, p. 109). Here is a more extended example designed to illustrate what is involved in local reliability and the role of the eliminative strategy described above.29 In experiments conducted in the late 1960s, Joseph Weber, an experimentalist at the University of Maryland, claimed to have successfully detected the phenomenon of gravitational radiation. The production of gravity waves by massive moving bodies is predicted (and explained) by general relativity. However, gravitational radiation is so weakly coupled to matter that detection of such radiation by us is extremely difficult. Weber’s apparatus initially consisted of a large metal bar which was designed to vibrate at the characteristic frequency of gravitational radiation emitted by relatively large scale cosmological events. The central problem of ⎯⎯⎯⎯⎯⎯⎯ 28
As with judgements about general reliability, we do not mean to suggest that there is some single method or algorithm to be employed in this ruling out of alternatives. For example, ruling out an alternative may involve establishing an observational claim that is logically inconsistent with the alternative (Popperian falsification), but might take other forms as well; for example, it may be a matter of finding evidence that renders the alternative unlikely or implausible or of finding evidence that the alternative should but is not able to explain. 29 The account that follows draws heavily on Collins (1975) and Collins (1981). Other accessible discussions of Weber’s experiment on which we have relied include Davis (1980), esp. pp. 102-117, and Will (1986).
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experimental design was that to detect gravitational radiation one had to be able to control or correct for other potential disturbances due to electromagnetic, thermal, and acoustic sources. In part, this was attempted by physical insulation of the bar, but this could not eliminate all possible sources of disturbance; for example, as long as the bar is above absolute zero, thermal motion of the atoms in the bar will induce random vibrations in it. One of the ways Weber attempted to deal with this difficulty was through the use of a second detector which was separated from his original detector by a large spatial distance – the idea being that genuine gravitational radiation, which would be cosmological in origin, should register simultaneously on both detectors while other sorts of background events which were local in origin would be less likely to do this. Nonetheless, it was recognized that some coincident disturbances will occur in the two detectors just by chance. To deal with this possibility, various complex statistical arguments and other kinds of checks were used to attempt to show that it was unlikely that all of the coincident disturbances could arise in this way. Weber also relied on facts about the causal characteristics of the signal – the gravitational radiation he was trying to detect. The detectors used by Weber were most sensitive to gravitational radiation when the direction of propagation of given radiation was perpendicular to the axes of the detectors. Thus if the waves were coming from a fixed direction in space (as would be plausible if they were due to some astronomical event), they should vary regularly in intensity with the period of revolution of the earth. Moreover, any periodic variations due to human activity should exhibit the regular twenty-four hour variation of the solar day. By contrast, the pattern of change due to an astronomical source would be expected to be in accordance with the sidereal day which reflects the revolution of the earth around the sun, as well as its rotation about its axis, and is slightly shorter than the solar day. When Weber initially appeared to find a significant correlation with sidereal, but not solar, time in the vibrations he was detecting, this was taken by many other scientists to be important evidence that the source of the vibrations was not local or terrestrial, but instead due to some astronomical event. Weber claimed to have detected the existence of gravitational radiation from 1969 on, but for a variety of reasons his claims are now almost universally doubted. In what follows, we concentrate on what is involved in Weber’s claim that his detection procedure was locally reliable and how he attempted to establish that claim. As we see it, what Weber was interested in establishing was a singular causal claim: he wanted to show that at least some of the vibrations and disturbances his data recorded were due to gravitational radiation (the phenomenon he was trying to detect) and (hence) that such radiation existed. The problem he faced was that a number of other possible causes or factors besides gravitational radiation might in principle have caused his data. Unless
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Weber could rule out, or render implausible or unlikely, the possibility that these other factors might have caused the disturbances, he would not be justified in concluding that the disturbances are due to the presence of gravitational radiation. The various experimental strategies and arguments described above (physical isolation of the bar, use of a second detector, and so forth) are an attempt to do just this – to make it implausible that the vibrations in his detector could have been caused by anything but gravitational radiation. For example, in the case of the sidereal correlation the underlying argument is that the presence of this pattern or signature in the data is so distinctive that it could only have been produced by gravitational radiation rather than by some other source. We will not attempt to describe in detail the process by which Weber’s claims of successful detection came to be criticized and eventually disbelieved. Nonetheless it is worth noting that we can see the underlying point of these criticisms as showing that Weber’s experiment fails to conform to the eliminative pattern under discussion – what the critics show is that Weber has not convincingly ruled out the possibility that his data were due to other causes besides gravitational radiation. Thus, for example, the statistical techniques that Weber used turned out to be problematic – indeed, an inadvertent natural experiment appeared to show that the techniques lacked general reliability in the sense described above. (Weber’s statistical techniques detected evidence for gravitational radiation in data provided by another group which, because of a misunderstanding on Weber’s part about synchronization, should have been reported as containing pure noise.) Because of this, Weber could no longer claim to have convincingly eliminated the possibility that all of the disturbances he was seeing in both detections were due to the chance coincidence of local causes. Secondly, as Weber continued his experiment and did further analysis of his data, he was forced to retract his claim of sidereal correlation. Finally, and perhaps most fundamentally, a number of other experiments, using similar and more sensitive apparatus, failed to replicate Weber’s results. Here the argument is that if in fact gravitational radiation was playing a causal role in the production of Weber’s data such radiation ought to interact causally with other similar devices; conversely, failure to detect such radiation with a similar apparatus, while it does not tell us which alternative cause produced Weber’s data, does undermine the claim that it was due to gravitational radiation. Much of what we have said about the advantages of the notion of general reliability vis-à-vis IRS-style accounts holds as well for local reliability. When we make a judgement of local reliability about certain data – when we conclude, for example, that some set of vibrations in Weber’s apparatus were or were not evidence for the existence of gravitational radiation – what needs to be established is not whether there obtains some appropriate formal or logical relationship of the sort IRS models attempt to capture, but rather whether there
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is an appropriate causal relationship leading from the phenomenon to the data. Just as with general reliability, the causal relationships needed for data to count as locally reliable evidence for some phenomenon can hold even if data lack a natural sentential representation that stands in the right formal relationship to the phenomenon-claim in question. Conversely, a sentential representation of the data can stand in what (according to some IRS accounts of confirmation) is the right formal relationship to a hypothesis and yet nonetheless fail to evidentially support it. Weber’s experiment also illustrates this point: Weber obtained data which (or so he was prepared to argue) were just what would be expected if general relativity were true (and gravitational radiation existed). On at least some natural ways of representing data by means of observation sentences, these sentences stand in just the formal relationships to general relativity which according to H-D and positive instance accounts, are necessary for confirmation. Nonetheless this consideration does not show that Weber’s data were reliable evidence for the existence of gravitational radiation. To show this Weber must show that his data were produced by a causal process in which gravitational radiation figures. This is exactly what he tries, and fails, to do. The causally driven strategies and arguments described above would make little sense if all Weber needed to show was the existence of some appropriate IRS-style formal relationship between a true sentential representation of his data and the claim that gravitational radiation exists. Similarly, as we have already had occasion to note, merely producing bubble chamber photographs that have just the characteristic patterns that would be expected if neutral currents were present – producing data which conform to this hypothesis or which have some description which is derivable from the hypothesis – is not by itself good evidence that neutral currents are present. To do this one must rule out the possibility that this data was caused by anything but neutral currents. And as we have noted, this involves talking about the causal process that has produced the data – a consideration which is omitted in most IRS accounts. As we have also argued, a similar point holds in connection with the Eddington solar eclipse expedition. What Eddington needs to show is that the apparent deflection of starlight indicated by the photographic plates is due to the causal influence of the sun’s gravitational field, as described by general relativity, rather than to more local sources, such as changes in the plates due to variations in temperature. Once we understand Eddington’s reasoning as reasoning to the existence of a cause in accordance with an eliminative strategy, various features of that reasoning that seem puzzling on IRS treatments – that it is not obvious how to represent all of the evidentially relevant features of the photographs in terms of true observation sentences and auxiliaries and that the values calculated from the photographs don’t exactly coincide with (E) but are nonetheless taken to support (E) – fall naturally into place.
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IX There is a common element to a number of the difficulties with IRS models that we have discussed that deserves explicit emphasis. It is an immediate consequence of our notions of general and local reliability that the processes that produce or generate data are crucial to its evidential status. Moreover, it is often hard to see how to represent the evidential relevance of such processes in an illuminating way within IRS-style accounts. And in fact the most prominent IRS models simply neglect this element of evidential assessment. The tendency within IRS models is to assume, as a point of departure, that one has a body of evidence, that it is unproblematic how to represent it sententially, and to then try to capture its evidential relevance to some hypothesis by focusing on the formal or structural relationship of its sentential representation to that hypothesis. But if the processes that generated this evidence make a crucial difference to its evidential significance, we can’t as IRS approaches assume, simply detach the evidence from the processes which generated it, and use a sentential representation of it as a premise in an IRS-style inductive inference. To make this point vivid, consider (P) a collection of photographs which qua photographs are indistinguishable from those that in fact constituted evidence for the existence of neutral current interactions in the CERN experiments of 1973. Are the photographs in (P) also evidence for the existence of neutral currents? Although many philosophers (influenced by IRS models of confirmation) will hold that the answer to this question is obviously yes, our claim is that on the basis of the above information one simply doesn’t know – one doesn’t know whether the photographs are evidence for neutral currents until one knows something about the processes by which they are generated. Suppose that the process by which the photographs were produced failed to adequately control for high energy neutrons. Then our claim is that such photographs are not reliable evidence for the existence of neutral currents, even if the photographs themselves look no different from those that were produced by experiments (like the CERN experiment) in which there was adequate control for the neutron background. It is thus a consequence of our discussion of general and local reliability that the evidential significance of the same body of data will vary, depending upon what it is reasonable to believe about how it was produced. We think that the tendency to neglect the relevance of the data-generating processes explains, at least in large measure, the familiar paradoxes which face IRS accounts. Consider the raven paradox, briefly introduced in section IV above. Given our discussion so far it will come as no surprise to learn that we think the culprit in this case is the positive instance criterion itself. Our view is that one just can’t say whether a positive instance of a hypothesis constitutes evidence for it, without knowing about the procedure by which the positive
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instance was produced or generated. A possibility originally introduced by Paul Horwich (1982) makes this point in a very striking way: suppose that you are told that a large number of ravens have been collected, and that they have all turned out to be black. You may be tempted to suppose that such observations support the hypothesis that (h1) all ravens are black. Suppose, however, you then learn how this evidence has been produced: a machine of special design which seizes all and only black objects and stores them in a vast bin has been employed, and all of our observed ravens have come from this bin. In the bin, we find, unsurprisingly, in addition to black shoes, old tires and pieces of coal, a number of black ravens and no non-black ravens. Recall that our interest in data is in using it to discriminate among competing phenomenon-claims. Similarly, when we investigate the hypothesis that all ravens are black, our interest is in obtaining evidence that differentially supports this hypothesis against other natural competitors. That is, our interest is in whether there is evidence that provides some basis for preferring or accepting this hypothesis in contrast to such natural competitors as the hypothesis that ravens come in many different colors, including black. It is clear that the black ravens produced by Horwich’s machine do not differentially support the hypothesis that all ravens are black or provide grounds for accepting it rather than such competitors. The reason is obvious: the character of the evidencegathering or data-generating procedure is such that it could not possibly have discovered any evidence which is contrary to the hypothesis that all ravens are black, or which discriminates in favor of a competitor to this hypothesis, even if such evidence exists. The observed black ravens are positive instances of the hypothesis that all ravens are black, but they do not support the hypothesis in the sense of discriminating in favor of it against natural competitors because of the way in which those observations have been produced or generated. If observations of a very large number of black ravens had been produced in some other way – e.g., by a random sampling process, which had an equal probability of selecting any raven (black or non-black) or by some other process which was such that there was some reason to think that the evidence it generated was representative of the entire population of ravens – then we would be entitled to regard such observations as providing evidence that favors the hypothesis under discussion. But in the absence of a reason to think that the observations have been generated by some such process that makes for reliability, the mere accumulation of observations of black ravens provides no reason for accepting the hypothesis that all ravens are black in contrast to its natural competitors. Similar considerations apply to the question of whether the observation of non-black, non-ravens supports the hypothesis that (h2), “All non-black things are non-ravens.” As a point of departure, let us note that it is less clear than it is in the case of (h1) what the “natural” serious alternatives to (h2) are. The hypothesis (h3) that “All non-black things are ravens” is a competitor to (h2) – it
