1148 00319 8975
MINNESOTA STUDIES IN THE PHILOSOPHY OF SCIENCE
Minnesota Studies in the
PHILOSOPHY OF SCIENCE
VOLUME Concepts, Theories,
and
the
II
Mind-Body Problem
EDITED BY
HERBERT AND
FEIGL,
MICHAEL SCRIVEN
DROVER MAXWELL
FOR THE MINNESOTA CENTER FOR PHILOSOPHY OF SCIENCE
UNIVERSITY OF MINNESOTA PRESS, MINNEAPOLIS
Copyright 1958 by the
UNIVERSITY OF MINNESOTA All rights reserved
PRINTED IN THE UNITED STATES OF AMERICA Third printing 1967 Library of Congress Catalog Card
Number: 57-12861
PUBLISHED IN GREAT BRITAIN, INDIA, AND PAKISTAN BY THE OXFORD UNIVERSITY PRESS, LONDON, BOMBAY, AND KARACHI
Preface
This second volume of Minnesota Studies in the Philosophy of Science presents further results of the collaborative research of the Minnesota
Center for the Philosophy of Science in the area of the philosophical and methodological problems of science in general, psychology in particular. Again, some of the essays concern the broader philosophical foundations while others concentrate on more circumscribed logical or methodological issues.
In the course of the Center's work in recent years it has become increasingly clear that our publications will continue to reflect the sustained efforts of the research staff and some of its collaborators toward
an
analysis
and
clarification of a
number
of difficult and controversial
We
expect to return to some of these in future volumes. For while it is example, expected that most of the material which will appear in the next volume will grow out of our current research in the phitopics.
losophy of physics, some of it will undoubtedly still be concerned with the general foundations of science and the philosophy of psychology.
Although none of the following essays presuppose knowledge of the contents of any of the others, there are a number of common themes which provide a large measure of integration. Some of these common concerns are suggested in the Synopsis which follows this preface and which also contains brief abstracts of all the papers which appear in the volume.
Despite a certain
common
methodology of science
basic orientation in logical analysis
among
the
staff
and
its
and the
collaborators, there re-
main divergencies which even very extensive and
intensive discussion
did not remove. But, this is hardly surprising in philosophy. Even in the philosophy of science, individual differences in background, training,
in the finished product, no out before their embodiare thrashed ideas the thoroughly
and predilections manifest themselves
matter
how
777794 JUN
1 6 1976
KANSAS CITY (MO) PUBUC LIBRARY
Preface
ment
in written
and printed form.
advantageous to the reader self
which
ideas
he
finds
who
most
We are confident that this will prove
will, after all,
valid
and
have to decide for him-
fruitful.
stated in the preface to the first volume, the core staff of the first three years of operation was drawn from the University of Minnesota's faculty and consisted of Paul E. Meehl (Chair-
As
Center during the
man, Psychology Department), Wilfrid
S. Sellars (Chairman, Philosophy Department), Michael Scriven (Philosophy Department; Center Research Associate; currently at Swarthmore College), and Herbert Feigl
(Philosophy Department; Director of the Center). Additional research members since the summer or autumn of 1956 were H. Gavin
staff
Alexander (M.A., Oxford, Lecturer in Philosophy, University of Manchester), Dr. Grover Maxwell, Dr. William R. Rozeboom (Ph.D., Psychology, University of Chicago), and Professor Adolf Griinbaum (Lehigh University; visiting professor at the Center, autumn semester 19561957) Three conferences (1954, 1955, and 1956) were held at Princeton .
University where
we
profited
from the collaboration,
later greatly ex-
tended by correspondence, with Professors C. G. Hempel, Henry Mehlberg, Hilary Putnam, and Dr. Paul Oppenheim. Some of the results are incorporated in the essays of the present volume. Again, we wish to acknowledge with deep appreciation our indebtedness to the Louis
W.
and
Maud
Hill Family Foundation, to the administration of the
Uni-
Minnesota, and to its Graduate School, which generously provided a stipend for one of its research assistants, and to the visitors and collaborators named in the preface to the first volume of this series. versity of
We have received
invaluable assistance from our secretary, Betty Jacobfrom William H. Capitan, who prepared the index; from Alvin H. sen; who Miller, helped compile some of the bibliographies; and from the staff of the University of Minnesota Press.
Herbert Feigl, Director
Michael Scriven, Research Associate Grover Maxwell, Research Assistant
MINNESOTA CENTER FOR PHILOSOPHY OF SCIENCE June 1957
VI
Synopsis
The
following brief summaries are to provide a first orientation regarding the issues discussed in the essays contained in the present volume. The first essay deals with the very fundamental and contro-
question concerning the possibility of attaining a unified conceptual system and a unity of laws which will be necessary and sufficient for all fields of scientific explanation.
versial
1. Unity of Science as a Working Hypothesis: PAUL OPPENHEIM and HILARY PUTNAM. The aim of the paper is to formulate a precise concept
and to determine to what extent that unity can be the basis of precise definitions of the crucial concepts in-
of tJnity of Science attained.
volved,
On
it
hypothesis
is is
argued in detail that tentative acceptance of a working justified, according to which full empirical Unity of Science
can be attained. This
justification
grounds, partly because there
dence in
its
is
is
given, partly
a large
on methodological
mass of direct and indirect
evi-
favor.
A portion
of the third paper presents a view which differs on several points from that of the first in the analysis of reduction of one science to another. This essay and the one preceding it reflect partly divergent
views on a
number
of specific issues which arise in connection with
and the concepts which it employs. 2. The Theoretician's Dilemma: CARL G. HEMPEL. This essay examines the significance, for scientific theorizing, of terms which purport to
scientific explanation
refer to non-observable, or "hypothetical" things or events; it discusses
ways in which such terms servational vocabulary, in
what
and
may be it
interpreted by reference to an obthen deals with the question whether, and
sense, theoretical terms
might be altogether avoided in the
formulation of effective scientific theories.
and Theories: MICHAEL SCRIVEN. In an attempt to deal with such problems as the analysis of laws and disposi3.
Definitions, Explanations,
vii
Synopsis relation of theoretical concepts to the observation lanthe undertakes a rather extensive study of definitions. author guage, This approach to the formulation of the meaning of terms brings out
tions,
and the
the limitations there are on any brief summary of meaning such as a definition, and consequently the limitations on the programs of 'reducing'
one language
to another, for example, that of chemistry to that
of physics, that of meaning to that of descriptions of linguistic usage, mental states to behavior, laws to event descriptions, and in general,
theory to observations. Some interesting consequences appear for the usual analyses of scientific explanations, theories, and concepts, and also
names, rules, analyticity, and stipulative definitions. next three essays examine in detail some of the topics discussed in the preceding ones. It is interesting to note the important points of
for analyses of
The
agreement and disagreement. For example, although there is some divergence on the analysis of generalizations and scientific laws, most of the writers agree that
any purely extensional analysis of disposition terms
is
inadequate. 4.
Disposition Concepts and Extensional Logic;
jor attempts to analyze disposition concepts
ARTHUR PAP. The ma-
and counterfactual condi-
framework of extensional logic are critically examined. By an "extensional logic" is meant a logic that treats all compound
tionals within the
statements as truth-functional, in particular implications as so-called material implications. Analytical philosophers and logicians who have approached the problem more or less within this framework include
Bergmann, Hempel and Oppenheim, Carnap (reduction sentences), Kaila, Storer, Popper, and Braithwaite. But all such analyses are found inadequate for one reason or another. Instead it is proposed that the be built upon a primitive and nonextensional concept of "natural" implication (corresponding to A. Burks' "causal implication" and Reichenbach's "(synthetic) nomologianalysis of disposition concepts
W.
cal
implication")
.
With
adequate schema of structed. It
is
the help of this primitive concept an apparently explicit definition of disposition concepts is con-
emphasized, however, that the abandonment of extennot involve a
sional logic as a tool of analysis of causal language does
breach with any essential tenet of empiricism, such as the theory of the logical contingency of laws of nature.
Humean
5. Counterfactuals, Dispositions, and the Causal Modalities: WILFRED SELLARS. This paper consists of an introductory section describing the Vlll
Synopsis over-all structure of the II.
argument, and four parts: I. Counterfactuals, Properties, III. Causal Connection: The
Thing-Kinds and Causal
Dialectic of the Controversy, and IV. Toward a Theory of the Causal Modalities. Readers primarily interested in logical problems relating to scientific inference and in the controversy between the 'regularity' and 'entailment' analyses of lawlike statements should note that the discussion of these topics in Parts III and IV does not presuppose familiarity
with the arguments of the first two parts. Again, the discussion of thingkinds and causal properties in Part II is reasonably independent of the analysis and resolution of Goodman's puzzle about counterfactuals, which is the burden of Part I. 6.
General Statements as Rules of Inference?: H. GAVIN ALEXANDER.
The view
that general statements should be regarded as rules of inference or inference licenses has been supported in four ways. (1)
We
often infer directly from particular to particular with no major premise (Ryle). (2) The basis of induction must be a principle of inference rather than a statement of the uniformity of nature (Black, Braithwaite) (3) Laws in science are inference licenses not statements (Toulmin) (4)
.
.
Counterfactual conditionals can only be derived from general truths
which are expressed in the form of material rules of inference (Sellars). These four lines of argument are each examined carefully, and it is shown that none of them is at all conclusive.
The remaining papers are more directly relevant to the philosophy of psychology, specifically to the mind-body problem. The importance of the phenomenal field, emphasized in the Zener paper, is a theme which reappears
in the detailed analysis of the traditional
mind-body
problem contained in the essay by Feigl. 7. Persons: p. F. STRAWSON. The author argues that certain traditional of other philosophical problems ('the unity of the self/ 'knowledge
minds/ 'union of mind and body') are interdependent and can be
finally
resolved only by full recognition of the logical primacy of the concept of a person. This involves a complete repudiation both of the Cartesian
The argument pivots on the logical indiand notions of individual predicate, and on the requirement that viduals should be distinguishable and identifiable. tradition
and
its
'empiricist' variants.
The
for the Science of Significance of Experience of the Individual of current Psychology: KARL ZENER. This paper consists of a critique 8.
behavioristic
methodology from the point of view of Gestalt theory ix
Synopsis
and of suggestions for changes in outlook and emphasis in the general methodology of psychology. It is argued that conscious experiencesdirect awareness in the phenomenal field, including more rarely occurto mere verbal reports ring experiences are themselves (as opposed about them) not only legitimate as data but are of crucial importance for the science of psychology. It is contended that a too narrowly conceived principle of intersubjective testability has narrowed the range of experience accessible to scientific treatment, and a more liberal criterion is proposed and developed. Such changes "would involve clearer of psyrecognition of the peculiar necessity for the full development of its scientific observers number that a sufficient a science as chology
and experimenters themselves be highly developed in those characteristics which may be thought of as most essentially and significantly " 'human/ 9. The "Mental" and the "Physical": HERBERT FEIGL. The subject matter and the methods of psychology can be successfully clarified only through a comprehensive logical analysis of the relations of the mental and the plexity
physical. This problem, perhaps because of its extreme comits central place in the disputes between various "Weltan-
and
is nowadays frequently ignored (or repressed?) by psyand even by many philosophers. It is contended that the philosophies of phenomenalism, neutral monism, as well as behaviorism (American or recent British) cannot do justice to the problem because
schauungen" chologists
of their (respective)
reductionistic tendencies. Nevertheless, there
is
the possibility and plausibility of a monistic view based on a realistic, logical-empiricist analysis of the factual problems and the logical per-
mind-body puzzle. Through such an analysis, utilizing basic principles of logical syntax, semantics, and pragmatics, an identity or double-language view of the relation of the mental and the plexities of the
some
physical (anticipated in various metaphysical
and epistemological
ver-
by A. Riehl, M. Schlick, B. Russell and some American critical realists) can be more securely established. This requires, however, several sions
fairly radical revisions
of the traditional conceptions of acquaintance,
description, subjectivity, objectivity, spatiality, qualitative tive
knowledge, teleology, and reference (intentionality)
.
and quantita-
By
allocating
proper domains and by resolving them through logical analysis, the plausibility of dualistic doctrines (old and new) is greatly diminished. In the light of these clarifications a more the various
difficulties to their
Synopsis adequate understanding of the various approaches in current psychological theory can be achieved. in
The last article and the appendix, by treating themes which appeared Volume I, exemplify an important feature of this series the oppor-
tunity for sustained research and for the continuation of fruitful controspecific problems. Meehl's article supplements his own paper "Problems in the Actuarial Characterization of a Person" and some of
versy
on
the other papers of
Volume
I
which were concerned with methodologi-
psychology and psychoanalysis. The Appendix contributed Sellars and Chisholm concentrates on the problem of intentionality, by which is an important part of the mind-problem, and thus connects with cal issues of
a corresponding section in Feigl's essay. 10.
When
We
Shall
MEEHL. In making
may
Use Our Heads Instead of the Formula?;
his decision
p. E.
about an individual case the clinician
possess special information which,
combined with psychological
theory and plausible, "accepted" (but unverified) empirical generalizations, would lead to a prediction differing from that yielded by a tested statistical
function which provides no place for insertion of the special is argued that some circumstances justify a counter-
information. It
However, the present primitive state of theoretical knowledge in psychology does not justify "countermanding the formula"
actuarial prediction.
except in extremely clearcut cases. Appendix: Intentionality and the Mental: RODERICK M. CHISHOLM and
WILFRID SELLARS.
The
core of the
spondence between Wilfrid
Sellars
Appendix is an exchange of correand Professor Roderick Chisholm of
Brown
University concerning the account of the logical character of statements about mental episodes and dispositions (thoughts, beliefs, desires, attitudes, etc.), which was sketched by the former in his essay,
"Empiricism and the Philosophy of Mind," printed in Volume I of The correspondence is preceded by an introduction defining the problem in general terms, and by a reprinting, with additions and
this series.
omissions, of Professor Chisholm's recent paper, "Sentences about Believing," in Proceedings of the Aristotelian Society, 56:125-148 (1955-
1956).
XI
Contents
SYNOPSIS
vii
UNITY OF SCIENCE AS A WORKING HYPOTHESIS, Paul Oppenheim and Hilary
by
Putnam
3
1. Introduction, 3. 2. Unity of Science and Micro-Reduction, 5. 3. Reductive Levels, 9. 4. The Credibility of Our Working Hypothesis, 11. 5.
Past Successes at Each Level, 16. 6. Evolution, Ontogenesis, and SynConcluding Remarks, 27. Notes, 29. References, 32.
thesis, 23. 7.
THE THEORETICIAN'S DILEMMA: A Theory Construction, by Carl G.
Study in the Logic of 37
Hempel
1. Deductive and Inductive Systematization, 37. 2. Observables and Theoretical Terms? 43. 4. Structure Theoretical Entities, 41. 3. and Interpretation of a Theory, 46. 5. The Theoretician's Dilemma, 49. 6. Operational Definitions and Reduction Sentences, 50. 7. On the De-
Why
Means of an Observational Vocabufinability of Theoretical Terms by Functional Replaceability of lary, 53. 8. Interpretative Systems, 71. 9. Theoretical Terms, 75. 10. Meaning and Truth of Scientific Theo-
On
ries,
81. Notes, 87. References, 94.
DEFINITIONS, EXPLANATIONS,
AND
THEORIES, by 99
Michael Scriven 99.
Definitions: In-
1. General Introduction, 99. Analytic Method, troduction, 102. 4. Dictionary Definitions, 102. 5. Erroneous Definitions, 103. 6. Dictionaries versus Encyclopedias, 104. 7. Definitions as Substitution Rules, 105. 8. 'Undefinable' terms, 107. 9. Inter-categorical
2.
3.
The Definition of "Definition", 113. 11. The MisMathematical Definition; The Actual Limitations with leading Analogy on Redefinition, 116. 12. Definitions of Logical Constants in Symbolic 119. 13. Definitions as Analyses, 121. 14. Definability and ReDefinitions, 112. 10.
Logic,
ducibility, 122. 15.
The Concept
of 'Completed Science/ 127. 16.
The
Definitions in Terms of Acceptable Aspects of Reductionism, 128. 17. 18. The Analyticity of Definitions and StateLinguistic Function, 132. ments about Linguistic Function, 135. 19. Definitions as Rules, 139. xiii
Contents 20. Dictionary Definitions as Reports of Usage, 140. 21. The Truth of Rules, 142. 22. Stipulative Definitions, 145. 23. Final Assessment of Defimtions-as-Rules View, 149. 24. The Application and Invocation of Rules, 150. 25. Names of Individuals, 151. 26. The 'Stipulative' Definition of Individual Names, 1 55. 27. The Names of Fictitious Individuals, 156. 28. Existence as a Presupposition of Names, 158. 29. General
Names and
Scientific Concepts, 160. 30. Conditional Definitions, 164. Concepts and Vagueness, 175. 32. Dispositional Concepts,
31. Statistical
Theory Language, and Observation Language, 180. 33. The MicroConditional Equivalents of Macro-Properties, 187. 34. Complicated
The
Concepts; Psychological Dispositions, 188. 35.
lemma, 191.
Theoretician's Di-
36. Explanations, 192.
DISPOSITION CONCEPTS AND EXTENSIONAL LOGIC, Arthur Pap
...
.
by
...
196
COUNTERFACTUALS, DISPOSITIONS, AND THE CAUSAL MODALITIES, Introduction, 225.
by Wilfrid I.
Sellars
Counterfactuals, 227.
225
.
.
II.
Thing-Kinds and Causal
Properties, 248. III. Causal Connection: The Dialectic of the Controversy, 266. IV. Toward a Theory of the 'Causal' Modalities, 285. Ref-
erences, 307.
GENERAL STATEMENTS AS RULES OF INFERENCE? H. Gavin Alexander
PERSONS,
.
,
....
.
by P. F. Srrawson
by 309
330
.
THE SIGNIFICANCE OF EXPERIENCE OF THE INDIVIDUAL FOR THE SCIENCE OF PSYCHOLOGY, by Karl Zener
.
.
THE "MENTAL" AND THE "PHYSICAL/
7
.
by Herbert Feigl
A Preliminary
Survey of Some Perplexities and Their Repression, 370. and the Philosophical Strands in the Mind-Body Tangle, 374. III. Requirements and Desiderata for an Adequate Solution of the Mind-Body Problem. A Concise Statement of the Major Issues, 387. IV. Sorting Out the Various Meanings of "Mental" and I.
II.
The
Scientific
A
"Physical". Comparative and Critical Analysis, 397: A. "Subjective" versus "Objective", 397; B. Non-Spatial versus Spatial, 406; c. Quality versus Quantity, 409; D. "Purposive" versus "Mechanical", 411; E.
"Mnemic",
"Holistic",
"Emergent"
versus
"Non-Mnemic", "Atomis-
"Intentional" versus "Non-Intentional", 416. V. Mind-Body Identity. Explications and Supporting Arguments, 419: A. Review of the More Basic Meanings and Connotations of "Mentic",
"Compositional", 413;
F.
xiv
354 370
Contents taT and "Physical". Conclusions regarding their Respective Merits and Demerits, 419; B. The Inference to Other Minds, 425; c. The Cognitive Roles of Acquaintance, 431; D. Reduction and Identification in Scientific Theories, 438; E. Arguments Concerning the Identification of Sentience with Neural Events, 445. VI. A Budget of Unsolved Problems. Is There a PheSuggestions for Further Analyses and Research, 465: A.
nomenal Language? The Relations of Meaning, Evidence, and Reference, 466; B. Unitary or Dual Language Reconstruction? 468; c. Oneone Correspondence and the "Riddle of the Universe," 470; D. Some Remarks on the Philosophical Relevance of Open Scientific Questions in Psychophysiology, 478. Concluding Remark^ 482. Note and References, 483.
SHALL WE USE OUR HEADS INSTEAD OF THE FORMULA? by P. E. Meehl
WHEN
APPENDIX: INTENTIONALITY
498
AND THE MENTAL 507
Introduction, by Wilfrid Sellars
Sentences about Believing, by Roderick
M. Chisholm
Chisholm-Sellars Correspondence on Intentionality
510 521
NAME INDEX
540
SUBJECT INDEX
544
xv
MINNESOTA STUDIES IN THE PHILOSOPHY OF SCIENCE
PAUL OPPENHEIM
and
HILARY PUTNAM
Unity of Science as a Working Hypothesis
1.
1.1.
The
Introduction
expression "Unity of Science"
precise content
is
is
often encountered, but
difficult to specify in a satisfactory
manner.
It is
its
the
aim of
and
A
this paper to formulate a precise concept of Unity of Science; examine to what extent that unity can be attained. concern with Unity of Science hardly needs justification. are
to
We
guided especially by the conviction that Science of Science, i.e., the meta-scientific study of major aspects of science, is the natural means
by promoting the integration of
for counterbalancing specialization
knowledge. The desirability of this goal is widely recognized; many universities have programs with this end in view; often pursued by means different from the one just mentioned,
scientific
for example,
but
it is
and the conception of the Unity of Science might be especially suited as an organizing principle for an enterprise of this kind. 1.2.
As a
preliminary,
we
will
strength, three broad concepts of First,
to
distinguish,
all
the terms of science
order of increasing
Unity of Science:
Unity of Science in the weakest sense
which
in
l
is
attained to the extent
are reduced to the terms of
some
or psychology). This concept of Unity of be replaced by a number of sub-concepts dependLanguage (12) may one specifies the notion of "reduction" in which on manner the ing
one discipline
(e.g., physics,
involved. Certain authors, for example, construe reduction as the defi-
by means of those in the selected basic of biconditionals (47)); and some of means discipline (reduction by these require the definitions in question to be analytic, or "true in virtue nition of the terms of science
of the meanings of the terms involved" AUTHORS' NOTE: criticism.
The
We
(epistemological reduction);
wish to express our thanks to C. G. Hempel for constructive any shortcomings is, however, exclusively ours.
responsibility for
3
Paul Oppenheim and Hilaiy Putnam
upon the biconditionals effecting reshall employ is a wider one, and of biconditionals as a special means reduction to include by designed
others impose no such restriction duction. The notion of reduction is
we
case.
Second, Unity of Science in a stronger sense (because it implies is represented Unity of Language, whereas the reverse is not the case) the laws which to extent the It is attained to of Laws
by Unity
(12).
of science
become reduced
to the laws of
some one
discipline. If the
such an all-comprehensive explanatory system were realized,
ideal of
one could
call it
Unitary Science (18, 19, 20, 80). The exact meaning on the concept of "reduction" em-
of 'Unity of Laws' depends, again,
ployed.
Third, Unity of Science in the strongest sense is realized if the laws of science are not only reduced to the laws of some one discipline, but the laws of that discipline are in some intuitive sense "unified" or "connected." It is difficult to see how this last requirement can be made precise;
tions of
and
it
will not
be imposed here. Nevertheless, trivial realizabe excluded, for example, the simple branches of science does not reduce the par-
"Unity of Science" will
conjunction of several ticular branches in the sense
we
shall specify.
In the present paper, the term 'Unity of Science' will be used in two senses, to refer, first, to an ideal state of science, and, second, to 1.3.
a pervasive trend within science, seeking the attainment of that ideal. In the first sense, 'Unity of Science' means the state of unitary science. It involves the
two constituents mentioned above: unity of
vocabulary, or "Unity of Language"; and unity of explanatory principles, or "Unity of Laws." That Unity of Science, in this sense, can
be fully realized constitutes an over-arching meta-scientific hypothesis
which enables one
to see a unity in scientific activities that might otherwise appear disconnected or unrelated, and which encourages the construction of a unified body of knowledge.
In the second sense, Unity of Science exists as a trend within scieninquiry, whether or not unitary science is ever attained, and not-
tific
withstanding the simultaneous existence, (and, of course, legitimacy) of other, even incompatible, trends. 1.4.
The
senses, of
expression 'Unity of Science'
which two
them from the
will
be
briefly
sense with which
is employed in various other mentioned in order to distinguish
we
are concerned. In the
first
place,
UNITY OF SCIENCE AS A WORKING HYPOTHESIS what
sometimes referred to
is
something that we may call the Unity might be represented by the thesis that is
of
Method
all
the empirical sciences employ the same standards of explanation, of
in science. This
significance, of evidence, etc.
In the second place, a radical reductionist thesis (of an alleged "loginot an empirical kind) is sometimes referred to as the thesis of the Unity of Science. Sometimes the "reduction" asserted is the definacal,"
bility of all (10);
the terms of science in terms of sensationalistic predicates is wider (11) and predicates
sometimes the notion of "reduction"
referring to observable qualities of physical things arc taken as basic (12). These theses are epistemological ones, and ones which today appear
doubtful.
The
epistemological uses of the terms 'reduction', 'physical-
ism', 'Unity of Science', etc.,
should be carefully distinguished from
the use of these terms in the present paper. 2.
Unity of Science and Micro-Reduction
2.1. In this paper we shall employ a concept of reduction introduced by Kemeny and Oppenheim in their paper on the subject (47), to which the reader is referred for a more detailed exposition. The principal requirements may be summarized as follows: given two theories T! and T2 T2 is said to be reduced to TI if and only if: ,
(1)
The
(2)
Any
(3)
T!
is
T2
contains terms not in the vocabulary of TI. observational data explainable by 2 are explainable by TI.
vocabulary of
at least as well systematized as
complicated than
T2
;
but
this
is
T T2
.
(Ti
is
normally more
allowable, because the reducing theory
normally explains more than the reduced theory. However, the "ratio/' so to speak, of simplicity to explanatory power should be at least as the reduced great in the case of the reducing theory as in the case of 2
theory.)
Kemeny and Oppenheim also define science B 2 by another branch BI (e.g.,
the reduction of a branch of
the reduction of chemistry to
of physics). Their procedure is as follows: take the accepted theories B 2 at a given time t as T2 Then B f is reduced to Bj at time t if and .
some theory TI in BI only if some of the theories Analogously, if
there
is
at t such that
of
B2
TI reduces T2 (47) by some T! be.
are reduced
of B 2 longing to branch BI at t, we shall speak of a partial reduction to BI at t. This approach presupposes (1) the familiar assumption that some division of the total vocabulary of both branches into theoretical 5
Paul Oppenheim and Hilary Putnam
and observational terms is given, and the same observational vocabulary. 2.2.
The
two branches have
(2) that the
essential feature of a micro-reduction
that the branch BI
is
We
must suppose deals with the parts of the objects dealt with by B 2 of disuniverse a have we branch each to that corresponding specific .
