Peirce and the Economy of Research Nicholas Rescher Philosophy of Science, Vol. 43, No. 1. (Mar., 1976), pp. 71-98. Stable URL: http://links.jstor.org/sici?sici=0031-8248%28197603%2943%3A1%3C71%3APATEOR%3E2.0.CO%3B2-Y Philosophy of Science is currently published by The University of Chicago Press.
Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/ucpress.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission.
JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact
[email protected].
http://www.jstor.org Wed Jun 6 07:47:05 2007
PEIRCE AND THE ECONOMY OF RESEARCH*
NICHOLAS RESCHER University of Pittsburgh
The theory of the economics of research played a central role in the analysis of scientific method of Charles Sanders Peirce. The present paper describes Peirce's project as he saw it and then puts its machinery to work in an analysis of current issues in the philosophy of science. The aim is to show that, even apart from their historical interest, Peirce's ideas on this subject have a substantial systematic interest.
1. Peirce's Project. In his analysis of scientific method Charles Sanders Peirce gave the place of pride to a theory-indeed a discipline-of his own devising, namely to what he called the economy of research.' This Peircean project has been totally-and most unfortunatelyneglected by his commentators and by the subsequent course of development in the philosophy of science. The paper falls into three sections. The first consists of a description of Peirce's project as he saw it, and considers briefly his motivational arguments for its importance. The second, somewhat longer section of the paper is nonhistorical-it attempts to exhibit the value of Peirce's ideas by showing that they can actually be put to work in resolving several currently controverted issues in the theory of inductive reasoning. The third section of the paper considers some of the relationships
*Received April, 1975; revised August, 1975. 'Peirce's main paper on the subject is an 1878 essay of this title (7:139-157; but for the date see 5.601.) Compare also 7:720 and 1:122-125. Peirce returned to the subject at length in adetailed proposal (unsuccessfully) put before the Carnegie Institution in 1902 (7:158-161). All references of this form are to Peirce [22]. Peirce tended togive Ernst Mach credit as aprecursor or congener-quite erroneously. (See 5.601.) To be sure, Mach had given a widely circulated 1882 lecture on "The Economical Nature of Physical Inquiry," (See Mach [16], pp. 186-213.) But this succeeded Peirce's own 1876/9 investigations. And in any case, Mach's dCmarche came down to pushing his "convenient abbreviation" theory of physical laws as in (imperfect) compression of a mass of facts into a compact formula. The resort to "economy" was for Mach simply a convenient peg on which to hinge his doctrine of laws-he accorded economic considerations no formative role in the framework of scientific inquiry and inductive reasoning itself. In writing this paper I have been able to profit from the comments of my colleagues John Haugeland and Gerald J. Massey on an earlier version. Philosophy of Science, 43 f 19761, pp. 71-98.
Copyright 01976 by the Philosophy of Science Association.
72
NICHOLAS RESCHER
between Peirce's conception of the economy of research and certain cognate ideas relating to decision theoretic models of hypothesis-acceptance. Peirce divided the labor of scientific or inductive inquiry between two distinct processes or procedures. The first, abduction, has to do with the elaboration of possibilities and the provision of possible explanations and hypotheses for the solution of scientific problems. The second, induction proper, is concerned with the narrowing of this range of alternative possibilities in an endeavor to determine which is in fact correct (or at any rate is the most promising candidate for correctness in the epistemic circumstances at hand).2 Peirce was acutely alive to what has subsequently become a commonplace in the philosophy of science, the idea that data underdetermine theory-that an infinite variety of alternative hypotheses can conform equally well to any finite body of empirical data. If science is to proceed in its quest for adequate theories by testing hypotheses against the naturally available or experimentally contrived empirical facts, we must seek pre-experiential guidance through the embarras de richesses of alternative possibilities to determine priorities. The crucial first step of the inductive process of hypothesis testing will thus be to decide which hypotheses merit immediate check, which can be put off until tomorrow, and which can wait until Niagara runs dry. Peirce holds that it is to the economy of research that we are to look for guidance here. (See the concise statement of the issue at 6.530.) For whatever intrinsic appeal various individual items within the welter of abductively eligible hypotheses may possess, we must face up to the harsh reality of the limitations imposed by the cost of experimental research in expert time and material resources. Thus the methodology of inductive practice is-as Peirce sees it-crucially dependent on the intelligent deployment of economic consideration. Hypothesis testing is the very crux of induction, and-given the proliferation of possibilities-the selection of hypotheses for testing must be determined on an economic basis: Proposals for hypotheses inundate us in an over-whelming flood, while the process of verification to which each one must be subjected before it can count as at all an item, even of likely knowledge, is so very costly in time, energy, and money-and consequently in ideas which might have been had for that time, 2"Abduction furnishes all our ideas concerning real things . . . but is mere conjecture, without probative force. . . . Induction gives us the only approach to certainty concerning the real that we can have." (8.209)
PEIRCE AND T H E ECONOMY O F RESEARCH
73
energy, and money, that Economy would override every other consideration even if there were any other serious considerations. In fact there are no others. Peirce thus maintained that the economics of research is a pivotally determinative consideration in inductive reasoning. He proposed to construe the economic process at issue in terms of the sort of balance of assets and liabilities that we ourselves would call cost-benefit a n a l y ~ i s On . ~ the side of benefits he was prepared to cast his net widely: closeness of fit to data, explanatory value, simplicity, parsimony, concordance with other accepted theories, even antecedent likelihood and intuitive appeal are allowed to count for something on the side of assets. But in the other column there sit those hard-faced factors of "the dismal scienceH-time, effort, energy, and money. Peirce formulated the task of the enterprise in terms that can scarcely be improved upon a century later: The doctrine of economy, in general, treats of the relations between utility and cost. That branch of it which relates to research considers the relations between the utility and the cost of diminishing [the gaps and 1 the probable error of our knowledge. Its main problem is, how, with a given expenditure of money, time, and energy, to obtain the most valuable addition to our knowledge. (7.140) His words of commendation for this enterprise are unequivocal, for he insisted that "the economical science is particularly profitable to science; and that of all branches of economy, the economy of research is perhaps the most profitable . . . costing little beyond the energies of the researcher, and helping the economy of every other science" (7.161). One of the main advantages of economic analysis is its potential saving of effort and resources in the face of the operation of a principle of diminishing returns in inquiry, a conception to which Peirce returned again and again.5 To this idea of the economy of research-of cost-benefit analysis in inductive inquiry and reasoning-Peirce gave as central a place 35.602. Some of the lessons for hypothesis-testing which draw upon the economy of research are set out at 7.223-231. Compare also Peirce's invocation of the economy of research in defending the use of presumptions in science at 6.423. 4Besides its role in relation to hypothesis-testing, considerations of economy of research also enter in with respect to the costs of acting o n an hypothesis. (Cf. 7.142.) We shall not here treat this separable issue as separate. Successful application is, after all, a crucial aspect of testing. 5Peirce was perhaps the first writer to draw attention to the rising cost of experimental work as science matures in the course of its historical development. (Cf. 7.144.) On this issue see the present writer's [26].