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is inconsistent with (h2) on the supposition that there is at least one non-black thing – but not a serious competitor since every investigator will have great confidence that it is false prior to beginning an investigation of (h2). Someone who is uncertain whether (h2) is true will not take seriously the possibility that (h3) is true instead and for this reason evidence that merely discriminates between (h2) and (h3) but not between (h2) and its more plausible alternatives will not be regarded as supporting (h2). Thus while the observation of a white shoe does indeed discriminate between (h2) and (h3) this fact by itself does not show that the observation supports (h2). Presumably the best candidates for serious specific alternatives to (h2) are various hypotheses specifying the conditions (e.g., snowy regions) under which non-black ravens will occur. But given any plausible alternative hypothesis about the conditions under which a non-black raven will occur, the observation of a white shoe or a red pencil does nothing to effectively discriminate between (h2) and this alternative. For example, these observations do nothing to discriminate between (h2) and the alternative hypotheses that there are white ravens in snowy regions. As far as these alternatives go, then, there is no good reason to think of an observation of a white shoe as confirming (h2). There are other possible alternatives to (h2) that one might consider. For example, there are various hypotheses, (hp), specifying that the proportion of ravens among non-black things is some (presumably very small) positive number p for various values of p. There is also the generic, non-specific alternative to (h2) which is simply its denial (h4), “Some non-black things are ravens.” For a variety of reasons these alternatives are less likely to be of scientific interest than the alternatives considered in the previous paragraph. But even if we put this consideration aside, there is an additional problem with the suggestion that the observation of a white shoe confirms (h2) because it discriminates between (h2) and one or more of these alternatives. This has to do with the characteristics of the processes involved in the production of such observations. In the case of (h1), “All ravens are black,” we have some sense of what it would mean to sample randomly from the class of ravens or at least to sample a “representative” range of ravens (e.g., from different geographical locations or ecological niches) from this class. That is, we have in this case some sense of what is required for the process that generates relevant observations to be unbiased or to have good reliability characteristics. If we observe enough ravens that are produced by such a process and all turn out to be black, we may regard this evidence as undercutting not just those competitors to (h1) that claim that all ravens are some uniform non-black color but also those alternative hypotheses that claim that various proportions of ravens are non-black, or the generic alternative hypothesis that some ravens are non-black. Relatedly, observations of non-black ravens produced by such a process might confirm some alternative hypothesis to (h1) about the proportion
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of ravens that are non-black or the conditions under which we may expect to find them. By contrast, nothing like this is true of (h2). It is hard to understand even what it might mean to sample in a random or representative way from the class of non-black things and harder still to envision a physical process that would implement such a sampling procedure. It is also hard to see on what basis one might argue that a particular sample of non-black things was representative of the entire range of such things. As a result, when we are presented with even a very generous collection of objects consisting of white shoes, red pencils and so on, it is hard to see on what sort of basis one might determine whether the procedure by which this evidence was produced had the right sort of characteristics to enable us to reliably discriminate between (h2) and either the alternatives (hp) or (h4), and hence hard to assess what its evidential significance is for (h2). It is thus unsurprising that we intuitively judge the import of such evidence for (h2) to be at best unclear and equivocal. On our analysis, then, an important part of what generates the paradox is the mistaken assumption, characteristic of IRS approaches, that evidential support for a claim is just a matter of observation sentences standing in some appropriate structural or formal relationship to a hypothesis sentence (in this case the relationship captured by the positive instance criterion) independently of the processes which generate the evidence and independently of whether the evidence can be used to discriminate between the hypothesis and alternatives to it. It might be thought that while extant IRS accounts have in fact neglected the relevance of those features of data-generating processes that we have sought to capture with our notions of general and local reliability, there is nothing in the logic of such accounts that requires this omission. Many IRS accounts assign an important role to auxiliary or background assumptions. Why can’t partisans of IRS represent the evidential significance of processes of data generation by means of these assumptions? We don’t see how to do this in a way that respects the underlying aspirations of the IRS approach and avoids trivialization. The neglect of data generating processes in standard IRS accounts is not an accidental or easily correctable feature of such accounts. Consider those features of data generation captured by our notion of general reliability. What would the background assumptions designed to capture this notion within an IRS account look like? We have already argued that in order to know that an instrument or detection process is generally reliable, it is not necessary to possess a general theory that explains the operation of the instrument or the detection process. The background assumptions that are designed to capture the role of general reliability in inferences from data to phenomena thus cannot be provided by general theories that explain the operation of instruments or detection processes. The information that grounds judgements of general reliability is, as we have seen, typically
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information from a variety of different sources – about the performance of the detection process in other situations in which it is known what results to expect, about the results of manipulating or interfering with the detection process in various ways, and so forth. While all of this information is relevant to reliability, no single piece of information of this sort is sufficient to guarantee reliability. Because this is the case and because the considerations which are relevant to reliability are so heterogeneous and so specific to the particular detection process we want to assess, it is not clear how to represent such information as a conventional background or auxiliary assumption or as a premise in an inductive inference conforming to some IRS pattern. Of course we can represent the relevant background assumptions by means of the brute assertion that the instruments and detection processes with which we are working are generally reliable. Then we might represent the decision to accept phenomenon-claim P, on the basis of data D produced by detection process R as having something like the following structure: (1) If detection process R is generally reliable and produces data having features D, it follows that phenomenon-claim P will be true with high probability. (2) Detection process R is generally reliable and has produced data having features D; therefore (3) phenomenon-claim P is true with high probability (or alternatively (4) phenomenon-claim P is true). The problem with this, of course, is that the inference from data to phenomenon now no longer looks like an IRS-style inductive inference at all. The resulting argument is deductive if (3) is the conclusion. If (4) is the conclusion, the explicitly inductive step is trivial – a matter of adopting some rule of acceptance that allows one to accept highly probable claims as true. All of the real work is done by the highly specific subject-matter dependent background claim (2) in which general reliability is asserted. The original aspiration of the IRS approach, which was to represent the goodness of the inference as a matter of its conforming to some highly general, subject-matter independent pattern of argument – with the subject-matter independent pattern supplying, so to speak, the inductive component to the argument – has not been met.30 ⎯⎯⎯⎯⎯⎯⎯ 30
Although we lack the space for a detailed discussion, we think that a similar conclusion holds in connection with judgements of local reliability. If one wished to represent formally the eliminative reasoning involved in establishing local reliability, then it is often most natural to represent it by means of the deductively valid argument pattern known as disjunctive syllogism: one begins with the premise that some disjunction is true, shows that all of the disjuncts save one are false, and concludes that the remaining disjunct is true. But, as in the case of the representation of the argument appealing to general reliability considered above, this formal representation of eliminative reasoning is obvious and trivial; the really interesting and difficult work that must be done in connection with assessing such arguments has to do with writing down and establishing the truth of their premises: has one really considered all the alternatives, does one really have good grounds for considering all but one to be false? Answering such questions typically requires a great deal of subject-matter specific causal knowledge. Just as in the case of general reliability, the original IRS
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Here is another way of putting this matter: someone who accepts (1) and (2) will find his beliefs about the truth of P significantly constrained, and constrained by empirical facts about evidence. Nonetheless the kind of constraint provided by (1) and (2) is very different from the kinds of non-deductive constraints on hypothesis choice sought by proponents of IRS models. Consider again the passage quoted from Hempel in section II. As that passage suggests, the aim of the IRS approach is to exhibit the grounds for belief in hypotheses like (3) or (4) in a way that avoids reference to “personal” or “subjective” factors and to subject-matter specific considerations. Instead the aim of the IRS approach is to exhibit the grounds for belief in (3) or (4) as resulting from the operation of some small number of general patterns of non-deductive argument or evidential support which recur across many different areas of inquiry. If (2) is a highly subject-matter specific claim about, say, the reliability of a carbon-14 dating procedure when applied to a certain kind of fossil or (even worse) a claim that asserts the reliability of a particular pathologist in correctly discriminating benign from malignant lung tumors when she looks at x-ray photographs, reference to “subject-matter specific” or “personal” considerations will not have been avoided. A satisfactory IRS analysis would begin instead with some sentential characterization of the data produced by the radioactive dating procedure or the data looked at by the pathologist, and then show us how this data characterization supports (3) or (4) by standing in some formally characterizable relationship to it that can be instantiated in many different areas of inquiry. That is, the evidential relevance of the data to (3) or (4) should be established or represented by the instantiation of some appropriate IRS pattern, not by a highly subject-matter specific hypothesis like (2). If our critique of IRS is correct, this is just what cannot be done. As the passage quoted from Hempel makes clear, IRS accounts are driven in large measure by a desire to exhibit science as an objective, evidentially constrained enterprise. We fully agree with this picture of science. We think that in many scientific contexts, evidence has accumulated in such a way that only one hypothesis from some large class of competitors is a plausible candidate for belief or acceptance. Our disagreement with IRS accounts has to do with the nature or character of the evidential constraints that are operative in science, not with whether such constraints exist. According to IRS accounts these constraints derive from highly general, domain-independent, formally characterizable patterns of evidential support that appear in many different areas of scientific investigation. We reject this claim, as well as Hempel’s implied suggestion that either the way in which evidence constrains belief must be capturable within an
aspiration of finding a subject-matter independent pattern of inductive argument in which the formal features of the pattern do interesting, non-trivial work of a sort that might be studied by philosophers has not been met.
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IRS-style framework or else we must agree that there are no such constraints at all. On the contrasting picture we have sought to provide, the way in which evidence constrains belief should be understood instead in terms of non-formal subject-matter specific kinds of empirical considerations that we have sought to capture with our notions of general and local reliability. On our account, many well-known difficulties for IRS approaches – the various paradoxes of confirmation, and the problem of explaining the connection between a hypothesis’s standing in the formal relationships to an observation sentence emphasized in IRS accounts and its being true – are avoided. And many features of actual scientific practice that look opaque on IRS approaches – the evidential significance of data generating processes or the use of data that lacks a natural sentential representation, or that is noisy, inaccurate or subject to error – fall naturally into place.31 James Bogen Department of Philosophy Pitzer College (Emeritus) and University of Pittsburgh
[email protected] James Woodward Division of Humanities and Social Sciences California Institute of Technology
[email protected]
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We have ignored Bayesian accounts of confirmation. We believe that in principle such accounts have the resources to deal with some although perhaps not all of the difficulties for IRS approaches described above. However, in practice the Bayesian treatments provided by philosophers often fall prey to these difficulties, perhaps because those who construct them commonly retain the sorts of expectations about evidence that characterize IRS-style approaches. Thus while there seems no barrier in principle to incorporating information about the process by which data has been generated into a Bayesian analysis, in practice many Bayesians neglect or overlook the evidential relevance of such information – Bayesian criticisms of randomization in experimental design are one conspicuous expression of this neglect. For a recent illustration of how Bayesians can capture the evidential relevance of data generating processes in connection with the ravens paradox, see Earman (1992); for a rather more typical illustration of a recent Bayesian analysis that fails to recognize the relevance of such considerations, see the discussion of this paradox in Howson and Urbach (1989). As another illustration of the relevance of the discussion in this paper to Bayesian approaches, consider that most Bayesian accounts require that all evidence have a natural representation by means of true sentences. These accounts thus must be modified or extended to deal with the fact that such a representation will not always exist. For a very interesting attempt to do just this, see Jeffrey (1989).