UB
course
3 i;
and that we have
a part-whole relation, Pt (75; 76, especonditions we shall say that the
91). Under the following reduction of B 2 to BI 4 is a micro-reduction; cially p.
the objects in the universe of discourse of
B2
B2
is
reduced to BI; and
are wholes
which
possess
a decomposition (75; 76, especially p. 91) into proper parts all of which let us suppose belong to the universe of discourse of BI. For example,
B2
a branch of science which has multicellular living things as its universe of discourse. Let BI be a branch with cells as its universe of is
discourse.
decomposed of BI.
we
B 2 can be things in the universe of discourse of into proper parts belonging to the universe of discourse
Then the
in addition,
If,
shall say that
We
shall also
it is
the case that BI reduces
Bj micro-reduces B say that a branch BI
B2
at the time
t,
at
time
is
a potential micro-reducer of a
t.
the objects in the universe of discourse of B 2 are wholes which possess a decomposition into proper parts all of which belong to the universe of discourse of BI. The definition is the same as the
branch
B2
if
definition of 'micro-reduces' except for the omission of the clause 'B 2
reduced to BI/
is
micro-reduction constitutes a step in the direction of Unity if BI reduces B 2 it explains everything that
Any
of Language in science. For,
,
does (and normally, more besides). Then, even if we cannot define in BI analogues for some of the theoretical terms of B 2 we can use Bj
B2
,
in place of
B. Thus
any reduction, in the sense explained, permits a
"reduction" of the total vocabulary of science by making it possible to 5 dispense with some terms. Not every reduction moves in the direction of Unity of Science; for instance reductions within a branch lead to a simplification of the vocabulary of science, but they do not necessarily
lead in the direction of Unity of Science as we have characterized it (although they may at times fit into that trend). However, micro-reductions,
and even
replace
partial micro-reductions, insofar as
some of the terms
do move
of
they permit us to
one branch of science by terms of another,
in this direction.
Likewise, the micro-reduction of
B2
to BI
moves
in
the direction of
UNITY OF SCIENCE AS A WORKING HYPOTHESIS Unity of Laws; for
making
it
"reduces" the total
number
possible, in principle, to dispense
it
of scientific
with the
kws
kws by
of
B 2 and
explain the relevant observations by using BI. The relations 'micro-reduces' and 'potential micro-reducer' have very
simple properties: (1) they are transitive (this follows from the transitivity of the relations 'reduces' and Tt'); (2) they are irreflexive (no branch can micro-reduce itself); (3) they are asymmetric (if BI micro-
B 2 B 2 never
The two
ktter properties are not purely formal; however, they require for their derivation only the (certainly true) empirical assumption that there does not exist an infi-
reduces
,
micro-reduces BI).
a series of things Xi, x2 , x3 a proper part of x2 , etc.
nite descending chain of proper parts,
i.e.,
such that x2
is
is
a proper part of Xi, x 3
.
.
.
The its
just-mentioned formal property of the relation 'micro-reduces' transitivity is of great importance for the program of Unity of
means that micro-reductions have a cumulative character. a branch B 3 is micro-reduced to B 2 and B 2 is in turn micro-
Science. It
That
is, if
,
reduced to BI, then B 3 is automatically micro-reduced to BI. This simple fact is sometimes overlooked in objections 6 to the theoretical possibility of attaining unitary science by means of micro-reduction. Thus it has been contended that one manifestly cannot expkin human behavior by reference to the laws of atomic physics. It would indeed be fantastic to suppose that the simplest regularity in the field of psychology could be explained directly i.e., "skipping" intervening branches of science
by employing subatomic
theories.
But one may
believe in the attaina-
oneself to this bility of unitary science without thereby committing It is not absurd to suppose that psychological kws may absurdity.
eventually be explained in terms of the behavior of individual neurons in the brain; that the behavior of individual cells including neuronsmay eventually be explained in terms of their biochemical constitution;
including the macro-molecules that be explained in terms of atomic eventually may achieved, then psychological laws will have, in prin-
and that the behavior of molecules
make up
living cells
physics. If this
is
of atomic physics, although it would neverciple, been reduced to kws theless be hopelessly impractical to try to derive the behavior of a single
human being directly from his
constitution in terms of elementary
particles. 2.3.
Unitary science certainly does not exist today. But will
be attained?
It
is
useful to divide this question into
it
ever
two subquestions:
Paul Oppenheim and Hilary Putnam unitary science can be attained at be attained at all?
(1) If
Can
all,
how
can
it
be attained?
(2)
it
First of all, there are various abstractly possible ways in which unitary science might be attained. However, it seems very doubtful, to say the if the things least, that a branch B 2 could be reduced to a branch BI, universe of in the themselves are not in the universe of discourse of B 2
do not possess a decomposition into parts in the universe of discourse of BI. ("They don't speak about the same
and
discourse of BI
also
things/')
does not follow that BI must be a potential micro-reducer of all reductions are micro-reductions.
It i.e.,
B2
,
that
which the reducing theory and the reduced the same branch, or to branches with the same uni-
There are many theory belong to
cases in
When we
come, however, to branches with different universes say, physics and psychology it seems clear that the possiof a structural connection bility of reduction depends on the existence verse of discourse.
Thus one cannot plausibly that the behavior of inorganic matter reference to psychological laws; for inorganic materials
between the universes suppose
via the Tt' relation.
for the present at least
explainable by do not consist of is
One
supposes that psychology may be reducible to physics, but not that physics may be reducible to psyliving parts.
chology!
Thus, the only method of attaining unitary science that appears to be seriously available at present is micro-reduction.
To
turn
now
to our second question, can unitary science be attained?
We certainly do
not wish to maintain that
the case. But
it
has been established that
does not follow, as some philosophers seem to think, that a tentative acceptance of the hypothesis that unitary science this
is
can be attained hypothesis
is
is
it
therefore a
credible;
7
mere
and we
"act of faith."
shall
We believe
that this
attempt to support this in the
by providing empirical, methodological, and in reason^ its therefore think the assumption pragmatic support. that unitary science can be attained through cumulative micro-reduction
latter part of this paper,
We
8
itself as a working hypothesis. That is, we believe that it in accord with the standards of reasonable scientific judgment to
recommends is
tentatively accept this hypothesis
and to work on the assumption that
further progress can be made in this direction, without claiming that its truth has been established, or denying that success may elude us. finally
8
UNITY OF SCIENCE AS A WORKING HYPOTHESIS 3.
As a
3.1.
Reductive Levels
basis for our further discussion,
we
wish to consider
now
the possibility of ordering branches in such a way as to indicate the major potential micro-reductions standing between the present situation
and the
state of unitary science.
their universes of discourse.
We
The most
natural
offer, therefore,
way
to
do
this
is
by
a system of reductive
chosen that a branch with the things of a given level as its universe of discourse will always be a potential micro-reducer of any branch with things of the next higher level (if there is one) as its universe of discourse. levels so
Certain conditions of adequacy follow immediately from our aim.
Thus: (1)
There must be
(2)
Thd number
(3)
There must be a unique lowest
several levels.
of levels
must be
finite.
level
(i.e.,
under the relation 'potential micro-reducer');
a unique ''beginner"
this
means that
success
at transforming all the potential micro-reductions connecting these branches into actual micro-reductions must, ipso facto, mean reduction to a single branch.
thing of any level except the lowest must possess a decomposition into things belonging to the next lower level. In this sense (4)
each
Any
level, will
be
immediately above
as it
were a
"common denominator"
for the level
it.
Nothing on any level should have a part on any higher level. levels must be selected in a way which is "natural" 9 and justifiable from the standpoint of present-day empirical science. In par(5)
(6)
The
the step from any one of our reductive must correspond to what is, scientifically
ticular,
level
in the trend
toward
levels to
the next lower
speaking, a crucial step
over-all physicalistic reduction.
The accompanying list gives the levels we shall may verify that the six conditions we have listed
employ; are
10
the reader
all satisfied.
6
Social groups
5
(Multicellular) living things Cells
4 3
Molecules
2
Atoms
1
Elementary
Any whole which
particles
into parts all of possesses a decomposition
which
Paul Oppenheim and Hilary Putnam are
on a given
level, will
each level includes
be counted levels.
all
as also belonging to that level.
Thus
However, the highest level to which
higher a thing belongs will be considered the "proper" level of that thing. This inclusion relation among our levels reflects the fact that scientific
laws which apply to the things of a given level and to of those things also apply to all things of higher level.
all
combinations
Thus a
physicist,
7
about speaks about "all physical objects/ is also speaking living things but not qua living things. maintain that each of our levels is necessaiy in the sense that
when he
We
would be Utopian to suppose that one might reduce all of the major theories or a whole branch concerned with any one of our six levels
it
to a theory concerned with a lower level, skipping entirely the immeare sufficient in the diately lower level; and we maintain that our levels sense that
would not be Utopian to suppose that a major theory on levels might be directly reduced to the next lower level.
it
any one of our
(Although this is not to deny that it cases, to introduce intervening steps.)
However,
this contention
of predicates to
be
may be
convenient, in special
significant only if
is
we suppose some
set
associated with each of these levels. Otherwise, as
has been pointed out, 11 trivial micro-reductions would be possible; e.g., we might introduce the property "Tran" (namely, the property of being an atom of a transparent substance) and then "explain the trans-
parency of water in terms of properties on the atomic level," namely, all atoms of water have the property Tran. More
by the hypothesis that explicitly,
the explanation would consist of the statements
(a)
(x)(x
is
transparent
(b)
(x)(x
is
water
To
exclude such
each level there
D
===
(y)(y
trivial
(y) is
(y is an atom of x D Tran(y) an atom of x D Tran(y) )
"micro-reductions,"
associated a
we
shall
)
suppose that with
of the theoretical predicates normally characterize to on that level at present (e.g., with employed things level 1, there would be associated the predicates used to specify spatiois
list
temporal coordinates, mass-energy, and electric charge).
And when we
speak of a theory concerning a given level, we will mean not only a theory whose universe of discourse is that level, but one whose predicates belong to the appropriate
concerning level n is
+
1
list. Unless the hypothesis that theories can be reduced by a theory concerning level n
restricted in this way, it lacks
any 10
clear empirical significance,
UNITY OF SCIENCE AS A WORKING HYPOTHESIS the "part-whole" (Tf) relation is understood in the wide xPty holds if x is spatially or temporally contained in y, then everything, continuous or discontinuous, belongs to one or an3.2.
If
sense, that
other reductive level; in particular to level
1
(at least), since it
is
a
whole consisting of elementary particles. However, one may wish to understand Vhole' in a narrower sense (as "structured organization of elements"
12 ).
Such
a specialization involves
two
essential steps:
the construction of a calculus with such a narrower notion as
and
tive concept,
its
(1)
primi-
(2) the definition of a particular Tt' relation satisfy-
ing the axioms of the calculus.
Then the problem will arise that some Hence a theory dealing with such
things do not belong to any
things might not be microthe micro-reductions indicated by our system of levels were accomplished; and for this reason, unitary science might
level.
reduced even
if
all
not be attained.
For
man in a phone booth" is an aggregate of which we would not regard as a whole in
a trivial example, "a
things on
different levels
such a narrower sense. Thus, such an "object" does not belong to any reductive level; although the "phone booth" belongs to level 3 and the man belongs to level 5.
The problem posed by such aggregates safely make the assumption that the
may
is
not
serious,
however.
"man
behavior of
in
We
phone
booths" (to be carefully distinguished from "men in phone booths") could be completely explained given (a) a complete physicochemical theory
(i.e.,
a theory of levels
up
to
3,
including "phone booths"), and
(b) a complete individual psychology (or more generally, a theory of levels up to 5). With this assumption in force, we are able to say: If
we can in
construct a theory that explains the behavior of all the objects levels, then it will also handle the aggregates of such
our system of
objects. 4. 4.1.
The
Credibility of
Our Working Hypothesis
John Stuart Mill asserts (55,
Book VI, Chapter
7) that since (in
our wording) human social groups are wholes whose parts are individual from and persons, the "laws of the phenomena of society" are "derived
may be
resolved into the laws of the nature of individual man." In our
terminology, this
concerning
is
to suggest that
social groups
it
is
a logical truth that theories
theories (level 6) can be micro-reduced by 11
Paul Oppenheim and Hilary Putnam concerning individual living things (level 5); and, mutatis mutandis,
it
would have to be a logical truth that theories concerning any other level can be micro-reduced by theories concerning the next lower level. As a consequence, what we have called the "working hypothesis that unitary science can be attained would likewise be a logical truth. 7*
however, not so much wrong as it is vague. What is one to count as "the nature of individual man"? As pointed out above (section 3.1) the question whether theories concerning a Mill's contention
is,
the next given reductive level can be reduced by a theory concerning lower level has empirical content only if the theoretical vocabularies are have supspecified; that is, only if one associates with each level, as we
posed to be done, a particular
T2
set of theoretical concepts.
Given,
e.g.,
the question whether there exists a true psy2 is an chological theory TI in a particular vocabulary which reduces empirical question. Thus our "working hypothesis" is one that can only
a sociological theory
,
T
on empirical grounds. the factors on which the degree of credibility of any empiriAmong cal hypothesis depends are (45, p. 307) the simplicity of the hypothesis, the variety of the evidence, its reliability, and, last but not least, the
be
justified
factual support afforded
by the evidence.
We
proceed to discuss each
of these factors. 4.2.
be
As
for the simplicity 13 of the hypothesis that unitary science can
attained,
to consider the traditional alternatives
it suffices
mentioned
by those who oppose it. "Hypotheses" such as Psychism and NeoVitalism assert that the various objects studied by contemporary science have special parts or attributes, unknown to present-day science, in addition to those indicated in our system of reductive levels. For example, men are said to have not only cells as parts; there is also an immaterial "psyche"; living things are animated by "entelechies" or "Vital forces"; social
of these cases are
groups are
we
moved by "group minds."
provided at present
But, in none
with postulates or coordinat-
ing definitions which would permit the derivation of testable predictions. Hence, the claims made for the hypothetical entities just men-
tioned lack any clear scientific meaning; and as a consequence, the question of supporting evidence cannot even be raised.
On fail,
the other hand,
we cannot
ently
unknown
if
the effort at micro-reduction should seem to
preclude the introduction of theories postulating presrelevant parts or presently unknown relevant attributes 12
UNITY OF SCIENCE AS A WORKING HYPOTHESIS for
some
or
all
of the objects studied
by
science.
Such theories are
per-
fectly admissible, provided they have genuine explanatory value. For example, Dalton's chemical theory of molecules might not be reducible to the best available theory of atoms at a given time if the latter theory
ignores the existence of the electrical properties of atoms. Thus the 14 as the meaning is specified at a parhypothesis of micro-reducibility, ticular time, may be false because of the insufficiency of the theoretical
apparatus of the reducing branch.
Of
course, a
new working
hypothesis of micro-reducibility, obtained
by enlarging the list of attributes associated with the lowest level, might then be correct. However, if there are presently unknown attributes of a more radical kind (e.g., attributes which are relevant for explaining the behavior of
simple "repair"
living,
but not of non-living things), then no such
would seem
possible. In this sense,
an alternative to the view that
it
will eventually
Unity of Science is be necessary to bifurcate
the conceptual system of science, by the postulation of new entities or new attributes unrelated to those needed for the study of inanimate
phenomena.
The requirement
4.3.
simple form
that there be variety of evidence assumes a
in our present case. If all the past successes referred to a
would be poor evidence indeed that be reduced by theories concerning all the past successes were on the atomic
single pair of levels, then this
theories concerning each level can a lower level.
For example,
if
we should
hardly regard as justified the inference that laws consocial cerning groups can be explained by reference to the "individual the members of those groups. Thus, the first requireof psychology"
level,
ment is that one should be able to provide examples of successful microreductions between several pairs of levels, preferably between all pairs. Second, within a given level what is required is, preferably, examples of different kinds, rather than a repetition of essentially the same ex-
ample many times. In
phenomena
We
short,
one wants good evidence that be micro-reduced.
all
the
of the given level can
below a survey of the past successes in each level. of is, course, only a sketch; the successful micro-reductions and projected micro-reductions in biochemistry alone would fill a large shall present
This survey
book. But even from this sketch
it
will
be apparent, we
great the variety of these successful micro-reductions respects discussed.
13
is
believe,
in
how
both the
Paul Oppenheim and Hilary Putnam 4.4.
Moreover,
we
shall,
of course, present only evidence from authorifrom which the theory or
as reliable in the particular area
ties
regarded experiment involved
is
drawn.
The important factor because we shall devote to 4.5.
factual support it
many
is
discussed only briefly now,
of the following pages and
otherwise interrupt our presentation. The first question raised in connection with any hypothesis
what
course,
factual support
it
possesses; that
is,
would
is,
of
what confirmatory
is available. The evidence supporting a into that providing direct and subdivided conveniently hypothesis that providing indirect factual support. By the direct factual support
or disconfirmatory evidence is
15
we mean, roughly, the proportion of confirmatory to disconfirmatory instances. By the indirect factual support, opposed we mean the inductive support obtained from other well-confirmed for a hypothesis
as
hypotheses that lend credibility to the given hypothesis. While intuitively adequate quantitative measures of direct factual support have been worked out by Kemeny and Oppenheim, 16 no such measures exist for indirect factual support.
The
judgments of these magnitudes, explicata will
be worked
present paper will rely only on intuitive and will not assume that quantitative
out.
As our hypothesis is that theories of each reductive level can be micro-reduced by theories of the next lower level, a "confirming instance"
our
is
levels.
simply any successful micro-reduction between any two of direct factual support for our hypothesis is thus provided
The
by the past successes at reducing laws about the things on each level by means of laws referring to the parts on lower (usually, the next lower) levels.
In the sequel,
each pair of
we
shall survey
the past successes with respect to
levels.
As indirect factual support, we shall cite evidence supporting the hypothesis that each reductive level is, in evolution and ontogenesis (in a wide sense presently to be specified) prior to the one above it.
The
hypothesis of evolution means here that (for n
=
1
.
.
.
5) there
was a time when there were things of level n, but no things of any higher level. This hypothesis is highly speculative on levels 1 and 2; fortunately the micro-reducibility of the molecular to the atomic level
and of the atomic
level to the
elementary particle level
is
relatively well
established on other grounds. Similarly, the hypothesis of ontogenesis
14
is
that, in certain cases, for
UNITY OF SCIENCE AS A WORKING HYPOTHESIS any particular object on level n, there was a time when it did not exist, but when some of its parts on the next lower level existed; and that it 17 developed or was causally produced out of these parts. The reason for our regarding evolution and ontogenesis as providing indirect factual support for the Unity of Science hypothesis may be
formulated as follows:
Let
customary in science, assume causal determination as a guiding principle; i.e., let us assume that things that appear later in time can be accounted for in terms of things and processes at earlier us, as is
Then, if we find that there was a time when a certain whole did and that things on a lower level came together to form that
times.
not
exist,
it is very natural to suppose that the characteristics of the whole can be causally explained by reference to these earlier events and parts; and that the theory of these characteristics can be micro-reduced by a
whole,
theory involving only characteristics of the parts. For the same reason, we may cite as further indirect factual support for the hypothesis of empirical Unity of Science the various successes at synthesizing things of each level out of things
on the next lower
Synthesis strongly increases the evidence that the characteristics
level.
of the
whole
in question are causally determined
by the
characteristics,
including spatio-temporal arrangement, of its parts by showing that the object is produced, under controlled laboratory conditions, whenever parts with those characteristics are arranged in that way.
The ment
consideration just outlined seems to us to constitute an arguagainst the view that, as objects of a given level combine to form
there appear certain new phenomena (35, p. 151; 76, p. 93) in the sense of being forever irreducible to laws governing the phenomena on the level of
wholes belonging to a higher
level,
which are "emergent"
the parts. What our argument opposes is not, of course, the obviously true statement that there are many phenomena which are not reducible available theories pertaining to lower levels; our working hypothesis rejects merely the claim of absolute irreducibility, unless such a claim is by a theory which has a sufficiently high degree of
by currently
supported thus far we are not aware of any such theory. It is not suffifor cient, example, simply to advance the claim that certain phenomena considered to be specifically human, such as the use of verbal language, credibility;
in an abstract and generalized way, can never be explained on the basis of neurophysiological theories, or to make the claim that this conceptual
15
Paul Oppenheim and Hilary Putnam capacity distinguishes non-human animals.
man
and not only
in principle
in degree
from
Let us mention in passing certain pragmatic and methodological points of view which speak in favor of our working hypothesis: 4.6.
of practical value, because it provides a good synopsis of scientific activity and of the relations among the several scientific disciIt is
(1)
plines. (2) It
is,
as has often
many
lating
fruitful in the sense of stimu-
been remarked,
different kinds of scientific research.
belief in the irreducibility of various
of contrast,
By way
phenomena
has yet to yield a
single accepted scientific theory.
corresponds methodologically to what might be called the "Democritean tendency" in science; that is, the pervasive methodologi(3)
cal
It
tendency
similar
18
to try, insofar as
phenomena
is
possible, to explain apparently dis-
in terms of qualitatively identical parts
and
their
spatio-temporal relations.
5.
5.1.
Past Successes at
By comparison with what we
Each Level
shall
find
on lower
levels,
micro-reduction of level 6 to lower ones has not yet advanced very especially in regard to
reasons: First of
all,
human
societies.
This
may have
at least
the far,
two
the body of well established theoretical knowledge
rather rudimentary, so that there is not much to be micro-reduced. Second, while various precise theories concerning certain special types of phenomena on level 5 have been developed, it
on
level 6
seems
good deal of further theoretical knowledge concerning on the same level will be needed before reductive success
as if a
other areas
on a
is still
larger scale
can be expected. 19 However, in the case of certain
very primitive groups of organisms, astonishing successes have been achieved. For instance, the differentiation into social castes among certain kinds of insects has
been tentatively explained in terms of the
secretion of so-called social
hormones (3).
Many writers
20
believe that there are
some
laws
common
to all forms
of animal association, including that of humans. Of greater potential relevance to such laws are experiments dealing with "pecking order"
among domestic
fowl (29). In particular, experiments showing that the can be influenced by the amount of male hormone in individual birds suggest possible parallels farther up the evolutionary scale. social structure
16
UNITY OF SCIENCE AS A WORKING HYPOTHESIS
With respect to the problems of human social organization, as will be seen presently, two things are striking: (1) the most developed body of theory is undoubtedly in the field of economics, and this is at present entirely micro-reductionistic in character; social theory are all likewise of this
(2) the
character.
main approaches
(The
to
technical term
'micro-reduction' is not, of course, employed by writers in these fields. However, many writers have discussed "the Principle of Methodological 21 and this is nothing more than the special form our Individualism";
working hypothesis takes in application to In economics, to represent the
if
very
way
in
human
weak assumptions
social groups.)
are satisfied,
which an individual orders
it
is
his choices
possible
by means
of an individual preference function. In terms of these functions, the economist attempts to explain group phenomena, such as the market, to account for collective
welfare economics, etc.
consumer behavior, to solve the problems of theories for which a micro-reductionistic
As
accepted in economics we could cite all the standard macro-theories; e.g., the theories of the business cycle, theories of curderivation
is
rency fluctuation (Gresham's law to the effect that bad money drives out good is a familiar example), the principle of marginal utility, the law of demand, laws connecting change in interest rate with changes in inventory, plans, equipment, etc.
The
relevant point
is
while the econ-
no longer dependent on the oversimplified assumption of "economic man," the explanation of economic phenomena is still in terms of the preferences, choices, and actions available to individuals. omist
is
In the realm of sociology, one can hardly speak of any major theory But it is of interest to survey some of the major theo-
as "accepted." retical
On Marx
approaches from the standpoint of micro-reduction. the one hand, there is the economic determinism represented by and Veblen. In the case of Marx the assumptions of classical eco-
nomics are openly made: Individuals are supposed at least on the and in the long run to act in accordance with their material
average,
From this assumption, together with a theory of the business for all its undoubted originality, Marx based on the classiwhich, cycle cal laws of the market, Marx derives his major laws and predictions. Thus Marxist sociology is micro-reductionistic in the same sense as interests.
classical
economics, and shares the same basic weakness (the assump-
tion of "economic
man").
Veblen, although stressing
class interests
17
and
class divisions as
did
Paul Oppeiiheim and Hilary Putnam Marx, introduces some non-economic factors in his sociology. His account is ultimately in terms of individual psychology; his hypothesis of "conspicuous consumption"
is
a brilliant
and characteristicex-
ample.
Max Weber
produced a sociology strongly antithetical to Marx's. Yet each of his explanations of group phenomena is ultimately in terms of individual psychology; e.g., in his discussion of political parties, he argues that people enjoy working under a "charismatic" leader, etc. Indeed the psychological (and hence micro-reductionistic) character of the major sociologies (including those of Mannheim, Simmel, etc., as
well as the ones mentioned above (54, 86, 94, 103) ) is often recognized. Thus one may safely say, that while there is no one accepted sociological theory,
of these theoretical approaches represent attempted micro-
all
reductions.
52. Since Schleiden and Schwann (1838/9),
it
is
known
that
all
living things consist of cells. Consequently, explaining the laws valid
on
level 5
by those on the
cell level
means micro-reducing
all
phe-
nomena
of plants and animals to level 4. As instances of past successes in connection with level 5 we have chosen to cite, in preference to other types of example, micro-reductions
and projected micro-reductions dealing with central nervous systems as wholes and nerve cells as parts. Our selection of these examples has not been determined by anthropocentrism. First of all, substantially similar arise in the case of multicellular animals, as nearly all of them a nervous system; and, second, the question of micro-reducing possess those aspects of behavior that are controlled by the central nervous
problems
system in (85, p. 1)
man and one
the higher animals
at this level,
is
easily the
and therefore most worth
most
significative
discussing.
Very great activity is, in fact, apparent in the direction of microreducing the phenomena of the central nervous system. Much of this very recent; and most of it falls under two main headings: neurology, and the logical design of nerve nets. (Once again, the techniactivity
cal
is
term 'micro-reduction' Instead, one
is
not actually employed by workers in these
widespread and lasting discussion concerning the advantages of "molecular" versus "molar" 22 explanations, and con23 cerning "reductionism." ) fields.
finds
Theories constructed by neurologists are the product of highly dework in neuroanatomy, neurochemistry, and neuro-
tailed experimental
18
UNITY OF SCIENCE AS A WORKING HYPOTHESIS physiology, including the study of electric activity of the nervous sys24
tem,
electroencephalography. it has proved possible to advance more hypothetical explanations on the cellular level for such phe-
e.g.,
As
a result of these efforts,
or less
nomena as association, memory, motivation, emotional disturbance, and some of the phenomena connected with learning, intelligence, and perception. For example, a theory of the brain has been advanced by Hebb (32)
which accounts
for all of the
A
above-mentioned phenomena.
the Weber-Fechner law (insofar as
cal psychological law,
it
classi-
seems to
apply), has likewise been micro-reduced, as a result of the work of
Hoagland (36).
We turn now to the logical design of nerve nets: The logician Turing 25 proposed (and solved) the problem of giving a characterization of computing machines in the widest sense mechanisms for solving problems effective series of logical operations.
by
of seeing
whether
a
This naturally suggests the idea consist of the elements
"Turing machine" could
used in neurological theories of the brain; that is, whether it could conof a network of neurons. Such a nerve network could then serve as
sist
a hypothetical
Such
a
model
for the brain.
network was
basic element
first
constructed by McCulloch and Pitts. 26
The
the neuron, which, at any instant, is either firing or not firing (quiescent). On account of the "all or none" character of the activity of this basic element, the nerve net designed by McCulloch
and
is
Pitts constitutes, as
it
were, a digital computer.