74
NICHOLAS RESCHER
in his methodology of science as words can manage to a ~ s i g n Yet .~ no other part of this great man's philosophizing has fallen on stonier ground. The Peirce-bibliographies now run to over 800 entries and currently add some 40 items per a n n ~ m Yet . ~ all this flood of writing-extending over the century since Peirce flourished 8-contains not one single significant item devoted to the analysis of this aspect of his theory of ~ c i e n c e . ~ This is a great misfortune. For there is virtually no part of Peirce's philosophy which has ampler current relevancy and which is capable of rendering greater services to the solution of current disputes.1° In my considered opinion, it is no grave exaggeration to say that Peirce's project of the economy of research is an instrument that can cut through much of the recent disputes about inductive reasoning like a well-honed knife through butter. This, of course, is a large claim that needs substantiation. It will, hopefully, prove possible to convince the reader, by way of a rapid guided tour over some of the main controversies of the recent theory of inductive reasoning, that Peirce's idea affords an instrumentality of impressive power.
2. Carnap's Requirement of Total Evidence. Let us begin by considering one of the major controverted principles of recent inductive logic, Carnap's requirement of total evidence. Carnap states this requirement as follows: 6He referred to it as that "which really is in all cases the leading consideration in Abduction, which is the question of Economy-Economy of money, time, thought, and energy" (5.600). 'About one third of this current material appears in the quarterly Transactions of the Charles S. Peirce Society, and the rest elsewhere. For the bibliography regarding Peirce see Fisch [9], which contains ca. 400 entries, and its two supplements of 1966 (ca. 100 entries) and 1974 (ca. 350 entries). 8Peirce lived from 1839-1914. His 40th year-the inception of the Greek akmZ or Roman floruit-thus began in 1878. 9Cushen [7] is only a seeming exception. Actually it is a reprint of Peirce's own essay. Murphey [20] has no subject-index entry for "economy of research." The 1968 doctoral dissertation by Raymond M. Herbenick, and the article entitled "Peirce on Systems Theory," which was based on it (Herbenick [ l I]), are in small part relevent to the topic. Fann [8] has a brief section (pp. 47-51) on economy of research, which, however, consists of bare summarizing of some Peircean passages without much elaboration or analysis. Sharpe [31] contains a few incidential observations on the economy of research. (I am indebted to Professors Max Fisch and Arthur Burks for useful bibliographical suggestions.) 'OIt is, moreover, highly topical in extra-philosophical contexts. For "research planningn-operations research as applied to scientific research and development-is an active enterprise in current technological-administrative studies. Economists have also become interested in the macrolevel aspects of the issue. Cf. Norris and Vaizey m1.
PEIRCE AND THE ECONOMY OF RESEARCH
75
Requirement o f total evidence: in the application of inductive logic to a given knowledge situation, the total evidence available must be taken as basis for determining the degree of confirmation. Given a body of (relevant and correct) evidence e the conscientious scientist will never settle for an assessment of the degree of confirmation of a hypothesis h as having the value d c ( h / e ) as long as there is a further available item of (relevant and correct) evidence e ' , so that d c ( h / e & e ' ) , would represent the appropriate quantity. Thus the confirmationists work, like that of the proverbial housewife, is virtually never done. The point at issue is quite clear in the case of statistically based probabilities.12 Suppose we inquire regarding the chances of X ' s having cardiac problems of a certain type by a particular age. How far are we to carry the issue of extracting the evidence that is "available" from a suitable reference class? Is this to be Americans in general, American males, male Pennsylvanians, members of X's profession, members of X's family, members of X's family with X's reading habits, etc.? Where is the introduction of fuller and more complex information ever to stop? We are thus brought to the standard objection to total evidence as an inherently impracticable demand. There is no theoretical limit to the relevant information that is (in principle) actually "available." Ultimately an evidential totalitarianism leads ultimately ad absurdum, since it carries us to the statistically vitiating conclusion of narrowing in on the single case itself. The Carnapian total evidence requirement is in fact the signpost of a crucial tension. On the one hand, it would be rationally indefensible to neglect some crucial available datum-X's mode of employment as an asbestos-factory worker, say, or as a devott of cigarettes. And so to be sure of getting enough into the evidence-base Carnap insists that we put in everything. But on the other hand, we can hardly be expected to go off on an endless goose-chase through the whole gamut of X ' s characteristic properties, including his penchant for blondes or preference for peaches over pears. It seems somehow neurotic to insist on the literal totalitarianism of working everything into the account. But the minute we intrpduce the economic aspect, the situation "See Carnap [3], p. 211. For a most useful survey of the recent literature of inductive inference see Kyburg [14]. A particularly illuminating discussion of the total evidence requirement is given in Salmon [29]. I2ln these instances, the Carnapian requirement is tantamount to Reichenbach's rule of basing statistical probabilities on the narrowest reference class for which statistics can be had. See Reichenbach [25].
76
NICHOLAS RESCHER
is transformed. On the basis of purely theoretical considerations we are entrapped in the dilemma that a total evidence requirement is indispensable on the one hand and unworkable on the other. But once economic factors are introduced, these can supply the necessary definiteness needed to secure a workable approach to this aspect of the methodology of inductive inquiry. The evidence-problem now obtains a new definiteness and workability. For it at once becomes clear that total evidence is not the real issue, but rather the maximal volume of relevance-endowed evidence that one can obtain relative to the available resources (or better, relative to the resources it makes sense to make available considering the intrinsic importance of the issue for which the probability at issue is being determined). l 3 3. Hempel's Paradox of the Ravens. A substantial literature has grown up over a problem of inductive reasoning first posed by C. G. Hempel in 1946, the so-called "Paradox of the Ravens." (See [lo] and [3], pp. 223-224.) It roots in the observation of deductive logic that "All X is Y" is deductively equivalent by contraposition to "All Y is x." Accordingly, "All ravens ( R ) are black (B)" is deductively equivalent to "All non-black-objects (B) are non-ravens (R)." Given this equivalence, why should it be that in inductive contexts one is inclined to accept black ravens as confirming instances of the claim but not white tennis shoes? Regard the situation from the angle of a Venn Diagram:
"It is very important in this context to realize that economic considerations do not necessarily militate towards narrow reference classes. In a statistics-gathering day and age, information may be more readily and cheaply accessible on a nationally aggregated basis than in a more localized and highly disaggregated level. We have the interesting (if paradoxical-seeming) situation that information at a high level of generality and large-scale aggregation is usually more cheaply and easily come by than more relevant, case-specific information.
PEIRCE AND THE ECONOMY OF RESEARCH
77
The emptiness of (2) is as equivalently checked by going to the R's = (2) (3) and seeing that only (3)'s are encountered as by going to the B'S = (1) + (2) and seeing that only (1)'s are encountered. Either way, we are simply checking the emptiness of compartment (2). There seems to be no logico-theoretical reason for granting one of these approaches a preferred status over the other. But the fact is that there is a crucial economic difference between the two approaches. To check emptiness of (2) via the "natural" approach means going to the R ' s = (2) (3) and checking their color. To establish it via the "unnatural" approach we mean going to the B ' S = (1) + (2) and checking their type. Now let's make a few assumptions to delineate the structure of the situation.