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REFERENCES Bogen, J. and Woodward, J. (1988). Saving the Phenomena. The Philosophical Review 97, 303-52. Bogen, J. and Woodward, J. (1992). Observations, Theories, and the Evolution of the Human Spirit. Philosophy of Science 59, 590-611. Braithwaite, R. (1953). Scientific Explanation. Cambridge: Cambridge University Press. Collins, H. M. (1975). The Seven Sexes: A Study in the Sociology of a Phenomenon, or the Replication of Experiments in Physics. Sociology 9, 205-24. Collins, H. M. (1981). Son of Seven Sexes: The Social Deconstruction of a Physical Phenomenon. Social Studies of Science 11, 33-62. Conant, J. B. (1957). The Overthrow of the Phlogiston Theory: The Chemical Revolution of 17751789. In: J. B. Conant and L. K. Nash (eds.), Harvard Case Histories in Experimental Science, vol. 1. Cambridge, Mass.: Harvard University Press. Davis, P. (1980). The Search for Gravity Waves. Cambridge: Cambridge University Press. Donovan, A., Laudan, L., and Laudan, R. (1988). Scrutinizing Science. Dordrecht: Reidel. Earman, J. (1992). Bayes or Bust? A Critical Examination of Bayesian Confirmation Theory. Cambridge, Mass.: The MIT Press. Earman, J. and Glymour, C. (1980). Relativity and Eclipses. In: J.L. Heilbron (ed.), Historical Studies in the Physical Sciences, vol. 11, Part I. Feyerabend, P. K. (1985). Problems of Empiricism. Cambridge: Cambridge University Press. Franklin, A. (1990). Experiment, Right or Wrong. Cambridge: Cambridge University Press. Friedman, M. (1979). Truth and Confirmation. The Journal of Philosophy 76, 361-382. Galison, P. (1987). How Experiments End. Chicago: University of Chicago Press. Glymour, C. (1980). Theory and Evidence. Princeton: Princeton University Press. Goldman, A. (1986). Epistemology and Cognition. Cambridge, Mass: Harvard University Press. Hacking, I. (1983). Representing and Intervening. Cambridge: Cambridge University Press. Hempel, C. G. (1965) Aspects of Scientific Explanation. New York: The Free Press. Howson, C. and Urbach, P. (1989). Scientific Reasoning: The Bayesian Approach. La Salle, Ill.: Open Court. Humphreys, P. (1989). The Chances of Explanation. Princeton: Princeton University Press. Jeffrey, R. (1989). Probabilizing Pathology. Proceedings of the Aristotelian Society 89, 211-226. Lavoisier, A. (1965). Elements of Chemistry. Translated by W. Creech. New York: Dover. Lewin, R. (1987). Bones of Contention. New York: Simon and Schuster. Mackie, J. L. (1963). The Paradox of Confirmation. The British Journal for the Philosophy of Science 13, 265-277. Merrill, G. H. (1979). Confirmation and Prediction. Philosophy of Science 46, 98-117. Miller, R. (1987). Fact and Method. Princeton: Princeton University Press. Pais, A. (1982). ‘Subtle is the Lord. . .’: The Science and Life of Albert Einstein. Oxford: Oxford University Press. Popper, K. R. (1959). The Logic of Scientific Discovery. New York: Harper & Row. Priestley, J. (1970). Experiments and Observations on Different Kinds of Air, and Other Branches of Natural Philosophy Connected with the Subject. Vol. 1. Reprinted from the edition of 1790 (Birmingham: Thomas Pearson). New York: Kraus Reprint Co. Reichenbach, H. (1938). Experience and Prediction: An Analysis of the Foundations and the Structure of Knowledge. Chicago: University of Chicago Press. Schlesinger, G. (1976). Confirmation and Confirmability. Oxford: Clarendon Press. Taylor, J. (1982). An Introduction to Error Analysis. Oxford: Oxford University Press. Will, C. (1986). Was Einstein Right? New York: Basic Books. Woodward, J. (1983). Glymour on Theory Confirmation. Philosophical Studies 43, 147-157. Woodward, J. (1989). Data and Phenomena. Synthese 79, 393-472.
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M. Norton Wise REALISM IS DEAD
1. Introduction In Explaining Science: A Cognitive Approach (1988), Ron Giere is attempting to deal with three opponents at once: the sterility of philosophy of science over the last thirty years, so far as its having any relevance to scientific practice; the pragmatic empiricism of Bas van Fraassen with its associated anti-realism (van Fraassen, 1980); and the “strong program” of social construction, with its radical relativism. Thus he is playing three roles. With respect to irrelevance he is playing reformer to the profession, if not heretic, while vis-à-vis van Fraassen he is one of the knights of philosophy engaged in a friendly joust; but relativism is the dragon that must be slain, or at least caged if it cannot be tamed. Cognitive science is Giere’s steed and realism his lance, suitable both for the joust and the battle with the dragon. While the mount is sturdy, I shall suggest, the lance of realism is pure rubber. Since van Fraassen is well able to defend himself, and since I have no pretensions to being one of the knights of philosophy, I will play the dragon of social construction. Let me begin, however, by generating a historical context for this new approach to philosophy of science.
2. A New Enlightenment Anyone familiar with the naturalistic philosophy of science propagated during the French enlightenment by d’Alembert, Condillac, Lavoisier, Condorcet and many others will recognize that Explaining Science announces a new enlightenment. Like the old one it depends on a psychological model. While the old one was based on the sensationalist psychology of Locke and Condillac, the new one is to be based on cognitive science. Thereby the faculties of memory, reason, and imagination are to be replaced by those of representation and judgement. The old “experimental physics of the mind,” to borrow Jean
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 269-285. Amsterdam/New York, NY: Rodopi, 2005.
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d’Alembert’s phrase for Lockean psychology, is to be replaced by a new science, more nearly a “theoretical physics” of the mind, but in both cases the faculties of the mind ground a naturalistic philosophy (Giere 1988). The two philosophies are most strikingly parallel in that both rely on a triadic relation between a linguistic element, a perceptual element, and the real world. The old philosophy presented the three aspects of knowledge as words, ideas, and facts. Lavoisier, in his Elements of Chemistry, essentially quoting Condillac, put it as follows: “every branch of physical science must consist of three things; the series of facts which are the objects of the science, the ideas which represent these facts, and the words by which these ideas are expressed. Like three impressions of the same seal, the word ought to produce the idea, and the idea to be a picture of the fact” (Lavoisier 1965). In the new philosophy, in place of word, idea, and fact, we have relational correlates: proposition, model, and real system. model (idea)
proposition (word)
real system (fact)
The heart of the new scheme is “representation,” which refers to our everyday ordinary ability to make mental maps or mental models of real systems and to use those models to negotiate the world. With models replacing ideas, representation replaces reason, especially deductive reason, which seems to play a very limited role in the problem solving activity of practical life, whether of cooks, carpenters, chess players, or physicists. Given the stress on everyday life, practice is the focus of analysis. Explaining Science: A Cognitive Approach explains scientific practice in terms of mental practice. It is therefore critical for Giere to change our conception of what scientific practice is, to show us, in particular, that the understanding and use of theories is based on representation, not reason, or not deductive reason. Similarly, there can be no question of universal rational criteria for accepting or rejecting a theory. There is only judgement, and judgement is practical. It cannot, however, according to Giere, be understood in terms of the rational choice models so prominent today in the social sciences. Instead, he develops a “satisficing” model. I am going to leave the critique of this model of judgement to others and content myself with representation. I would observe, however, that in Giere’s model of science the traditional categories of theory and theory choice get translated into
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representation and judgement, respectively. Thus I am going to be discussing only the nature of theory, which he treats in chapters 3-5. Theory choices are made in chapters 6-8. I would also observe that science in Giere’s model is highly theorydominated. Experiment is regularly described as providing data for theory testing; it has no life of its own. To appreciate his project, therefore, we must extract the term “practice” from the practical activity of the laboratory, where knowledge of materials, instruments, apparatus, and how to make things work is at issue, and transfer it to the use of theories, to theoretical practice. Here the practical activity is that of producing and using theoretical models, or representations. The basic idea is that theoretical models function much like apparatus. They are schemata of the real systems in nature, such as springs, planets, and nuclei, which allow us to manipulate those systems and generally to interact with them. Now I want to applaud this attention to practice, which is so prominent in recent history of science. And I want especially to applaud its extension to theoretical practice, which has not been so prominent. But Giere’s treatment has a consequence which I think unfortunate. It completely reduces theory to practice. This reduction will provide the first focus of my critical remarks. The second will be his realism and the third his use of this realism to defeat social constructivists. The relation of these three issues can be understood from the diagram above. First, a theory is to consist, as it does for Nancy Cartwright in How the Laws of Physics Lie, not merely of linguistic propositions – such as Newton’s laws – but also of a family of abstract models – such as the harmonic oscillator – which make sense of the propositions and which relate them to the world (Cartwright 1983, esp. chs. 7, 8). These models are constructs, or ideal types. They embody the propositions and thereby realize them. In Giere’s view, however, the propositions as such have no independent status. They are to be thought of as implicit in the models and secondary to them. And in learning to understand and use the theory one learns the models, not so much the propositions. This is the reduction of theory to practice. Secondly, the relation of the models to real systems is one of similarity. A model never captures all aspects of a real system, nor is the relation a one-to-one correspondence between all aspects of the model and some aspects of the real system. But in some respects and to some degree the model is similar to the real system. This simulacrum model, so far as I can tell, is also the same as Cartwright’s, but while she calls it anti-realism, Giere calls it realism (Cartwright 1983, ch. 8; Giere 1988, chs. 3, 4). I will call the difference a word game and conclude that realism is dead. Thirdly, the similarity version of realism is supposed to defeat the relativism of social constructivists. Perhaps it does, but it is far too heavy a weapon. Just before getting into these issues it may be useful to give one more contextual reflection. It is difficult today to discuss notions of representation
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without simultaneously discussing postmodernism, which has made representation into the shibboleth of the present. But the ideals of the Enlightenment – unity, simplicity, communicability, rationality, certainty – are precisely what postmodernism has been ridiculing for the last decade. Thus we ought to suspect that Giere in some sense shares the postmodern condition. Simplicity is no longer the name of nature, complexity is. Indeed I believe he does share this condition and that it is basically a healthy one. He thoroughly rejects the Enlightenment dream of the one great fact, or the one law which would subsume all knowledge under a unified deductive scheme. He recognizes that theoretical practice is not unified in this way; it is not a set of abstract propositions and deductions but a collection of models and strategies of explanation which exhibit the unity of a species, an interbreeding population containing a great deal of variation and evolving over time. To extend the metaphor, the relations within and between theories, between subdisciplines, and between disciplines will take us from varieties and species to entire ecological systems evolving over time. Cognitive science provides the right sort of model for this practical scheme because it is not a unified discipline in the usual sense. It is a loose cluster of disciplines, or better, of parts of disciplines, a veritable smorgasbord with a bit of logic here, of artificial intelligence there, and a smattering of anthropology on the side. It is a collection of techniques of investigation and analysis, developed originally in a variety of disciplines, which are now applied to a common object, the mind. The cluster of practices is held together only by the desire to understand mental function. Cognitive science is an excellent example of the patchwork systems of postmodern theory. It also represents the mainstream direction in contemporary universities of much research organization and funding, the cross-disciplinary approach to attacking particular issues. Thus Giere’s introductory chapter, “Toward a Unified Cognitive Theory of Science” (1988, ch. 1) is appropriately titled if we remember that the unity involved is not unity in the Enlightenment sense. He is hostile to disciplinary identification of the object of study, as in philosophy’s hang-up on rationality and sociology’s on the social. Entities like cognitive science will hold together only so long as their components fertilize each other intellectually or support each other institutionally, that is, so long as fruitful interaction occurs at the boundaries between its component practices. Here, if the evolutionary metaphor pertains, we should expect to find competition, cooperation, and exchange. That is, we should expect to find that social processes are the very heart of the unity of practice. But that is what we do not find. Seen in the light of postmodern theories of practice, my problems with Giere’s theory come at its two ends: in the complete reduction of the old Enlightenment unity of ideas to a new enlightenment unity of practices, and in the failure to make the unity of practices into a truly social interaction.