The
various relations
be represented by instituting suitable connections between neurons; and in this way the hypothetical net can of prepositional logic can
be "programmed" to solve any problem that will yield to a predetermined sequence of logical or mathematical operations. McCulloch and
employ approximately 10 they are well below the upper Pitts
since the
number
elements in their net; in this respect limit set
by neurological
of neurons in the brain
order of magnitude of 10 10 ever, unrealistic:
4
.
is
investigation,
estimated to be of the
In other respects, their model was, how-
no allowance
is
made
for time delay, or for
random
error, both of which are important features of all biological processes. Nerve nets incorporating both of these features have been designed
by von Neumann.
Von Neumann's model
employs bundles of nerves
rather than single nerves to form a network; this permits the simultaneous performance of each operation as many as 20,000 times as a
19
Paul Oppenheim and Hilary Putnam check against error. This technique of constructing a computer is impractical at the level of present-day technology, voa Neumann admits,
"but quite practical for a perfectly conceivable, more advanced tech-
and
nology, for
on
for the natural relay-organs (neurons).
micro-componentry which this level"
is
(97, p. 87). Still
I.e.,
it
merely
calls
unnatural as a concept further advances in the direction of
not at
all
adapting these models to neurological data are anticipated. In terms of such nerve nets it is possible to give hypothetical micro-reductions for memory, exact thinking, distinguishing similarity or dissimilarity of stimulus patterns, abstracting of "essential" components of a stimulus pattern, recognition of shape regardless of form and of chord regardless of great importance in Gestalt psychology (5, pp. 128, 129, 152)), purposeful behavior as controlled by negative feed-
of pitch
(phenomena
back, adaptive behavior, and mental disorders. It is the task of the neurophysiologist to test these
models by
investi-
gating the existence of such nets, scanning units, reverberating networks, and pathways of feedback, and to provide physiological evidence of their
functioning. Promising studies have been made in this respect. 5.3. As past successes in connection with level 4 (i.e. as cases in
phenomena involving whole
cells
27
which
have been explained by theories
concerning the molecular level) we shall cite micro-reductions dealing with three phenomena that have a fundamental character for all of science: the decoding, duplication, and mutation of the information that is ultimately responsible for the development genetic and maintenance of order in the cell. Our objective will be to show biological
that at least one well-worked-out micro-reducing theory has been advanced for each phenomenon. 28 (The special form taken by our working
hypothesis on this level is "methodological mechanism.") had good evidence indicating that the genetic Biologists have lon information in the /cell's nucleus acting as an "inherited message" control over cell biochemistry through the production of specific protein catalysts (enzymes) that mediate particular steps (reactions) in the chemical order that is the cell's life. The problem of exerts
its
"decoding" the control information in the nucleus thus reduces to
how
the specific molecules that comprise it serve to specify the construction of specific protein catalysts. The problem of duplication (one aspect of the over-all problem of inheritance) reduces to how the
molecules of genetic material can be copied
20
like so
many
"blueprints."
UNITY OF SCIENCE AS A WORKING HYPOTHESIS
And
the problem of mutation (elementary step in the evolution of new reduces to how "new" forms of the genetic molecules can arise. inheritable messages)
In the
twenty years evidence has accumulated implicating desoxy(DNA) as the principal "message-carrying" molecule
last
ribose nucleic acid
and constituting the genetic material of the chromosomes. Crick and Watson's 29 brilliant analysis of DNA structure leads to powerful microreducing theories that explain the decoding and duplication of DNA. It is known that the giant molecules that make up the nucleic acids have, like proteins (49, 66, 67), the structure of a backbone with side groups attached. But, whereas the proteins are polypeptides, or chains of amino-acid residues (slightly over 20 kinds of
amino
acids are
known);
the nucleic acids have a phosphate-sugar backbone, and there are only 4 kinds of side groups all of which are nitrogen bases (purines and pyrimidines)
.
Crick and Watson's model contains a pair of
DNA chains
wound around a common axis in the form of two interlocking helices. The two helices are held together (forming a helical "ladder") by hydrogen bonds between pairs of the nitrogen bases, one belonging to each helix. Although 4 bases occur as side groups only 2 of 16 conceivable pairings are possible, for steric reasons. These 2 pairs of bases recur molecule and thus invite a picturesque along the length of the with the and of the Morse code. They can be dots dashes analogy
DNA
arranged in any sequence: there
is
human body
way 1000
to encode in this
DNA in
enough
a single cell of the
large textbooks.
The model
can be said to imply that the genetic "language" of the inherited constructrol message is a "language of surfaces": the information in
DNA
sequence of amino acids in the proteins which are control. The surface structure of the ultimate under synthesized the dictated helix, by sequence of base pairs, specifies like a ture
is
decoded
as a
DNA
DNA
template
30
the sequence of amino acids laid
down end
to
end
in the
fabrication of polypeptides.
Watson and
Crick's
model immediately suggests how the DNA might itself for transmission as an inherited message
produce an exact copy of
to the succeeding generation of cells.
above, consists of
two interwoven
The
helices,
ment of the other. Thus each chain
DNA
molecule, as noted
each of which
may
act as a
is
the comple-
mold on which
a
DNA
complementary chain can be synthesized. The molecule need only unwind and separate. Each begins to build a new
two chains of a
21
Paul Oppenheim and Hilary Putnam
complement onto
as loose units, floating in the cell, attach
itself,
them-
DNA
chain. When the process is com31 where before there was only one! there chains two of are pleted, pairs Mutation of the genetic information has been explained in a molecu-
selves to the bases in the single
32
(micro-reduction) theory advanced some years ago by Delbruck. Delbriick's theory was conceived long before the newer knowledge of
lar
DNA
was
available;
but
it is
a very general
by Crick and Watson's model
model
in
no way
vitiated
of the particular molecule constituting
the genetic material. Delbruck, like many others, assumed that the gene is a single large "nucleo-protem" molecule. (This term is used for macromolecules, such as viruses and the hypothetical "genes," which consist of protein and nucleic acid. Some recent theories even assume that an
chromosome
a single such molecule.) According to Delbruck' s theory, different quantum levels within the atoms of the molecule cormutation is simply a respond to different hereditary characteristics. entire
is
A
of a rare type (i.e., one with a high activation energy). observed variation of the spontaneous mutation rate with tempera-
quantum jump
The
is in good quantitative agreement with the theory. Such hypotheses and models as those of Crick and Watson, and of Delbruck, are at present far from sufficient for a complete micro-
ture
reduction of the major biological generalization, e.g., evolution and general genetic theory (including the problem of the control of develop
But they constitute an encouraging start towards this ultimate to this extent, an indirect support for our working hypothesis. and, goal 5.4. Only in the twentieth century has it been possible to micro-reduce
inent)
.
to the atomic
and
in
some
cases directly to the
subatomic
level
most of
the macro-physical aspects of matter (e.g., the high fluidity of water, the elasticity of rubber, and the hardness of diamond) as well as the
chemical phenomena of the elements, i.e. those changes of the peripheral electrons which leave the nucleus unaffected. In particular, electronic theories explain, e.g., the laws governing valence, the various types of bonds, and the "resonance" of molecules between several equivalent
electronic structures.
A
complete explanation of these phenomena and is possible only with the help of Pauli's
those of the Periodic Table
exclusion principle which states in one form that
the same atom can be alike in
all
of
no two electrons of
4 "quantum numbers." While some
molecular laws are not yet micro-reduced, there is every hope that further successes will be obtained in these respects. Thus Pauling (63, 64) writes: 22
UNITY OF SCIENCE AS A WORKING HYPOTHESIS There are
still problems to be solved, and some of them are great an example is the problem of the detailed nature of catalytic can feel sure, however, that this problem will in the course
problems activity.
We
of time
be solved
in terms of
quantum theory
as
it
now
there
exists:
seems little reason to believe that some fundamental new principle mains to be discovered in order that catalysis be explained (64)
re-
.
5.5.
Micro-reduction of level 2 to level
1
has been mentioned in the
preceding section because
many molecular phenomena are at present the atomic (skipping level) explained with reference to laws of ele33 mentary particles. Bohr's basic (and now somewhat outdated) model atom
of the
as a
kind of "solar system" of elementary particles
is
today
part of everyone's conceptual apparatus; while the mathematical development of theory in its present form is formidable indeed! Thus we shall
not attempt to give any
details of this success.
of progress in this field certainly gives reason to
But the high
rate
hope that the unsolved
the forces that hold the nucleus together, will problems, likewise be explained in terms of an elementary particle theory. especially as to
Evolution, Ontogenesis, and Synthesis
6.
6.1.
As pointed out
in section 4.5, evolution provides indirect factual
support for the
working hypothesis that unitary science is attainable. Evolution (in the present sense) is an over-all phenomenon involving all levels, from 1 through 6; the mechanisms of chance variation and "selection" operate throughout in ways characteristic for the evolution-
34 ary level involved.
Time
scales have,
various scientists showing the times
indeed, been worked out by first things of each level
when the
35 (These times are, of course, the less hypothetical the appeared. the level involved.) But even if the hypothesis of evolution higher first
should
fail
to hold in the case of certain levels,
it is
important to note
whenever it can be shown that things of it does hold a given level existed before things of the next higher level came into existence some degree of indirect support is provided to the particular
that whenever
special case of our
The
hypothesis of "evolution"
cerns levels
undergoing
by
working hypothesis that concerns those two
Gamow
1
to
3.
(24, 25,
most speculative
levels.
insofar as
it
con-
Various cosmological hypotheses are at present 35
According to one of these, strongly urged 26), the first nuclei did not form out of elementary to thirty minutes after the start of the universe's
lively discussion.
particles until five
is
23
Paul Oppenheim and Hilary Putnam expansion; molecules
may not have been
Most
able to exist until considerably
subscribe to such evolutionary present-day cosmologists views of the universe; i.e., there was a "zero point" from which the evolution of matter began, with diminishing density through expansion.
later.
still
Hoyle have advanced a conflicting idea, the "steady state" theory, according to which there is no "zero conpoint" from which the evolution of matter began; but matter is However, H. Bondi, T. Gold, and
density remains constant in spite of exseems to be hope that these rival hypotheses will be
tinuously created, so that pansion. There
submitted to
F.
its
the specific empirical tests in
near future. But, fortunately,
we do not have to depend on hypotheses that are still so highly controversial: as we have seen, the micro-reducibility of molecular and atomic today not open to serious doubt. Less speculative are theories concerning the origin of
phenomena from
is
life
(transition
Fox, 22) points out that four mechanisms have been discovered which lead to the formation of amino level
?
to level 4). Calvin
(9;
and other organic materials
in a mixture of gases duplicating the 37 These have, in the terrestrial of composition primitive atmosphere. been tested with results. fact, Many biologists positive experimentally
acids
today accept with Oparin (61) the view that the evolution of life as such was not a single chance event but a long process possibly requiring as first
many
as
two
billion years, until precellular living organisms
appeared.
According to such views, "chemical evolution" gradually leads in an appropriate environment to evolution in the familiar Darwinian sense. hardly has meaning to speak of a point at which day controversies exist concerning the "dividing appeared." line" between living and non-living things. In particular, viruses are classified by some biologists as living, because they exhibit self-duplica-
In such a process,
"life
To
it
this
and mutability; but most biologists refuse to apply the term to them, because viruses exhibit these characteristic phenomena of life only due to activities of a living cell with which they are in contact. But, tion
wherever one draws the living
line,
substance, and the
38
non-living molecules preceded primordial evolved gradually into highly organized
latter
living units, the unicellular ancestors of all living things.
The
"first
complex molecules endowed with the faculty of reproducing their own kind" must have been synthesized and with them the beginning of evolution in the Darwinian sense
a few billion years ago,
24
Goldschmidt
UNITY OF SCIENCE AS A WORKING HYPOTHESIS (27, p. 84) asserts: "all
the facts of biology, geology, paleontology, biothis statement but actually
chemistry, and radiology not only agree with
prove it." Evolution at the next two levels (from level 4 to level 5, and from 5 to 6) is not speculative at all, but forms part of the broad line of
Darwinian evolution, so well marked out by the various kinds of
The
dence referred to in the statement
evi-
line of develop-
just quoted. 39 and it is to some extent arbitrary (as again a continuous one; in the case of "living" versus "non-living") to give a "point" at which true multicellulars first appeared, or at which an animal is "social" rather
ment
is
than "solitary." But in spite of (a)
cells;
this arbitrariness,
it is
safe to say that:
what were originally competing single the "selection" by the environment was in this case determined
Multicellulars evolved from
by the superior (b) Social
40 survival value of the cooperative structure.
animals evolved from solitary ones for similar reasons; and,
indeed, there were millions of years during which there were only solitary animals on earth, and not yet their organizations into social structures.
41
6.2. To illustrate ontogenesis, we must show that particular things of a particular level have arisen out of particular things of the next lower level. For example, it is a consequence of most contemporary cosmologi-
whether of the evolutionary or of the "steady state" typethat each existent atom must have originally been formed by a union of elementary particles. (Of course an atom of an element may subsecal theories
quently undergo "transmutation.") However, such theories are extremely of atoms to form speculative. On the other hand, the chemical union molecules
Coming
is
commonplace
in nature.
to the higher levels of the reductive hierarchy,
we have
un-
Individual cells do not, as far
fortunately a hiatus at the level of cells. our observations go, ever develop out of individual molecules; on the
as
contrary, "cells
come only from
cells," as
Virchow
stated about
one
hundred years ago. However, a characteristic example of ontogenesis of the next lower level is afforded by things of one level out of things of the development of multicellular organisms through the process of mitosis and cell division. All the hereditary characteristics of the organism are specified in the "genetic information" carried in the chromosomes of each individual cell, and are transmitted to the resultant organism
through
cell division
and
mitosis.
25
Paul Oppenheim and Hilary Putnam
A
more
startling
example of ontogenesis at this level is provided by These are isolated amoebae; (3)-.
the slime molds studied by Bonner
but, at a certain stage, they "clump" together chemotactically and form a simple multicellular organism, a sausage-like "slug"! This "slug" crawls with comparative rapidity and good coordination. It even has senses of a sort, for it is attracted by light.
As
we have some
to the level of social groups,
ontogenetic data, how-
ever slight; for children, according to the well-known studies of Piaget on child behavior), acquire the capacity (70, 71) (and other authorities to cooperate with welfare,
and
only after a
one another, to be concerned with each other's treat one another as peers,
form groups in which they
number
of years (not before seven years of age, in Piaget's in a rudimentary form what we are looking
Here one has
studies). for:
to
the ontogenetic development of progressively more social behavior
(level 6)
by what begin
as relatively "egocentric"
and unsocialized
indi-
viduals (level 5).
63. Synthesis affords factual support for micro-reduction much as ontogenesis does; however, the evidence is better because synthesis usually takes place under controlled conditions. Thus it enables one to
show that one can obtain an object of the kind under variably
by
instituting the appropriate causal relations
investigation in-
the parts
among
that go to make it up. For this reason, we may say that success in synthesizing is as strong evidence as one can have for the possibility of micro-reduction, short of actually finding the micro-reducing theory. To begin on the lowest level of the reductive hierarchy, that one can
obtain an is
atom by bringing together the appropriate elementary
a basic consequence of elementary nuclear physics.
from the operation of atomic piles proceeds as one bombards protons
particles
A common example
the synthesis of deuterium. This (in, e.g., hydrogen gas) with neu-
is
trons.
The
synthesis of a molecule
by chemically uniting atoms
mentary laboratory demonstration.
One
familiar
is
is
an
ele-
the union
example an electric spark
of oxygen and hydrogen gas. Under the influence of one obtains the appearance of 2 molecules.
HO
The
next level
Thus success would qount
is
that of
life.
"On
the borderline" are the viruses.
at synthesizing a virus out of non-living macro-molecules as a first step to the synthesis of cells (which at
present
seems to be an achievement for the 26
far distant future)
.
UNITY OF SCIENCE AS A WORKING HYPOTHESIS
While
success at synthesizing a virus out of atoms is not yet in sight, out of synthesis non-living highly complex macro-molecules has been
accomplished. At the University of California Virus Laboratory (23), protein obtained from viruses has been mixed with nucleic acid to obtain active virus.
The
protein does not behave like a virusit
is
com-
However, the reconstituted virus has the same "natural" virus, and will produce the tobacco mosaic disease
pletely non-infectious.
structure as
when
applied to plants. Also new "artificial" viruses have been produced by combining the nucleic acid from one kind of virus with the protein from a different kind. Impressive results in synthesizing proteins have
been accomplished: e.g., R. B. Woodward and C. H. Schramm (107; see also Nogushi and Hayakawa, 60; and Oparin, 61 ) have synthesized "protein analogues"
giant polymers containing at least 10,000
ammo-
acid residues.
At the next cellular
level,
no one has of course synthesized a whole multicells; but here too there is an im-
organism out of individual
pressive partial success to report. Recent experiments have provided detailed descriptions of the manner in which cells organize themselves
into
whole multicellular
whole
tissues.
These studies show that even
isolated
when brought
together in random groups, could effectuate the characteristic construction 6f such tissues. 42 Similar phenomena are cells,
known
in the case of sponges and fresh-water polyps. the Lastly, "synthesis" of a new social group by bringing together previously separated individuals is extremely familiar; e.g., the organiza-
well
tion of
new
clubs, trade unions, professional associations, etc.
even the deliberate formation of whole
new
societies, e.g.,
One
has
the formation
Oneida community of Utopians, in the nineteenth century, or of the state of Israel by Zionists in the twentieth. There have been experimental studies in this field; among them, the
of the
pioneer work of Kurt Lewin and his school 7.
is
especially well
known. 43
Concluding Remarks
The
possibility that all science may one day be reduced to microphysics (in the sense in which chemistry seems today to be reduced to it), and the presence of a unifying trend toward micro-reduction run-
ning through
much
by
in the various sciences
specialists
of scientific activity, have often
and by
opinions have, in general, been expressed in a
27
been noticed both
meta-scientists.
more
But these
or less vague
manner
Paul Oppenheim and Hilary Putnam
and without very deep-going
justification. It
has been our aim,
first,
to
provide precise definitions for the crucial concepts involved, and, second, to made accusations that belief in the attainato the frequently is "a mere act of faith/'
reply
bility of unitary science
that,
ance of is
We hope to have shown
contrary, a tentative acceptance of this belief, an acceptas a working hypothesis, is justified, and that the hypothesis
on the it
on methodological grounds
credible, partly
(e.g.,
the simplicity of
the hypothesis, as opposed to the bifurcation that rival suppositions create in the conceptual system of science), and partly because there is
really a large
The
mass of direct and indirect evidence in
idea of reductive levels
may plausibly be regarded
employed
its
favor.
in our discussion suggests
as a natural order of sciences.
For
what
this pur-
to take as "fundamental disciplines" the branches corresponding to our levels. It is understandable that many of the wellknown orderings of things 4 * have a rough similarity to our reductive it suffices
pose,
levels,
and that corresponding orderings of sciences are more or
less
"fundamental disciplines." Again, several sucbe grouped together (e.g. physics today convention-
similar to our order of 6 cessive levels
may
ally deals at least
least levels
with
levels
1,
2,
and
3;
just as biology deals
with at
5). Thus we often encounter a division into simply and social sciences. But these other efforts to solve a
4 and
physics, biology,
45 have apparently been made problem which goes back to ancient times on more or less intuitive grounds; it does not seem to have been realized
that these orderings are "natural" in a deeper sense, of being based on the relation of potential micro-reducer obtaining between the branches
of science.
should be emphasized that these six "fundamental disciplines" are, largely, fictitious ones (e.g., there is no actual branch whose universe of It
molecules and combinations thereof)
If one wishes one may utilize a concept in semantical information theory which has been defined by one of us (3). This is the
discourse
is
strictly
.
a less idealized approach,
semantical functor: 'the
C
amount
of information the statement S con-
C) ) Then one can charS if we are any theory (or any branch, willing to identify a branch with a conjunction of theories) by a sextuple: namely, inf(S, tains
about the
class
(or, in symbols: inf (S,
.
acterize
level 1), inf(S, level 2)
...
inf(S, level 6). This sextuple can
be
re-
garded as the "locus" of the branch S in a six-dimensional space. The axes are the loci of the imaginary "fundamental disciplines" just referred 28
UNITY OF SCIENCE AS A WORKING HYPOTHESIS any
to;
real
branch
tion not quite
present-day biology) will probably have a posiaxis, but nearer to one than to the others.
(e.g.,
on any
Whereas the
orderings to which we referred above generally begin with the historically given branches, the procedure just described reverses this tendency. First a continuous order is defined in which any imaginable branch can be located; then one investigates the relations
the actually existing branches. These positions may be expected to change with time; e.g. r as micro-reduction proceeds, "biology" will
among
occupy a position
The
branches.
continuous order
than "Linnean"; tuitive or
closer to the "level 1" axis,
it
derives
customary
its
may be
naturalness, not
classifications,
in the light of the hypothesis that
and so
will all the other
described as "Darwinian" rather
but from
from agreement with
its
in-
high systematic import
Unity of Science
is
attainable.
NOTES 1
Science, in the wider sense, may be understood as including the formal disciplines, mathematics, and logic, as well as the empirical ones. In this paper, we shall be concerned with science only in the sense of empirical disciplines, including the socio-
humamstic ones.
*By a "theory" (in the widest sense) we mean any hypothesis, generalization, or law (whether deterministic or statistical), or any conjunction of these; likewise by "phenomena" (in the widest sense) we shall mean either particular occurrences or theoretically formulated general patterns. Throughout this paper, "explanation" ("explainable" etc.) is used as defined in Hempel and Oppenheim (35). As to "explanatory power," there is a definite connection with "systematic power." See Kemeny and Oppenheim (46, 47). *
we
are willing to adopt a "Taxonomic System" for classifying all the things by science, then the various classes and subclasses in such a system could represent the possible "universes of discourse." In this case, the UBI of any branch would be associated with the extension of a taxonomic term in the sense of OppenIf
dealt with
heim (62). *
we shall as a rule omit the clause 'at time t'. Oppenheim (62, section 3) has a method for measuring such a reduction. Of course, in some cases, such "skipping" does occur in the process of Henceforth,
B
6
micro-
reduction, as shall be illustrated later on. 7 As to degree of credibility, see Kemeny and
Oppenheim (45, especially p. 307). "acceptance, as an overall fundamental working hypothesis, of the reduction theory, with physical science as most general, to which all others are reducible; with biological science less general; and with social science least general of all," has been 8
The
emphasized by Hockett (37, especially
"As to
natural, see
Hempel
p. 571).
(33, p. 52),
and Hempel and Oppenheim (34, pp.
107,110). 10
Many well known hierarchical orders of the same kind (including some comIt suffices to give the following patible with ours) can be found in modern writings. in the modern quotation from an article by L. von Bertalanffy (95, p. 164) : "Reality, appears as a tremendous hierarchical order of organized entities, leading, conception, in a superposition of many levels, from physical and chemical to biological and of Science is granted, not by an Utopian reduction of all sociological systems. Unity
29
Paul Oppenheim and Hilary Putnam sciences to physics and chemistry, but by the structural uniformities of the different the last paragraph of section 2.2 levels of reality," As to the last sentence, we refer to the problem noted. Von Bertalanffy has done pioneer work developing a General of some differences of emphasis, is an interesting conwhich,
m
m
m
spite System Theory tribution to our problem. 11 The following example is
m
the one given Hempel and 93, 94). (76, pp. Oppenheim 13 See Rescher and Oppenheim (76, p. 100), and Rescher (75). Of course, nothing as "wholes" is the characterization of certain is intrinsically a "true" whole; ^things of the particular Tt relation selected. For always a function of the point of view, i.e. define Tt' so that the instance, if a taxonomic system is given, it is very natural to "wholes" will correspond to the things of the system. Similarly for aggregate see Rescher and Oppenheim (76, p. 90, n. 1 ) 13 See Kemeny and Oppenheim (47, n. 6). A suggestive characterization of simof the "entropy" of a theory has been put forward by Rothstem (78). plicity in terms the direction moves Using Rothstem's terms, we may say that any micro-reduction a slight modification of
(35, p. 148). See also Rescher and
Oppenheim
7
.
m
of lower entropy (greater organization) 14 The statement that B 2 is micro-reducible to Bi means (according to the analysis we adopt here) that some true theory belonging to Bi i.e., some true theory with and universe of discourse, whether accepted or not, and the .
appropriate vocabulary
whether it is ever even written down or not micro-reduces every true theory of B 2 This seems to be what people have in mind when they assert that a given B 2 may not be reduced to a given JBi at a certain time, but may nonetheless be reducible ( micro.
reducible) to
it.
like (45, p. 307); also for "related concepts," Carnap's "degree of confirmation" see Carnap (13). 16 As to degree of credibility see Kemeny and Oppenheim (45, especially p. 307). 17 in such a case: any Using a term introduced by Kurt Lewin (48), we can also say with these parts. particular object on level n is genidentfcal
"See Kemeny and Oppenheim
"Though we cannot accept Sir Arthur Eddington's idealistic implications, we quote from his Philosophy of Physical Science (17, p. 125) "I conclude therefore that our engrained form of thought is such that we shall not rest satisfied until we are able to represent all physical phenomena as an interplay of a vast number of structural units intrinsically alike. All the diversity of phenomena will be then seen to correspond to different forms of relatedness of these units or, as we should usually :
say, different configurations." 18 Scriven has set forth
M. "A
essay,
some suggestive considerations on this subject in his Possible Distinction between Traditional Scientific Disciplines and the Study
Human
Behavior" (79 ). See e.g. Kartman (43), with many quotations, references, and notes, some of them micro-reduction istic. 21 This term has been introduced by F. A. Hayek (31). See also Watkins (98, owe valuable information in ecoespecially pp. 729-732) and Watkins (99). of
20
We
nomics to W. J. Baumol, Princeton University. 22 This distinction, first made by C. D. Broad (6, p. 616), adopted by E. C. Tolman (90), C. L. Hull (39), and others, is still in use, in spite of objections
against this terminology. 23
This is the form our working hypothesis takes on this level in this field. See in connection the often quoted paper by K. MacCorquodale and P. E. Meehl, "On a Distinction between Hypothetical Constructs and Intervening Variables" (52), and some of the discussions in the "Symposium on the Probability Approach in Psycholthis
ogy" (73), C. C. Pratt. 24
As
as well as references therein, to
to neuroanatomy, see e.g.
W.
H.
Feigl,
W.
Koehler, D. Krech, and
Penfield (69); as to neurochemisrry, see e.g.
30
UIN11 I
U*
^JJUNUfc.