+
+
the # of R's is approximately 10' the # of B's is approximately 1040 the average cost of finding an R is -$I the cost of determining the blackness of an R-in-hand is approximately 1$ = $.01 (e) the average cost of finding a B is . l $ = -9i.001 (f) the cost of determining the ravenhood of a B-in-hand is approximately .l$ = s.001
(a) (b) (c) (d)
Nothing much hinges on the particular numbers here. Specifically as regards (b), I don't propose to offer some Eddington-reminiscent estimate of the number of molecules in the universe-all that we need for present purposes is that the number of identifiable objects in the world is rather big. Let it be assumed further that to get adequate statistical control of a population of size X we need to have a sample of size V X . (As the result will prove highly insensitive to the exact form of this "control-size" assumption, its details are not worth quarreling over.) Two courses of action now lie before us: (I) Find (108)'/2 ravens and check their blackness:
Contrast (11): Find (lo4') ravenhood: c o s t : lo2' x $2 x
'I2
=
non-black objects and check their
$2 x 101'
There is a shocking difference between two strategies of verification from the economic point of view. And this economic difference puts black ravens and white tennis shoes on an altogether different plane. If someone hands us a verified black raven he has contributed one hundredth of one percent to the cost of the whole project of verification.
78
NICHOLAS RESCHER
If he hands us the white tennis shoe, his contribution is vanishingly small. The natural course of approach is massively cheaper-with it, expenditure at any given level goes enormously further towards adequacy (that is, it buys us vastly more by way of confirmation/disconfirmation). Reliance on the "natural" instances wins hands down in point of cost-effectiveness as an inductive strategy. The Peircean approach to the economic dimension once again renders good service. 4. Goodman's Grue Paradox. Let me now turn to Goodman's "new riddle of induction." In an influential essay of 1953, Nelson Goodman set afoot yet another "paradox" in the theory of inductive inference. Few problems in this area have occasioned a larger literature. Goodman's puzzle is based on a somewhat unorthodox pair of (phenomenal) color concepts
examined before the temporal reference-point to and is green or not examined before to and is blue. (to is an otherwise arbitrary moment of time that is not in the past.) bleen = examined before the temporal reference-point to and is blue or not examined before to and is green. grue
=
If we do our inductive reasoning on the basis of this color taxonomy, we shall seemingly obtain excellent inductive support for the thesis that all emeralds will eventually have the appearance we have standardly indicated by the description "blue" (viz., after to)-since all that have been examined to date are grue. On this basis, our "normal" inductive expectations would be totally baffled, and we arrive at a Hume-like result from a totally un-Humean point of departure. l4 Various considerations mark this issue as an inductive puzzle that cuts deeper than one might think on first view. (1) No amount of empirical evidence can help us choose between the "abnormal" grue /bleen color taxonomy and the normal green/blue one. Empirical evidence relates in the nature of things to past-or-present and there is (ex hypothesi) no difference here. (2) We cannot object that grue and bleen make explicit reference to time (viz., to to), because this only seems so from the parochial I4The situation would be quite otherwise if the "big change" came about in a gradual and unnoticed way, as a slow shift with no rude shocks to our memory of how things used to look, or else with a gradual "readjustment," so that the recollection of discrepancies would fade away in the pattern of an image-inversion experiment. For then we would continue to make our indicative projections on the old basis-e.g., grass would still be described as green, even though it "really" looks blue.
PEIRCE AND THE ECONOMY O F RESEARCH
79
standpoint of our familiar color-terminology . From the grue / bleen standpoint, the shoe is on the other foot, for, from the perspective of the grue-bleeners, it is our color taxonomy that appears as timedependent: green
=
blue
=
examined examined examined examined
before before before before
to and to and to and to and
grue or not
bleen.
bleen or not
grue.
The situation is entirely symmetric from their perspective and what's sauce for the goose is sauce for the gander as far as any theoretical objections on the basis of general principles go. The situation thus looks to be one of total parity as between our color-talk and that of the grue-bleeners, with no theoretical advantage available to decide the choice between them and us. Goodman himself in effect gives up on finding a preferential rationale of choice on a theoretical basis of general principle, and falls back on an appeal to "entrenchmentm-the fact (in the final analysis) that custom and habit has settled the issue preemptively in favor of our established color-language habits. (Few commentators have found this resolution convincing.) But the whole issue wears a rather different aspect when one approaches it from the direction of economic considerations. To operate with gruejbleen it would not suffice for the application of one's color taxonomy merely to recall that the thing looked "just like" this or like that, if one forgot whether one saw it before or after to. Again, it would not serve to have phenomenologically faithful color photographs of the thing if one had no record of when they were taken-and so cannot decide (say) whether one was taken before to and the other after to, or whether both are merely different prints of one and the same picture. In the orthodox green/blue color-taxonomy all that ever mattersnot only with current perception but also when one introduces pictorial records, memory and (even precognition)-is the strictly phenomenal issue of the perceived appearance of things. In the ordinary case, but not with grue/bleen, it transpires that ostension is an adequate apparatus for learning and teaching because the surface usual appearI5For a survey of objections and positions see Kyburg [14]. He summarizes his discussion with the observation "The problem of finding some way of distinguishing between sensible predicates like 'blue' and 'green' and the outlandish ones suggested by Goodman, Barker, and others, is surely one of the most important problems to come out of recent discussions of inductive logic" (p. 266).
80
NICHOLAS RESCHER
ance is the only issue. l 6 Thus green/blue can be handled by purely ostensive surrogates (colored just like this-pointing to grass-or like that-pointing to the sky), while grue/bleen involves the additional issue-the additional complication-of the time of observation relative to the great divide at to. The orthodox case involves simply the ostensively manipulable phenomenology of observation, the unorthodox case also calls for the chronometric recourse to temporal data. It is a matter of economy-not of chance!-that the "normal" taxonomy is normal. These considerations indicate a deep asymmetry between the two cases. The orthodox color taxonomy is in principle cheaper to operate than the latter as a basis for accommodating our descriptive and-above all-our inductively projective purposes. In one case color-talk can be carried on wholly in an ostensively taught language where all that matters is the surface appearance of things-in a perfectly uniform way vis-8-vis time. In the other case we have a two-factor mechanism which adds to this ostensively accessible phenomenology also a layer of chronometric issues at the level of learning, teaching, explanation, and application. Thus the orthodox taxonomy is easier and cheaper to operate. I want to stress that this is not an externalized issue that involves an invidious comparison of one color taxonomy case from the unfairly conceded vantage point of the other. It is a strictly internal issue of what it takes-not just de facto but in principle, in "every possible world," so to speak-to operate with the machinery of these rival color taxonomies. We now do not have an invidious comparison of one color taxonomy from the standpoint of a precommitment to the other, but simply the question of the resources or mechanisms needed for making the one taxonomy or the other work out-so to speak "from within." One is accordingly enabled to push the issue one step deeper than Goodman himself. For we are not left at the brute fact of entrenchment itself-that the orthodox taxonomy is entrenched vis-a-vis its alternatives. Rather we get some insight into its rationale-why it has become entrenched-namely that it is in principle less complex and more convenient (i.e., economical !) to operate. Entrenchment is thus rendered-not a matter of mere sociology, but-a factor that obtains a perfectly sound rationale in considerations of economy. l 7 I6This idea of utilizing ostension as a device for tackling Goodman's paradox is originally due to Salmon [28]. "As Israel Scheffler-perhaps the ablest of Goodman's expositors and defendershas remarked: "The most natural objection to Goodman's new approach is that it provides no explanation of entrenchment itself." (Scheffler [30] .)