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3. Reduction of Theory to Practice in Mechanics Because Giere sets up his scheme with respect to classical mechanics, I will discuss in some detail his rendering of it. He has examined a number of textbooks at the intermediate and advanced level and contends that the presentation conforms to his scheme, that physicists understand and use classical mechanics in the way they ought to if representation via models is the real goal of the theory. I will attempt to show that these claims are seriously distorting, both historically and in the present. The problems begin at the beginning, when he throws into one bag intermediate and advanced textbooks, which are designed for undergraduate and graduate courses, respectively. The intermediate ones are intermediate rather than elementary only because they use the vector calculus to develop a wide range of standard problems, which I agree function as models in the above sense. But these texts base their treatment on Newton’s laws of motion and on the concept of force, that is, on the principles of elementary mechanics. What most physicists would call advanced texts, which are based on extremum conditions like the principle of least action and Hamilton’s principle, are said to differ from the sort based on Newton’s laws “primarily in the sophistication of the mathematical framework employed” (Giere 1988, p. 64). Nothing could be farther from the truth. The entire conceptual apparatus is different, including the causal structure. And it includes large areas of experience to which Newton’s laws do not apply. Thus Giere’s phrase “the Hamiltonian version of Newton’s laws,” rather than the usual “Hamiltonian formulation of mechanics,” betrays a serious distortion in the meaning that “advanced” mechanics has had for most physicists since around 1870 (Giere 1988, p. 99). This is significant in the first instance because Giere wants us to believe that the reason it doesn’t seem to matter much in mechanics textbooks, and in the learning and doing of physics, whether or which of Newton’s laws are definitions, postulates, or empirical generalizations is that the theory is to be located not so much in these laws themselves as in the model systems which realize them, like the harmonic oscillator and the particle subject to an inversesquare central force. But a more direct explanation would be that these laws are not actually considered foundational by the physicists who write the textbooks. These writers are teaching the practical side of a simplified theory which has widespread utility. Foundations are discussed in advanced texts, where extremum conditions, symmetry principles, and invariance properties are at issue. Debate within a given context, I assume, normally focuses on what is important in that context. We should not look to intermediate textbooks for a discussion of foundations. If we do we will be in danger of reducing theory to practice, and elementary practice at that.
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I would like to reiterate this first point through a brief glance at the content of mechanics texts in historical terms. If we look at the great French treatises and textbooks of Lagrange, Laplace, Poisson, Duhamel, Delaunay and others through the nineteenth century we will not find Newton’s laws at all. The foundations of French mechanics, including the standard textbooks of the École Polytechnique, were d’Alembert’s principle and the principle of virtual velocities, a generalized form of the balance principle which Lagrange used to reduce dynamics to statics. In Britain, of course, Newton’s laws were foundational, and judging from the amount of ink spilt, their status mattered considerably: from their meaning, to how many were necessary, to their justification. William Whewell’s Cambridge texts are instructive here (1824, 1832). After mid-century Newton’s laws did take on a standard form, at least in Britain, but only when they had been superseded. In the new physics, which for simplicity may be dated from Thomson and Tait’s Treatise on Natural Philosophy of 1867, energy functions replace force functions and extremum principles replace Newton’s laws (Kelvin and Tait 1879-83). Force is still a meaningful concept, but a secondary one, literally derivative, being defined as the derivative of an energy function (Smith and Wise 1989). Now this is all rather important because the new theory promised to penetrate thermodynamics and electromagnetic fields. In these areas Newton’s laws had little purchase. My point is that the value of the new theory lay not so much in supplying a more powerful way to solve old problems, as in suggesting a different conceptual base which might encompass entirely new realms of experience. The value of theory lay not so much in its power to solve problems as in its power to unify experience. The monolithic attempt to reduce theory to practice misses this central point. Cartwright and I may fully agree with Giere that theories consist in the general propositions and idealized model systems together, indeed we may agree that so far as use of the theory to solve problems is concerned, the models are what count. But one does not thereby agree that the general propositions ought to be thought of as what is implicit in the models. The propositions are what enable one to recognize the diversity of models as of one kind, or as having the same form. The power of theory lies in its unifying function. In this sense, theoretical strategy is not the same as practical strategy. Inventing a chess game is not the same as playing chess. Similarly, theoretical physicists are not the same sort of bird as mathematical physicists and neither is of the same sort as an experimentalist. Although they all interbreed, the evolution of physics has produced distinct varieties. I suspect that at the level of professional physicists Giere’s naturalism reduces the theoretical variety to the mathematical one. To capture the essential difference between theoretical and practical strategies the diagram below may be helpful. The top wedge represents the strategy of a theorist in attempting to encompass as many different natural systems as
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possible under one set of propositions. If the propositions are taken as the Hamiltonian formulation of mechanics, then the theorist hopes to include not only classical mechanics itself, but thermodynamics, geometrical optics, electromagnetic theory, and quantum mechanics. The ideal is unity under deduction, although the deduction must be constructed in each case by factoring in a great deal of specialized information not contained in the propositions.
Hamilton’s principle
Logic Psychology Anthropology Artificial intelligence Neurology
Classical mechanics Thermodynamics Electromagnetism Geometrical optics Quantum mechanics
Mental function
The lower wedge, directed oppositely, represents the practical strategy of solving a particular problem (at the point of the wedge) by bringing to bear on it whatever resources are available: bits of theory, knowledge of materials, phenomenological laws, standard apparatus, mathematical techniques, etc. One assembles a wide variety of types of knowledge and tries to make them cohere with respect to a single object of interest. If classical mechanics epitomizes the theoretical wedge, cognitive science epitomizes the practical one. Of course neither strategy is ever fully realized in a pure form. But as strategies they seem to be very different in kind and to serve very different purposes. Perhaps a naturalist would argue that that is why the theoretical and the practical are so ubiquitously differentiated in everyday life.
4. Similarity Realism The historical picture takes on a somewhat different tint with respect to realism. Giere argues that theoretical models represent real systems in some respects and to some degree and that in these respects and degrees they are realistic. Nearly
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all of the formulators of the new mechanics, however, rejected precisely this version of the realism of theories. Thomson and Tait labeled their theoretical development “abstract dynamics” to differentiate it from the realistic theory they lacked, namely “physical dynamics.” Abstract dynamics worked with rigid rods, frictionless surfaces, perfectly elastic collisions, point particles and the like, not with the properties of real materials. They were singularly unimpressed with the fact that abstract dynamics yielded approximately correct results in certain idealized situations, because the theory actually violated all experience. Most simply, its laws were reversible in time, which meant that it contradicted the second law of thermodynamics and therefore could not be anything like correct physically. They suspected that its fundamental flaw lay in the fact that it dealt with only a finite number of variables. It could be formulated, therefore, only for a finite system of discrete particles and would not apply to a continuum, which Thomson especially believed to be the underlying reality (Smith and Wise 1989, chs. 11, 13, 18). But the argument does not depend on this continuum belief. As I interpret Thomson, he would say that the realist position is vitiated not by the fact that the theory fails to reproduce natural phenomena in some respect or to some degree but by the fact that it straightforwardly contradicts all empirical processes in its most fundamental principles. He would not understand the point of Giere’s contention with respect to the ether that its non-existence is “not [a good basis] for denying all realistically understood claims about similarities between ether models and the world” (Giere 1988, p. 107; emphasis in original). Why not, pray tell? Why not simply call the similarities analogies and forget the realism? Thomson was a realist, most especially about the ether. But to get at reality he started at the far remove from abstract theory and abstract models, namely at the phenomenological end, with the directly observable properties of known materials. For example, he argued for the reality of his elastic-solid model of ether partly on the grounds that the ether behaved like Scotch shoemaker’s wax and caves-foot jelly. He attempted always to construct realistic models which relied on the practical reality of familiar mechanical systems rather than on the mathematical structure of idealized hypothetical models. From the perspective of this contrast between abstract dynamics and practical reality, the point of reformulating mechanics in terms of energy functions and extremum conditions was not to obtain a more realistic theory but to obtain a more general one, and one that was thus more powerful in the sense of organizing a greater range of experience. To make abstract mechanics subsume thermodynamics one could represent matter as composed of a finite number of hard atoms interacting via forces of attraction and repulsion, but then one would have to add on a randomizing assumption in order to get rid of the effects of finiteness and timereversibility in the equations of mechanics. The resulting theory, doubly false,
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certainly did not count as realistic among its British analysts: Thomson, Tait, Maxwell, and others. Maxwell put this point in its strongest form, to the effect that the goal of theoretical explanation in general, and especially of the new mechanics, was not to discover a particular concrete model which reproduced the observed behavior of the system in question but to discover the most general formulation possible consistent with this observed behavior. Thus one sought the most general energy function for the system, a Lagrangian or a Hamiltonian, which would yield empirically correct equations for its motion, this energy function being specified in terms of observable coordinates alone, like the input and output coordinates of a black box, or more famously like the bell ropes in a belfry, independent of any particular model of the interior workings of the belfry. For every such Lagrangian or Hamiltonian function, Maxwell observed, an infinite variety of concrete mechanical models might be imagined to realize it. He himself exhibited uncommon genius in inventing such models, but unlike his friend Thomson, he was much more sanguine about the value of unrealistic ones, regarding them as guarantors of the mechanical realizability of the Lagrangian in principle. He did not suppose that a similarity between the workings of a given model and observations on a real system indicated that the system was really like the model, but only analogous to it. Being analogous and being like were two different things. Similar remarks could be made for the perspective on generalized dynamics and on mechanical models of Kirchhoff, Mach, Hertz, and Planck. Even Boltzmann, the most infamous atomistic-mechanist of the late nineteenth century expressed himself as in agreement with Maxwell on the relation of models to real systems. Since Boltzmann, in his 1902 article on “Models” for the Encyclopaedia Britannica, cites the others to support his view, I will let him stand for them all. Boltzmann remarks that “On this view our thoughts stand to things in the same relation as models to the objects they represent . . . but without implying complete similarity between thing and thought; for naturally we can know but little of the resemblance of our thoughts to the things to which we attach them.” So far he does not diverge strikingly from Giere on either the nature or the limitations of similarity. But while Giere concludes realism from limited similarity, Boltzmann concludes that the “true nature and form” of the real system “must be regarded as absolutely unknown” and the workings of the model “looked upon as simply a process having more or less resemblance to the workings of nature, and representing more or less exactly certain aspects incidental to them.” Citing Maxwell on mechanical models, he observes that Maxwell “did not believe in the existence in nature of mechanical agents so constituted, and that he regarded them merely as means by which phenomena could be reproduced, bearing a certain similarity to those actually existing . . . The question no longer being one of ascertaining the actual internal structure of
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matter, many mechanical analogies or dynamical illustrations became available, possessing different advantages.” For Maxwell, “physical theory is merely a mental construction of mechanical models, the working of which we make plain to ourselves by the analogy of mechanisms we hold in our hands, and which have so much in common with natural phenomena as to help our comprehension of the latter” (Boltzmann 1974, p. 214, 218, emphasis added). Structural analogy, not realism, is the relation of similarity between models and natural phenomena. I do not see that Giere has shown more. His appeal to the category of representation in cognitive science does not help. To drive one last nail in this coffin of realism, let me tell a little story about G. F. Fitzgerald, a second generation Maxwellian who attempted in 1896 to convince his friend William Thomson, Lord Kelvin since 1892, of the wrong-headed nature of Thomson’s elastic-solid model of the ether. The debate between them had been going on for twenty years already, with Thomson insisting that the ether had to be like an elastic solid, given the nature of all known materials, and complaining that Maxwell’s equations did not give a sufficiently definite mechanical model based on force and inertia. To rely on Maxwell’s equations as the basis of electromagnetic theory Kelvin regarded as “nihilism,” the denial that reality could be known. Fitzgerald in turn argued that the elastic-solid supposition was unwarranted. In spite of a limited analogy, the ether might not be at all like any known matter. The matter of the ether, to him, was simply that which obeyed the mathematical laws invented by Maxwell and corroborated by experiment. “To work away upon the hypothesis” that the ether was an elastic solid, therefore, was “a pure waste of time” (Smith and Wise 1989, ch. 13). To this condemnation of his realistically interpreted analogy, Kelvin retorted: the analogy “is certainly not an allegory on the banks of the Nile. It is more like an alligator. It certainly will swallow up all ideas for the undulatory theory of light, and dynamical theory of E & M not founded on force and inertia. I shall write more when I hear how you like this.” The answer came, “I am not afraid of your alligator which swallows up theories not founded on force and inertia . . . I am quite open to conviction that the ether is like and not merely in some respects analogous to an elastic solid, but I will . . . wait till there is some experimental evidence thereof before I complicate my conceptions therewith.” Oliver Heaviside put it more succinctly, remarking to Fitzgerald that Lord Kelvin “has devoted so much attention to the elastic solid, that it has crystallized his brain” (Smith and Wise 1989, ch. 13). Now I am not suggesting that Ron Giere’s realism has crystallized his brain; but like Fitzgerald, I fail to see what the claim of realism about theories adds to that of analogy. I would suggest further, that a naturalistic theory of science, which is supposed to represent the actual behavior of theoretical physicists, ought to consider the history of that behavior. I have attempted to show with the above examples that a very significant group of theoreticians over a fifty-year
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period examined the similarity relations that Giere considers an argument for realism and drew the opposite conclusion. They opted for nihilism. Given the prominent role of these people in the evolution of physics, it seems that an evolutionary naturalism in particular, ought not to make the successful pursuit of physics depend on realism about theories. I therefore advocate following their nihilistic example with respect to the realism-antirealism game. But this conclusion does not follow only from history. A reading of many contemporary theorists supports it. Stephen Hawking, for example, in his popular little book, A Brief History of Time (1988), contends that theoreticians are merely engaged in making up more or less adequate stories about the world. The same view appears at length in a book called Inventing Reality: Physics as Language (1988), by Bruce Gregory, associate director of the Harvard-Smithsonian Center for Astrophysics. “A physicist is no more engaged in painting a ‘realistic’ picture of the world than a ‘realistic’ painter is,” Gregory opines, and again, “[p]hysical theories do not tell physicists how the world is; they tell physicists what they can predict reliably about the behavior of the world.” The preceding two sections suggest that Giere’s reduction of theory to practice and his similarity realism are linked. Actually I think that if we reject the former we automatically reject the latter. I will illustrate this linkage with a final example from mechanics, again emphasizing the more sophisticated versions which rely on extremum conditions and the variational calculus. The most important theoretical goal in using such formulations is to be able to encompass within a single formalism a wide variety of quite different fields of physics which employ different mathematical relations, such as Newton’s laws, Maxwell’s equations, and the Schrödinger equation. Goldstein, the author of one of Giere’s advanced textbooks and the one my entire generation of physicists was brought up on, remarks that “[c]onsequently, when a variational principle is used as the basis of the formulation, all such fields will exhibit, at least to some degree, a structural analogy” (Goldstein 1950, p. 47). This is the same view that Maxwell promoted about formal analogy. It means, to give Goldstein’s simple example, that an electrical circuit containing inductance, capacitance, and resistance can be represented by a mechanical system containing masses, springs, and friction. The similarity, however, has never induced physicists to call the representation realistic. The same argument applies to the relation between theoretical models and real systems.