Ab
A
WUKJKJJNU
Rosenblueth
(77,- especially Chapter 26 for acetylcholine and the summaries on pp. 134-135, 274-275); as to The Electric Activity of the Nervous System, see the book of this title by Brazier (5). See this last book also for neuroanatomy, neurophysiology, neurochemistry. See Brazier (5, pp. 128, 129, 152) for micro-reduction of Gesralt mentioned below. phenomena ^Turing (91, 92). For an excellent popular presentation, see Kemeny (44). 28 See the often quoted paper by McCulloch and Pitts (53), and later publications
by these authors,
as well as other papers in this field in tie same Bulletin of Mathee.g. by N. Rashevsky. See also Platt (72) for a "complementary
matical Biophysics,
approach which might be called amplifier theory." For more up to date details, see Shannon and McCarthy's (82) Automata Studies, including von Neumann's model, discussed by him (82, pp. 43-98). 27 Throughout this paper, "cell" is used in a wide sense, i.e., "Unicellular" organism or single cell in a multicellular organism. 28 For more details and much of the following, see Simpson, Pittendrigh and Tiffany (87), Goldschmidt (28), and Horowitz (38). For valuable suggestions we are indebted to C. S. Pittendrigh who also coined the terms "message carrying
molecule" and "languages of surface" used in our text. 29 See in reference to the following discussion Watson and Crick (100), also (101), and (102), and Crick (15). 80 Pauling and Delbriick ( 68 ) A micro-reducing theory has been proposed for these activities using the "lock-key" model. See Pauling, Campbell and Pressman (65), .
andBumet 31
(8).
Neumann (96) and Jacobson (40). See Timoteeff-Ressovsky (89, especially pp. 108-138). It should, however, be noted that since Delbruck's theory was put forward, his model has proved inadequate for explaining genetic facts concerning mutation. And it is reproduced here only as For a mechanical model, see von
83
a historical case of a micro-reducing theory that, in 83
level
We is
its
day, served valuable functions.
think that, throughout this paper, our usage of thing language also on this
admissible in spite of well-known difficulties and refer e.g. to Born (4), and
Johnson (42). 84 See e.g. Broad (6, especially p. 93), as to "a general tendency of one order to combine with each other under suitable conditions to form complexes of the next order." See also Blum (1, and 2, especially p. 608); Needham (59, especially pp. 184-185); and Dodd (16). 88 This wording takes care of "regression," a reversal of trend, illustrated e.g. by parasitism. 80
For a
clear survey of cosmological hypotheses see the 12 articles published in the
American cited under Gamow (26) Perhaps the most sensational method is an experiment suggested by H. C. Urey and made by S. L. Miller (56, 57), according to which ammo acids are formed when an electric discharge passes through a mixture of methane, hydrogen, ammonia, and issue of Scientific
.
87
water. *8
attributes, almost any one of which we can reproduce in only when they all appear to a greater or lesser degree in the same system simultaneously that we call it living" (Calvin, 9, p. 252). Thus the an underdividing line between "living" and "non-living" is obtained by transforming 65lying "multidimensional concept of order" (see Hempel and Oppenheim, 34, pp. 77), in a more or less arbitrary way, into a dichotomy. See also Stanley (88, especially
"Actually
life
has
a nonliving system. It
many
is
pp. 15 and 16 of the reprint of this article). 80 See note 38 above. 40
For details, see Lindsey (50, especially pp. 136-139, 152-153, 342-344). See Burkholder (7). 41 See e.g. the publications (104, 105, 106) by Wheeler. See also Haskins (30,
also
31
Paul Oppenheim and Hilary Putnam especially pp. 30-36). Since we are considering evolution on level 6 as a whole, we can refrain from discussing the great difference between, on the one hand, chance mutations, natural selection, and "instinctive" choices and, on the other hand, the
m
time man of consciously and willfully directing social evolution stretches of specifically small orders of magnitude (see Zilsel, 108). 42 See Moscana (58) and his references, especially to work by the same author and
specific faculty of
by Paul Weiss. 43 See Lippitt (51). For recent experiments, and 9), and Sherif (83).
44
see
Shenf and Sherif
(
84, Chapters 6
See note 10 above,
45
For details, see Flint (21), and Vannerus (93). Auguste Comte in his GOUTS de Philosophic Positive, Premiere et Deuxieme Lemons (14), has given a hierarchical order of 6 "fundamental disciplines" which, independently from its philosophical background, is amazingly modem in many respects, as several contemporary authors recognize.
REFERENCES 1.
Blum, H. F. Time's Arrow and Evolution. Princeton: Princeton Univ.
Press,
1951. 2.
Blum, H. F. "Perspectives
3.
(1955). Bonner,
4.
5.
6.
7.
8.
in
Evolution,"
American
Scientist,
43:595-610
T. Morphogenesis. Princeton: Princeton Univ. Press, 1952. Interpretation of Quantum Mechanics," British Journal for the Philosophy of Science, 3:95-106 (1953). Brazier, M. A. B. The Electric Activity of the Nervous System. London: Sir Isaac Pitman & Sons, Ltd., 1951. Broad, C. D. The Mind and its Place in Nature. New York: Harcourt, Brace, 1925. Burkholder, P. R. "Cooperation and Conflict among Primitive Organisms," American Scientist, 40-601-631 (1952). Burnet, M. "How Antibodies are Made," Scientific American, 191:74-78 J.
Bom, M. "The
(November 1954). M. "Chemical Evolution and the Origin of Life," American Scientist, 44-248-263 (1956). 10. Carnap, R. Der logische Aufbrau der Welt. Berlm-Schlachtensee: Im WeltkreisVerlag, 1928. Summary in N. Goodman, The Structure of Appearances, pp 114-146. Cambridge: Harvard Univ. Press, 1951. 11 Carnap, R. "Testability and Meaning," Philosophy of Science, 3.419-471 (1936), and 4:2-40 (1937). Reprinted by Graduate Philosophy Club, Yale University, New Haven, 1950. 12. Carnap, R. Logical Foundations of the Unity of Science, International Encycloof Unified Science. Vol. I, pp. 42-62. Chicago: Univ. of Chicago Press, ?edia 938. 13. Carnap, R. Logical Foundations of Probability. Chicago: Univ. of Chicago 9. Calvin,
Press, 1950.
14.
Comte, Auguste. Cours de Philosophic
Positive. 6 Vols.
Pans
Bachelier,
1830-
42.
H. C. "The Structure of Hereditary Material," Scientific American, 191: 54-61 (October 19 54). 16. Dodd, S. C. "A Mass-Time Triangle," Philosophy of Science, 11-233-244 15. Crick, F.
(1944). 17. Eddington, Sir Arthur. The Philosophy of Physical Science. Cambridge: Cambridge University Press, 1949. D. D. Runes (ed.), Twentieth Century 18. Feigl, H. "Logical Empiricism,"
m
32
UNITY OF SCIENCE AS A WORKING HYPOTHESIS
New York: Philosophical Library, 1943. Reprinted H. Feigl and W. Sellars (eds.), Readings in Philosophical Analysis. New York: Appleton-Centuiy-Crofts, 1949. Feigl, H. "Unity of Science and Unitary Science/' m H. Feigl and M. Brodbeck (eds.), Readings in the Philosophy of Science, 382-384. New York:
Philosophy, pp. 371-416. in
19.
pp.
Appleton-Century-Crofts, 1953. H. "Functionalism, Psychological Theory and the Uniting Sciences- Some Discussion Remarks," Psychological Review, 62-232-235 (1955). 21. Flint, R. Philosophy as Scientia Scientiarum and the History of the Sciences. New York: Scnbner, 1904 20. Feigl,
W. "The Evolution of Protein Molecules and Thermal Synthesis of Biochemical Substances," American Scientist, 44:347-359 (1956). Fraenkel-Conrat, H. "Rebuilding a Virus," Scientific American, 194:42-47 (June 19 56). Gamow, G. "The Origin and Evolution of the Universe," American Scientist, 39:393-406 (1951). Gamow, G. The Creation of the Universe. New York: Viking Press, 1952. Gamow, G. "The Evolutionary Universe," Scientific American, 195:136-154 (September 19 56). Goldschmidt, R. B. "Evolution, as Viewed by One Geneticist," American Scientist, 40:84-98 (1952). Goldschmidt, R. B. Theoretical Genetics. Berkeley and Los Angeles: Univ. of California Press, 1955. Guhl, A. M. "The Social Order of Chickens/' Scientific American, 194.42-46
22. Fox, S. 23.
24.
25.
26. 27.
28.
29.
(February 1956). 30. Haskins, C. P. Of Societies 31. Hayek, F. A. Individualism
and Man. New York: Norton & Co., 1951. and the Economic Order. Chicago: Univ. of Chi-
cago Press, 1948. 33.
Hebb, D. O. The Organization of Behavior. New York: Wiley, 1949. Hempel, C. G. Fundamentals of Concept Formation in the Empirical Sciences, Vol II, No. 7 of International Encyclopedia of Unified Science. Chicago: Univ.
34.
of Chicago Press, 1952. Hempel, C. G., and P. Oppenheim. Der Typusbegriff Logik; wissenschaftstheoretische Untersuchungen zur
32.
35.
im Lichre der neuen Konsritutionsforschung
und Psychologic. Leiden: A. W. Sythoff, 1936. Hempel, C. G., and P. Oppenheim. "Studies in the Logic of Explanation,"
Philosophy of Science, 15:135-175 (1948). Hoagland, H. "The Weber-Fechner Law and the All-or-None Theory," Journal of General Psychology, 3:351-373 (1930). 37. Hockett, C. H. "Biophysics, Linguistics, and the Unity of Science," American Scientist, 36:558-572 (1948). 38. Horowitz, N. H. "The Gene," Scientific American, 195.78-90 (October 1956). 39 Hull, C. L. Principles of Animal Behavior. New York: D. Appleton-Century, Inc., 1943. 40. Jacobson, H. "Information, Reproduction, and* the Origin of Life," American 36
Scientist,
43:119-127 (1955).
41. feffress, L. A. Cerebral
Mechanisms
in Behavior; the
Hixon Symposium
New
York: Wiley, 1951. 42. Johnson, M. "The Meaning of Time and Space in Philosophies of Science," American Scientist, 39:412-431 (1951). 43. Kartman, L. "Metaphorical Appeals in Biological Thought," American Scientist, 44:296-301 (1956). 44. Kemeny, J. G. "Man Viewed as a Machine," Scientific American, 192-58-66 (April 19 55).
33
Paul Oppenheim and Hilary Putnam P. Oppenheim. "Degree of Factual Support/' Philosophy J. G., and of Science, 19:307-324 (1952). 46. Kemeny, }. G., and P. Oppenheim. "Systematic Power/' Philosophy of Science,
45.
Kemeny,
22:27-33 (1955). Kemeny, J. G., and P. Oppenheim. "On Reduction/' Philosophical Studies, 7:6-19 (1956). 48. Lewm, Kurt. Der Begriff der Genese. Berlin: Verlag von Julius Springer, 1922. 49. Linderstrom-Lang, K. U. "How is a Protein Made?" American Scientist, 41: 100-106 (1953). 50. Lindsey, A. W. Organic Evolution. St. Louis: C. V. Mosbey Company, 1952. 51. Lippitt, R. "Field Theory and Experiment in Social Psychology/' American Journal of Sociology, 45:26-79 (1939). 52. MacCorquodale, K., and P. E. Meehl. "On a Distinction Between Hypothetical Constructs and Intervening Variables," Psychological Review, 55:95-105 (1948). 53. McCulloch, W. S., and W. Pitts. "A Logical Calculus of the Ideas Immanent in Nervous Activity/' Bulletin of Mathematical Biophysics, 5:115-133 (1943). 54. Mannheim, K. Ideology and l/topia. New York: Harcourt, Brace, 1936. 55. Mill, John Stuart. System of Logic. New York: Harper, 1848 (1st ed. London,
47.
1843). 56. Miller, S. L.
"A
Production of
Amino Acids Under
Possible Primitive Earth
Conditions," Science, 117:528-529 (1953). 57. Miller, S. L. "Production of Some Organic Compounds Under Possible Primitive Earth Conditions," Journal of the American Chemical Society, 77.2351-
2361 (1955). Moscana, A. "Development of Heterotypic Combinations of Dissociated Embryonic Chick Cells," Proceedings of the Society for Experimental Biology and Medicine, 92.410-416 (1956). 59. Needham, }. Time. New York: Macmillan, 1943. 60. Nogushi, J., and T. Hayakawa. Letter to the Editor, Journal of the American Chemical Society, 76:2846-2848 (1954). 61. Oparin, A. I. The Origin of Life. New York: Macmillan, 1938 (Dover Publica58.
tions, Inc. edition,
62.
1953).
Oppenheim, P. "Dimensions of Knowledge/' Revue Internationale de Philoso-
phic, Fascicule 40, Section 7 (1957). 63. Pauling, L. "Chemical Achievement
and Hope for the Future," American
36:51-58 (1948). 64. Pauling, L. "Quantum Theory and Chemistry," Science, 113:92-94 (1951). 65. Pauling, L., D. H. Campbell, and D. Pressmann. "The Nature of Forces between Antigen and Antibody and of the Precipitation Reaction," Physical Review, 63:203-219 (1943). 66. Pauling, L., and R. B. Corey. "Two Hydrogen-Bonded Spiral Configurations of the Polypeptide Chain," Journal of the American Chemical Society, 72:5349 Scientist,
(1950). 67. Pauling, L., and R. B. Corey. "Atomic Coordination and Structure Factors for Two Helical Configurations," Proceedings of the National Academy of Science
(U.S.), 37:235 (1951). 68. Pauling, L., and M. Delbriick. "The Nature of Intermolecular Forces Operative in Biological Processes," Science, 92.585-586 (1940). 69. Penfield, "The Cerebral Cortex and the Mind of Man," in P. Laslett (ed.), The Physical Basis of Mind, pp. 56-64. Oxford: Blackwell, 1950. 70. Piaget, J. The Moral Judgment of the Child. London: Kegan Paul, Trench,
W.
Trubner and Company, Ltd., 1932. The Language and Thought of the Child. London: Kegan Paul, }. Trench, Trubner and Company; New York: Harcourt, Brace, 1926.
71. Piaget,
34
UNITY OF SCIENCE AS A WORKING HYPOTHESIS R. "Amplification Aspects of Biological Response and Mental Activity," J. American Scientist, 44 180-197 (1956).
72. Platt,
Approach in Psychology (Symposium), Psychological Review, 62: 193-242 (1955). 74. Rashevsky, N. Papers m general of Rashevsky, published in the Bulletin of Mathematical Biophysics, 5 (1943). 75. Rescher, N. "Axioms of the Part Relation," Philosophical Studies, 68-11
73
Probability
(1955). 76. Rescher, N. and P. Oppenheim. ''Logical Analysis of Gestalt Concepts," British Journal for the Philosophy of Science, 6:89-106 (1955). 1
77. Rosenblueth, A.
The
Transmission of Nerve Impulses at NeuroefTector Junctions New York: Technological Press of MIT and Wiley,
and Peripheral Synapses. 1950.
78. Rothstein, }. Communication, Organization, rado: Falcon's Wing Press, 1957.
and Science. Indian
Hills,
Colo-
M
"A Possible Distinction between Traditional Scientific Disciplines and the Study of Human Behavior," in H. Feigl and M. Scriven (eds ), Vol. I, Minnesota Studies in the Philosophy of Science, pp. 330-339. Minneapolis: Univ. of Minnesota Press, 1956. 80. Sellars, W. "A Semantical Solution of the Mind-Body Problem," Methodos, 545-84 (1953). 81. Sellars, W. "Empiricism and the Philosophy of Mind," in H. Feigl and M. Scriven (eds.), Minnesota Studies in the Philosophy of Science, Vol. I, pp. 253-329. Minneapolis: Univ. of Minnesota Press, 1956. 82. Shannon, C. E., and McCarthy (eds.), Automata Studies. Princeton: Prince-
79. Scnven,
J.
ton Univ. Press, 1956. 83. Sherif,
84.
M.
"Experiments in Group Conflict,"
(November 1956). Shenf, M., and C.
W.
Sherif.
An
Scientific
American, 195:54-58
Outline of Social Psychology.
New
York:
Harper, 1956. 85. Sherrington, Charles. The Integrative Action of the Nervous System. New Haven- Yale Univ. Press, 1948. 86. Simmel, G. Sociologie. Leipzig: Juncker und Humblot, 1908. G. G., C. S. Pittendrigh, and C. H. Tiffany. Life. New York: Har87.
Simpson,
court, Brace, 1957.
W.
M. "The Structure of Viruses," reprinted from publication No. 14 88. Stanley, of the American Association for the Advancement of Science, The Cell and Protoplasm, pp. 120-135 (reprint consulted) (1940). N. W. Experimentelle Mutationsforschung in der Vererbungslehre. Dresden und Leipzig: Verlag von Theodor Steinkopff, 1937. 90. Tolman, E. C. Purposive Behavior in Animals and Men. New York: The Century Company, 1932. 91. Turing, A. M. "On Computable Numbers, With an Application to the Ser. Entscheidungsproblem," Proceedings of the London Mathematical Society, 2,42:230-265 (1936). 92. Turing, A. M. "A Correction," Proceedings of the London Mathematcial So-
89. Timoteeff-Ressov'sky,
ciety, Ser. 2, 43:544-546 (1937). Vannerus, A. VerensJcapssystematik. Stockholm: Aktiebolaget Ljus, 1907. 94. Veblen, T. The Theory of the Leisure Class. London: Macmillan, 1899. 95. Von Bertalanffy, L. "An Outline of General System Theory," The British Journal for the Philosophy of Science, 1:134-165 (1950). 96. Von Neumann, John. "The General and Logical Theory of Automata," in L. A.
93
Teffress
20-41.
(ed.), Cerebral
New
Mechanisms
in Behavior;
The Hixon Symposium,
York: John Wiley and Sons, Inc., 1951.
35
pp.
Paul Oppenhenu and Hilary Putnam 97.
Von Neumann,
98.
W. N. "Ideal Types and Historical Explanation/' in H. Feigl and J. Brodbeck (eds.), Readings in the Philosophy of Science, pp. 723-743. New York Appleton-Century-Crofts, 1953. Watkms, }. W. N. "A Reply/' Philosophy of Science, 22:58-62 (1955). Watson, J. D., and F. H. C. Crick. "The Structure of DNA," Cold Spring Harbor Symposium on Quantitative Biology, 18:123-131 (1953). Watson, J. D., and F. H. C. Crick. "Molecular Structure of Nucleic Acids A Structure for Desoxynbosenucleic Acid," Nature, 171:737-738 (1953). Watson, J. D., and F. H. C. Crick. "Genetical Implications of the Structure of Desoxynbosenucleic Acid," Nature, 171:964-967 (1953). Weber, M. The Theory of Social and Economic Organization, translated by A. M. Henderson and T. Persons. New York: Oxford Univ. Press, 1947. Wheeler, W. M. Social Life Among the Insects. New York: Harcourt, Brace,
John. "Probabilistic Logics and the Synthesis of Reliable Organisms from Unreliable Components," in C. E. Shannon and J. McCarthy (eds. ), Automata Studies. Princeton- Princeton Univ. Press, 1956.
Watkms,
M
99.
100 101 102. 103.
104.
1923. 105. Wheeler,
W. M.
Emergent Evolution and the Development of
Societies.
New
& Co., 1928. Wheeler, W. M. "Animal Societies," Scientific Monthly, 39:289-301 (1934). Woodward, R. B., and C. H. Schramm. Letter to the Editor, Journal of the
York: Norton 106. 107.
American Chemical Society, 69:1551 (1947). and Biological Evolution," Philosophy of Science, 7-121-128
108. Zilsel, E. "History
(1940).
CARL
The
G.
HEMPEL
Dilemma A STUDY IN THE LOGIC OF THEORY CONSTRUCTION
1.
Theoretician's
Deductive and Inductive Systematization
Scientific research in its various branches seeks
not merely to record
particular occurrences in the world of our experience: it tries to discover regularities in the flux of events and thus to establish general laws which 1
may be used for prediction, postdiction, and explanation. The principles of Newtonian mechanics, for example, make
it
pos-
sible, given the present positions and momenta of the celestial objects that make up the solar system, to predict their positions and momenta
for a specified future
time or to postdict them for a specified time permit an explanation of the
in the past; similarly, those principles
present positions and
momenta by
reference to those at
some
earlier
time. In addition to thus accounting for particular facts such as those just mentioned, the principles of Newtonian mechanics also explain i.e., empirical uniformities such as Kepler's laws of planetary motion; for the latter can be deduced from the former. 2
certain "general facts,"
and postdiction all have the same that the fact under consideration can be
Scientific explanation, prediction, logical character: they
inferred
show
from certain other
facts
by means of specified general laws. In may be schematized as a deduc-
the simplest case, this type of argument tive inference of the following form: (i.i)
d, c 2 I* L2
.
.
.
.
.
.
ck Lr
AUTHOR'S NOTE: I am indebted to the Council of the Humanities at Princeton Uniaward of a Senior Fellowship for the academic year 1956-57, which, by reducing my teaching load, gave me additional time for research. The present study is part of the work done during my tenure as a Senior Fellow.
versity for the
37
Carl G. Here, Ci,
C2 Ck
Hempel
are statements of particular occurrences (e.g., of the
,
position and momenta of certain celestial bodies at a specified time), and LI, L2 Lr are general laws (e.g., those of Newtonian mechan.
.
.
E
is a sentence stating whatever is being explained, preforce only or dicted, postdicted. And the argument has its intended 3 from the if its conclusion, E, follows deductively premises. While explanation, prediction, and postdiction are alike in their logi-
ics); finally,
cal structure,
they
differ in certain
other respects. For example, an argu-
only if E refers to than that at which the argument is offered; in the case of a postdiction, the event must occur before the presentation of the argument. These differences, however, require no fuller study here, for the purpose of the preceding discussion was simply to point out
ment
of the
form
(1.1)
an occurrence at a time
will qualify as a prediction
later
the role of general laws in scientific explanation, prediction, and postdiction.
For these three types of
scientific procedure,
we
will use the
common
term '(deductive) systernatization'. More precisely, that term will be used to refer, first, to any argument of the form (1.1) that meets the requirements indicated above, no matter whether
it
serves as
an explana-
tion, a prediction, a postdiction, or in still some other capacity; second, to the procedure of establishing arguments of the kind just character-
ized.
So
far,
we have
considered only those cases of explanation, prediction,
and related procedures which can be construed as deductive arguments. There are many instances of scientific explanation and prediction, how-
which do not
For example, the measles, this might be explained by pointing out that he caught the disease from his sister, who is just recovering from it. The particular antecedent facts here invoked are ever,
fall
into a strictly deductive pattern.
when Johnny comes down with
that of Johnny's exposure and, let us assume, the further fact that
Johnny had not had the measles previously. But to connect these with the event to be explained, we cannot adduce a general law to the effect that under the specified circumstances, the measles
is
invariably trans-
mitted to the exposed person: what can be asserted is only a high probability (in the sense of statistical frequency) of transmission. The same type of argument can be used also for predicting or postdicting the occurrence of a case of the measles. Similarly, in a psychoanalytic explanation of the neurotic behavior of
38
THE THEORETICIAN'S DILEMMA an adult by reference to certain childhood experiences, the generalizations which might be invoked to connect the antecedent events with those to be explained can be construed at best as establishing more or high probabilities for the connections at hand, but surely not as
less
expressions of unexceptional uniformities.
Explanations, predictions, and postdictions of the kind here illustrated from those previously discussed in two important respects: The
differ
laws invoked are of a different form, and the statement to be established does not follow deductively from the explanatory statements adduced.
We will now consider
these differences
somewhat more
closely.
The
laws referred to in connection with the schema (1.1), such as the laws of Newtonian mechanics, are what we will call statements of strictly universal
this all
kind
cases
is
form, or
an assertion
which meet
strictly universal statements.
which may be true or
crows are black'
A
statement of
to the effect that
certain specified conditions will unexceptionally
have such and such further 'All
false
is
characteristics.
For example, the statement and so is
a sentence of strictly universal form;
first law of motion, that any material body which is not acted an external force upon by persists in its state of rest or of rectilinear motion at constant speed.
Newton's
The
laws invoked in the second type of explanatory and related arguments, on the other hand, are, as we will say, of statistical form; they are statistical probability statements. statement of this kind is an
A
assertion
which may be true or falseto the
effect that for cases
which
meet conditions of a
specified kind, the probability of having such and such further characteristics is so-and-so much. 4
A
To put the distinction in a nutshell: strictly universal statement of the simplest kind has the form 'All cases of P are cases of Q'; a statistical probability statement of the simplest kind has the form 'The probability for a case of
P
to
be a case of
Q
is r.'
While the former
implies
an assertion about any particular instance of P namely, that it is also an instance of the latter implies no similar assertion concerning any of P or even concerning any finite set of such ininstance particular
Q
stances. 5 This circumstance gives rise to the second distinctive characteristic
mentioned above: the statement
E
describing the occurrence
under explanation or prediction or postdiction (for example, Johnny's catching the measles) is not logically deducible from the explanatory statements adduced (for example,
(Ci) Johnny was exposed to the
39
Carl G.
Hempel
Johnny had not previously had the measles; (L) For not previously had the measles and are exposed to persons it, the probability is .92 that they will contract the disease); rather, on
(C2
measles;
)
who have
the assumption that the explanatory statements adduced are true, it is very likely, though not certain, that E is true as well. This kind of
argument, therefore, is inductive rather than strictly deductive in character: it calls for the acceptance of E on the basis of other statements for it. An partial, if strongly supporting, grounds it is used for whether no matter of this kind explanation, argument prediction, or postdiction, or for yet another purpose will be called an inductive sysrematizarion. In particular, we will assume of an inductive
which constitute only
systematization that the conclusion is not logically implied by the 6 premises. Again, the procedure of establishing an argument of the kind just described will also be called inductive systematization.
By way
of further illustration, let us note here two explanatory argujust characterized. They are
ments which are of the inductive kind
adduced by von Mises in a statement to the
effect that the everyday notion of causal explanation will eventually adjust itself to changes in the logical form of scientific theories (especially to the use of statistical
"We
think," von probability statements as explanatory principles): Mises says, that "people will gradually come to be satisfied by causal
statements of this kind:
It is
because the die was loaded that the
'six'
shows more frequently (but we do not know what the next number will be); or: Because the vacuum was heightened and the voltage increased, the radiation
number
precise
became more intense (but we do not know the
of scintillations that will occur in the next minute)
both of these statements can be construed
Clearly,
tions of certain physical
."
7
as inductive explana-
phenomena.
All the cases of scientific systematization we have considered share this characteristic: they make use of general laws or general principles either of strictly universal or of statistical form. These general laws have the function of establishing systematic connections among empirical facts in such a way that with their help some empirical occurrences may
be inferred, by way of explanation, prediction, or postdiction, from other such occurrences. When, in an explanation, we say that the event described
by
Ck
E
occurred "because" of the circumstances detailed in Ci, C 2 if it can be construed as referring
that phrase has significance to general laws which render Ci, 2 .
.
.
,
C
40
.
.
.
Ck
relevant to
E
in the sense
THE THEORETICIAN that, granted the truth of the former,
S
DILEMMA make
they
the truth of the latter
either certain (as in a deductive systematization) or inductively probable (as in
an inductive systematization).
tablishment of general laws
is
It is for this
reason that the
es-
of crucial importance in the empirical
sciences. 2.