81
PEIRCE AND THE ECONOMY OF RESEARCH
It thus appears that the problem of validating inductive recourse to the orthodox color taxonomy vis-a-vis its Goodmanian rivals-on a Humean "future unlike past" footing-can be resolved on matters of principle rather than "mere facts" like custom with Hume or entrenchment with Goodman (to be sure of practical-i.e., econommic-rather than theoretical principle). And the considerations needed to cut through the Gordian knot are precisely those revolving about the economic factors of efficiency and convenience operative in the Peircean economy of inductive inquiry. 5. Generality-Preference and Falsificationism. To begin with, it will be clear that generality-simple extensiveness of reach and range-is going to play a central role in any cost-effective minded theory of economy of research. On the orthodox approach, science is interested in general theses because they are maximally informative. On a Popperian basis, science is generality-oriented because general theses are more vulnerable, more falsifiable-more testable. On a Peircean approach science is generality-oriented because general theses are the most cost-effective. Thus consider the sequence
(1) (2) (3) (4)
All All All All
(10) lions in the zoo have +. (1,000) lions in the USA have (100,000) living lions have 4. (100,000,000) lions who have ever lived have
+.
+
Two considerations now enter in: (i) The (previously supposed) fact that to have reasonably good statistical control over a population of size N we must check a sample of (say) V N of that population (given reasonable randomness of selection); (ii) In selecting Xindividuals of a certain sort, the average cost of the operation decreases with the size of X by a mass-production effect (say that the average unit cost a 1/log X subject to the well-established principle of the economics of success-production that the cost of the nth unit is proportional to l/n). Thus in comparing (1)-(4) above, it becomes clear that one will get a 10,000,000-fold increase in the range of application for a 500-fold increase in expenditure. Generality is obviously very advantageous from the cost-effectiveness standpoint. Thus while from the orthodox standpoint, general hypotheses are the most informative, and on a Popperian approach they are the most testable, on a Peircean approach they are superior because they combine these desiderata: they offer the most content per unit effort to be invested in testing. (The more general the thesis, the larger will be the "epistemic bang for the buck," other things being equal.) So far so good. But exactly how decisive is generality as a factor
82
NICHOLAS RESCHER
in scientific inquiry? In this context let us focus on some of the issues revolving about the theories of Karl Popper regarding the methodology of science, and begin with the Popperian thesis that the rational agenda of inquiry calls for science to address itself with prime priority to the most general (daring yet vulnerable) hypotheses in a problem-situation. Popper sets the stage of the problem in the following terms: "It is this interest [in the testability of hypotheses] which leads . . . to my demand that . . . statements of a high level of universality should be chosen" ([23], p. 273). The case stands as follows: Issue: The choice of subset-of-initial-concern among mutually exclusive hypotheses of different levels of generality. Question: Are we to choose the less general (safest and most cautious) or the more general (riskiest and most ambitious) as having prime priority-claims to investigation? Suppose now that we are confronted by a scientific problem-issue for which we have 110 alternative hypothetically available solutions, falling in two groups as per Table 1. Suppose further that 120 units TABLE 1 . ASSUMED SITUATION O F TWO GROUPS O F PROBLEM-RESOLVING HYPOTHESES Group A Number Probability of each (on the basis of a "best estimate" relative to the evidence-at-hand) Generality of each* Resource-cost of testing
10 .05 20 10 units
Group B 100 ,005 80 1 unit
"For simplicity we suppose that generality may be ranked on a scale from 0 to 100 (say for the percentage of the theoretically relevant species of individuals to which hypotheses of the range at issue might conceivably apply).
of funding/resources are at our disposal. We are to put x hypotheses of Group A, y of Group B to the test. How are we to decide on specific values for x and y? If we are true Popperians, we turn straightaway to Group B where the more vulnerable possibilities are obviously to be found. But is this reasonable? Note that the expected value we will obtain in point of generality is given by the quantity:
And-so let let us suppose-we to the basic constraints
should try to maximize this subject
PEIRCE AND THE ECONOMY OF RESEARCH
The result is a nifty little linear-programming problem:
So x + .4y is maximized with a value of 42 at (2,100) and we are to work through all 100 of the Group B hypotheses and 2 (randomly chosen?) Group A hypotheses. The low-probability hypotheses definitely wind up in the preferred position here. But, of course, had the case been somewhat different, the upshot would differ too. Thus if the Group A hypotheses were a bit more general and the Group Bones a bit less so (say 40 and 50, respectively) then the case would be reversed. For then the expected generality is:
And this is maximized at (10, 20), so that the Group A hypotheses would now enjoy priority. The point is that our economically oriented approach is wholly undogmatic in the issue of generality-preference. We replace Popper's purely logical concern with universality for its own sake with an economico-methodological concern for universality-relative-to-cost. If we take this economic line, and do sensible decision-making on the basis of the reasonable-seeming economic precept "Maximize generality subject to the constraints of affordability," then our basic concern is one of cost/benefit analysis, seeking to optimize returns subject
84
NICHOLAS RESCHER
to resource outlays. Is From this (certainly not unreasonable) perspective, it becomes an altogether secondary issue whether our priority attention is given to the more or the less general alternatives. The dispute of generality-priority versus specificity-priority now looks rather like a doctrinaire bit of unrealism. Once due heed is paid to the economic aspects of the matter, ideological attachment on the basis of "general principles" to highly general (or highly specific) hypotheses will become a luxury we can no longer afford.