5. Realism in the Laboratory Very briefly, I shall comment on a different kind of realism which appears in a chapter of Giere’s book entitled “Realism in the Laboratory.” The focus shifts from theoretical models to theoretical entities and the argument for realism
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shifts from similarity to manipulation and control. Here comparisons with Ian Hacking’s Representing and Intervening are unavoidable, as Giere acknowledges. One thinks particularly of Hacking’s phrase “If you can spray it, it’s real,” for which Giere’s alternative is, “Whatever can be physically manipulated and controlled is real” (Hacking 1983; Giere 1988). He has as little time for philosophers and sociologists who don’t believe in protons as he would have for soldiers who don’t believe in bullets, and for much the same reasons. Both can be produced and used at will with predictable effect. Protons, in fact, have the status in many experiments, not of hypothetical theoretical entities, but of research tools. The part of this discussion I like best is the three pages on technology in the laboratory. The subject has become a popular one in the last five years, at least in the history of science. In Giere’s naturalistic scheme, technology provides the main connector between our cognitive capacity for representation and knowledge of, for example, nuclear structure. He suggests that the sort of knowledge bound up in technology is an extension of our sensorimotor and preverbal representational systems. It is both different in kind and more reliable than knowledge requiring symbolic and verbal manipulation. It is knowledge of the everyday furniture of the laboratory, which allows one to act in the world of the nucleus. Here we seem finally to be talking about experimental practice and the life of an experimental laboratory. Theory testing is certainly involved, but is by no means the essence. I can only complain that three pages hardly count in a subject so large as this one. I do have two reservations, however. First, there seems to be a tendency to slide from the reality of a thing called a proton to the reality of the model of the proton, including its properties and characteristics. The model, even for the simplest purposes, involves a quantum mechanical description of elusive properties like spin, which is not spin at all in our everyday sense of a spinning ball. Does this assigned property have the same reality status as the proton itself? One need not get into the status of quantum mechanical models to raise this problem. Historically, many entities have been known to exist, and have been manipulated and controlled to an extraordinary degree, on the basis of false models. Electric current is an outstanding example. Our ability to manipulate and control a proton may well guarantee the reality of the proton without guaranteeing the reality of any model of it. This point goes back immediately to the previous remarks about similarity realism and theoretical models. My second reservation has to do with tool use. How are we to differentiate between material tools like magnets, detectors, and scattering chambers, on the one hand, and intellectual tools like mathematical techniques, on the other hand? Both are used as agents of manipulation and control of protons and both are normally used without conscious examination of principles or foundations.
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Both are the stuff of practice. Once again then, any arguments about laboratory practice are going to have to tie back into those about theoretical practice. A more thoroughgoing analysis will be required to show their similarities and differences.
6. Social Construction and Constrained Relativism If it is true, as I have argued, that Giere’s realism about theories is just a game with words, why does he pursue the game? The only answer I can see is that he is anxious to defeat the radical relativism which he associates with sociologists or social constructivists. That is, Giere’s realism serves primarily as a guard against relativism in the no-constraints version, which maintains that nature puts no constraints on the models we make up for explaining it. All models are in principle possible ones and which one is chosen is merely a matter of social negotiation. The problem of explaining the content of science, therefore, is exclusively that of explaining how one scheme rather than another comes to have currency among a particular social group. To move all the way to a realist position to defeat this form of relativism, however, seems to be bringing up cannons where peashooters would do. A simpler argument would be to reject no-constraints relativism on pragmatic grounds, on the grounds that there is no evidence for it and a great deal of evidence against it. It is so difficult to make up empirically adequate theories of even three or five different kinds, that we have no reason to believe we could make up ten, let alone an infinite number, and much less every conceivable kind. Constructing castles in the air has not proved a very successful enterprise. The construction of magnetic monopoles has fared little better. Arguing from all experience with attempts to construct adequate models, therefore, particularly from the empirical failure of so many of the ones that have been constructed, we must suppose that nature does put severe constraints on our capacity to invent adequate ones. Radical relativism, for a naturalist, ought to be rejected simply because it does not conform to experience. This argument leaves a social constructivist perfectly free to claim that, within the limits of empirical consistency, even though these limits are severe, all explanations are socially constructed. Among the reformed school, Andrew Pickering, Steven Shapin, Simon Schaffer, and Bruno Latour all hold this view. As Pickering puts it, nature exhibits a great deal of resistance to our constructions. Almost no social constructivists, to my knowledge, presently subscribe to the no-constraints relativism of the strong program except a few devotees
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remaining in Edinburgh and Bath.1 For those interested in the new constellation of social construction I would recommend a recent issue of Science in Context, with contributions from Tim Lenoir, Steve Shapin, Simon Schaffer, Peter Galison, and myself, among others. Bruno Latour’s Science in Action (1987) also presents an exceedingly interesting position. He extends the social negotiations of the old strong program to negotiations with nature. For all of these investigators, nature exhibits such strong resistance to manipulation that no-constraints relativism has become irrelevant. And the constrained relativism which they do adopt does not differ significantly from what Giere calls realism. There are, however, significant reasons for not calling it realism. Constraints act negatively. They tell us which of the options we have been able to invent are possibly valid ones, but they do not invent the options and they do not tell us which of the possible options we ought to pursue. This suggests immediately that in order to understand how knowledge gets generated we must analyze the social and cultural phenomena which, over and above the constraints which nature is able to exert, are productive of scientific knowledge. Actually this position seems to be Giere’s own. Noting that his constructive realism was invented to counter van Fraassen’s constructive empiricism, he adds, “The term emphasizes the fact that models are deliberately created, ‘socially constructed’ if one wishes, by scientists. Nature does not reveal to us directly how best to represent her. I see no reason why realists should not also enjoy this insight” (Giere 1988, p. 93). They should, but having savored its delights, they should give up realism. The position I am advocating has strong instrumentalist aspects. People use what works, or what has utility. But the instrumentalism of philosophers does not normally take into account the social relativity of utility. What works is relative to what purposes one has, and purposes are generally social. Thus it is no good explaining the growth of Maxwellian electromagnetic theory in Britain simply in terms of the fact that it gave a satisfactory account of the behavior of light. Satisfactory to whom? Certainly not to all mathematical physicists in Britain and certainly not to any mathematical physicists on the Continent between 1863, when Maxwell first published his theory, and the mid-1890s when it was superseded by Lorentz’s electron theory. Social historians contend that differences like these require a social interpretation of how scientific explanations get constituted. Philosophers of science, including instrumentalists and pragmatists, have generally had nothing to offer. They do not incorporate the social into the essence of science, but leave it on the borders, perpetuating the internal-external dichotomy. ⎯⎯⎯⎯⎯⎯⎯ 1
Shapin, one of the original Edinburgh group, never accepted the social determinist position. He has removed to San Diego. Pickering has removed to Illinois, but not before feuding with Bloor on the subject. Latour has been similarly sparring with Collins.
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Ron Giere is somewhat unique on this score, in that he is anxious not to exclude the social and historical contingency of science, but he too offers little that is explicitly social. Representation is for him an activity of individuals. They may achieve their individual representations in a social setting but the process of interaction is not a constitutive part of their representations. With this issue I would like to return to my starting point in the Enlightenment. The new enlightenment shares a standard flaw with the old. Based on individual psychology, it remains individualist in its philosophy of science. It allots no conceptual space, for example, to the political economy that permeates the practice of science and acts as a highly productive force in its advancement. It does not explicitly recognize that individuals are socially constructed, just as the objects are that individuals explain. Until the social process is brought in explicitly, philosophy of science will have little to offer to the social history of science.
7. Realism Is Dead In conclusion, I would like to return once more to the simulacrum model in order to suggest a somewhat different view of it. Previously I have attempted to show that if the behavior of physicists is to be our arbiter, then similarity between theoretical models and real systems cannot be used as an argument for the realism of theories. On the other hand, the similarity remains, and remains highly useful, whether we play the realist-antirealist game or not. It is just a game. But suppose we take the nihilist view a bit more seriously, and that we remodel Nietzsche’s famous line about God. The question is no longer whether God exists or not; God is dead. Similarly, we are beyond realism and antirealism. The question is no longer whether reality speaks to us through our models or not. Realism is dead. We have collapsed reality into our models and they have become reality for us. That seems to me the proper attitude to take to the simulacrum scheme. Here I am borrowing the argument of one of the more notorious postmodernists, Jean Baudrillard, who uses the term ‘simulacrum’ to describe the relation between image and reality in contemporary film and literature. I find his attitude particularly appropriate to Giere’s argument just because the argument identifies realism with similarity. It rescues reality by turning it into its opposite, the image. It thereby collapses reality into our models of it. Like film images, the models become more real than reality itself. They become “hyperreal,” to use Baudrillard’s term. One could easily take a critical view of this process. I would like instead to look at its positive side. It means that our models are reality-forming. They are so detailed, so technically perfect, that we lose the consciousness of their being representations. They function for us as total simulacra, or reality itself. Of
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course we know that models pick out certain aspects for emphasis, subordinate others, and ignore or even suppress the remainder, but if the model is our means for interacting with the world then the aspects that it picks out define the reality of the world for us. This attitude gains its strongest support from technology. Whenever we embody models in material systems and then use those systems to shape the world, we are shaping reality. Prior to the twentieth century, it might be argued, technology merely enhanced or modified already existing materials and energy sources. But that is certainly no longer the case. We regularly produce substances and whole systems that have no natural existence except as artifacts of our creation. This is most startling in the case of genetic engineering, where life itself is presently being shaped, but it applies equally to Teflon and television. I would stress that we typically accomplish these creations by manipulating models which we attempt to realize in the world. Often nature is recalcitrant and we have to return to our models. But far from representing a preexisting nature, the models create the reality that we then learn to recognize as natural. The process of creation is most obvious with respect to computer simulations. They have become so sophisticated, and so essential to basic research in all of the sciences, that they often substitute for experimental research. A computer-simulated wind tunnel can have great advantages over a “real” one as a result of increased control over relevant variables and elimination of irrelevant ones. More profoundly, the entire field of chaos theory has emerged as a result of computer simulations of the behavior of non-linear systems. The computer-generated pictures make visible distinct patterns of behavior where previously only chaotic motion appeared. They show how such patterns can be generated from simple codes iterated over and over again. Of course, it is possible to hold that the computer simulations merely discover a reality that was actually there all along. But this way of talking is precisely the target of the assertion that realism is dead. I prefer to say that the simulations create one of the constructions of reality possible under the constraints of nature. They show that it is possible coherently to represent chaotic systems in terms of iterated codes. But this representation is an artifact of the computer, or an artifact of an artifact. Herein lies the lesson of the simulacrum scheme. We are the creators. M. Norton Wise Department of History University of California, Los Angeles
[email protected]
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REFERENCES Boltzmann, L. (1974). Theoretical Physics and Philosophical Problems: Selected Writings. Edited by B. McGuinness, with a foreword by S. R. de Groot; translated by P. Foulkes. Dordrecht: Reidel. Cartwright, N. (1983). How the Laws of Physics Lie. Oxford: Clarendon Press. Giere, R. N. (1988). Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press. Goldstein, H. (1950). Classical Mechanics. Cambridge, Mass.: Addison-Wesley. Gregory, B. (1988). Inventing Reality: Physics as Language. New York: Wiley. Hacking, I. (1983). Representing and Intervening: Introductory Topics in the Philosophy of Natural Science. Cambridge: Cambridge University Press. Hawking, S. W. (1988). A Brief History of Time: From the Big Bang to Black Holes. Toronto, New York: Bantam. Latour, B. (1987). Science in Action: How to Follow Scientists and Engineers through Society. Cambridge, Mass.: Harvard University Press. Lavoisier, A.-L. (1965). Elements of Chemistry: In a New Systematic Order, Containing all the Modern Discoveries. Translated by R. Kerr. New York: Dover. Kelvin, W. Thomson and Tait, P. G. (1879-83). Treatise on Natural Philosophy. New edition. 2 vols. Cambridge: Cambridge University Press. Smith, C. and Wise, M. N. (1989). Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge: Cambridge University Press. Van Fraassen, B. C. (1980). The Scientific Image. Oxford: Clarendon Press. Whewell, W. (1824). An Elementary Treatise on Mechanics: Designed for the Use of Students in the University. 2nd edition. Cambridge: Printed by J. Smith for J. Deighton. Whewell, W. (1832). On the Free Motion of Points, and on Universal Gravitation, including the Principal Propositions of Books I. and III. of the Principia; the First Part of a New Edition of a Treatise on Dynamics. Cambridge: For J. and J. J. Deighton.