Observables and Theoretical Entities
is ultimately aimed at establishing explanaand order predictive tory among the bewilderingly complex "data" of
Scientific systematization
our experience, the phenomena that can be directly "observed" by us. It is a remarkable fact, therefore, that the greatest advances in scientific systematization have not been accomplished by means of laws referring explicitly to observables, i.e., to things and events which are ascertain-
able by direct observation, but rather by means of laws that speak of various hypothetical, or theoretical, entities, i.e., presumptive objects, events, and attributes which cannot be perceived or otherwise directly
observed by
For a
us.
fuller discussion of this point,
familiar distinction
between two
level of empirical generalization,
The
it
will
be helpful to
refer to the
levels of scientific systematization: the
and the
level of theory formation.
8
early stages in the
development of a scientific discipline usually belong to the former level, which is characterized by the search for laws the (of universal or statistical form) which establish connections among directly observable aspects of the subject matter
advanced stages belong to the second comprehensive
level,
laws, in terms of hypothetical entities,
for the uniformities established
on the
first level.
find everyday physical generalizations such is
under study.
where research
heat,' 'Iron rusts in
damp
but we might assign to
it
air/
also
Galileo's, Kepler's, Hooke's,
'Wood
as
floats
which
On
the
'Where there on water,
The more
is
aimed
will
we
first level, is
light there
iron sinks in
such more precise quantitative laws
and
at
account
Snell's laws, as well as botanical
it';
as
and
the concomitance of certain observable zoological generalizations about and other characteristics in the memfunctional, anatomical, physical, bers of a given species; generalizations in psychology that assert correladiverse observable aspects of learning, of perception, and tions
among
and various
in economics, sociology, descriptive generalizations and anthropology. All these generalizations, whether of strictly universal or of statistical form, purport to express regular connections among
so forth;
41
Carl G.
Hempel
phenomena, and they lend themselves, explanatory, predictive, and postdictive use.
directly observable
On
therefore, to
we encounter
general statements that refer to and a electric, gravitational fields, to molecules, atoms, sublimato or of subatomic ego, id, superego, libido, variety particles; tion, fixation, and transference; or to various not directly observable
the second
level,
magnetic, and
entities
invoked in recent learning theories.
In accordance with the distinction here made,
we
will
assume that the
or of any of its branches, (extra-logical) vocabulary of empirical science, is divided into two classes: observational terms and theoretical terms. In regard to an observational term it is possible, under suitable circumstances, to decide by means of direct observation whether the term does or does not apply to a given situation.
Observation
may
here be construed so broadly as to include not only
perception, but also sensation and introspection; or it may be limited to the perception of what in principle is publicly ascertainable, i.e., perceivable also by others. The subsequent discussion will be independent of
how
narrowly or
how
liberally
the notion of observation
is
construed;
may be worth noting, however, that empirical science aims for a system of publicly testable statements, and that, accordingly, the ob-
it
servational data
whose
correct prediction
is
the hallmark of a successful
theory are at least thought of as couched in terms on whose applicability in a given situation different individuals can decide, with high agree-
ment, by means of direct observation. Statements which purport to describe readings of measuring instruments, changes in color or odor accompanying a chemical reaction, utterances made, or other kinds of
overt behavior
shown by
ditionsthese
all illustrate
a given subject
under specified observable con-
the use of intersub/ectively applicable ob-
servational terms. 9
Theoretical terms, on the other hand, usually purport to refer to not and their characteristics; they function, in a
directly observable entities
manner soon to be examined more
closely, in scientific theories
intended
to explain empirical generalizations.
The vague;
preceding characterization of the two vocabularies it offers
no
may be retical
to
obviously
by means of which any scientific term as an observational term or as a theo-
precise criterion
unequivocally classified one. But no such precise criterion
be examined
is
in this essay are
needed here; the questions independent of precisely where the
42
is
dividing line between the terms of the observational and the theoretical vocabularies is drawn.
3.
Why
Theoretical Terms?
The
use of theoretical terms in science gives rise to a perplexing should science resort to the assumption of hypothetical problem:
Why
entities
when
interested in establishing predictive and explanatory observables? Would it not be sufficient for the
it is
connections
among and much
less extravagant at that, to search for a system of purpose, laws general mentioning only observables, and thus expressed in terms of the observational vocabulary alone?
Many
general statements in terms of observables have indeed been
formulated; they constitute the empirical generalizations mentioned in the preceding section. But, vexingly, many, if not all, of them suffer
from definite shortcomings: they usually have a rather limited range of application; and even within that range, they have exceptions, so that actually they are not true general statements. Take, for example, one of our earlier illustrations of an empirical generalization: (3.1)
Wood
floats
on water; iron
sinks in
it.
This statement has a narrow range of application in the sense that it refers only to wooden and iron objects and concerns their floating behavior only in regard to water. 10 And, what is even more important, it has exceptions: certain kinds of wood will sink in water, and a hollow iron sphere of suitable dimensions will float on it.
As the history
of science shows, flaws of this kind can often be
remedied by attributing to the phenomena under study certain further constituents or characteristics which, though not open to direct observaconnected in specified ways with the observable aspects of the matter under investigation, and which make it possible to estabsubject lish systematic connections among the latter. By way of illustration tion, are
though
it
is
admittedly an oversimplified one
A much
more
satisfactory generalization
is
the concept of the specific gravity of a body the quotient of its weight and its volume:
x,
(3.1).
(3.2)
Def.:s(x)
consider the sentence
obtained by means of
which
is
definable as
= w(x)/v(x)
Let us assume that
w
and v have been characterized operationally, outcomes of specified measuring
in terms of the directly observable
43
i.e.,
pro-
Carl G.
and that therefore they
cedures,
Then is
s,
determined by
as
are counted
we
will classify
s
the observables.
as a characteristic that
as a hypothetical entity.
which
state the following generalization,
of
among
might be viewed
observable; and, just for the sake of obtaining a simple
less directly
illustration,
(3.1),
Hempel
is
For
we may now
s,
a corollary of the principle
Archimedes:
A
(3.3)
solid
body
floats
on a liquid
if its
specific gravity
is
less
than
that of the liquid.
the exceptions we noted above as predicts correctly the behavior of a piece of heavy refuting (3.1): wood and of a hollow iron sphere. Moreover, it has a much wider scope:
This statement avoids,
first
of
all,
it
solid object and concerns its floating behavior Even the new generalization has certain limitaany liquid. further improvement. But instead of of and thus invites course, tions, pursuing this process, let us now examine more closely the way in which it refers
any kind of
to
in regard to
a systematic connection tion,
by the law
(3.3),
among
observables
which involves
is
achieved, in our illustra-
a detour
through the domain of
unobservables.
Suppose that we wish to predict whether a certain solid object b will on a given body 1 of liquid. will then first have to ascertain,
We
float
by appropriate operational procedure, the weight and the volume of b and 1. Let the results of these measurements be expressed by the following four statements Oi,
(0!)w(b)=w
(3.4)
i;
(0 8 )w(l)=w2 where
w w2 i?
definition
and
;
O2 O O ,
3,
4
:
(02 )v(b)=v1 (0 4 )v(l)=v2
v2 are certain positive real numbers. By means of the can infer, from (3.4), the specific gravities of b (3.2), ,
YI,
,
we
1:
S(b)=wi/v1 ;s(l)=w2 /v2 Suppose now that the first of these (3.5)
values
is
less
than the second; then
(3.4), via (3.5) implies that
(3.6)
s(b)<s(l)
By means (3.7)
b
of the law (3.3),
floats
on
we can now
infer that
1
This sentence will also be called
O
5.
The
sentences
d, O 2 O 3 O 4 O 5 ,
,
,
then share the characteristic that they are expressed entirely in terms of
44
THE THEORETICIAN'S DILEMMA
V
V
the observational vocabulary; for on our and are ob assumption, servational terms, and so are and T, which name certain observable
V
bodies; finally, 'floats on'
is
an observational term because under
able circumstances, direct observation will
show whether
suit-
a given ob-
on a given observable liquid. On the other hand, the sentences (3.2), (13), (3 5), and (3.6) lack that characteristic, for they all contain the term Y, which, in our illustration, belongs to the servable object floats
theoretical vocabulary.
The
systematic- transition
from the "observational data"
listed in (3.4)
to the prediction (3.7) of
an observable phenomenon is schematized in the accompanying diagram. Here, an arrow represents a deductive in(3.9)
I
I-
Prediction in
terms of
observables
ference; mention, above an arrow, of a further sentence indicates that
the deduction
is
effected
clusion stated at the right
by means of that sentence, i.e., that the conend follows logically from the premises listed
at the left, taken in conjunction
arrow.
Note
with the sentence mentioned above the
that the argument just considered illustrates the schema
O O O
2, 4 constituting the statements of particular facts, 3, (1.1), with Oi, the sentences (3.2) and (3.3) taking the place of the general laws, and 11 5 that of E.
O
Thus, the assumption of non-observable entities serves the purposes it provides connections among observables in the
of systematization:
form of laws containing theoretical terms, and
domain of hypothetical
this
entities offers certain advantages,
detour via the
some of which
were indicated above. In the case of our illustration, however, brief reflection will show that
the advantages obtained by the "theoretical detour" could just as well have been obtained without ever resorting to the use of a theoretical
45
Carl G.
Hempel
term. Indeed, by virtue of the definition (3.2), the law (3.3) can be restated as follows: (3.3')
A
body floats on a liquid if the quotient of its weight and volume is less than the corresponding quotient for the liquid.
solid
its
This alternative version clearly shares the advantages we found (3.3) to have over the crude generalization (3.1); and, of course, it permits the deductive transition from Oi,
O O O 2,
3,
4
to
O
5
just as well as does (3.3)
with (3.2).
in conjunction
The
question arises therefore whether the systematization achieved by general principles containing theoretical terms can always be duplicated by means of general statements couched exclusively in observational terms.
we must
first
To
prepare for an examination of this important problem, consider more closely the form and function of a scientific
theory. 4.
Structure
and Interpretation of
a
Theory
Formally, a scientific theory may be considered as a set of sentences T of a expressed in terms of a specific vocabulary. The vocabulary, consist of the terms of T, be to will understood theory extralogical
V
,
T
those which do not belong to the vocabulary of pure logic. Usually, some of the terms of are defined by means of others; but, on pain can be so deof a circle or an infinite regress, not all the terms of
i.e.,
V
V
V
Hence, may be assumed to be divided into two subsets: primiterms those for which no definition is specified and defined terms.
fined. tive
Analogously,
many
of the sentences of a theory are derivable
from others
by means
of the principles of deductive logic (and of the definitions of the defined terms); but, on pain of a vicious circle or an infinite
regress in the deduction,
not
all
of the theoretical sentences can be
T
falls into thus established. Hence, the set of sentences asserted by subsets: primitive sentences, or postulates (also called axioms), and
two
derivative sentences, or theorems. Henceforth, ries are
by
we
will
assume that theo-
form of axiomatized systems as here described; i.e., the primitive and the derivative terms and the defini-
given in the
listing, first,
tions for the latter, second, the postulates. In addition, the theory will
always be thought of as formulated within a linguistic framework of a clearly specified logical structure, which determines, in particular, the rules of deductive inference.
The
classical
paradigms of deductive systems of this kind are the
46
THE THEORETICIAN'S DILEMMA axiomatizations of various mathematical theories, such as Euclidean, and various forms of non-Euclidean geometry, and the theory of groups and other branches of abstract algebra; 12 but by now, a number of theories in empirical science have likewise been put into axiomatic form, or approximations thereof; among them, parts of classical and relativistic 13 certain segments of biological theory 14 and some theoretimechanics, cal systems in psychology, especially in
nomic
theory, the concept of utility,
the
field of learning;
among
15
in eco-
others, has received axio-
matic treatment. 16 If the primitive terms and the postulates of an axiomatized system have been specified, then the proof of theorems, i.e., the derivation of further sentences from the primitive onescan be carried out by means
of the purely formal canons of deductive logic, and thus, without any reference to the meanings of the terms and sentences at hand; indeed,
development of an axiomatized system, no meanings need be assigned at all to its expressions, primitive or derived. However, a deductive system can function as a theory in empirical science only if it has been given an interpretation by reference to emfor the deductive
pirical
phenomena. We may think of such interpretation as being by the specification of a set of interpretative sentences, which
effected
connect certain terms of the theoretical vocabulary with observational terms. 17 The character of these sentences will be examined in considerable detail in subsequent sections; at present
merely
as
may be mentioned,
an example, that interpretative sentences might take the form
of so-called operational definitions, i.e., of statements specifying the meanings of theoretical terms with the help of observational ones; of of theospecial importance among these are rules for the measurement retical quantities
by
reference to observable responses of measuring in-
struments or other indicators.
The manner connections
which a theory establishes explanatory and predictive among statements couched in observational terms ca,n now in
illustrated in outline by the following example. Suppose that the Newtonian theory of mechanics is used to study the motions, under the exclusive influence of their mutual gravitational attraction, of two
be
components of a double-star system, or the moon and a rocket coasting freely 100 miles above the moon's surface. On the basis of appropriate observational data, each of the two bodies may
bodies, such as the
be assigned a certain mass, and, at a given instant
47
t
,
a certain position
Carl G.
and velocity taken which
some
in
specified
Hempel
frame of reference. Thus, a
leads, via interpretative sentences in the
first
form of
step
is
rules of
O k which describe measurement, from certain statements Oi, O 2 observable instrument readings, to certain theoretical statements, say H 6 which assign to each of the two bodies a specific numeri2 HI, .
H
.
.
.
.
.
value of the theoretical quantities mass, position, and velocity. From these statements, the law of gravitation, which is couched entirely in cal
H
theoretical terms, leads to a further theoretical statement, specifies
7,
which
the force of the gravitational attraction the two bodies exert
H
upon each other at t ; and 7 in conjunction with the preceding theoretical statements and the laws of Newtonian mechanics implies, via a deductive argument involving the principles of the calculus, certain statements 9 HI O Hn, which give the positions and velocities of 8
H H
,
,
,
the two objects at a specified later time, say ti. Finally, use in reverse of the interpretative sentences leads, from the last four theoretical state-
ments, to a set of sentences O'i, O' 2 able
.
.
.
O' m which describe observ,
phenomena, namely, instrument readings that are indicative of the
predicted positions and velocities. By means of a schema analogous to
may be
the procedure
(3.8),
represented as follows: (4.1)
iO*
2
.
.
.
O k i, .[Ha, H LM > ^H H H 10 2
8,
Here,
R
is
9,
.
,
.
.
H^ -2+ iU H
H^
lf
2
.
.
.
H H e,
7^
R
>
iO\, 0' 2
.
.
.
0' m V
the set of the rules of measurement for mass, position,
G
and
is velocity; these rules constitute the interpretative sentences; are the Newtonian laws of motion. Newton's law of gravitation, and
LM
In reference to psychology, similar schematic analyses of the function of theories or of hypotheses involving "intervening variables" have re18 Here, the peatedly been presented in the methodological literature. observational data with which the procedure starts usually concern certain observable aspects of an initial state of a given subject, plus certain observable stimuli acting upon the latter; and the final observational statements describe a response made by the subject. The theoretical
statements mediating the transition from the former to the latter refer to various hypothetical entities, such as drives, reserves, inhibitions, or
whatever other not directly observable characteristics, qualities, or psychological states are postulated by the theory at hand.
48
THE THEORETICIAN 5.
The
The preceding account
S
DILEMMA
Theoretician's
Dilemma
of the function of theories raises
anew the
problem encountered in section 3, namely, whether the theoretical detour, through a domain of not directly observable things, events, or characteristics cannot be entirely avoided. Assume, for example, that as will often
be the
laws asserted
by the theory have the form
the interpretative sentences as well as the of equations which connect
case
certain expressions in terms of theoretical quantities either with other
such expressions, or with expressions in terms of observable quantities. Then the problem can be stated in Hull's succinct formulation: "If you
have a secure equational linkage extending from the antecedent observable conditions through to the consequent observable conditions, why, even though to do so might not be positively pernicious, use several 19 Skinner makes the same point in equations where one would do?"
more
when he
general form
theories, of causal chains in
criticizes
which a
the construction, in psychological link consisting of an observable
first
and controllable event
is connected with a final ("third") one of the same kind by an intermediate link which usually is not open to observation and control. Skinner argues: "Unless there is a weak spot in our
not lawfully determined by the first, or the third by the second, then the first and third links must be lawfully related. If we must always go back beyond the second link for causal chain so that the second link
is
we may avoid many
tiresome and exhausting of the first." 20 link as a function the third digressions by examining The conclusion suggested by these arguments might be called the prediction
and
control,
paradox of theorizing.
It asserts
that
if
the terms and the general prin-
they establish definite connections among observable phenomena, then they can be dispensed with since any chain of laws and interpretative statements ciples of a scientific theory serve their purpose,
i.e.,
if
law establishing such a connection should then be replaceable by a conseto observational antecedents links observational directly
which
quents.
By adding
to this crucial thesis
two further statements which
are
obviously true, we form of a dilemma:
obtain the premises for an argument in the classical
(5.1.)
the terms and principles of a theory serve their purpose they are unnecessary, as just pointed out, and if they don't serve their
If
49
Carl G.
Hempel
purpose they are surely unnecessary. But given any theory, its terms and principles either serve their purpose or they don't. Hence, the terms and principles of any theory are unnecessary.
This argument, whose conclusion accords well with the views of extreme methodological behaviorists in psychology, will be called the theoretician's
dilemma.
However, before yielding to glee or to gloom over the outcome of this argument, it will be well to remember that the considerations support of the crucial first premise were formulated rather sketchily. In order to form a more careful judgment on the issue, it will therefore be necessary to inquire whether the sketch can be filled
adduced so
far in
in so as to yield a cogent
6. It will
argument.
To
this task
we now
turn.
Operational Definitions and Reduction Sentences be well to begin by considering more closely the character of
interpretative sentences. In the simplest case, such a sentence could
be
explicit definition of a theoretical expression in terms of observa-
an
tional ones, as illustrated
(3.2). In this case, the theoretical
by
term
unnecessary in the strong sense that it can always be avoided in favor of an observational expression, its definiens. If all the primitives of a can be stated entirely in obare thus defined, then clearly theory is
T
T
general principles will indeed be laws that directly connect observables with observables. This would be true, in particular, of any theory that meets the standservational terms,
and
all its
ards of operationism in the narrow sense that each of
its
terms
is
intro-
duced by an explicit definition which states an observable response whose occurrence is necessary and sufficient, under specified observable test conditions, for
the applicability of the term in question. Suppose,
for example, that the theoretical
erty term, 'Q'.
Then an
term
is
a one-place predicate, or prop-
operational definition of the kind just
men-
tioned would take the form (6.1)
Def.Qx
= (CxDEx)
an object x has (by definition) the property Q if and only if it if it is under test conditions of kind C, then it exhibits an effect, or response of kind E. Tolman's definition of expectancy of i.e.,
is
such that
food provides an at L,
what we
illustration:
assert
is
that
"When we
if
(1)
he 50
is
assert that a rat expects
deprived of food, (2)
food
he has
THE THEORETICIAN
S
DILEMMA
been trained on path P, (3) he is now put on path P, (4) path P is now blocked, and (5) there are other paths which lead away from path P, one of which points directly to location L, then he will run down
We
the path which points directly to location L." 21 can obtain this formulation by replacing, in (6.1), 'Qx' by Vat x expects food at location L/ 'Cx' by the conjunction of the conditions (1), (2), (3), (4),
and L/
(5) for rat x,
to location
'Ex'
by
'x
runs
down the path which
points directly
been shown by Carnap in a now classical argument, 22 manner of defining scientific terms, no matter how natural it may
However, this
as has
seem, encounters a serious
difficulty.
interpretation, a conditional sentence, false
only
if its
antecedent
is
true and
For on the standard extensional such as the definiens in (6.1), is its consequent false. Hence, for
any object which does not satisfy the test conditions C, and for which therefore the antecedent of the definiens is false, the definiens as a
whole erty
is
true; consequently,
Q. In terms of our
such an object will be assigned the propof any rat not exposed to the
illustration:
we would have to say that he expected matter what kind of behavior the rat might exhibit. One way out of this difficulty is suggested by the following consideration. In saying that a given rat expects food at L, we intend to conditions (l)-(5) just stated,
food at
L no
attribute to the animal a state or a disposition which, under circum-
stances
(l)-(5), will cause the rat to run
down
the path pointing
directly to L; hence, in a proper operational definition,
C
E must
be
tied
by virtue of general laws of the kind expressing nomologically, /which requires causal connections. The extensional 'if ... then neither logical nor nomological necessity of connection would thereto
i.e.,
.
fore have to
.
be replaced in (6.1) by a stricter, nomological counterpart worded perhaps as 'if ... then, with causal necessity,
that might be
However, the ideas of law and of causal or nomological necessity as here invoked are not clear enough at present to make this approach seem promising.23 .
.
.'
24
has proposed an alternative way of meeting the difficulty encountered by definitions of the form (6.1); it consists in providing a partial rather than a complete specification of meaning for 'Q'. This
Carnap
done by means of so-called reduction sentences; in the simplest case, the following bilateral reduction sentence: (6.1) would be replaced by
is
(6.2)
CxD(Qx = Ex) 51
Carl G.
Hempel
if an object is under test conditions of kind C, then it has the if and property only if it exhibits a response of kind E. Here, the use of extensional connectives no longer has the undesirable aspects it ex-
i.e.,
Q
hibited in (6.1);
if
entire formula (6.2)
an object is
true of
is it,
not under
but
test conditions
this implies
nothing
C, then the whether
as to
the object does, or does not ? have the property Q. On the other hand, while (6.1) offers a full explicit definition of 'Q\ (62) specifies the
meet partly, namely, for just those objects that condition C; for those which don't, the meaning of 'Q' is left unspecified. In our illustration, for example, (63) would specify the meaning
meaning of 'Q' only
expects food at L' only for rats that meet conditions (l)-(5); for them, running down the path which pointed to L would be a necessary of
'x
and
sufficient condition of
food expectancy. In reference to
rats that
meet the test conditions (l)-(5), the meaning of 'x expects food at L' would be left open; it could be further specified subsequently by means of additional reduction sentences. In fact, it is this interpretation which is required for Tolman's condon't
cept of food expectancy. For while the passage quoted above seems to have exactly the form (6.1), this construal is ruled out by the following sentence which immediately follows the one quoted earlier: "When we assert that he does not expect food at location L, what we assert is that,
under the same conditions, he
down
the path which total interpretation thus given to
will
not run
points directly to location L." The 'rat x expects food at L' is most satisfactorily formulated in terms of a
sentence of the form (6.2), in the manner outlined in the preceding 25
paragraph.
As
this
example vividly
illustrates,
reduction sentences offer an excel-
way of formulating precisely the intent of operational definitions. construing the latter as merely partial specifications of meaning, this
lent
By
"open"; and the provision for and mutually supplementary, reduction sentences given term reflects the availability, for most theoretical terms,
approach
treats theoretical concepts as
a set of different, for a
of different operational criteria of application, pertaining to different contexts. 26
should be noted, however, that while an analysis in terms of reduction sentences construes theoretical terms as not fully defined by reference to observables, it does not prove that a full explicit definition It
in observational x terms
cannot be achieved for theoretical expressions. 52
THE THEORETICIAN
And
even be significantly asked
some
in
7.
The
The
for.
could
this effect
next section deals with this issue
detail.
On first,
Means
the Definability of Theoretical Terms by an Observational Vocabulary quite general, point to be
of any term, say
Vn
DILEMMA
seems questionable whether a proof to
it
indeed,
S
V, by means
have to
of a set
made here
is
this:
of
the definition
V of other terms, say V^, V
'
2
.
.
.
', definiens, a necessary and sufficient condition for the applicability of expressed in terms of some or all of the members of V. And in order to be able to judge whether this can
will
state, in
its
V
be done in a given
case,
we
have to
will
know how
the terms under
consideration are to be understood. For example, the vocabulary consisting of the terms 'male' and 'offspring of permits the formulation of a necessary
of
and
sufficient condition of application for the
but not in
term 'son
How
the given terms are to be understood can be indicated by specifying a set of sentences which are to be considered as true, and which connect the given terms in its biological,
legal sense.
its
U
with each other and perhaps with other terms. Thus, of sentences containing
V,
'v^
.
.
.
Vn
'
and possibly
U
will
be a
set
also other extra-
For example, in the case of the biological use of the 'male', and 'offspring', in reference to humans, the follow-
logical constants.
terms
'son',
ing set of sentences male,'
'No daughter
let us call it is
'x is
male/
might be given: 'Every son an offspring of y if and only if x
Ui
is
is
a son or a daughter of y/
U
Generally, the sentences of specify just what assumptions are to in the search for a definition, concerning the concepts under consideration; and the problem of definability now turns into the ques-
be made,
vn , a it is possible to formulate, in terms of Vi, v2 condition which, in virtue of the assumptions included in U, will be tion whether
.
both necessary and
V by means
it is
of 'vi,
V2
explicitly relativized
tions.
That
precise
.
Thus, using an idea set forth and we see that the concept of definability
sufficient for v.
developed technically by Tarski, of
.
'
'
by
27
.
acquires a precise meaning only if of specifying assumpreference to a set as follows: be now stated may .
meaning means
.
'vn
U
V = V, V VF the relative to a finite set U of statements containing, at least, V and (7.1)
V
is
definable by
of the vocabulary
{
.
-
.
all
53
Carl G. elements of
V
if
from
U there
is
Hempel
deducible at least one sentence stating no other extralogi-
a necessary and sufficient condition for v in terms of cal constants than the members of V. If all
the terms under study are one-place predicates of the first order, then a sentence of the required kind could most simply
for example,
be
stated in the
(7.2)
form
v(x)^D(x,
Vl ,
v2
.
.
.
O,
where the expression on the right-hand side stands for a sentential function whose only free variable is V, and which contains no extralogical constants other than those included in V. Similarly, in the case of our illustration, the set
Ui
specified
above
implies the statement:
x
is
a son of y ss (x
is
so that, relatively to Ui, 'son'
male and x is
is
an
offspring of y),
definable as 'male offspring'.