6. Probabilism vs. Improbabilism. I shall turn next to the Popperian thesis that the rational agenda of scientific inquiry calls on science to address itself with prime priority to the less probable (more vulnerable) hypothesis in a given problem-situation. The case stands as follows: Issue: We are confronted with a series of alternative hypotheses to resolve a given problem. All these are supposed to lie on the same level in point of generality. We are to put their respective tenability to the test. Question: Do we want to test the hypotheses in order of their probability or their improbability? Are the serious candidates for priority concern the probable or the improbable ones? Here, then, we confront the issue of a Carnapian probability-preference versus a Popperian improbability preference in relation to scientific hypotheses. l9 Consider, for the sake of an example, the case of three alternative hypotheses which are credited with the following probabilities in the face of the evidence-at-hand: hypothesis: probability:
HI
H2
.1
.2
H3 .7
Suppose we are to proceed in a series of pairwise tests of these '*Looking on theories as intellectual instrumentalities (for explanation, prediction, etc.), one can apply to them the usual economic considerations of many sided versatility vs. case-specific power that applies to tools in general. On the economic aspect of this latter issue compare the suggested discussion of "The Law of Diminishing Returns in Tools" in Zipf [32], pp. 66ff. and 182ff. "Popper put the issue as follows: "Thus if we aim, in science, at a high informative content-if the growth of knowledge means that we know more, that we know a and b rather than a alone, and that the content of our theories thus increases-then we have to admit that we also aim at a low probability . . . and since a low probability means a high probability of being falsified, it follows that a high degree of falsifiability, or refutability, or testability, is one of the aims of science." (Popper [24], p. 219.)
PEIRCE A N D T H E ECONOMY OF RESEARCH
85
H i against one another. And suppose further that the possible outcomes of these pairwise test-comparisons simply have a likelihood determined by the relative weights of their initial probabilities. We now pose the question of whether to test ihe probables against the probables first, or the improbables against the improbables. The supposition just made leads to the following tabulation of test-outcome probabilities:
There, of course, remains the question of the cost of these comparison tests. We shall make a very simple assumption here, that of the intrinsically plausible principle:
Ceteris paribus, the cost of pairwise tests decreases monotonically with the distance between the likelihoods of the competitors involved. We shall thus suppose-for the sake of the simplicity of our illustration-the simple proportionality principle: 20 cost(Hi vs H i ) = 1 - A ( H i , H j ) and so = k [1 - A ( H i , H i ) ] where A ( H i , H i ) = Ilpr(Hi / H i vs H i ) - p r ( H i / H i vs Hj)II We thus arrive at the following tabulation of test costs:
Test H , vs H z H , vs H , H z vs H ,
Cost .67k .26k .44k
( 1 ) Popperian Strategy: Work on unlikeliest first:
ZoNothingfundamental to the structure of the discussion would be altered by taking the cost to be governed by some other reasonable principle, such as proportionality to the ratio of the largest of p r ( H , / H , vs H i ) and p r ( H j / H , vs H i ) to the smaller of these two.
86
hTICHOLASRESCHER
Expected cost:
(2) Orthodox Strategy: Work on likeliest first:
Expected cost:
In this example, then, the orthodox strategy of first testing the more probable alternatives against one another proves superior on an expected-cost basis. But there is nothing inevitable about this. In other cases the situation could eventuate differently. Thus consider the preceding example subject to a change of probabilities: hypothesis: probability:
H I H2 .1 .4
H, .5
The conditions of the problem are now changed to:
Test H, vs H , H , vs H , H , vs H ,
(1) Popperian Strategy:
Expected cost:
Cost .4k .34k .88k
PEIRCE A N D T H E ECONOMY OF RESEARCH
(2) Orthodox strategy:
Expected cost: .44(.88k + .4k) + .56(.88k + .34k) = 1.25k So in this case the Popperian strategy of giving priority to the least probable hypothesis proves to be the more cost-effective. To summarize: The economic approach is eminently "pragmatic;" it does not accord general superiority either to a strategy of probability-priority or improbability-priority. It is neutral on this particular ideological issue, and lets the chips fall where they may-or rather, as indications of the economic sort mooted by Peirce indicate they should. It seems worth adding, however, that this entire discussion regarding probability-preference vs. improbability-preference differs in a fundamental way from the earlier discussion of generality-preference. For what was at issue there was the economic advantageousness of selecting a certain hypothesis for ADOPTION (or "rational acceptance") while what is at issue here has to do with the issue of selecting a certain hypothesis for TESTING. (The distinction between "research-worthy hypotheses" and "credible theories" is crucial here, our present concern with probability-priority not being oriented at theory-acceptance at all, but dealing with the much prior stage of the design of a "research program. ") 7. Simplicity. It is recognized by theoreticians on all sides that simplicity must play a prominent part in the methodology of science. There is as widespread agreement as there ever is on philosophical matters on the principle that simple hypotheses enjoy a preferred status in point of plausibility and credibility in inductive contexts. But on the other hand, when one pushes the issue back to first principles and presses the question of the rationale of this simplicitypreference, one meets with a wavering note of indecisiveness. One acute commentator has remarked as follows on the position of affairs:
The whole discussion of simplicity has been curiously inconclusive. Not only has there been no growing body of agreement concerning the measurement of simplicity, but there has been no agreement concerning . . . the precise role that simplicity should play in the acceptance of scientific hypotheses. ([14], pp. 267-268)
88
NICHOLAS RESCHER
Discussions of the issues are replete with indications of queasiness at the acceptance of a principle that seems less congenial to toughminded scientific analysts than to old-school metaphysicians with a penchant toward quasi-theological ideas like the principle of the simplicity of nature. It is difficult to justify simplicity-preference on grounds either of informativeness or of fal~ifiability;~' but it is easy to justify on grounds of economy. If one claims a phenomenon to depend not just on certain distances and weights and sizes but also (say) on temperature and magnetic forces, then one must operate a more co~nplextesting apparatus, and contrive to take readings over this enlarged range of physical parameters. Or again, in a certain curve-fitting case compare the thesis that the resultant function is linear
with the thesis that it is linear up to a point and sinusoidally wave-like thereafter:
Now think of writing a computer program to check whether empirically determined point-coordinates fit the specified function. This is clearly Z I I tis dogma among the Popperians that a simple theory is more readily falsified than a complex one. (Compare Chapter VII of Popper [23].) But this is true only if the complex theory is ad hoc designed specifically so as to eliminate the falsifiers of the simple one-i.e., if the complex theory is a bad theory. It is certainly not true in general. Is it really more difficult to show that a collection of points fail to be on a certain curved line than on a certain straight one? (Compare Barker [I] .)