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1. A New Enlightenment? I appreciate Norton Wise’s comparison of my project in Explaining Science (1988) with that of Enlightenment scientists and philosophers (Wise, this volume). When rejecting one’s immediate philosophical predecessors, it is comforting to be able to portray oneself not as a heretic who has abandoned philosophy, but as a reformer who would return philosophy to the correct path from which his predecessors had strayed. But we cannot simply return to the ideals of the Enlightenment. Some doctrines that were fundamental to the Enlightenment picture of science must be rejected. In particular, I think we must reject the idea that the content of science is encapsulated in universal laws. And we must reject the notion that there are universal principles of rationality that justify our belief in the truth of universal laws. As Wise notes, these latter are typically “postmodern” themes, and, as such, are usually posed in explicit opposition to the modernism of the Enlightenment. It is my view that this opposition must be overcome. The overall project for the philosophy of science now is to develop an image of science that is appropriately postmodern while retaining something of the Enlightenment respect for the genuine accomplishments of modern science. To many the idea of an “enlightened postmodernism” may seem contradictory. I see it merely as an example of postmodern irony.
2. Mechanics Wise has most to say about my discussion of theories based on an analysis of classical mechanics seen through the eyes of contemporary textbooks. I will not argue with Wise about the history of mechanics, since he is an expert on that subject and I am not. I concede the point that the difference between intermediate and advanced mechanics texts is not just that the advanced texts
In: Martin R. Jones and Nancy Cartwright (eds.), Idealization XII: Correcting the Model. Idealization and Abstraction in the Sciences (Poznań Studies in the Philosophy of the Sciences and the Humanities, vol. 86), pp. 287-293. Amsterdam/New York, NY: Rodopi, 2005.
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use a more sophisticated mathematical framework. I can safely admit, as Wise claims, that the Hamiltonian formulation of mechanics “includes large areas of experience to which Newton’s laws do not apply.” What I do not see is how this makes any difference to my main point, which was that scientific theories are not best understood as sets of universal statements organized into deductive systems. They are better understood as families of models together with claims about the things to which the models apply (Giere 1988, ch. 3). Wise and I seem to agree that Newton’s laws may best be thought of as providing a recipe for constructing models of mechanical systems. I do not see why moving up in generality from Newton’s laws to Hamilton’s equations should move one from mere recipes to fundamental laws. Rather, it seems to me that Hamilton’s equations merely provide a more general recipe for model building. One simply has a bigger family of models. Having said that, I am inclined to agree that there is something to Wise’s preference for the Hamiltonian formulation. The problem is to capture that difference within my particularistic view of scientific theories. Wise refers to the power of theory to “unify experience.” Newton’s theory is traditionally credited with possessing this virtue. It unified terrestrial and celestial motions, for example. My first inclination is to say that this unity consists primarily in the fact that “Newton’s laws” provide a single recipe for constructing models that succeed in representing both terrestrial and celestial systems. The unity provided by Hamilton’s equations is just more of the same. In short, unity may best be understood simply as scope of application. Yet there still seems something more to the Hamiltonian version of mechanics. The word “foundational,” however, does not seem to capture the difference. As Wise himself notes, what counts as “foundational” at any particular time may depend on whether one is in Britain or France. The difference, I think, is that the Hamiltonian approach is more fundamental. That is to say, energy is more fundamental than force. But what does “fundamental” mean in this context? Here I am tempted to invoke a realist framework. The conviction that energy is more fundamental than force is the conviction that energy is the causally deeper, and more pervasive, quantity in nature. Forces are merely the effects of changes in energy. On this understanding, wide scope of application turns out to be not only pragmatically valuable, but an indicator of something fundamental in nature. Does this mean that I persist in “reducing theory to practice”? And would that be a bad thing? I do not know how to answer these questions. Nor am I convinced it is important to do so. What matters to me is whether this is the right account of the nature and role of theory in science as we now know it.
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3. Realism In Explaining Science I distinguish several varieties of empiricism and several varieties of realism (1988, ch. 4). Whether to call my view “realist” or not depends on which variety one has in mind. And whether the label is important depends on the variety of non-realism being denied. Wise’s discussion is informed by nineteenth century intellectual distinctions with which I am only vaguely familiar. When he quotes Boltzmann writing that the “true nature and form” of real systems “must be regarded as absolutely unknown,” I hear echoes of Kant. And I think of Hilary Putnam’s (1981) characterization of “metaphysical realism.” If realism is the view that nature has a definite nature apart from any conceptualization and, moreover, that we could somehow know that nature “directly” without any mediating perceptual and conceptual structures, then I am an anti-realist. Again, if realism is the view that there must be complete isomorphism between model and thing modeled, so that, for example, the ether would have to be regarded as literally containing little wheels, then I am an anti-realist. Our differences come out clearly when Wise writes: Structural analogy, not realism, is the relation of similarity between models and natural phenomena. As I understand it, “structural analogy” is probably the most important kind of similarity between models and real systems. Constructive realism, for me, includes the view that theoretical hypotheses assert the existence of a structural analogy between models and real systems. I might even be pressed into claiming that “similarity of structure” is the only kind of similarity between models and reality that matters. I call this a kind of realism. Wise says that is an empty word; we might as well call it anti-realism. Whether the label is significant depends on the work it does. Wise thinks it is mainly a weapon in the battle against social constructivism. It is that, but much more. It is central to my understanding of a large part of post-positivist philosophy of science. For the moment I will drop the word “realism” in favor of what for me is a more fundamental notion, representation. Logical empiricism was representational in the strong sense that it regarded scientific hypotheses as true or false of the world. Moreover, logical empiricists dreamt of constructing an inductive logic that would provide the rational degree of belief, relative to given evidence, in the truth of any hypothesis. Beginning with Kuhn (1962), a major strain of post-positivist thinking denied the representational nature of science. For Kuhn, science is a puzzle solving activity which provides, at most, a way of looking at the world, but not literally a representation of it – certainly not in the sense that science makes claims about what is true or false of the world. One of the major lines of reaction to Kuhn, that of Lakatos (1970) and Laudan (1977), agrees with Kuhn about the non-representational nature of
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science. For Lakatos, progressive research programs are those that generate new empirical (not theoretical) content. Laudan remained closer to Kuhn in maintaining that more progressive programs are those with greater problem solving effectiveness. Both Lakatos and Laudan identified progress with rationality so as to recover the philosophical position that science is rational, in opposition to Kuhn who denied any special rationality for science. There is one more distinction to be made before I can conclude my defense of realism. Laudan, for example, claims that his account of science is representational in the sense that scientific hypotheses are statements that are in fact true or false. He calls this “semantic realism.” But he goes on to argue that there are no, and perhaps can be no, rational grounds for any claims one way or the other. In short, the basis of Laudan’s anti-realism is not semantic, but epistemological. The same is true of van Fraassen’s (1980) anti-realism. My realism has two parts. First, it rejects notions of truth and falsity as being too crude for an adequate theory of science. Taken literally, most scientific claims would have to be judged false, which shows that something is drastically wrong with the analysis. Rather, I regard scientific hypotheses as typically representational in the sense of asserting a structural similarity between an abstract model and some part of the real world. (I say “typically” because I want to allow for the possibility of cases where this is not so. Parts of microphysics may be such a case.) The second part is the theory of scientific judgment, and the theory of experimentation, which Wise, for reasons of exposition, put to one side. As elaborated in Explaining Science, I think there are judgmental strategies for deciding which of several models possesses the greater structural similarity with the world. Typically these strategies involve experimentation. And they are at least sometimes effective in the sense that they provide a substantial probability for leading one to make the right choice (1988, ch. 6).
4. Scientists’ Theories of Science Before turning to social constructivism, I would like to indulge in one methodological aside. Wise suggests “that a naturalistic theory of science, which is taken to mirror the views of theoretical physicists about theory, would do well to consider the history of physicists’ attitudes” (Wise, this volume). That suggestion is ambiguous and can be quite dangerous. Everybody has theories about the world. And most people also have theories about themselves and what they are doing in the world. But one’s theories about oneself are only loosely descriptive of one’s real situation. These theories also, perhaps mainly, serve to rationalize and integrate one’s interests, activities, and ambitions. Thus, as a general rule, actors’ accounts of their own activities
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cannot be taken as definitive. These accounts provide just one sort of evidence to be used in the investigation of what the actors are in fact doing. Scientists are no different. The theories scientists propound about their scientific activities do not have a privileged role in the study of science as a human activity. What scientists will say about the nature of their work depends heavily on the context, their interests and scientific opponents, the supposed audience, even their sources of funding. Newton’s claim not to feign hypotheses may be the most famous case in point. The claim is obviously false of his actual scientific practice. It may make more sense when considered in the context of his disputes with Leibniz and the Cartesians. But I am no historian. Let me take a more mundane example from my own experience studying work at a large nuclear physics laboratory (1988, ch. 5). One of my “informants” claimed that physics is like poetry and that physicists are like poets. I don’t know if he ever propounded this theory to his physicist friends. But he told me, most likely because he thought that this is the kind of thing that interests philosophers of science. Well, maybe there is poetry, as well as music, in the hum of a well-tuned cyclotron. But the truth is that this man began his academic life as an English major with strong interests in poetry. I am sure that this fact had more to do with sustaining his theory about the nature of physics than anything going on in that laboratory. I can only speculate about the details of the psychological connections.
5. The Case against Constructivism In my present exposition, the rejection of social constructivist sociologies of science comes out not as a main battle, but as a mopping up operation. Karin Knorr-Cetina (1981), a leading social constructivist, agrees with Laudan that scientists often intend their statements to be true or false of the world. She calls this “intentional realism.” Her argument is that if one examines in detail what goes on in the laboratory, one will find that what might be true or false of the world has little or no effect on which statements come to be accepted as true or false. That is more a matter of social contingency and negotiation than interaction with the world. I do not deny the existence of contingency and social negotiation in the process of doing science. Nor do I deny the power of personal, professional, and even broader social interests. My claim is that experimental strategies can, in some circumstances, overwhelm social interactions and interests, leaving scientists little freedom in their choice of the best fitting model. The final chapter of Explaining Science (1988, ch. 8), which deals with the 1960s revolution in geology, was intended to illustrate this point.