We
A
should add here an amplifying remark. definition, when it is not simply a convention introducing an abbreviatory notation (such as 5'
be short
for 'xxx-x-x') is usually conof two synonymy expressions, or, as it is often put, the identity of their meanings. Now the question of the definability of a given term of other terms surely is not simply by means of a set
the convention to let
'x
sidered as stating the
V
one of notational
V
fiat;
and indeed
it will
normally be construed as con-
V
cerning the possibility of expressing the meaning which the term possesses with the help of the meanings of the members of V. If this
conception is adopted, then naturally the information needed to answer the question of definability will concern the meanings of and of the members of V; accordingly, the statements in U, which provide this
V
information, will then be required not simply to be true, but to be analytic, i.e., true by virtue of the intended meanings of the constituent terms. In this case, the statements in
U
would have the character of
28 meaning postulates in the sense of Kemeny and Carnap. But in a study of the definability of theoretical expressions by means of observational terms, it is neither necessary nor even advisable to con-
strue definition in this intensional manner. For,
first
of
all,
the idea of
meaning, and related notions such as those of analyticity and synonymy, are by no means as clear as they have long been considered to be, 29 and it will
be
better, therefore, to avoid
Secondly, even
if
them when
this
is
possible.
those concepts are accepted as clearly intelligible,
54
THE THEORETICIAN the definability of a theoretical term
S
DILEMMA
still
cannot be construed exclu-
sively as the existence of a
servational terms:
than a
it
synonymous expression containing only obwould be quite sufficient if a coextensive (rather
synonymous) expression in terms of observables were forthcoming. For such an expression would state an empirically necessary and sufficient observational condition of applicastrictly
cointensive,
or
the theoretical term; and this is all that is required for our In fact, the sentence stating the condition which might have purposes. the form (7.2), for example can then be given the status of a truth-
bility for
by-definition, It
is
by
a suitable reformalization of the theory at hand.
of interest to note here that a necessary
and
discovered even
sufficient observa-
might be inductively
tional condition for a theoretical term, say 'Q',
only a partial specification of the meaning of 'Q' in terms of observables were available. Suppose, for example, that a set of alternative conditions of application for 'Q has been specified by if
7
means (7.3)
of bilateral reduction sentences:
C lX D(Qx^E lX C 2 x D (Qx E x) )
=====
C nxD where
all
(Qx
2
sE
nx)
predicates except 'Q' are observational. Suppose further that
suitable investigations lead to the following empirical generalizations: (7.4)
dxD(Ox C 2x D
E xx)
(Ox = E
2 x)
C nxD (Ox==E n x) where 'Ox' stands for
a sentential function in
V
which contains no
non-observational extralogical terms. These findings, in combination with (7.3), would inductively support the hypothesis (7.5)
Qx^Ox
which presents a necessary and sufficient observational condition for Q. However, (7.5) even if true (its acceptance involves the usual "inductive risk") clearly does not express a synonymy; if it did, no empirical investigations it
would be needed
states that, as a
or,
that
O
is
in the first place to establish
matter of empirical
fact, 'Q' is
an empirically necessary and 55
it.
Rather,
coextensive with 'O',
sufficient condition for
Q.
30
Carl G.
And
we
if
wish,
we may
Hempel
then imagine the theory-plus-interpretation at of a deductive system in which (7.5)
hand to be thrown into the form becomes a definitional truth, and
(7.3)
assumes the character of a
set
of empirical statements equivalent to those listed in (7.4). It might be mentioned here in passing that a similarly broad extensions! interpretation of definability is called for also in the context of the problem whether a given scientific discipline, such as psychology,
can be "reduced" to another, such as biology or even physics and chemof this problem is the question whether the istry. For one component
term* of the latter;
first
and what
is
discipline can
wanted
be defined by means of those of the
for this purpose
is
again a set of empirical
and
hypotheses providing, for each psychological term, a necessary
suffi-
cient condition of application expressed in the vocabulary of biology,
or of physics
When we
and chemistry.
example, that the concepts of the various chemical elements are definable in physical terms by a characterization of the specific
say, for
ways in which their molecules are composed of elementary
physical particles, we are clearly referring to results of experimental research rather than of a mere analysis of what is meant by the terms
naming the various elements. If the latter were the case, it would indeed be quite incomprehensible why the problems pertaining to the definability of scientific terms should present any difficulty, and why they should be the objects of much conjecture and controversy.
The
preceding considerations have important implications for our question whether all theoretical terms in empirical science can be defined in terms of observables. First of elliptical: to complete statements as referred to in (7.1).
as stated
is
for this purpose?
One
it,
all,
What
natural choice
they show that the question
we have set
to specify
some
terization
is
by no means
Now,
precise
this
U
of
could reasonably be chosen
would be the
set of all statements,
in theoretical or observational terms, that are accepted as
true by contemporary science.
set
presumably
pragmatic-historical charac-
and unambiguous; there it cannot be
border area containing statements for which
is
a
wide
clearly de-
termined whether they are accepted by contemporary science. But no matter how the claims of these border-area statements are adjudicated,
and no matter wherewithin reason the borderline between observational and theoretical terms is drawn, it is at least an open question whether the
set of presently accepted scientific statements implies for
56
THE THEORETICIAN'S DILEMMA every theoretical term a necessary and sufficient condition of applicaterms of observables. Certainly those who have asserted such
bility in
definability
have not supported their claim by actually deducing such for the possibility reasons by presenting cogent general
conditions, or
of doing so.
There
another way in which the claim of definability may be construed, namely as the assertion that as our scientific knowledge becomes is
more comprehensive, it will eventually be possible to deduce from it necessary and sufficient conditions of the required kind. (This is the sense in which definability is usually understood by those who claim the eventual definability of the concepts of psychology in terms of those of biology or of physics and chemistry; for that all the requisite definition statements even in an extensional, empirical sensecannot be deduced from current psychological, biological, and chemical 31 principles seems clear. )
in this sense
to
make
But
physical, to assert definability of a theoretical
a twofold claim:
term
that the term in question will not be abandoned in the further development of scientific theois
first,
and second, that general laws will be discovered which establish certain necessary and sufficient conditions, expressible in observational terms, for the applicability of the theoretical term at hand. Clearly, the rizing;
truth of these claims cannot be established
but at best by the
by philosophic arguments,
results of further scientific research.
Despite the precariousness of the problem, various claims and counterclaims have been advanced by philosophers of science and by methodologically interested scientists
theoretical terms
by
concerning the possibility of defining
reference to observables.
Some among
the philosophers have simply urged that nothing short of explicit definition in terms of a vocabulary that is clearly understood can provide an acceptable method of introducing new terms into the language of science; and the argument supporting this view is to the effect that otherwise the new terms are not intelligible. 32 To this question
we
will return later.
assertion, then,
The
protagonists of this view do not
make an
about the actual definability of the theoretical terms used
in contemporary empirical science; rather, they stress the importance of clarifying the ideas of science by restating them, as far as possible, in
a language with a clear and simple logical structure, and in such a way as to introduce all theoretical terms by means of suitable definitions.
Other
writers,
however, have argued, in 57
effect, that scientific theories
Carl G.
Hempel
and the way in which they function have certain pervasive logical or methodological characteristics which presumably are not affected by changes in scientific knowledge, and which provide a basis on which the question as to the definability of theoretical terms can be settled without the need either to examine all the statements accepted by contemporary science or to wait for the results of further research.
An is
illuminating example of a careful use of this type of procedure provided by Carnap' s argument, referred to in the beginning of sec-
tion 6 above,
which shows that
definitions of the
form
cannot
(6.1)
serve to introduce scientific concepts of the kind they were meant to in the sense that it does specify. The argument is limited, however,
not show (and does not claim to show) that an explicit definition of theoretical terms by means of observational ones is generally impossible. 33 Recently, Carnap has extended his examination of the problem in the following direction. Suppose that a given object, b, exhibits this kind of lawful behavior: whenever b is under conditions of a certain
observable kind C, then
kind E.
it
shows a response of a specified observable
We
let us call
then say that b has the disposition to react to C by E; this dispositional property Q for short. Clearly, our earlier
discussion in section 6 concerns the problem of precisely defining *Q' in terms of 'C'
either
and 'E
7
;
we noted
there, following Carnap, that
have to resign ourselves to a
partial specification of
we
meaning
will
for
by means of the bilateral reduction sentence (6:2); or, if we insist on an explicit complete definition, we will have to use causal modalities 'Q'
in the definiens.
But no matter which
of these alternative courses
is
chosen, the result-
ing disposition term 'Q' has this characteristic: if a given object b is under condition C and fails to show response E, or briefly, if Cb but
b lacks the property Q, This characteristic, Carnap argues, distinguishes "pure disposition terms/' such as 'Q', from the theoretical terms used in science; for though the latter are connected with the observational
~Eb, then
this establishes conclusively that
or briefly that
^Qb.
vocabulary by certain interpretative sentences Carnap calls them Crules those rules will not, in general, permit a set of observational data (such as 'Cb' and
'~EV
above) to constitute conclusive evidence
for or against the applicability of the theoretical tion.
There are two reasons
term in a given
situa-
for this assertion. First, the interpretative
sentences for a given theoretical term provide an observational interpre-
58
THE THEORETICIAN'S DILEMMA tation only within a certain limited range; thus, for example, in the case of the theoretical term 'mass', no C-rule is directly applicable to a
sentence S m ascribing a certain value of mass to a given body, if the is either so small that the body is not directly observable or so 34 large that the observer cannot "manipulate the body." value
And
second, a direct observational interpretation for a theoretical
term always involves the tacit understanding that the occurrence or absence of the requisite observable response in the specified test situato serve as a criterion only
if
provided that "the environment
is
tion
is
there are in a
no
disturbing factors, or,
normal
state."
35
Thus, for
example, a rule of correspondence might specify the deflection of a magnetic needle as an observable symptom of an electric current in a
nearby wire, but with the tacit understanding that the response of the needle is to count only if there are no disturbing factors, such as, say, a sudden magnetic storm.
Generally, then, Carnap holds that "if a scientist has decided to use a certain term 'M* in such a way, that for certain sentences about M, any possible observational results can never be absolutely conclusive
evidence but at best evidence yielding a high probability," then the 36 appropriate place for 'M' is in the theoretical vocabulary.
Now we
should note,
first
of
all,
that
if
Carnap's arguments are
sound, they establish that the theoretical terms of science
cannot be
construed as pure disposition terms, and thus even if, by the use of causal modalities, explicit definitions of the latter should be achieved, this
method would be
unavailing for theoretical terms.
But the
argu-
ments do not show and are not claimed to show that theoretical terms can in no way be explicitly defined in terms of observables. In Carnap's statement quoted in the preceding paragraph is accepted, then many terms that can be explicitly defined by means of the observational vocabulary must be qualified as theoretical. For exfact, if
be a two-place observational predicate, and predicate 'Mi be defined as follows:
ample,
(7.6)
let *R'
let a one-place
Def.M!x^(3y)Rxy
it stands in relation R i.e., an object x has the property MI just in case for 'x is less heavy stands for to at least one object y. If, example, 'Rxy' than y', then MI is the property of being exceeded in weight by at least
one
the heaviest of all objects. object, or, of not being 59
Carl G.
Hempel
domain of objects under study not been assigned any definite maximum number of elements. Consider now the possibility of conclusive observational Let us assume,
is
as customary, that the
infinite or at least has
evidence for or against the sentence 'Mia', which attributes MI to a certain object a. Obviously, a single observational finding, to the effect
R to
that a bears
a certain object b, or that Rab,
would
suffice to verify
'M^' completely. But no finite set of observational data 'Raa', 'Rab', 'Rac', and so forth would suffice for a conclusive refutation of 'Mia'. According to Carnap's
though defined in terms be classified as a theohave to might
criterion, therefore, 'Mi',
of the observational predicate 'R', retical
term.
quoted above, Carnap meant to require no observaof a theoretical term 'M' that for certain sentences about
But
possibly, in the passage
tional results can
M
be conclusively
verificatory or falsificatory evidence.
requirement can be explicitly defined in be a three-place observational predicate; for
Yet even terms meeting
this
terms of observables. Let
'S'
example, 'Sxyz' might stand for 'x is farther away from y than from let 'M 2 be defined as follows:
z.'
'
And
Def
(7.7)
.
Mx
Qy)
2
(z)
(~ (z
= y)
D
Sxyz)
.
M
In our example, an object x has 2 just in case there is an object y it is farther away than from any other object z. Consider
from which
now
the sentence
'M 2 a'. As
is
readily seen,
no
finite set of observational
findings (all the relevant ones would have the form 'Sabc' or '^Sabc') can be conclusive evidence, either verificatory or falsificatory, concern-
ing
'M2 a'. Hence, though
tional predicate
'S',
explicitly defined in
the term
'M2
terms of the observa-
'
is
theoretical according to the cri-
terion suggested
by Carnap. preceding discussion
The
illustrates
an elementary but important
when
a term, say a one-place predicate 'Q', is defined in terms of observables, its definiens must state a necessary and sufficient condition for the applicability of 'Q', i.e., for the truth of sentences of the form point:
'Qb'.
But even though that condition
servational terms,
it still
may
is then stated completely in obnot enable us to decide, on the basis of
number
of observational findings, whether 'Q' applies to a given object b; for the truth condition for 'Qb' as provided by the definiens may not be equivalent to a finite set of sentences each of
a finite
which expresses a potential observational 60
finding.
THE THEORETICIAN'S DILEMMA
To add one more example 7
property term
to those given before: suppose that the
and the
'iron object
and
'in
Then
the
relation terms 'attracts'
the vicinity of are included in the observational vocabulary. definition
Def x .
(7.8) is
a
is
magnet
= x attracts every iron object in
in terms of observables;
but the criterion
it
its
provides for
being a magnet cannot be expressed in terms of any
vicinity
an object b
finite
number
of
observational findings; for to establish that b is a magnet, we would have to show that any piece of iron which, at any time whatever, is brought into the vicinity of b, will be attracted by b; and this is an assertion about
To
an
infinity of cases.
express the idea
more
formally, let us
assume that our observa-
tional vocabulary contains, in addition to individual
names
for observable
objects, just first-order predicates of (i.e.,
small
properties or relations)
number
any degree, representing attributes which are observable in the sense that a
of direct observations will suffice, under suitable condi-
whether a given object or group of objects exhibits the attribute in question. Now let us adopt the following definitions: An atomic sentence is a sentence, such as Ta', 'Red', 'Sadg', which ascribes an observable tions, to ascertain
attribute to a specified object or group of objects.
A
basic sentence
is
an atomic sentence or the negation of an atomic sentence. A molecular sentence is a sentence formed from a finite number of atomic sentences
by means
of truth-functional connectives. Basic sentences will
sidered as included
among
be con-
the molecular sentences.
Basic sentences can be considered as the simplest statements describing potential results of direct observation: they assert that some specified set of (one or
more) objects
has, or lacks,
such and such an
observable attribute.
Now
by virtue of
a
theorem of truth-functional
logic, there exist for
every molecular statement S certain finite classes of basic statements which imply S, and certain other such classes which imply the negation of S. Thus, the molecular sentence Ta v(^Pa Rab)' is implied by
and
also
-{'^Pa', 'Rab'j*, for example; whereas
negation is implied by the set -}'~Pa '~Rab')-. This shows that for each molecular sentence S, it is possible to specify a set of basic sentences whose truth *{Ta')*
by
its
>
,
would conclusively
verify S,
and
also a set of basic sentences
61
whose
Carl G.
would
truth
Hempel
verify the negation of S,
refute S. Thus, a molecular sentence servational verification
is
and would thus conclusively capable both of conclusive obfalsification "in
and of conclusive observational
data can be described whose principle," i.e., in the sense that potential occurrence would verify the sentence, and others whose occurrence
would
falsify
but not of course in the sense that the two kinds of
it;
data might occur jointly indeed, they are incompatible with each other. But molecular sentences are the only ones which have this charac-
A sentence which
contains quantifiers non-vacuously verifiable and falsifiable in the sense just indicated. teristic.
Returning
now
to the definition of scientific terms,
is
not both
we may
accord-
molecular ingly distinguish two kinds of explicit definitions, those with all the extraand those with non-molecular definiens. In both cases, terms in the definiens belong to the observational vocabulary; but in the former, the definiens contains truth-functional connectives
logical
as the only logical terms; in the latter,
definitions (7.6), (7.7),
the molecular type (7.9)
Son xy
and
a (Male x
also contains quantifiers.
The
above are of the non-molecular type;
(7.8)
is illustrated
it
by
Offspring xy)
.
We may say now that all and only definitions with molecular definiens provide finite observational criteria of application for the terms they define: in the case of a non-molecular definiens, the ascription of the defined attribute to a given case cannot be conclusively based finite set of observational findings.
Definition by
means
introduce
suffice to
all
might seem to be
on a
of a molecular observational definiens does not
non-observational terms of science.
That
this
is
from the preceding discussion, for surely terms of the kind defined in (7.6) and (7.7) will be permissible and
so
clear
indeed needed in science. This reason
is
not conclusive, however. For
the circumstance that a term, say 'M' , is originally introduced by a definition with non-molecular definiens does not preclude the possibility that
cate, or
this
is
'M'
There
in fact coextensive with a certain observational prediof such predicates, say 'O M '. And if
might be discovered by further (re-) defined by 'O M '.
the case,
then be
is
some molecular compound
is
it
research,
and *M' could
another argument, however, which shows that, granting cer-
tain plausible general assumptions concerning the observational vocabu-
62
THE THEORETICIAN lary,
not
all
S
DILEMMA
non-observational scientific terms can be defined by means
We
of molecular observational expressions. will now briefly consider this argument. 37 The observational vocabulary will be assumed to be finite. It
contain individual names designating certain observable terms with any finite number of places,
may
objects; first-order predicate
representing properties and relations of observable objects; and also i.e., terms expressing quantitative aspects grams, volume in cubic centimeters, age in days
functors,
objects.
we
will
such
as
weight in
of the observable
However, in accordance^ with our assumption of observability, suppose that each of the |unctors can take on only a finite num-
ber of different values; this corresponds to the fact that only a finite number of different weights, for example, can be ascertained and distinguished by direct observation. In contrast to these functors in the observational vocabulary, the theoretical vocabulary of physics, for example, contains a large number of functors
over
all real
whose permissible numbers within a
values range over
real
all
numbers or
certain interval.
Thus, for example, the distance between two points may theoretically have any non-negative value whatever. Now a definition of the required kind for a theoretical functor would have to specify, for each of its permissible values, a finite observational criterion of application. For example, in the case of the theoretical functor length , a necessary and sufficient condition, in the form of a finite observational criterion, would 7
have to be forthcoming for each of the the form
The
=
briefly, 1 (x,y)
infinitely
many
statements of
between points x and y some real number.
distance, in centimeters, 7
r
,
where
r is
Hence, we would have to
specify, for
7
is r
or
each value of Y, a corresponding
finitely ascertainable configuration of observables. But this is impossible because in view of the limits of discrimination in direct observation, only
a finite, though very large, number of finitely observable configurations can altogether be ascertained and distinguished.
However, if we drop the requirement of a molecular equivalent, in observational terms, for each permissible value of a theoretical functor, 38 then an infinity of different values may become available. Consider, for example, the functor 'the
of cells contained in organism y 7
7
7
If 'x is a cell
number
,
'y is
an organism , and then it is possible to give a separate 'x is
as observational expressions,
contained in y are
.
admitted criterion
of applicability, in terms of observables, for each of the infinitely
63
7
many
Carl G. values
1?
2, 3
.
.
.
Hempel
39 which that functor may theoretically assume. This
can be done by means of the Frege-Russell analysis of cardinal numand sufficient condition is bers. For 1, for example, the necessary
n~
the following:
(3n)
(7 10)
(
v ) (y
an organism
is
-
((v
is
a
v
cell
is
contained in
y)
D
All extralogical constants occurring in this definiens are, on our assumpcontains two quantifiers and tion, observation terms; but the expression definiens for any value n the thus is clearly non-molecular. Generally, will require
n
+
1 quantifiers.
of observables, even Thus, the reach of explicit definition in terms in the first-order functional calculus,
is
greatly extended
if
quantifica-
are And stronger logical means permitted in the definiens. For example, countenanced, vast further extensions may be obtained.
tion
if
is
the functor 'the fined (7,1 1)
by the
number
of cells contained in
f
can be explicitly de-
single expression
a (a sim x (x
is
a
x
cell
Here, the circumflex accent
is
is
contained in y )
)
.
the symbol of class abstraction, and 'sim'
the symbol for similarity of classes (in the sense of one-to-one matchaboth of these of their belong to the vocabu-
symbols
elements);
bility
(more specifically, of the logic of classes). So far, we have examined only functors whose values are integers. Can functors with rational and even irrational values be similarly de-
lary of pure logic
fined in terms of observables? Consider, for example, the theoretical
in observapossible to express, sufficient condition for
functor length in centimeters'. tional terms, a necessary (7.12)
l(x,y)
=
and
Is
it
r
We
might try to develop a suitable definition which would correspond to the fundamental method of measif our observational uring length by means of rigid rods. And indeed, meter for the standard name a contains bar, and furthermore vocabulary for every non-negative value of r?
the (purely qualitative)
measuring procedure, or irrational value of
terms required to describe the fundamental
it is r,
possible to state, for
any
specified rational
a necessary and sufficient condition for (7.12).
However, the definiens will in most cases be far from molecular in form: it will be teeming with symbols of quantification over individuals
64
THE THEORETICIAN'S DILEMMA
We
relations of various types. 40 brief outline, the way in which such definitions may
and over
pressions
classes
and
assumed
will indicate, in
be obtained. Ex-
to belong to the observational vocabulary will
be
italicized. First,
the segment determined by points x,y will be said to have a
length of 100 centimeters
if it is
congruent with
(i.e.,
can be
made
to
coincide with) the segment marked off on the standard meter bar. This definiens is even of molecular form. But consider next the observational criterion for l(x,y) .25. It may be stated in the following form, which begins with a quantificational phrase: there are four segments, each marked of! on a rigid body, such that (i) all four are congruent with
each other;
sum
the segment obtained by placing them straight line) is congruent with the segment marked off on the standard meter bar; of the four segments is con(iii) any
end
to
(ii)
their
(i.e.,
end along a
gruent with the segment determined by points x,y. Analogously, an explicit observational definiens can be formulated for any other value
n that
of
a rational multiple of 100,
is
and hence,
for
any rational value
of n.
Next, the consideration that an irrational number can be construed as the limit of a
sary
and
sequence of rational numbers yields the following neces-
sufficient condition for l(x,y)rz:r,
where
r
is
irrational:
the
segment determined by points x,y contains an infinite sequence of points such that (i) Xi is between x and y, x2 between x x and y, Xi, x2 x 3 ,
and
.
.
.
(ii) given any segment S of rational length, there is a point, say xn , in the sequence such that the segments determined by xn and y, xn 1 and y, and so forth are all shorter than S, (iii) the lengths
so forth;
+
of the segments determined by x and x ly x and x27 and so forth, form a sequence of rational numbers with the limit r. Finally, the idea underlying the preceding definition can
be used
to
formulate an explicit definiens for the expression *l(x,y)' in such a way that its range of values is the set of all non-negative numbers. Definitions of the kind here outlined are attainable only at the cost of using a strong logical apparatus, namely, a logic of sets adequate for the development of the theory of real numbers. 41 This price will be considered too high by nominalists, who hold that many of the logi-
concepts and principles here required, beginning with the general concept of set, are intrinsically obscure and should not, therefore, be used in a purported explication of the meanings of scientific terms. This
cal
65
Carl G.
Hempel
not the place to discuss the nominalistic strictures, however; and beadvance sides, it would no doubt be generally considered a worthwhile is
in clarification
if
for a set of theoretical scientific expressions explicit
definitions in terms of observables can
be constructed
at
all.
Another objection that might be raised against the definitional procedure here outlined is that it takes a schematic and oversimplified view
and that terms needed
of the fundamental measurement of length, in construing as observational certain
such as
term
'rigid
bod/ and
'point'
.
This
is
quite true.
for 'point' in the observational vocabulary,
points as directly observable physical objects; terion for
two points
x,y determining a
it is
rather liberal
in the definiens,
By including the
example,
we
construed
but our observational
segment
cri-
of irrational length
berequired that there should be an infinite sequence of other points the never satisfied observable tween x and y. This condition is by
"points" in the form of small physical objects, or marks on rigid which are used in the fundamental measurement of length. As
bodies,
a consequence, the actual performance of fundamental measurement as represented in the above definition will never yield an irrational value for the length of a segment. But this does not show that no meaning has been assigned to irrational lengths; on the contrary, our outline of the definition shows that a meaning can indeed be formulated in
observational terms for the assignment of any specified irrational value to the length of a physical line segment, as well as for the functor length in
cm
7
in general.
However, the concept of length thus defined is not adequate for a physical theory which incorporates geometry, say in its Euclidean form. For the
latter requires that certain
to direct
measurementsuch
segments which are well accessible
as the diagonal of a square whose sides
have a length of 100 centimetershave an irrational length value; and statements to this effect will always turn out to be false if the criterion
made strictly definitory of length; for that procedure, noted, will always yield a rational value for the length of a given
just discussed is as
we
segment.
What
the preceding argument about quantitative terms (represented by functors) shows, then, is this: the fact that the set of permissible values of a theoretical functor term is denumerably infinite or even has
the cardinality of the continuum does not exclude the possibility of an explicit definition for
it
by means of a 66
finite
vocabulary containing only
THE THEORETICIAN qualitative terms
which
are,
S
by reasonably
DILEMMA liberal standards, observational
The argument
does not show, however, that such a definition is available for every functor term required by science (even our illustrative definition of length' turned out not to meet the needs of in character.
and indeed,
was pointed out early in this seccannot be expected. A number of writers have taken the position that even if in principle theoretical terms could be avoided in favor of observational ones, methodit would be practically impossible orwhat is more serious
theoretical physics);
as
tion, a general proof to this effect
ologically disadvantageous or even stultifying to
There
is,
for
do
so.
example, the answer given by Tolman and by Spence
to
the problem considered by Hull, which was mentioned in section 5 if intervening theoretical variables can establish a secure link-
above:
age between antecedent and consequent observable conditions, why should we not use just one functional connection that directly links
antecedents and consequents? Spence adduces as one reason, also sug42 the following consideration: the mathematical gested by Tolman, function required to express the connection will be so complex that it is humanly impossible to conceive of it all at once; we can arrive at it only by breaking it down into a sequence of simpler functional connections, mediated by intervening variables. This argument, then, attributes to the introduction of unobservable theoretical entities
an
important practical role in the context of discovering interdependencies among observables, and presumably also in the context of actually perof forming the calculations required for the explanation or prediction specific occurrences
on the
basis of those interdependencies.
An
to hypothetical important methodological function is attributed an interesting passage of Hull's essay on intervening variables 43 The crucial in molar behavior theory. point of Hull's argument is
entities in
this:
of a Suppose that in order to explain or predict the response time at the the to attribute ti we in a subject, situation,
given subject of his response, a certain habit strength, which has the status of a hypoThat strength is, in Hull's theory, "merely a quantitative thetical entity.
after-effects" of certain earlier observrepresentation of the perseverative able events, such as observable stimuli received in temporally remote if reference to the hypothetical entity, learning situations. Consequently, habit strength, were avoided by linking the subject's observable response
at ti directly to the observable stimuli received earlier
67
then
we would
Carl G.