PEIRCE AND THE ECONOMY O F RESEARCH
89
a vastly less complex-and so more economical-process in the linear case as compared with its more convoluted congener. And comparable considerations of operative economy attach to simplicity on the side not just of substantiation but also of utilization, and render simpler alternatives more advantageous to select for adoption as well as for testing. The concerns of economy provide a straightforward and reasonable basis for simplicity-preference. On such an approach, no claim is made (tacitly or otherwise) of any sort of ontological linkage between simplicity and (probable) truth. Simplicity-preference is based on the strictly practical consideration that the simple hypotheses are the cheaper-the most advantageous for us to put to use in the context of our purposes. There is thus no recourse to a substantive (or constitutive) postulate of the simplicity of nature; it suffices to have recourse to a regulative (or practical) precept of economy of means. This amounts to a theoretical defense of simplicity that in fact rests on practical considerations. Peirce himself offered a closely analogous metaphysicomethodological justification for simplicity-preference. He maintained that the combination of relatively good probability of correctness with a relatively low cost of testing gave simple hypotheses a preferred status, since the expected-value calculations of the economy of research indicate that (when other things are anything like equal) simple hypotheses can be put into operation more advantageously than others. (For Peirce's argumentation see 6.530-532.) On this approach, considerations of the economics of inductive inquiry provide a relatively unproblematic rationale of the methodological merits of simplicity as a desideratum in the theory of inductive reasoning. 8. Conclusion. Enough has now been said to substantiate the main conclusions I would like to draw from these various illustrations. The conception of the economy of research in the actual conduct of inductive inquiry provides an instrument of considerable power. Even in a very rudimentary form, the economic perspective emphasized by Peirce can straightforwardly resolve some of the key disputed issues in the recent theory of inductive reasoning, including problems regarding Carnap's requirement of total evidence, Hempel's paradox of the ravens, Goodman's grue paradox, the concept of simplicitypreference, and some of the key issues controverted between Popper and his opponents. It is interesting and significant to note that a common thread runs through many of the major controversial points in the recent theory of inductive reasoning. Time and again, the theoreticians put before
90
NICHOLAS RESCHER
us one sort of story where common sense says something quite different. And so there arises a to-and-fro of great length with such issues as grue versus blue or black ravens versus white shoes, issues where the whole tradition of ordinary practice tells us that there is no realistic occasion for worry. It now becomes clear why the theoreticians encounter perplexity where others do not. For they have all too commonly left out of consideration one of the very central factors of this (and any other) enterprise-the economic element. In consequence, a gap has opened up between the theoreticians' ideas as to how matters should stand in the abstract logic of things, and the ordinary practitioner's sense of the natural way to go at it. Recourse to a consideration of the economic aspect of inductive practice can neatly close this gap in many cases. Peirce had a clearer vision here than many of his successors. Of course, a great deal remains to be said both as to the economy of research itself and about Peirce's ideas of this matter. But I trust that what has been put forward here is enough to persuade the reader that in giving this subject a central place in his theory of inductive inquiry Peirce was well ahead of his contemporaries-and indeed of ours as well. 22
9. Pragmatist Epistemology and Latter-Day Decision-Theory Models of
Propositional Acceptance. Having reproached it in the preceding section of ignoring the economy of research, I should like in this section to do the contemporary methodology of science somewhat ampler justice in this regard. Contemporary epistemologists of science incline to approach the issue of the acceptarzce of hypotheses from a decision-theoretic point of view. This approach originated with Carnap's 1950 treatise on The Logical Foundations of Probability, where he discussed the utility-maximizing acceptance rule. 23 He envisages a situation of the following sort: we are given several competing hypotheses; we know their probabilities in the light of the available evidence; we now can assess the respective utilities that flow from their acceptance. On 22Recentinductive theorists who have proposed cognitive decision models concerned with accepting hypotheses have generally ignored problems that arise in designing experiments on collecting data. Statisticians, on the other hand, have done much better at facing up to these issues. Peirce had the good fortune to be as much one as the other. 23Since Carnap's day these problems have been widely canvassed-especially in publications by C. G. Hempel, I. Levi, J. Hintikka, R. Hilpinen, and Juhani Pietarinen. For references to the literature see the works cited in footnote 9.
PEIRCE AND T H E ECONOMY O F RESEARCH
91
this basis, we are enjoined by the decision-rule at issue to accept that hypothesis H whose expected utility
is at a maximum. On such an approach, propositional acceptance will be a straightforward matter of a decision-theoretic combination o f probability and utility considerations. In somewhat more formal terms, a decision-theory model of thesisacceptability takes on a shape that can best be apprehended by introducing a bit of symbolic machinery. Let P, Q, R, etc., represent theses. There will now be two correlative modes of "cognitive action" in terms of an acceptance-operator a . a ( P ) = accepting the thesis P G ( P ) = not accepting the thesis P (Note that not accepting P, i.e., &(P), is very different from accepting not-P, i.e., a ( P ) . ) Let us begin on this basis by contemplating the four theoretically available alternatives: (i) a ( P ) & G(P); (ii) a ( P ) & & ( P ) ; (iii) a ( P ) & a ( P ) ; and (iv) G(P) & G(P). Since rational acceptance is to be at issue, the principles of operation for the acceptance-operator a must clearly embody the rule: If a ( P ) , then G(P). We thus arrive at the following upshot: Case (i) is tantamount simply to a ( P ) itself, and case (ii) simply to a ( ~ itself. ) Moreover, case (iii) is rationally impossible. The alternatives regarding the acceptability of P are thus reduced to three mutually exclusive and exhaustive cases:
Only three possibilities exist: acceptance, rejection, and agnosticism. At this stage, the issue of utilities comes to the foreground. Here, most recent writers in the subject join in making the following suppositions: (1) The only utilities that concern us are to be cognitive utilities: knowledge, ignorance, error. We shall deal with belief or acceptance on a purely theoretico-cognitive basis, where the aspect of practical or affective implications can be put aside. The operative utility-goal is the theoretico-cognitive one of gaining information, and we shall abstract from any issues relating to the application of this information in practice. (2) Correct acceptance thus brings us a positive utility, a benefit, viz., information. Errors on the other hand come in two froms: ( I ) Errors of the first kind. These are errors of omission:
92
NICHOL,AS RESCHER
we don't accept P when P is in fact the case. They involve the sanction (negative utility) of ignorance. (2) Errors of the second kind. These are errors of commission: we accept P when in fact P. They involve the sanction (negative utility) of actual mistakes.