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6. Social versus Individual In a review of Explaining Science, the philosopher of science Richard Burian (1988) voices the worry that my account of science leaves too much room for social factors. Wise objects that there is not enough. Actually I think Wise is more nearly correct. But Burian’s worry indicates that there is considerable room for the social in my account. Throughout Explaining Science there are hints of an ecological, or evolutionary, model of the growth of science (1988, pp. 12-26, 133-37, 222, and 24849). At one time I had intended to develop this model in greater detail, but that proved not to be feasible, and was put off, hopefully to be taken up as a later project. It is in this context that I would begin explicitly to model the social processes of science. I am convinced, however, that I have the priorities right. An adequate theory of science must take individuals as its basic entities. This means primarily, but not exclusively, scientists. I even have a theoretical argument for this position (1989). A scientific theory of science must in the end be a causal theory. In the social world the only active causal agents are individuals. This is not to deny that there is a socially constructed social reality. Individuals are enculturated and professionalized. But nothing happens unless individuals act. In particular, nothing changes unless individuals change it. And science is nothing if not changing. So no theory of science that reduces individuals, and their cognitive capacities, to black boxes can possibly be an adequate theory of science. In spite of his social history rhetoric, Wise in practice follows this strategy. His recent work (Wise and Smith 1988) attempts to show how machines like the steam engine and the telegraph provided a means by which the culture of late nineteenth century British commerce and industry became embodied in the content of the physics of the day. But even more important than the machines is the individual scientist, in this case William Thomson, who performed the translation. In the social world of science, as in the social world generally, there are no actions without actors.
7. Is Realism Dead? Since I finished writing Explaining Science, there has been some softening in the sociological position, as Wise notes. Perhaps there is no longer a significant substantive difference between my position and the consensus position among sociologists and social historians of science. Since I am not yet sure that convergence has in fact occurred, let me conclude by stating what I would regard as the minimal consensus on the starting point for developing an adequate theory of science. It is this: We now
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know much more about the world than we did three hundred, one hundred, fifty, or even twenty-five years ago. More specifically, many of the models we have today capture more of the structure of various parts of the world, and in more detail, than models available fifty or a hundred years ago. For example, current models of the structure of genetic materials capture more of their real structure than models available in 1950. The primary task of a theory of science is to explain the processes that produced these results. To deny this minimal position, or even to be agnostic about it, is to misconceive the task. It is to retreat into scholasticism and academic irrelevance. If this is the consensus, it marks not the death, but the affirmation of a realist perspective. The good news would be that we could at least temporarily put to rest arguments about realism and get on with the primary task. That would be all to the good because the primary task is more exciting, and more important.* Ronald N. Giere Department of Philosophy and Center for Philosophy of Science University of Minnesota
[email protected]
REFERENCES Burian, R. (1988). Review of Giere (1988). Isis 79, 689-91. Giere, R. N. (1988). Explaining Science: A Cognitive Approach. Chicago: University of Chicago Press. Giere, R. N. (1989). The Units of Analysis in Science Studies. In: S. Fuller, M. DeMey, T. Shinn, and S. Woolgar (eds.), The Cognitive Turn: Sociological and Psychological Perspectives on Science. Sociology of the Sciences, vol. 13. Dordrecht: Kluwer Academic. Knorr-Cetina, K. D. (1981). The Manufacture of Knowledge. Oxford: Pergamon Press. Kuhn, T. S. (1962). The Structure of Scientific Revolutions. 2nd edition: 1970. Chicago: University of Chicago Press. Lakatos, I. (1970). Falsification and the Methodology of Scientific Research Programmes. In: I. Lakatos and A. Musgrave (eds.), Criticism and the Growth of Knowledge, pp. 91-196. Cambridge: Cambridge University Press. Laudan, L. (1977). Progress and Its Problems. Berkeley: University of California Press. Putnam, H. (1981). Reason, Truth, and History. Cambridge: Cambridge University Press. Smith, C. and M. N. Wise (1988). Energy and Empire: A Biographical Study of Lord Kelvin. Cambridge: Cambridge University Press. Van Fraassen, B. C. (1980). The Scientific Image. Oxford: Clarendon Press.
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The author gratefully acknowledges the support of the National Science Foundation and the hospitality of the Wissenschaftskolleg zu Berlin.
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POZNAŃ STUDIES IN THE PHILOSOPHY OF THE SCIENCES AND THE HUMANITIES
Contents of Back Issues of the Idealization Subseries
VOLUME 1 (1975) No. 1 (Sold out) The Method of Humanistic Interpretation – J. Kmita, Humanistic Interpretation; W. Ławniczak, On a Systematized Interpretation of Works of Fine Arts; J. Topolski, Rational Explanation in History. The Method of Idealization – L. Nowak, Idealization: A Reconstruction of Marx’s Ideas; J. Brzeziński, Interaction, Essential Structure, Experiment; W. Patryas, An Analysis of the “Caeteris Paribus” Clause; I. Nowakowa, Idealization and the Problem of Correspondence. The Application: The Reconstruction of Some Marxist Theories – J. Topolski, Lenin’s Theory of History; J. Kmita, Marx’s Way of Explanation of Social Processes; A. Jasińska, L. Nowak, Foundations of Marx’s Theory of Class: A Reconstruction.
VOLUME 2 (1976) No. 3 (Sold out) Idealizational Concept of Science – L. Nowak, Essence – Idealization – Praxis. An Attempt at a Certain Interpretation of the Marxist Concept of Science; B. Tuchańska, Factor versus Magnitude; J. Brzeziński, Empirical Essentialist Procedures in Behavioral Inquiry; J. Brzeziński, J. Burbelka, A. Klawiter, K. Łastowski, S. Magala, L. Nowak, Law and Theory. A Contribution to the Idealizational Interpretation of Marxist Methodology; P. Chwalisz, P. Kowalik, L. Nowak, W. Patryas, M. Stefański, The Peculiarities of Practical Research. Discussions – T. Batóg, Concretization and Generalization; R. Zielińska, On Inter-Functional Concretization; L. Nowak, A Note on Simplicity; L. Witkowski, A Note on Implicational Concept of Correspondence.
VOLUME 16 (1990) IDEALIZATION I: GENERAL PROBLEMS (Edited by Jerzy Brzeziński, Francesco Coniglione, Theo A.F. Kuipers and Leszek Nowak) Introduction – I. Niiniluoto, Theories, Approximations, and Idealizations. Historical Studies – F. Coniglione, Abstraction and Idealization in Hegel and Marx; B. Hamminga, The Structure of Six Transformations in Marx’s Capital; A.G. de la Sienra, Marx’s Dialectical Method; J. Birner, Idealization and the Development of Capital Theory. Approaches to Idealization – L.J. Cohen, Idealization as a Form of Inductive Reasoning; C. Dilworth, Idealization and the Abstractive-Theoretical Model of Explanation; R. Harré, Idealization in Scientific Practice; L. Nowak, Abstracts Are Not Our Constructs. The Mental Constructs Are Abstracts. Idealization and Problems of the Philosophy of Science – M. Gaul, Models of Cognition or Models of Reality?; P.P. Kirschenmann, Heuristic Strategies: Another Look at Idealization and Concretization; T.A.F. Kuipers, Reduction of Laws and Theories; K. Paprzycka, Reduction and Correspondence in the Idealizational Approach to Science.
VOLUME 17 (1990) IDEALIZATION II: FORMS AND APPLICATIONS (Edited by Jerzy Brzeziński, Francesco Coniglione, Theo A.F. Kuipers and Leszek Nowak) Forms of Idealization – R. Zielińska, A Contribution to the Characteristic of Abstraction; A. Machowski, Significance: An Attempt at a Variational Interpretation; K. Łastowski, On Multi-Level Scientific Theories; A. Kupracz, Concretization and the Correction of Data; E. Hornowska, Certain Approach to Operationalization; I. Nowakowa, External and Internal Determinants of the Development of Science: Some Methodological Remarks. Idealization in Science – H. Rott, Approximation versus Idealization: The KeplerNewton Case; J. Such, The Idealizational Conception of Science and the Law of Universal Gravitation; G. Boscarino, Absolute Space and Idealization in Newton; M. Sachs, Space, Time and Motion in Einstein’s Theory of Relativity; J. Brzeziński, On Experimental Discovery of Essential Factors in Psychological Research; T. Maruszewski, On Some Elements of Science in Everyday Knowledge.
VOLUME 25 (1992) IDEALIZATION III: APPROXIMATION AND TRUTH (Edited by Jerzy Brzeziński and Leszek Nowak) Introduction – L. Nowak, The Idealizational Approach to Science: A Survey. On the Nature of Idealization – M. Kuokkanen and T. Tuomivaara, On the Structure of Idealizations; B. Hamminga, Idealization in the Practice and Methodology of Classical Economics: The Logical Struggle with Lemma’s and Undesired Theorems; R. Zielińska, The Threshold Generalization of the Idealizational Laws; A. Kupracz, Testing and Correspondence; K. Paprzycka, Why Do Idealizational Statements Apply to Reality? Idealization, Approximation, and Truth – T.A.F. Kuipers, Truth Approximation by Concretization; I. Nowakowa, Notion of Truth for Idealization; I. Nowakowa, L. Nowak, “Truth is a System”: An Explication; I. Nowakowa, The Idea of “Truth as
a Process.” An Explication; L. Nowak, On the Concept of Adequacy of Laws. An Idealizational Explication; M. Paprzycki, K. Paprzycka, Accuracy, Essentiality and Idealization. Discussions – J. Sójka, On the Origins of Idealization in the Social Experience; M. Paprzycki, K. Paprzycka, A Note on the Unitarian Explication of Idealization; I. Hanzel, The Pure Idealizational Law – The Inherent Law – The Inherent Idealizational Law.
VOLUME 26 (1992) IDEALIZATION IV: INTELLIGIBILITY IN SCIENCE (Edited by Craig Dilworth) C. Dilworth, Introduction: Idealization and Intelligibility in Science; E. Agazzi, Intelligibility, Understanding and Explanation in Science; H. Lauener, Transcendental Arguments Pragmatically Relativized: Accepted Norms (Conventions) as an A Priori Condition for any Form of Intelligibility; M. Paty, L’Endoreference d’une Science Formalisee de la Nature; B. d’Espagnat, De 1’Intelligibilite du Monde Physique; M. Artigas, Three Levels of Interaction between Science and Philosophy; J. Crompton, The Unity of Knowledge and Understanding in Science; G. Del Re, The Case for Finalism in Science; A. Cordero, Intelligibility and Quantum Theory; O. Costa de Beauregard, De Intelligibilite en Physiąue. Example: Relativite, Quanta, Correlations EPR; L. Fleischhacker, Mathematical Abstraction, Idealization and Intelligibility in Science; B. Ellis, Idealization in Science; P.T. Manicas, Intelligibility and Idealization: Marx and Weber; H. Lind, Intelligibility and Formal Models in Economics; U. Maki, On the Method of Isolation in Economics; C. Dilworth, R. Pyddoke, Principles, Facts and Theories in Economics; J.C. Graves, Intelligibility in Psychotherapy; R. Thom, The True, the False and the Insignificant or Landscaping the Logos.
VOLUME 34 (1994) Izabella Nowakowa IDEALIZATION V: THE DYNAMICS OF IDEALIZATIONS Introduction; Chapter I: Idealization and Theories of Correspondence; Chapter II: Dialectical Correspondence of Scientific Laws; Chapter III: Dialectical Correspondence in Science: Some Examples; Chapter IV: Dialectical Correspondence of Scientific Theories; Chapter V: Generalizations of the Rule of Correspondence; Chapter VI: Extensions of the Rule of Correspondence; Chapter VII: Correspondence and the Empirical Environment of a Theory; Chapter VIII: Some Methodological Problems of Dialectical Correspondence.