Hempel
be invoking, as causal determinants for the response, certain observable events which at the time of the response, have long ceased to exist. And rejects this notion, apparently inevitable when intervening hypothetical entities are eschewed, of causal action over a temporal distance:
Hull
"it
hard to believe that an event such
is
as stimulation in a
remote
has ceased to act
learning situation can be causally active long after on the receptors. I fully agree with Lewin that all the factors alleged it
to
be
causally influential in the determination of
any other event must 44
The hypothetical of the the habit subject at the time ti of strength by his response permits an explanation that accords with this principle. Though the concluding part of the passage just quoted sounds quite
be
in existence at the
time of such causal action."
factor represented
metaphysical, the basic import of Hull's argument is methodological. It credits the assumption of explanatory hypothetical entities with an accomplishment that is well described by Feigl in another context: "the
discontinuous and historical character (action at a spatial and/or temporal distance) of the phenomenalistically restricted account vanishes replaced by a spatio-temporally continuous (contiguous) and nomologically coherent formulation on the level of hypothetical con-
and
is
struction." 45
Such
spatio-ternporally continuous theories appear to rec-
ommend
themselves for at least two reasons: first, they possess a certain formal simplicity, which at present can hardly be characterized in precise terms, but which is reflected, for example, in the possibility of using the powerful and elegant mathematical machinery of the calculus for the deduction, from the postulates of the theory, of explanatory and predictive connections among particular occurrences. And second, as
was mentioned in section
3, the past development of empirical science seems to show that explanatory and predictive principles asserting discontinuous connections among (spatio-temporally separated) observ-
able events are likely to be found to have limited scope and various The use of theories in terms of hypothetical entities
kinds of exceptions.
frequently makes it possible to account for such exceptions by means of suitable assumptions concerning the hypothetical entities involved.
Another, more general, argument that must be considered here has been developed in a lucid and precise manner by Braithwaitc, 46 who gives credit to
Ramsey
for the basic principle. 47 Braithwaite's
main con-
that "theoretical terms can only be defined by means of observable properties on condition that the theory cannot be
tention
is
adapted
68
THE THEORETICIAN'S DILEMMA properly to apply to erence to a simple, terpreted theory.
new
situations." 4S
He
elaborates this idea
by refmodel of an inof that model which
precisely formulated, miniature
Without going
into the details
would require too long a digression here
Braithwaite's claim can be
by the following example: suppose that interpreted, at a certain stage of scientific re-
illustrated, it seems,
adequately the term 'temperature'
is
by reference to the readings of a mercury thermometer. If this observational criterion is taken as just a partial interpretation
search, only
(namely
as a sufficient
bility is left
but not necessary condition), then the
open of adding further
partial interpretations,
possi-
by reference
to other thermometrical substances
which are usable above the boiling point or below the freezing point of mercury; and this permits a vast increase in the range of application of such laws as those connecting
the temperature of a metal rod with its length or with sistance, or the temperature of a with its or
its electric re-
its volume. If, gas pressure however, the original criterion is given the status of a complete definiens, then the theory is not capable of such expansion; rather, the original definition has to be abandoned in favor of another one, which is
incompatible with the
first.
49
The concept
of intelligence lends itself to a similar argument: if test criteria which presuppose, on the part of the subject, the ability to read or at least to use language extensively are accorded the status of full definitions, then difficulties of the sort just indicated arise when the
concept and the corresponding theory are to be extended to very young children or to animals.
However, the argument here outlined can hardly be said to establish what is claimed, namely that "A theory which it is hoped may be expanded in the future to explain more generalizations than it was originally designed to explain
must allow more freedom
to
its
theoretical
terms than would be given them were they to be logical constructions out of observable entities" 50 (and thus defined in terms of the latter) .
For
the procedure of expanding a theory at the cost of changthe definitions of some theoretical terms is not ing logically faulty; nor can it even be said to be difficult or inconvenient for the scientist, for clearly,
the problem at
hand
is
rather
one
for the methodologist or the logician,
who
seeks to give a clear "explication" or 'logical reconstruction" of the changes occurring in an expansion of a given theory. And in the type of case discussed by Braithwaite, for example, this can be done in alter-
69
Carl G.
Hempel
native ways either in terms of additions to the original partial interpretation, or in terms of a total change of definition for some theoretical expressions.
And
if it is
held that this latter method constitutes, not an
expansion of the original theory, but a transition to a
would
raise
more
new
one, this
a terminological question than a methodological ob-
jection.
against definition does not have the throws into relief an important heuristic
But though the above argument intended systematic weight,
it
aspect of scientific theorizing:
such as
entities
when
electric currents,
a scientist introduces theoretical
magnetic
chemical valences, or
fields,
subconscious mechanisms, he intends them to serve as explanatory factors which have an existence independent of the observable symptoms
by which they manifest themselves; or, to put it in more sober terms: whatever observational criteria of application the scientist may provide are intended by him to describe just symptoms or indications of the presence of the entity in question, but not to give an exhaustive characit. The scientist does indeed wish to leave open the possi-
terization of
adding to his theory further statements involving his theoretical statements which may yield new interpretative connections be-
bility of
terms
tween theoretical and observational terms; and yet he will regard these assumptions about the sam6 hypothetical entities to which
as additional
the theoretical terms referred before the expansion. This way of looking at theoretical terms appears to have definite heuristic value. It stimulates the invention and use of powerfully explanatory concepts for which only links with experience can be indicated at the time, but which are
some
fruitful in suggesting further lines of research that
may
lead to addi-
tional connections with the data of direct observation. 61
The
survey
argument
made
in the present section has yielded
no conclusive
for or against the possibility of explicitly defining all theo-
terms of empirical science by means of a purely observational vocabulary; and in fact we have found strong reasons to doubt that any retical
argument can
As
settle the question
once and for
all.
for the theoretical terms currently in use,
we
present to formulate observational definientia for to
make them,
retical
are quite unable at of them, and thus
all
in principle, unnecessary. In effect, therefore,
most theo-
terms are presently used in science on the basis of only a partial
experiential interpretation;
and
this use, as
distinct heuristic advantages.
70
we
noted, appears to offer
THE THEORETICIAN'S DILEMMA In view of the importance that thus attaches to the idea of partial interpretation, we will now consider somewhat more closely what kind
might be given of it, and we will then turn to the what sense, the verdict of dispensability as proclaimed by the "theoretician's dilemma," applies also to theoretical terms which have been only partially interpreted, and which, therefore, cannot be dispensed with simply by virtue of definition. of formal account
question whether, or in
8.
Interpretative Systems Carnap's theory of reduction sentences is the first systematic study of the logic of partial definition. The introduction of a term by means of a chain of reduction sentences differs in
the use of a chain of definitions.
two
significant respects
from
specifies the meaning of the term only partially and thus does not provide a way of eliminating the term from all contexts in which it may occur. Second, as a rule, it does First, it
not amount just to a notational convention, but involves empirical assertions. If, for example, the term 'Q' is introduced by the two reduction sentences
C lX D C 2 xD
(8.1)
(8.2)
(Qx (Qx
then the following empirical law
(x)((C lX .E lX)D (C 2
(8.3) i.e.,
the
is
asserted
by implication:
xDE x)) 2
roughly speaking: any object that shows a positive response under test condition will, when put into the second test condition,
first
show
Thus, a chain of reduction sentences term normally combines two functions of language that are often considered as sharply distinct: the stipulative assignment of meana positive response as well.
for a given
ing,
and the assertion
or description of empirical fact.
Reduction sentences,
as
we saw
earlier,
are very well suited for the
formulation of operational criteria of application as partial definitions.
But they are subject to rather severe limitations as to logical form and thus do not seem sufficient to provide a satisfactory general schema for the partial interpretation of theoretical terms. 62 A broader view of insuggested by Campbell's conception of a physical theory as consisting of a "hypothesis," represented by a set of sentences in theoretical terms, and a "dictionary," which relates the latter to conterpretation
is
cepts of experimental physics (which
71
must be interconnected by env
Carl G.
Hempel
53
In contrast to the standard conception of a dictionary, Campbell's dictionary is assumed to contain, not definitions for the theoretical terms, but statements to the effect that a theoretical senpirical laws).
tence of a certain kind
is
true
sentence of a specified kind
is
if
and only
true.
54
is
made
that a translation
a corresponding empirical
Thus, rather than definitions, the
dictionary provides rules of translation;
claim
if
and
must be
for partial rules at that,
no
specified for each theoretical
statement or for each empirical statement. This latter feature accords well, for example, with the consideration that a particular observable macro-state of a given physical system may number of theoretically distinguishable microto a
correspond
large
sentence describing just one of those micro-states, the sentence describing the corresponding macro-state does states; so that, for a theoretical
not express a necessary and sufficient condition, and hence provides no translation. 55
The
statements in Campbell's dictionary evidently do not have the character of reduction sentences; they might be formulated, however, as biconditionals in
by an
"if
and only
which a sentence in theoretical terms
if" clause,
is connected, with a sentence in observational terms.
In other contexts, neither reduction sentences nor such biconditionals to be adequate. For as a rule, the presence of a hypothetical entity such as a certain kind of electric field, will have observable symptoms H,
seem
only
if
certain observational conditions, Oi, are satisfied, such as the
presence of suitable detecting devices, which will then have to show observable responses, 2 A sentence stating this kind of criterion would
O
.
have the character of a generalized reduction sentence; into the form (8.4)
where
d D (H D XV
it
might be put
2)
and 'O 2
'
are sentences
terms of observables, and 'H'
is
possibly quite complex ones in a sentence which is expressed in theo-
retical terms.
But there
is
no good reason
to limit interpretative statements to just
the three types here considered. In order to obtain a general concept of partial interpretation, we will now admit as interpretative statements
any sentences, of whatever observational terms.
logical form,
which contain theoretical and
On the assumption that the theoretical
and observa-
tional statements of empirical science are formulated within a specified
72
THE THEORETICIAN framework,
logical
this idea
S
DILEMMA
can be stated more precisely and explicitly
as follows: (8.5)
Let
T
be
a theory characterized fay a set of postulates in terms of a finite theoretical B be a second set T , and let vocabulary of extra-logical terms, to be called the basic vocabulary, which shares no term with with T . By an interpretative system for
V
V
V
VB
we
T
then understand a set J of sentences which is finite, is (i) (ii) logically compatible with T, (iii) contains no B (iv) contains T or extra-logical term that is not contained in T and B essentially, i.e., it is not logically every element of T equivalent to some set of sentences in which some term of 56 or B does not occur at all. the basis
will
V
V
V
,
V
V
V
In applying the concept here defined to the analysis of scientific we will have to assume, of course, that B consists of terms
V
theories,
which are antecedently understood. They might be observational terms, in the somewhat vague sense explained earlier; but we need not insist on
this.
One might
well take the view, for example, that certain dis-
position terms such as 'malleable
7
,
'elastic',
strictly observation terms, and are not
'hungry*,
known
to
be
and
'tired'
are not
explicitly definable
by means of observation terms; and yet, such terms might be taken to be well understood in the sense that they are used with a high degree of agreement by different competent observers. In this case, it would be quite reasonable to use these terms in interpreting a given B theory, i.e., to admit them into
V
.
Campbell's conception of the function of his "dictionary" illustrates and shows that it comes closer to actual scien-
this possibility very well
tific procedure. Campbell specifies that the interpretation provided by the dictionary must be in terms of what he calls "concepts," such as the terms 'temperature', 'electrical resistance', 'silver', and 'iron* as used in
experimental physics and chemistry. These are hardly observational in the narrow sense, for they are specifically conceived as representing clusters of empirical laws: "Thus, if we say anything about electrical
we assume that Ohm's Law is true; bodies for which Ohm's Law is not true, gases for example, have no electrical resistance." 57 And when we qualify a given body as silver, we attribute to it certain kinds resistance
of lawful behavior concerning solubility in various liquids, melting point, forth. But even though one might not wish to qualify these
and so terms
as observational,
one may
still
73
consider
them
as well understood,
Carl G.
Hempel
and
as used with high intersubjective agreement, by scientific experiB menters; and thus, they might be admitted into as include defined as special cases all the Interpretative systems just
V
.
types of interpretation we considered earlier, namely, interpretation by chains of reduction senexplicit definitions for all theoretical terms, by
bell's
by biconditional translation statements in the sense of Campof the form dictionary, and by generalized reduction sentences
(8.4);
but of course they also allow for interpretative statements in a
tences,
large variety of other forms.
Interpretative systems have the
same two
characteristics
which
dis-
tinguish chains of reduction sentences from chains of definitions First, an interpretative system normally effects only a partial interpretation of :
VT
the terms in
;
i.e., it
does not lay
logical implication), for every
down (by
VT
term in
condition of application in terms of
VB
.
explicit
statement or by
a necessary and sufficient Second, like a chain of reduc,
an interpretative system will but will imply certain in not be character, normally purely stipulative statements in terms of B alone which are not logical truths, and which, on the conception of VB as consisting of antecedently understood emtion sentences for a given theoretical term,
V
pirical terms,
may be viewed
as expressing empirical assertions.
Thus,
here again, we find a combination of the stipulative and the descriptive use of language. But, to turn to a third point of comparison, an interpretative system need not provide an interpretation complete or incomplete for each term in T individually. In this respect it differs from a set of defini-
V
tions,
which
and from
specifies for
each term a necessary and sufficient condition,
a set of reduction sentences,
and a
a necessary
usually different
which provides
term
for each
sufficient condition.
It
is
quite
an interpretative system provides, for some or even all of the terms in T no necessary or no sufficient condition in terms of B possible that
V
V
,
or indeed neither of the two; instead,
ment of
or
by
VB only
it
might
specify,
by
,
explicit state-
logical implication, sufficient or necessary conditions in terms for certain expressions containing several
terms of
manner of Campbell's dictionary. therefore, when a theory T is interpreted by an
VT
for
example, in the
As
a rule,
interpreta-
the theoretical terms are not dispensable in the narrow sense of eliminability from all contexts, in favor of defining expressions tive
system
in terms of
J,
VB
.
Nor
are they generally dispensable in the sense that J
74
THE THEORETICIAN'S DILEMMA
H that can be formed by means of VT VB a sentence O in terms of VB such H = O 58 logically deducible from
provides, for every sentence a "translation" into terms of
the the biconditional
,
,
i.e.,
is
}.
Are theoretical terms, then, altogether indispensable on
this
broad
conception of interpretation so that the "paradox of theorizing" formulated in section 5 no longer consider this question applies to them? in the next section.
We
Functional Replaceability of Theoretical Terms
9.
The
systematizing function of a theory T, as interpreted by an in-
terpretative system J will consist in permitting inferences from given "data" in terms of B to certain other (e.g., predictive) statements in
V
terms of
VB
If
.
Oi
is
the statement expressing the data, C>2 the inferred
statement, then the connection (9.1)
(d-T.J)
may be symbolized
thus:
2
T
stands for the set of postulates Here, as in similar contexts below, of the theory at hand; the arrow represents deductive implication.
Now,
(9.1) holds
so that (9.1) (9.2)
is
if
>(0 1
(T.J)
and only
if
T- J
implies the sentence
Oi D
O2
;
tantamount to
DQ
8)
Whatever systematization is achieved among the VB-sentences is clearly accomplished by T in conjunction with J. It will be convenient
T
therefore to consider the postulates of together with the sentences of J as the postulates of a deductive system T', which will be called
V
V
an interpreted theory. Its vocabulary \V will be the sum of T and B What was noted in connection with (9.1) and (9.2) may now be restated thus: If
tion
from Oi to
(9.3)
(Oi-T)
an interpreted theory T' establishes a deductive
O2
,
i.e.,
.
transi-
if
>02
then (9.4)
T
>(OiD0 2
)
and conversely, where T'
is
the set of postulates of the interpreted
theory.
Now it can exactly the
the set of
readily
be shown that an interpreted theory T' establishes
same deductive connections among VB -sentences as does those theorems of T' which are expressible in terms of
all
75
Carl G.
V B alone; we will call and
of T',
this
Hempel
the set of V^-theorems, or Wconseguences,
will designate it
by
XV.
This means, that for
all
purposes
of deductive systematization, T' is, as we will say, functionally equivalent to the set T -, which contains not a single theoretical term.
O
The proof is as follows: The deductive transition, represented in (9.3), from Oi to O 2 can be achieved just as well by using, instead of T', D O 2 which by virtue of (9.4) belongs to (V; simply the sentence for we have, by modus ponens,
d
,
>0 2
(CMOiDOO)
(9.5)
And since O T
-
surely contains
all
the
O
VB -sentences
form Oi
of the
D
O
2
that are implied by T', the set T suffices to effect all the deductive T systematizations achievable by means of T'. On the other hand, -
O
is
no
stronger in this respect than T'; for
O
O2 D O2
OT
'
permits the deductive
'
D O2
but in this case, x only implies which means, in view of the equivalence of T' also implies Oi deductive transition from (9.4) with (93), that T' will permit the
from
transition
to
if it
Oi
;
,
to
O2
d
.
Thus, the deductive systematization that an interpreted theory T' among sentences expressed in terms of a basic vocabulary V# T of those stateexactly the same as that accomplished by the set
achieves is
O
>
ments (theorems) of T' which can be expressed in terms of V^ alone. In this sense, the theoretical terms used in T can be dispensed with.
But
OT
'
is
normally an unwieldy infinite set of statements, and the
is some generally applicable more and manageable perspicuous by putting it making into the form of an axiomatized theoretical system T' B which would be formulated in terms of V B alone. A theorem in formal logic which
question
method
arises
therefore whether there
of
it
,
was recently proved by Craig shows that vided only that T'
satisfies
this
is
indeed the case, pro-
certain extremely liberal
and unconfining
conditions. 59
Thus
Craig's theorem has a definite bearing upon the problems raised the by "paradox of theorizing/' which was stated in section 5 in somewhat vague terms. The theorem at hand points out one way in which the "paradox" can be given a clear and precise interpretation and a
rigorous proof: It shows that for
any theory T' using both theoretical terms and non-theoretical, previously understood ones, there exists, under certain very widely satisfied conditions, an axiomatized theoreti76
THE THEORETICIAN
S
DILEMMA
system T' B which uses only the non-theoretical terms of T' and yet
cal
functionally equivalent with T' in the sense of effecting, among the sentences expressible in the non-theoretical vocabulary, exactly the same is
T
deductive connections as
7 .
Should empirical science then
avail itself of this method and replace theories involving assumptions about hypothetical entities by functionally equivalent theoretical systems couched exclusively in terms
all
its
which have direct observational reference or which clearly
are,
at
any
rate,
understood? There are various reasons which make this inadvis-
able in consideration of the objectives of scientific theorizing.
To
begin with, let us consider the general character of Craig's method. Disregarding many subtle points of detail, the procedure may be described as follows:
the
all
By means
of a constructive procedure, Craig arranges T' in a sequence. This sequence is highly reof contains, for any sentence occurring in it, also all its
VB -theorems
dundant, for
it
V
B ). Craig prethey are expressible in not even all, of these many, though
logical equivalents
(as far as
scribes a
for eliminating
procedure
duplications.
The remaining sequence
therefore
still
contains each
VB
-
theorem of T' in at
least one of its various equivalent formulations. the in this remaining sequence are made postulates sentences Finally, of T'B. Thus, the set of B -theorems of T' is "axiomatized" in T' B only all
V
in a rather Pickwickian sense,
some
namely by making every sentence of the
equivalent formulations, a postulate of T' B whereas normally, the axiomabzation of a set of sentences is intended to select as postulates just a small subset from which the rest can then in
set,
be
of
its
many
;
logically derived as theorems. In this
manner, the axiomatization
expresses the content of the whole set "in a form which cally or mathematically
in effect includes all
more perspicuous."
sentences that are to
60
And
be axiomatized
postulates of T' B , the latter, as Craig himself puts
or to provide genuine insight."
The
loss in simplicity
terms of T'
is
which
is
psychologi-
since Craig's
method
among
the
"fail to simplify
it,
61
results
from discarding the
theoretical
reflected in the circumstance that the set of postulates
which Craig's method yields for T' B is always infinite. Even in cases where actually there exists some finite subset of O T of B -theorems of from which all the rest can be deduced, Craig's procedure will '
V
T
not yield such a subset: that
is
the price of the universal applicability
of Craig's method.
77
Carl G.
Now
Hempel
there are cases where an infinity of postulates may not be exwhen the axioms are specified by means of
cessively unwieldy; notably
axiom-schemata,
62 i.e.,
that has one of a finite is
example)
by stipulations to the effect that any sentence number of specified forms (such as 'x x', for
=
But the manner
to count as an axiom.
or postulates, of T' B are specified by Craig's
and the
in
method
which the axioms, is
vastly
more
in-
system would be
resulting practically unmanageable to say nothing of the loss in heuristic fertility and suggestiveness which
tricate,
results
from the elimination of the theoretical concepts and hypotheses.
For empirical
method of dispensing with theowould be quite unsatisfactory. we have examined the eliminability of theoretical concepts science, therefore, this
retical expressions
So
far,
and assumptions only in the context considered an interpreted theory T' lishing deductive transitions
such theories
may
among
the sense outlined in section yield a further
sions
by means
1
) ;
:
we
exclusively as a vehicle of estab-
observational sentences. However,
means
also afford
of deductive systematization
of inductive systematization
and an
(in
analysis of this function will
argument against the elimination of theoretical expresof Craig's method.
of illustration,
we
will refer to the following example, which in order the more deliberately oversimplified clearly to exhibit the essentials: we will assume that T contains the term 'white
By way
is
V
or
T'
states
for short,
no
phosphorus',
and that the
interpretative system incorporated into T' sufficient observational conditions of for it, but
application
several necessary ones.
These
be assumed to be independent of though in the case of white phosphorus will
each other in the sense that, they occur jointly, any one of them will in certain other cases occur in the absence of one or more of the others. Those necessary conditions might be the following: white phosphorus has a garlic-like odor; it is soluble in turpentine, in vegetable burns. In symbolic notation: (9.6) (9.7)
oils,
and in
ether;
it
produces skin
(x)(PxDGx) (x)(PxDTx) (Px
D Vx)
(9.8)
(x)
(9.9)
(x)(PxDEx)
(9.10)
(x)
(Px
D
Sx)
All predicates other than T' that occur in these sentences will belong then, to B
V
.
78
THE THEORETICIAN'S DILEMMA
Now
let
VT contain
just
ignition temperature of 30
one term
C,
or
in addition to
T
for short;
and
T' namely be y
let there
'has
an
exactly
one interpretative sentence for T, to the effect that if an object has the property I then it will burst into flame if surrounded by air in
which a thermometer shows a reading above 30 C. This property will be considered as observable and will be represented by the predicate
T'
in
VB
.
The
interpretative sentence for
(x)(IxDFx) Finally, we will assume
T,
then,
is
(9.11)
that the theoretical part of
T
7
contains one
single postulate, namely, (9.12)
(x)
(Px
D
Ix)
white phosphorus has an ignition temperature of 30 C. Let the seven sentences (9.6)-(9.12) represent the total content of T'. i.e.,
Then,
as
is
readily seen, T' has
no consequences
in terms of
VB except
T' will permit a deductive tranB -sentence to another only if the latter is logically
for purely logical truths; consequently, sition
from one
V
implied by the former, so that T' is not required to establish the connection. In other words: T' effects no deductive systematization among
VB-sentences at lishing,
all.
among the
play an essential role in estabB -sentences, certain explanatory or predictive con-
Nevertheless, T'
V
may
nections of an inductive kind. Suppose, for example, that a certain object, b, has been found to have all the characteristics G, T, V, E, S.
In view of the sentences (9.6)-(9.10), according to which these characsymptomatic of P, it might then well be inferred that b
teristics are
white phosphorus. This inference would be inductive rather than deductive, and part of its strength would derive from the mutual in-
is
dependence which we assumed to
exist
among
symptoms of white phosphorus. The sentence arrived at inductively leads, via
those five observable
TV
which has thus been in (9.12), to the prediction 'IV, which
turn, in virtue of (9.11), yields the forecast
TV.
Thus, T' permits the
from the observational data 'GV, 'TV, 'W, <EV, 'SV to the observational prediction TV. But the transition requires an inductive on the strength of the five data step, consisting of the acceptance of TV transition
sentences, establish,
which support, but which, of course, do not conclusively
TV.
On
the other hand, the system T' B obtained by Craig's method does not lend itself to this inductive use; in fact, all its sentences are logical
79
Carl G. truths
Hempel
and thus T'B makes no empirical the
all
above,
VB-theorems
of
T
assertion at
all, for,
as
was noted
are logically true statements.
63
the systematizing use of an interpreted theory T' is conceived as involving inductive as well as deductive procedures, then the correif
Thus,
sponding system T' B cannot, in general, replace T'. Another, inductively simpler, method of obtaining a functional equivaT' is provided lent, in observational terms, of a given interpreted theory
by an idea of Ramsey's. In
the
effect,
method amounts
to treating
theoretical terms as existentially quantified variables, so that all
all
the
Ramsey's manner of formulating
occur in extra-logical constants that
64 a theory belong to the observational vocabulary. Thus, for example,
the interpreted theory determined by our formulas (9.6)-(9.12) would be expressed by the following sentence, which we will call the Ramseysentence associated with the given theory.
(3<) (3
(9.13)
(($xD0K).foxD (Gx-Tx.Vx.Ex.Sx)).(,/oc
DFx)) equivalent to the expression obtained
This sentence
is
the sentences
(9.6)-(9.12), replacing T' and
variables
V
and
V
T
and prefixing
respectively,
by conjoining
throughout by the
existential
quantifiers
with regard to the latter. Thus, (9.13) asserts that there are two properties, 4> and ^, otherwise unspecified, such that any object with the property
also has the property
if/,
and any object with the property G, T, V, E, S, and
also has the (observable, fully specified) properties
any object with the property
\f/
also has the (observable, fully specified)
property F.
An
interpreted theory T' as
we have been
course, logically equivalent with
more than T' B ; in
T
fact,
it
is
conceiving
it
is
not, of
associated Ramsey-sentence any with the associated Craig-system implied by, but does not in turn imply, its
logically equivalent
each of the two
is
7
But though the Ramsey-sentence contains, apart from variables and logical constants, only terms from V B it can be shown to imply exactly the same VB -sentences as does T'; hence, it establishes exactly the same .
,
deductive transitions
among
VB -sentences
as
does T'. In this respect
then, the Ramsey-sentence associated with T' is on a par with the Craigsystem T' B obtainable from T'. But its logical apparatus is more ex-
travagant than that required by T' or by T' B In our illustration, (9.6)(9.12), for example, T' and T' B contain variables and quantifiers only .
80
THE THEORETICIAN
S
DILEMMA
with respect to individuals (physical objects), whereas the Ramseysentence (9.13) contains variables and quantifiers also for properties of individuals; thus, while culus, the
But
this
T and T' B require only a
Ramsey-sentence
calls for
first-order functional cal-
a second-order functional calculus.
means that the Ramsey-sentence
associated with an inter-
preted theory T' avoids reference to hypothetical entities only in letter replacing Latin constants by Greek variables rather than in spirit. For it still
asserts the existence of certain entities of the
kind postulated by
without guaranteeing any more than does T that those entities are observable or at least fully characterizable in terms of observables. Hence, 7
T',
Ramsey-sentences provide no satisfactory way of avoiding theoretical concepts.