On the purely cognitive approach we take a narrow view of benefits and costs. Utility now amounts to information-content. The only benefit is the engrossment of truth-content, the sole costs envisaged are the losses of truth through non-acceptance or-worse-through the acceptance of conflicting falsehoods. How serious a matter is error? Some regard it as akin to a heinous crime. W. K. Clifford certainly thought so. In his classic 1877 essay on "The Ethics of Belief" (to which William James's even more famous essay of 1895 on "The Will to Believe" offers a reply) Clifford maintained that: It is wrong, always. everywhere, and for anyone, to believe anything upon insufficient evidence. 24 Some writers have even gone so far as to push this sort of judgment to its logical conclusion by pressing it towards the boundaries that separate the morally reprehensible from the legally criminal. " William James quite properly argued against Clifford that the enterprise of inquiry is governed not only by the negative injunction "Avoid error!" but no less importantly by the positive injunction "Achieve truth!" And, in the factual area-where the content of our claims outstrips the evidence we can ever gather from them-this (so he insists) demands the risk of error. There is nothing irrational about this risk, quite to the contrary: "a rule of thinking which would absolutely prevent one from acknowledging certain kinds of truth, if those kinds of truth were really there, would be an irrational rule."'" 24Clifford [ 6 ] . For a useful outline of the James-Clifford controversy and its background see Kauber [13], where the relevant issues are set out and further references to the literature are given. For a particularly interesting recent treatment see Chisholm [SI. 25For example, in Chance [4] one finds "the making of statements that outstrip the evidence" prominently enrolled on the register of this category of "crimes." (pp. 33-34.) I6See James [12], pp. 27-28. Clifford's tough line on belief in the religious sphere was not matched by a corresponding toughness in the sphere of scientific knowledge, where he took a confidently realistic position. Rejecting the possibility of certainty here, he stressed that what we accept as our "knowledge" of nature rests on various interpretative principles, which, though indemonstrable, are nevertheless necessary for man's survival, and whose acceptance is thus to be accounted for (though not established) in evolutionary terms. He held the uniformity of nature to be such a principle, maintaining that "Nature is selecting for survival those individuals and races
PEIRCE AND T H E ECONOMY OF RESEARCH
93
Let us look at the matter in a Jamesian perspective as one of combining balancing the desideratum of error-avoidance off against that of information-loss. We then arrive at a situation somewhat as follows (where cont ( P ) is to be a measure of the information-content of the thesis P):
Course 1 Actual Situation P obtains Pobtains
(Accept P ) (aP> + cont(P) K x -cont(P)
Schedule of Returns Course 2 (Accept P) K x -cont(P) + cont(P)
Course 3 (Suspend Judgment re. P ) (a*P) -cont(P) -cont(P)
Here K is a constant that fixes the seriousness of the penalty of "falling into errorM-the larger the value we assign to K, the more cautious we will be in running the risk of error, and the more weight we give to errors of the second kind vis-8-vis those of the first. (A Cliffordian will make K relatively large, a Jamesian relatively small .") Given any utility measure, one can implement a Bayesian decision program by guiding action in terms of a program of maximizing the expected utility of its outcome. On this approach, one applies the general decision-rule: Within the range of available action-alternatives choose that fo.r which the estimate of the resulting utility (or the expected value thereof) is a maximum. This decision-rule is usually called the "Bayesian criterion" for rational choice among action-alternatives. (See [IS], pp. 312-313.) Applying this rule to our special case of propositional acceptance, we recall three exclusive and exhaustive alternatives: a ( P ) , a ( ~ )a*(P) , = G(P) & G(P). At this stage we invoke the principle: Adopt that one among alternatives which maximizes the utility-results to be expected. who act as if they were uniform; and hence the gradual spread of this belief over the civilized world" ( [ 6 ] ,p. 209). James' own position against Clifford comes down to saying that what's sauce for the scientific goose is sauce for the religious gander as well. 27ButK would never be very small. As long as we keep our acceptance-set consistent, the inclusion of error will block further truths, while non-acceptance never blocks anything. Errors of the first kind are thus substantially more serious than those of the second.
94
NICHOL,AS RESCHER
Reverting back to our information-content utilities we can now do some expected-value calculations: Espectutions
E(aP) = X . c(P) + ( 1 - X ) . K . -c(P)
E(&) = x . K . - c ( P ) + ( 1 - X ) . C ( P )
E(a";P)= x . - c ( P ) + ( 1 - X ) . - c ( P )
Let us adopt the abbreviation Z for the content-measure of a thesis weighted by its probability:
Then we have
On the Bayesian approach to hypothesis-acceptance, these three quantities are to be our guide in the acceptance or nonacceptance of hypotheses. Thus we are to accept P i n the following circumstances:
E ( ~ P>) E ( & P ) iff
Z ( P ) - K . Z ( P )> - K . Z ( P ) + Z ( P )
Z ( P ) . ( 1 + K ) > Z(P). ( 1 + K )
Z(P)< Z(P)
And, of course, by symmetry
E ( ~ P>) E ( a P ) iff Z ( P ) < Z ( P ) Note that when it comes to the choice of P versus P, the value of the penalty-constant K does not matter. Let us next take up the case of a suspension of judgment E ( a " P ) > E ( a P ) iff
- Z ( P ) - Z ( P )> Z ( P ) - K . Z ( P )
z ( P )(.K - 1 ) > 2ZP
3
E ( a W p )> E ( ~ Piff )
- Z ( P ) - Z ( P )> - K . Z ( P ) + z ( P ) Z ( P )( K - 1 ) > 2Z(P)
a
L
Z ( P ) > --- Z ( P ) K-I
95
PEIRCE AND THE ECONOMY OF RESEARCH
Suspension of judgment secures a higher expected value than both these alternatives just when both of these conditions are satisfied.
Line 11:
/
z(P)
K-1 = ------
. Z(P)
2
Z(P)= Z ( P )
Line I:
z(P)
2
= -.
Z(P)
K- 1
Z(P) Figure 1
In the region below Line I, accepting P is preferable to a suspension of judgment. In the region above Line 11, rejecting P (accepting P) is preferable to a suspension of judgment. In the region between the lines a suspension of judgment is preferable to either alternative. is determined by the size of the quantity The width of the angle K which determines how serious a sanction "falling into error" actually is. When K = 3 we're in the straight comparison case. As K gets bigger, the region of enforced uncertainty grows, until as K -+ x it becomes all-pervasive. The broken central line indicates a crucial division-boundary corresponding to the K = 3 case. In the region above it we are better off accepting P, and below it we are better off accepting P i n a forced choice between P and P. (This, of course, is independent of K.) Thus K may be characterized as an index of caution-its magnitude reflects the extent to which one is loath to run the risk of possible error. Smallish values of K are correlated with a reasonably sensible policy of calculated risks. The fact that our capacity to accept anything as putative knowledge vanishes as K -+ x indicates that there is no risk-free avenue to empirical knowledge. In the epistemology of factual cognition, as in other areas of life, the dictum "Nothing ventured, nothing gained" applies. The picture of Figure I makes it graphically clear how telling James's argument against Clifford in fact is. In viewing "falling into error" as virtually a fate worse than death-taking K to be very large indeed-Clifford cuts himself off from Butler's view of probability as a guide to life. Any sort of calculated risks in the whole empirical
+
96
NICHOLAS RESCHEK
sphere of the inherently less-than-certain is now precluded. As James saw, a Cliffordian approach fails to sail between Scylla and Charybdis-it avoids error of the second kind (errors of commission) only at the price of massive errors of the first kind (errors of omission). These considerations in effect put before us the essentials of the Bayesian decision-theoretic approach to hypothesis acceptance as it is currently cultivated. Its guiding conception is that of the maximization of the expected value of the epistemic utilities of the theses at issue. This view of the recommended acceptance process brings to light both its strengths (in the maximization of expected returns) and its weaknesses (in its exclusive preoccupation with the merely cognitive utility of the results). The Bayesian decision-theoretic model of the acceptance of scientific hypotheses does undoubtedly introduce some economic elements into the picture. After all, it provides a framework for expected-value calculations and thus encompasses a range of utility-considerations on which such calculations will be based. Nevertheless, this remains a far cry from the issues of the economy of research as envisaged by Peirce. For Peirce is concerned with the economic aspects of the process of evidence-gathering and the methodology of hypothesistesting itself-and thus not merely with the decision-theoretic issue of the expected-utility-of-acceptance relative to the evidence-in-hand. In the decision-theory models of acceptance we do find a concern for maximizing the expected utility of the result of inquiry, but we do not find any indication of the need to accomplish this desideratum in the correlative context of a need t o minimize the cost of inquiry.28 Utility itself is the objective, and not utility-in-relation-to-cost. 29 The economic aspect is introduced only at the final stage of acceptance and not at the preliminary stages of inquiry itself. In this regard, 28However, while methodologists of science have yet to come to terms with the issue, statisticians have for sometime concerned themselves with the problems that arise in designing experiments and collecting data. (Historically, it was Peirce's work as an applied statistician that brought these issues to the forefront of his thinking.) 2%ome writers do-after a manner-explicitly introduce the cost-element. The pioneer among these is R. B. Braithwaite. (See Braithwaite [2].) Their approach envisages combining "the costs of various possible mistakes and the benefits of various possible mistakes and the benefits of various ways of being right." (See the summary of the position in Kyburg [14], p. 275.) Recent writings by Alex C. Michalos also revolve about this approach. (See Michalos [17], [18], [19].) However, Braithwaite, Michalos et al., still do not view the problem in its Peircean perspective. For their "costs" are those involved in the acceptance of an hypothesis (in effect simply the negative utilities of the usual decision-theory approach), while Peirce's "costs" relating to the process of inquiry as such, and relate to the state of affairs that precedes the stage at which an acceptance-choice is faced.