VOLUME 38 (1994) IDEALIZATION VI: IDEALIZATION IN ECONOMICS (Edited by Bert Hamminga and Neil B. De Marchi) Introduction – B. Hamminga, N. De Marchi, Preface; B. Hamminga, N. De Marchi, Idealization and the Defence of Economics: Notes toward a History. Part I: General Observations on Idealization in Economics – K.D. Hoover, Six
Queries about Idealization in an Empirical Context; B. Walliser, Three Generalization Processes for Economic Models; S. Cook, D. Hendry, The Theory of Reduction in Econometrics; M.C.W. Janssen, Economic Models and Their Applications; A.G. de la Sienra, Idealization and Empirical Adequacy in Economic Theory; I. Nowakowa, L. Nowak, On Correspondence between Economic Theories; U. Mäki, Isolation, Idealization and Truth in Economics. Part II: Case Studies of Idealization in Economics – N. Cartwright, Mill and Menger: Ideal Elements and Stable Tendencies; W. Balzer, Exchange Versus Influence: A Case of Idealization; K. Cools, B. Hamminga, T.A.F. Kuipers, Truth Approximation by Concretization in Capital Structure Theory; D.M. Hausman, Paul Samuelson as Dr. Frankenstein: When an Idealization Runs Amuck; H.A. Keuzenkamp, What if an Idealization is Problematic? The Case of the Homogeneity Condition in Consumer Demand; W. Diederich, Nowak on Explanation and Idealization in Marx’s Capital; G. Jorland, Idealization and Transformation; J. Birner, Idealizations and Theory Development in Economics. Some History and Logic of the Logic Discovery. Discussions – L. Nowak, The Idealizational Methodology and Economics. Replies to Diederich, Hoover, Janssen, Jorland and Mäki.
VOLUME 42 (1995) IDEALIZATION VII: IDEALIZATION, STRUCTURALISM, AND APPROXIMATION (Edited by Martti Kuokkanen) Idealization, Approximation and Counterfactuals in the Structuralist Framework – T.A.F. Kuipers, The Refined Structure of Theories; C.U. Moulines and R. Straub, Approximation and Idealization from the Structuralist Point of View; I.A. Kieseppä, A Note on the Structuralist Account of Approximation; C.U. Moulines and R. Straub, A Reply to Kieseppä; W. Balzer and G. Zoubek, Structuralist Aspects of Idealization; A. Ibarra and T. Mormann, Counterfactual Deformation and Idealization in a Structuralist Framework; I.A. Kieseppä, Assessing the Structuralist Theory of Verisimilitude. Idealization, Approximation and Theory Formation – L. Nowak, Remarks on the Nature of Galileo’s Methodological Revolution; I. Niiniluoto, Approximation in Applied Science; E. Heise, P. Gerjets and R. Westermann, Idealized Action Phases. A Concise Rubicon Theory; K.G. Troitzsch, Modelling, Simulation, and Structuralism; V. Rantala and T. Vadén, Idealization in Cognitive Science. A Study in Counterfactual Correspondence; M. Sintonen and M. Kiikeri, Idealization in Evolutionary Biology; T. Tuomivaara, On Idealizations in Ecology; M. Kuokkanen and M. Häyry, Early Utilitarianism and Its Idealizations from a Systematic Point of View. Idealization, Approximation and Measurement – R. Westermann, Measurement-Theoretical Idealizations and Empirical Research Practice; U. Konerding, Probability as an Idealization of Relative Frequency. A Case Study by Means of the BTL-Model; R. Suck and J. Wienöbst, The Empirical Claim of Probability Statements, Idealized Bernoulli Experiments and Their Approximate Version; P.J. Lahti, Idealizations in Quantum Theory of Measurement.
VOLUME 56 (1997) IDEALIZATION VIII: MODELLING IN PSYCHOLOGY (Edited by Jerzy Brzeziński, Bodo Krause and Tomasz Maruszewski) Part I: Philosophical and Methodological Problems of Cognition Process – J. Wane, Idealizing the Cartesian-Newtonian Paradigm as Reality: The Impact of New-Paradigm Physics on Psychological Theory; E. Hornowska, Operationalization of Psychological Magnitudes. Assumptions-Structure-Consequences; T. Bachmann, Creating Analogies – On Aspects of the Mapping Process between Knowledge Domains; H. Schaub, Modelling Action Regulation. Part II: The Structure of Ideal Learning Process – S. Ohlson, J.J. Jewett, Ideal Adaptive Agents and the Learning Curve; B. Krause, Towards a Theory of Cognitive Learning; B. Krause, U. Gauger, Learning and Use of Invariances: Experiments and Network Simulation; M. Friedrich, “Reaction Time” in the Neural Network Module ART 1. Part III: Control Processes in Memory – J. Tzelgov, V. Yehene, M. Naveh-Benjamin, From Memory to Automaticity and Vice Versa: On the Relation between Memory and Automaticity; H. Hagendorf, S. Fisher, B. Sá, The Function of Working Memory in Coordination of Mental Transformations; L. Nowak, On Common-Sense and (Para-)Idealization; I. Nowakowa, On the Problem of Induction. Toward an Idealizational Paraphrase.
VOLUME 63 (1998) IDEALIZATION IX: IDEALIZATION IN CONTEMPORARY PHYSICS (Edited by Niall Shanks) N. Shanks, Introduction; M. Bishop, An Epistemological Role for Thought Experiments; I. Nowak and L. Nowak, “Models” and “Experiments” as Homogeneous Families of Notions; S. French and J. Ladyman, A Semantic Perspective on Idealization in Quantum Mechanics; Ch. Liu, Decoherence and Idealization in Quantum Measurement; S. Hartmann, Idealization in Quantum Field Theory; R. F. Hendry, Models and Approximations in Quantum Chemistry; D. Howard, Astride the Divided Line: Platonism, Empiricism, and Einstein's Epistemological Opportunism; G. Gale, Idealization in Cosmology: A Case Study; A. Maidens, Idealization, Heuristics and the Principle of Equivalence; A. Rueger and D. Sharp, Idealization and Stability: A Perspective from Nonlinear Dynamics; D. L. Holt and R. G. Holt, Toward a Very Old Account of Rationality in Experiment: Occult Practices in Chaotic Sonoluminescence.
VOLUME 69 (2000) Izabella Nowakowa, Leszek Nowak IDEALIZATION X: THE RICHNESS OF IDEALIZATION Preface; Introduction – Science as a Caricature of Reality. Part I: THREE METHODOLOGICAL REVOLUTIONS – 1. The First Idealizational Revolution. Galileo’s-Newton’s Model of Free Fall; 2. The Second Idealizational Revolution. Darwin’s Theory of Natural Selection; 3. The Third Idealizational Revolution. Marx’s
Theory of Reproduction. Part II: THE METHOD OF IDEALIZATION – 4. The Idealizational Approach to Science: A New Survey; 5. On the Concept of Dialectical Correspondence; 6. On Inner Concretization. A Certain Generalization of the Notions of Concretization and Dialectical Correspondence; 7. Concretization in Qualitative Contexts; 8. Law and Theory: Some Expansions; 9. On Multiplicity of Idealization. Part III: EXPLANATIONS AND APPLICATIONS – 10. The Ontology of the Idealizational Theory; 11. Creativity in Theory-building; 12. Discovery and Correspondence; 13. The Problem of Induction. Toward an Idealizational Paraphrase; 14. “Model(s) and “Experiment(s). An Analysis of Two Homogeneous Families of Notions; 15. On Theories, Half-Theories, One-fourth-Theories, etc.; 16. On Explanation and Its Fallacies; 17. Testability and Fuzziness; 18. Constructing the Notion; 19. On Economic Modeling; 20. Ajdukiewicz, Chomsky and the Status of the Theory of Natural Language; 21. Historical Narration; 22. The Rational Legislator. Part IV: TRUTH AND IDEALIZATION – 23. A Notion of Truth for Idealization; 24. “Truth is a System”: An Explication; 25. On the Concept of Adequacy of Laws; 26. Approximation and the Two Ideas of Truth; 27. On the Historicity of Knowledge. Part V: A GENERALIZATION OF IDEALIZATION – 28. Abstracts Are Not Our Constructs. The Mental Constructs Are Abstracts; 29. Metaphors and Deformation; 30. Realism, Supra-Realism and Idealization. REFERENCES – I. Writings on Idealization; II. Other Writings.
VOLUME 82 (2004) IDEALIZATION XI: HISTORICAL STUDIES ON ABSTRACTION AND IDEALIZATION (Edited by Francesco Coniglione, Roberto Poli and Robin Rollinger) Preface. GENERAL PERSPECTIVES – I. Angelelli, Adventures of Abstraction; A. Bäck, What is Being qua Being?; F. Coniglione, Between Abstraction and Idealization: Scientific Practice and Philosophical Awareness. CASE STUDIES – D.P. Henry, Anselm on Abstracts; L. Spruit, Agent Intellect and Phantasms. On the Preliminaries of Peripatetic Abstraction; R.D. Rollinger, Hermann Lotze on Abstraction and Platonic Ideas; R. Poli, W.E. Johnson’s Determinable-Determinate Opposition and his Theory of Abstraction; M. van der Schaar, The Red of a Rose. On the Significance of Stout's Category of Abstract Particulars; C. Ortiz Hill, Abstraction and Idealization in Edmund Husserl and Georg Cantor prior to 1895; G.E. Rosado Haddock, Idealization in Mathematics: Husserl and Beyond; A. Klawiter, Why Did Husserl not Become the Galileo of the Science of Consciousness?; G. Camardi, Ideal Types and Scientific Theories.
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Democracy and the Post-Totalitarian Experience. Edited by Leszek Koczanowicz and Beth J. Singer. Frederic R. Kellogg and Łukasz Nysler, Assistant Editors. Amsterdam/New York, NY 2005. XIV, 224 pp. (Value Inquiry Book Series 167) ISBN: 90-420-1635-3
€ 48,-/US $ 67.-
This book presents the work of Polish and American philosophers about Poland’s transition from Communist domination to democracy. Among their topics are nationalism, liberalism, law and justice, academic freedom, religion, fascism, and anti-Semitism. Beyond their insights into the ongoing situation in Poland, these essays have broader implications, inspiring reflection on dealing with needed social changes.
USA/Canada: One Rockefeller Plaza, Ste. 1420, New York, NY 10020, Tel. (212) 265-6360, Call toll-free (U.S. only) 1-800-225-3998, Fax (212) 265-6402 All other countries: Tijnmuiden 7, 1046 AK Amsterdam, The Netherlands. Tel. ++ 31 (0)20 611 48 21, Fax ++ 31 (0)20 447 29 79
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Putting Peace into Practice
Evaluating Policy on Local and Global Levels Edited by Nancy Nyquist Potter Amsterdam/New York, NY 2004. XV, 197 pp. (Value Inquiry Book Series 164) ISBN: 90-420-1863-1
Paper
€ 42,-/US $ 55.-
This book examines the role and limits of policies in shaping attitudes and actions toward war, violence, and peace. Authors examine militaristic language and metaphor, effects of media violence on children, humanitarian intervention, sanctions, peacemaking, sex offender treatment programs, nationalism, cosmopolitanism, community, and political forgiveness to identify problem policies and develop better ones.
USA/Canada: One Rockefeller Plaza, Ste. 1420, New York, NY 10020, Tel. (212) 265-6360, Call toll-free (U.S. only) 1-800-225-3998, Fax (212) 265-6402 All other countries: Tijnmuiden 7, 1046 AK Amsterdam, The Netherlands. Tel. ++ 31 (0)20 611 48 21, Fax ++ 31 (0)20 447 29 79
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Operation Barbarossa
Ideology and Ethics Against Human Dignity André Mineau
Amsterdam/New York, NY 2004. XIV, 244 pp. (Value Inquiry Book Series 161)
ISBN: 90-420-1633-7
€ 52,-/US$ 68.-
This book purports that, given Operation Barbarossa’s concept and scope, it would have been impossible without Nazi ideology, that we cannot understand it in the absence of its reference to the Holocaust. It asks and attempts to answer whether we can describe ideology without reference to ethics and speak about genocide while ignoring philosophy.
The VALUE INQUIRY BOOK SERIES (VIBS) is an international scholarly program, founded in 1992 by Robert Ginsberg, that publishes philosophical books in all areas of value inquiry, including social and political thought, ethics, applied philosophy, aesthetics, feminism, pragmatism, personalism, religious values, medical and health values, values in education, values in science and technology, humanistic psychology, cognitive science, formal axiology, history of philosophy, post-communist thought, peace theory, law and society, and theory of culture.
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[email protected] Please note that the exchange rate is subject to fluctuations