PEIRCE AND THE ECONOMY O F RESEARCH
97
Peirce's ideas still have not been fully assimilated to present-day approaches. 30 REFERENCES
[ I ] Barker, S. F. "On Simplicity in Empirical Hypotheses." Philosophy of Science 28 (1961): 162-171; Reprinted in Probability, Confirmation and Simplicity. Edited by M. H. Foster and M. L. Martin. New York: Odyssey Press, 1966. (This anthology contains several good papers on this topic.) [2] Braithwaite, R. B. Scientific Explanation. Cambridge: Cambridge University Press, 1953. [3] Carnap, R. Logical Foundations of Probability. Chicago: University of Chicago Press, 1950 and 1962. [4] Chance, J. Intellectual Crime. London: N . Douglas, 1933. [5] Chisholm, R. "Lewis' Ethics of Belief." In The Philosophy of C. I. Lewis. Edited by P. A. Schilpp. La Salle: Open Court Publishing Co., 1968. [6] Clifford, W. K. "The Ethics of Belief." In Lectures and Essays. Vol. 11. London: Books for Libraries, 1879. Originally published in Contemporary Review 30 (1877): 42-54. [7] Cushen, W. E . "C. S. Peirce on Benefit-Cost Analysis of Scientific Activity." Operations Research 14 (1967): 641ff. [8] Fann, K. T . Peirce's Theory of Abduction. The Hague: Humanities Press, 1970. [9] Fisch, M. "A Draft of a Bibliography of Writings about C. S. Peirce." In Studies in the Philosophy of Charles Sanders Peirce. Edited by E. C. Moore and R. S. Robin. Amherst: University of Massachusetts Press, 1964. First supplement to the preceding in Transactions o f the Charles S. Peirce Society 2 (1966); second supplement in Transactions of the Charles S. Peirce Society 10 (1974). [lo] Hempel, C. G. "A Note on the Paradoxes of Confirmation." Mind 55 (1946): 79-82. [ I l l Herbenick, R. M. "Peirce on Systems Theory." Transactions of the Charles S. Peirce Society 6 (1970): 84-98. [12] James, W. The Will to Believe and Other Essays in Popular Philosophy. New York: Peter Smith, 1956. [13] Kauber, P. "The Foundations of James' Ethics of Belief." Ethics 84 (1974): 151-166. [14] Kyburg, H. E ., Jr. "Recent Work in Inductive Logic." American Philosophical Quarterly 1 (1964): 249-287. [15] Luce, R. D. and H. Raiffa. Games and Decisions. New York: Wiley, 1957. [16] Mach, E. Popular Scientific Lectures. Chicago: Open Court Publishing Co., 1894. [17] Michalos, A. C. Principles of Logic. Englewood Cliffs: Prentice-Hall, Inc., 1969. [18] Michalos, A. C. The Popper-Carnap Controversy. The Hague: Humanities Press, 1971. 301n a widely discussed 1953 paper Richard Rudner has posed the second-order research-design question: How long must inquiry be conducted to assure the (contextually appropriate) probabilification of a certain probability-assignment? (See Rudner [27] .) Implicit here-i.e., not present in Rudner's discussion itself but raised by its implications-is the problem of assessing the cost of continued research against the risks inherent in a mistaken acceptance of imperfect information. This sort of question is decidedly a Peircean issue and Rudner deserves credit for helping to keep it on the agenda. But I think it not unfair to say that having posed this sort of issue (which lies within the framework of Peircean concerns), Rudner does not do anything with it. Unlike Peirce himself, he neither poses the issue of costs, nor seems to be aware of how deeply this problem of making sure enough cuts into the very methodology of inductive inquiry. In this regard, Peirce not only maintains priority, but maintains primacy as well.
98
NICHOLAS RESCHER
[19] Michalos, A. C. Foundations o f Decision-Making. New York: Van Nostrand, 1976. [20] Murphey, M. G. The Development of Peirce's Philosophy. Cambridge: Harvard University Press, 1961. [21] Norris, K. and J. Vaizey. The Economics of Research and Technology. London: Beekman Publishers, 1973. [22] Peirce, C. S. Collected Papers of Charles Sanders Peirce. Edited by Charles Hartshorne et al. Cambridge: Harvard University Press, 1931-1958. [23] Popper, K. The Logic of Scientific Discovery. New York: Basic Books, 1959. [24] Popper, K. Conjectures and Refutations. London: Basic Books, 1962. [25] Reichenbach, H. The Theory of Probability. Berkeley and Los Angeles: University of California Press, 1949. [26] Rescher, N. Scientific Progress. Oxford: Basil Blackwell, 1976. [27] Rudner, R. "The Scientist Qua Scientist Makes Value Judgments." Philosophy of Science 20 (1953): 1-6. Reprinted in Reading in the Philosophy of Science. Edited by B. Brody. Englewood Cliffs: Prentice-Hall, Inc., 1970. [28] Salmon, W. C. "On Vindicating Induction." In Induction: Some Current Issues. Edited by H . Kyburg and E. Nagel. Middletown: Wesleyan University Press, 1963. [29] Salmon, W. C. Statistical Explanation and Statistical Relevance. Pittsburgh: University of Pittsburgh Press, 1969. [30] Scheffler, I. "Inductive Inference: ANew Approach." Science27 (1958): 177-181. [31] Sharpe, R. "Induction, Abduction, and the Evolution of Science." Transactions of the Charles S. Peirce Society 6 (1970): 12-33. [32] Zipf, G. K. Human Behavior and the Principle o f Least Effort. Boston: AddisonWesley Press, 1949.