And
indeed,
Ramsey himself made no such claim Rather,
strual of theoretical
his con-
terms as existentially quantified variables appears
have been motivated by considerations of the following kind: If theoretical terms are treated as constants which are not fully defined to
terms of antecedently understood observational terms, then the sentences that can formally be constructed out of them do not have the character of assertions with fully specified meanings, which can be
in
significantly held to
be either true or
false; rather, their status is
compa-
rable to that of sentential functions, with the theoretical terms playing
the role of variables. But of a theory, we want to be able to predicate truth or falsity, and the construal of theoretical terms as existentially quantified variables yields a formulation
and
at the
same time
which meets
this
requirement
retains all the intended empirical implications of
the theory. This consideration raises a further problem concerning the status of be discussed in the partially interpreted theories; that problem will
next section.
10.
On Meaning
and Truth
of Scientific Theories
The problem
suggested by Ramsey's approach is this: if, in the man8, we construe the theoretical terms of a theory as extrafor which the system J provides only a partial interpreconstants logical tation in terms of the antecedently understood vocabulary B can the
ner of section
V
,
sentences formed by means of the theoretical vocabulary nevertheless be considered as statements which make definite assertions, and which arc either true or false? 81
Carl G.
The tics,
Hempel
question might seem to come under the jurisdiction of semanof truth. But this specifically, of the semantical theory
and more
What
the semantical theory of truth provides (under a general definition of truth for the sentences of a given language L. That definition .is stated in a suitable metalanguage, M, of L and permits the formulation of a necessary and sufficient conis
not the case.
certain conditions)
is
dition of truth for any sentence S of L. This condition is represented 65 (To be suited for its purpose, simply by a translation of S into M.
M
must therefore contain a translation of every sentence of L and must meet certain other conditions which are precisely specified in the semanare to tical theory of truth.) But if the truth criteria thus stated in
M
be
M
all, then clearly all the translations of L-statements into must be assumed to be significant to begin with. Instead of deciding
intelligible at
the question of the significance of L-sentences, the semantical definition of truth presupposes that it has been settled antecedently. For quite analogous reasons, semantics does not enable us to decide in a given system T' do, or do not, have or or semantical, factual, ontological reference a characteristic which some writers have considered as distinguishing genuinely theoretical con-
whether the theoretical terms
structs
from
66 auxiliary or intervening theoretical terms.
with the claims and counter-claims that have been nection
lies
One
made
difficulty
in this con-
in the failure of the discussants to indicate clearly
what
they wish to assert by attributing ontological reference to a given term. Let us note here that from a purely semantical point of view, it is pos-
any term of a language L that taken to be understood: the referent can be specified in the same manner as the truth condition of a given sentence in L, namely by sible to attribute semantical reference to is
translation into a suitable metalanguage. For example, using English as a metalanguage, we might say, in reference to Freud's terminology,
that 'Verdraengung' designates repression, 'Subhmierung', sublimation, and so on. Plainly, this kind of information is unilluminating for those
who wish
to use existential reference as a distinctive characteristic of a
it help those who want to the entities sense, designated by theoretical terms can be said actually to exist a question to which we will return. Semantics, then, does not answer the question raised at the begin-
certain kind of theoretical terms; nor does
know whether,
ning of
or in
this section;
what
we have
for theoretical terms
to look elsewhere for criteria of significance
and sentences. 82
THE THEORETICIAN
S
DILEMMA
we might
qualify a theoretical expression as inhas been adequately explained in terms consider as antecedently understood. In our earlier discussion,
Generally speaking,
telligible or significant if it
which we
V
such terms were represented by the vocabulary B (plus the terms of But now the an "adequate" exWhat constitutes logic). question arises,
No
generally binding standards can be specified: the answer ultimately determined by one's philosophical conscience. The logical
planation? is
and epistemological puritan
what has been and he may impose further restricexample, on the logical apparatus that
will declare intelligible only
VB
explicitly defined in terms of
tions, in a nominalistic vein, for
;
may be used
in formulating the definitions. Others will find terms introduced by reduction sentences quite intelligible, and still others will even countenance an interpretation as tenuous as that afforded by an interpretative system. One of the most important advantages of definition lies in the fact that it ensures the possibility of an equivalent re-
V
statement of any theoretical sentence in terms of B Partial interpretation does not guarantee this; consequently it does not provide, for .
every sentence expressible in theoretical terms, a necessary and sufficient condition of truth that can be stated in terms which are antecedently
understood. This, no doubt, the
is
the basic difficulty that
critics find
with
method
of partial interpretation. In defense of partial interpretation,
on the other hand, it can be understand an expression is to know how to use it, and in a formal reconstruction the "how to" is expressed by means of rules. said that to
Partial interpretation as
show, for example,
we have
construed
it
provides such rules. These
VB
what sentences in terms of
alone
may be
in-
from sentences containing theoretical terms; and thus they specify, in particular, a set of B -sentences that are implied, and hence indirectly ferred
V
interpreted theory T'. (If the set is empty, the theory within the domain of empirical science.) Conversely, the
asserted,
by an
does not
fall
rules also
show that sentences
in theoretical terms
may be
inferred from
VB -sentences. cal
Thus, there are close resemblances between our theoretisentences and those sentences which are intelligible in the narrower
V
sense of being expressible entirely in terms of B a circumstance which into the class of of theoretical sentences in favor militates admitting significant statements. It
should be mentioned that
have to recognize
as significant
if
this policy
is
adopted, then
we
will
(though not, of course, as interesting 83
Carl G.
Hempel
or worth investigating) certain interpreted systems which surely
not qualify as potential
scientific theories.
For example,
let
would
L be
the
of empirical generalizations about of an observational vocabulary terms in formulated learning behavior, number of arbitrary senfinite a of the let P and be B,
conjunction of
some
number
finite
V
conjunction
tences formed out of a set
VT
of arbitrarily chosen uninterpreted terms the conjunction of the postulates of some
(for example, P might be axiomatization of elliptic geometry)
Then, by making P the postulates and by choosing the sentence P D L as the only member of our which "exinterpretative system J, we obtain an interpreted theory, of
plains" in a trivial
T
.
T
way
all
the given empirical generalizations, since would not be considered
L. Yet, needless to say, J plainly implies
T
67
The characteristic here illustrated does a satisfactory learning theory. not vitiate our analysis of partial interpretation, since the latter does not claim that every partially interpreted theoretical system is a potentially of interesting theory; and indeed, even the requirement of full definition all
theoretical terms
by means of
rewarding "theories/'
remind us is
necessary
good
if
scientific
still
our
leaves
room
for similarly un-
mock
"learning theory" simply having an empirical interpretation (which
Examples
that, in addition to
VB
like
there are to be any empirically testable consequences) a theory must satisfy various important further conditions;
VB -consequences
must be empirically well confirmed; it must effect a logically simple systematization of the pertinent B -sentences, it must suggest further empirical laws, and so forth. its
V
the sentences of a partially interpreted theory T' are granted the
If
status of significant statements, they can false.
And
be said to be either true or
then the question, touched upon
earlier in this section, as
to the factual reference of theoretical terms, can be dealt with in a
quite straightforward manner: To assert that the terms of a given theory have factual reference, that the entities they purport to refer to actually exist, is tantamount to asserting that what the theory tells us is true;
and
When
turn is tantamount to asserting the theory. we say, for that the of example, elementary particles contemporary physical theory actually exist, we assert that there occur in the universe particles of the this in
various kinds indicated cal laws,
and showing
by physical theory, governed by specified physicertain specific kinds of observable symptoms-
again indicated by physical theory of their presence in certain specified circumstances. But this is tantamount to asserting the truth of the (in-
84
THE THEORETICIAN
S
DILEMMA
terpreted) physical theory of elementary particles. Similarly, asserting the existence of the drives, reserves, habit strengths, postulated by a
given theory of learning amounts to affirming the truth of the system con88 sisting of the statements of the theory and its empirical interpretation. Thus understood, the existence of hypothetical entities with specified characteristics
examined
and
assumed by a given theory, can be same sense in which the truth of the theory
interrelations, as
inductively in the
can be examined, namely, by an empirical investigation of
itself
its
VB-
consequences.
According to the conception
just outlined,
we have to
attribute factual
the (extra-logical) terms of a theory if that theory is this characteristic provides no basis for a semantical dichottrue; hence, in the theoretical omy vocabulary. Also, the factual reference, as here reference to
all
construed, of theoretical terms does not depend on whether those terms couched in terms of B alone. Even
V
are avoidable in favor of expressions if all
the theoretical terms of a theory T' are explicitly defined in terms B , so that their use affords a convenient shorthand way of saying
V
of
what could reference
if
be said by means of VB alone, they what the theory says is true.
also
will
still
have factual
The
preceding observations on truth and on factual reference in regard to partially interpreted theories rest on the assumption that the sentences of such theories are accorded the status of statements. For
who find this assumption unacceptable, there are at least two other ways of construing what we have called an interpreted theory. The first of these is Ramsey's method, which was described in the those
an previous section. It has the very attractive feature of representing which contains in the form of fide a bona statement, interpreted theory
no
extra-logical constants other
than those contained in
VB
,
and
still
V
has exactly the same B -consequences as the interpreted theory stated in terms of incompletely interpreted theoretical constants. It is perhaps the most satisfactory way of conceiving the logical character of a sciento theory, and it will be objectionable mainly, or perhaps only, those who, on philosophical grounds, are opposed to the ontological commitments 69 involved in countenancing all the requisite variables tific
of the theory ranging over domains other than that of the individuals of physi(such as, for example, the set of all quantitative characteristics cal objects, or sets,
the set of
and so forth)
all
dyadic relations
.
85
among them,
or sets of such
Carl G.
Hempel
like the contemporary nominalists, reject such commitments, may adopt a conception of scientific strong ontological theories, not as significant statements, but as intricate devices for inin terms of an ferring, from intelligible initial statements, expressed
Those
finally,
who,
V
B , certain other, again intelligible, antecedently understood vocabulary statements in terms of that vocabulary. 70 The theoretical terms are then
construed as meaningless auxiliary marks, which serve as convenient statesymbolic devices in the transition from one set of experiential
ments
to another.
To be
sure, the
conception of laws and theories as
does not reflect the way in which extra-logical principles of inference In publications dealing with probscientists. theoretical are used by they lems of theoretical physics, or biology, or psychology, for example, sentences containing theoretical terms are normally treated on a par with those which serve to describe empirical data: together with the latter,
they function as premises and as conclusions of deductive and of inductive arguments. And indeed, for the working scientist the actual formulation
and use of
inference
theoretical principles as complex extra-logical rules of would be a hindrance rather than a help. However, the pur-
pose of those who suggest this conception is not, of course, to facilitate the work of the scientist but rather to clarify the import of his formulations; and from the viewpoint oFa philosophical analyst with nominalistic inclinations, for
example, the proposed view of scientific sentences intelligible statements, does represent
which by his standards are not an advance in clarification.
However, the question posed by the theoretician's dilemma can be two alternative conceptions of the status
raised also in regard to the
of a theory. Concerning Ramsey's formulation, we may ask whether it not possible to dispense altogether with the existentially quantified variables which represent the theoretical terms, and thus to avoid the is
commitment they require, without sacrificing any of the deductive connections that the Ramsey-sentence establishes among B-
ontological
V
sentences.
And
in regard to theories conceived as inferential devices,
we
may ask whether they cannot be replaced by a functionally equivalent set of rules i.e., one establishing exactly the same inferential transitions
among VB-sentences- which In both
cases,
Craig's
uses
none
theorem
of the "meaningless marks."
gives
an affirmative answer by de-
scribing a general method for constructing the desired kind of equivalent (provided only that the original formulation meets the very weak
86
THE THEORETICIAN'S DILEMMA requirements of that theorem). But again, in both cases, the result hasf the same shortcomings that were mentioned in section 8: First of all, the
method would
replace the Ramsey-sentence by an infinite set of
body of inferential rules by an infinite set of rules, in terms of V B and would thus lead to a loss of economy. Second, the resulting system of postulates or of inferential rules would not lend postulates, or the ,
to inductive prediction and explanation. And third, it would have the pragmatic defect, partly reflected already in the second point, of being less fruitful heuristically than the system using theoretical terms. itself
When
scientists or methodologists claim that the theoretical
terms
of a given theory refer to entities which have an existence of their own,
which
are essential constituents or aspects of the world
we
live in, then,
no matter what individual connotations they may connect with this adduce in support of it seem clearly
assertion, the reasons they could
to lie in the fact that those terms function in a well-confirmed theory
which
effects
an economical systematization, both deductive and induc-
tive, of a large class of particular facts
which
is
and empirical
generalizations,
heuristically fertile in suggesting further questions
hypotheses.
And
and new
as far as suitability for inductive systematization,
with economy and heuristic
fertility,
and
along
are considered essential charac-
teristics of a scientific theory, theoretical
terms cannot be replaced with-
out serious loss by formulations in terms of observables only: the theoretician's dilemma, whose conclusion asserts the contrary, starts with a false premise.
NOTES x
This term was suggested by a passage in Reichenbach's volume (70), where the word 'postdictabihty' is used to refer to the possibility of determining "past data in terms of given observations" (p. 13). In a similar context, Ryle uses the term 'retroof the historians' "business (see, for example, (78, p. 124) ), and Walsh speaks to 'retrodict' the past: to establish, on the basis of present evidence, what the past must have been like" (93, p. 41 ) According to a remark in Acton's review of Walsh's
diet'
.
62 (1953), pp. 564-565), the word 'retrodiction' was used in this sense already by J. M. Robertson in Buckle and his Critics (1895). 2 More accurately: it can be deduced from the principles of Newtonian mechanics that Kepler's laws hold in approximation, namely, on the assumption that the forces exerted upon the planets by celestial objects other than the sun (especially other
book (Mind,
vol.
planets) are negligible. 3 For a fuller presentation of this deductive schema of scientific explanation and section 12, and 63, Chapter 25), and Hempel and Oppenprediction, see Popper (62,
heim (36). * The distinction here made refers, then, exclusively to the form of the statements under consideration, and not to their truth status or to the extent to which they are
87
Carl G.
Hempel
supported by empirical evidence. If it were established, for example, that actually only 80 per cent of all crows are black, this would not show that 'all crows are black/ or Si for short, was a statistical probability statement, but rather that it was a false statement of strictly universal form, and that The probability for a crow to be black is .8,' or S 2 for short, was a true statement of statistical form. Furthermore, to be sure, neither Si nor S 2 can ever be established conclusively they available evidence, each of them thus has can be more or less \\ell
supported by
only
or less high logical, or inductive, probability, relative to that evidence But this again does not affect at all the fact that Si is of strictly universal and S 2 of statisti-
a
more
cal
form. 5
For a fuller discussion of this point, see, for example, Nagel (55, section 7), Reichenbach (71, sections 63-67), Cramer (18, Chapter 13). 6 The explanatory and predictive use of statistical laws constitutes perhaps the most important type of inductive systematization; but the occurrence of such laws among the premises is not required by our general concept of inductive systematization And indeed, as Carnap (11, pp. 574-575) has pointed out, it is sometimes possible to make information about a predictions of an inductive character exclusively on the basis of finite set of particular cases, without the mediation of any laws whatever. For example, information to the effect that a large sample of instances of P has been examined, that all of its elements have the characteristic Q, and that a certain case x, not included in the sample, is an instance of P, will lend high inductive support to the prediction that x, too, has the characteristic Q. Also, it is sometimes possible to base an inductive systematization on a set of piemises which include one or more strictly universal statements, but
no
statistical laws.
An
in Section 9, in the prediction based 7
example of such a systematization on the formulas (9.6)-(9.12).
will
be found
p. 188). Whether it is advisable to refer to explanations of this kind debatable: since the classical conception of causality is intimately bound up with the idea of strictly universal laws connecting cause and effect, it might be better to reserve the term 'causal explanation' for some or all of those explanatory arguments of form (1.1) in which all the laws invoked are of strictly universal form.
Mises (54,
as causal
is
8
Northrop (59, Chapters III and IV), for example, presents this distinction very suggestively; he refers to the two levels as "the natural history stage of inquiry" and "the stage of deductively formulated theory." very lucid and concise discussion of
A
the idea at hand will be found in Feigl (20) 9 In his essay on Skinner's analysis of learning (in Estes et al. (19) ), Verplanck throws an illuminating sidelight on the importance, for the observational vocabulary (the terms of the data-language, as he calls it), of high uniformity of use among different experimenters. Verplanck argues that while much of Skinner's data-language is sound in this respect, it is "contaminated" by the inclusion, in its vocabulary, of two kinds of terms that are not suited for the description of objective scientific data. The first kind includes terms "that cannot be successfully used by many others"; the second kind includes certain terms that should properly be treated as higher order .
theoretical expressions.
The non-precise and pragmatic character of the requirement of mtcrsubjcctive uniformity of use is nicely reflected Verplanck's conjecture "that if one were to work with Skinner, and read his records with him, he would find himself able to make the same discriminations as does Skinner and hence eventually give some of them at least
m
data-language status" (loc. 10
cit.,
p.
279n)
.
should be mentioned, however, that the idea of the range of application of a generalization is here used in an intuitive sense which it would be difficult to explicate.
The
It
range of application of (3.1), for example, might plausibly be held to be narrower than here indicated: it might be construed as consisting only of wooden-objectsplaced-in-water, and iron-objects-placed-m-water. On the other hand, (3.1) may be equivalently restated thus: Any object whatever has the two properties of either not
THE THEORETICIAN being wood this
S
DILEMMA
on water, and of either not being iron or sinking in water. In torm, the generalization might be said to have the largest possible range of applior floating
cation, the class of
all objects whatever. Since (3.2) was presented as a definition, it might be considered inappropriate to include it among the general laws 2, effecting the predictive transition from Oi, 3 , (X to Os. And indeed, it is quite possible to construe the concept of logical deduction as applied to ( 1 1 ) in such a way that it includes the use of any definition as an additional premise In this case, (3.3) is the only law imoked the prediction here considered. On the other hand, it is also possible to treat sentences such as (3.2), which are usually classified as purely definitional, on a par uith other statements of universal form, which are qualified as general laws. ITiis view is favored by the con11
O
O
m
when a theory conflicts \uth pertinent empirical data, it sometimes the "laws" and sometimes the "definitions" that are modified in order
sideration, for example, that is
to accommodate the evidence. Our analysis of deductive systematization is neutral with respect to this issue. rA lucid elementary discussion of the nature of axiomatized mathematical systems may be found in Cohen and Nagel (15, Chapter VI; also reprinted in Feigl and Brodbeck ( 24 ) ) For an analysis in a similar vein, w ith special emphasis on geometry, see also Hempel (30). An excellent systematic account of the axiomatic method is given in Tarski (84, Chapters VI-X); this presentation, which makes use of some concepts r
.
of elementary symbolic logic, as developed in earlier chapters, includes several simple illustrations from mathematics. careful logical study of deductive systems in em-
A
pineal science, with special attention to the role of theoretical terms, is carried out in the first three chapters of Braithwaite (4j, and a logically more advanced exposition of the axiomatic method, coupled with applications to biological theory, has been
given by
and (99).
especially in (98) for example, Hermes (37);
Woodger,
Walker (92); McKmsey, Sugar, and Suppes (53); Rubin and Suppes (75), and the further references given in these publications. An important pioneer work in the field is Reichenbach "See,
(52);
McKmsey and Suppes
(68). 11
See especially Woodger (98) and (99). See, for example, Hull et al. (39) For example, in von Neumann and Morgenstem (58, Chapter III and Appendix). 17 Statements effecting an empirical interpretation of theoretical terms have been the methodological literature under a variety of names. For example, discussed Reichenbach, who quite early emphasized the importance of the idea with special reference to the relation between pure and physical geometry, speaks of coordmarive definitions (69, section 4, also 72, Chapter VIII); Campbell (7, Chapter VI; an excerpt from this chapter is reprinted in Feigl and Broclbeck (24)) and Ramsey (67, pp. 212-236) assume a dictionary connecting theoretical and empirical terms (See 15
.
18
m
below). Margenau (48, especially Chapter 4) speaks of rules of correspondence, and recently Carnap (14) has likewise used the general term 'correspondence rules' Northrop's epistemic correlations (59, especially Chapter VII) may be viewed as a special kind of interpretative statements. For a discussion of interpreta-
also Section 8
tion as a semantical procedure, see Carnap (10, sections 23, 24, 25), and Hutten (40, fuller discussion of interpretative statements is included especially Chapter II ) sections 6, 7, 8 of the present essay. 18 lucid and concise presentation may be found, for example, in Bergmann and .
m
A
A
Spence (3).
"Hull -10
(38, p. 284). Skinner (80, p. 35).
^Tolman, Ritchie, and Kalish (88, p. 15). See also the detailed critical analysis of Tolman's characterization of expectancy in MacCorquodale and Meehl (47, pp. 179-181).
89
Carl G. 22
Hempe]
4) and on the general problem of explicating the concept of a law of nature, see Braithwaite (4, Chapter IX); Burks (6); Carnap (14, section 9); Goodman (28); Hempel and Oppenheim (36, Part III); Reichenbach (73). 24 In his theory of reduction sentences, developed in Carnap (8). There is a reduction question, however, whether certain conditions which Carnap imposes upon sentences do not implicitly invoke causal modalities. On this point, see Hempel (34, 23
See Carnap
On
(
8, section
.
this point,
section 3). 25 And in fact, the total specification of meaning effected by the passages quoted is then summarized by the authors in their "definition" II, which has exactly the form (6.2) of a bilateral reduction sentence for 'rat x expects food at L.' (Tolman, Ritchie, and Kalish (88, p. 15).) 20 For a fuller discussion, see Carnap (8, section 7) and Camap (14, section 10).
DF
27
See Tarski (83, especially pp. 80-83) (41) and (42); Carnap (12). On this point, see especially Quine (65); Goodman (26); White (95) and (96, Part II ) The significance of the notion of analyticity in special reference to theoretical statements is critically examined, for example, in Pap (60) and (61) and in Hempel (34). Arguments in defense of concepts such as analyticity and synonjmy are advanced in the following articles, among others: Carnap (12, 13); Grice and .
^SeeKemeny 29 .
Strawson (29); Martin (49); Mates (51); Wang (94). 30 Since the reduction sentences (7.3) determine the meaning of 'Q' for those and it might n only those cases which meet at least one of the conditions Ci, C 2 be argued that (7.4) in conjunction with (7.3) inductively supports, not (7.5), but only the following hypothesis, which limits the assertion of (7.5) to the cases just .
.
.
C
,
specified:
(CaXvOxv
(7.50
and that what (7.5)
.
.
asserts
-(CaXvCsxv
(7.5")
.
D
(Qx
beyond
this,
vCjc)
.
.
.
vCnx)
D
=
Ox)
namely,
(Qx
=
Ox)
constitutes a stipulation rather than an empirical hypothesis. But this does not alter the fact that (7.5), since it implies (7. 5'), is empirical in character, and that its acceptance requires therefore inductive support.
This point is discussed more fully in Hempel (32). On the problem of "reducing" the concepts of one discipline to those of another, the following publications have important bearing: Nagel (56) and (57); Woodger (100, pp. 271ff); Kemeny and Oppenheim (43). 32 One writer who is impelled by his "philosophical conscience" to take this view 31
Goodman (see 27, Chapter I; 28, Chapter II, section 1). A similar position was taken by Russell when he insisted that physical objects should be conceived as "logical constructions" out of sense-data, and thus as definable in terms of the latter (see, is
for example, 77, 33 34 85 38
See Carnap
Chapter VIII). (
14, especially sections
9,10).
Carnap (14, section 10).
Camap
(
14, section 10).
Carnap (14, section 10). An idea which is similar in spirit, but not quite as clear in its content, has been put forward by Pap in (60) and in (61, sections 10-13 and 70 , with the claim (not made by Carnap for his argument) that it establishes the "untenability" of the "thesis of explicit definability" (of theoretical terms by means of observational ones). Pap (60, p. 8). On the other hand, Bergmann (especially in 1 and 2) holds that many concepts of theoretical physics, including "even the particle )
notions of classical physics could, in principle, be introduced by explicit definitions. This, by the way, is also true of all the concepts of scientific psychology." Bergmann (2, section 1). In the same context Bergmann mentions that the method of partial
90
THE THEORETICIAN
S
DILEMMA
interpretation seems to be necessary in order to dissolve some of the puzzles concerning quantum theory. However, this strong assertion is supported chiefly by sketches of some sample definitions. Bergmann suggests, for example, that 'This place is in an electric field' can be defined by a sentence of the form 'If Ri then R/ where Ri stands for a sentence to the effect that there is an electroscope at the place in question, and Ra stands "for the description of the behavior of the electroscope (in an electric field)." (1, pp. 98-99.) However, this kind of definition may be questioned on the basis of Carnap's arguments, which have just been considered. And in addition, even if unobjectionable, some examples cannot establish the general thesis at issue. Thus, the question remains unsettled. 37 The basic idea was outlined earlier in Hempel (33, p. 30). 38 1 am grateful to Herbert Bohnert who, in a conversation some years ago, pro-
vided the stimulus for the development of the ideas here outlined concerning the definability of functors with infinitely many permissible values. Mr. Bohnert remarked on that occasion that explicit definition of such functors in terms of an observational vocabulary should be possible along lines indicated by the Frege-Russell theory of natural 89
and of
real
numbers.
should be objected that 'cell' and 'organism' are theoretical rather than observational terms, then they may be replaced, without affecting the crux of the argument, by terms whose observational character is less controversial, such as 'marble' and If it
'bag', for 40
example.
was mistaken, therefore, when in an earlier essay I asserted that "no sentence expressible in observation terms and logical terms alone can state a sufficient condition (let alone a necessary and sufficient one) for a sentence of the form 'the length of 1
interval
i
is
r
centimeters.'"
Hempel
(35, p. 68.)
The
consideration that led
me
to
66-68) overlooked the point made above (between (7.7) and (7.8) ), namely that a sentence expressed in observational and logical terms alone may represent a necessary and sufficient condition for the truth of a given theoretical sentence without providing finite observational truth criteria for that sentence: it may be non-molecular in form. 41 The argument can readily be extended to functors taking complex numbers or this assertion (loc. cit., pp.
number of components as values. Our reasoning has relied essentially on the Frege-Russell method of defining the various kinds of numbers (integers, rational, irrational, complex numbers, etc.) in terms of the concepts of the logic of sets. For a detailed outline of the procedure, see Russell (76); fuller technical accounts may be found in many works on symbolic logic. "See Tolman (87, as reprinted in Marx, 50, p. 89); and Spence (82, p. 65n). vectors of any
"Hull (38). 44
Hull (38, p. 285).
46
Feigl (21, p. 40). 46
Braithwaite (4, Chapter III) See the essay "Theories" (1929) in Braithwaite (4, p. 76). .
47
48
Ramsey (67).
40
This point is also made in Carnap (8, section 7) in a discussion of the advantages of reduction sentences over definitions in the introduction of scientific terms. And Feigl eloquently argues in the same vein in his essay (23), in which the general principle is illustrated by various suggestive examples taken from physics and psychology. 60 Braithwaite (4, p. 76). 51 An excellent concise synopsis of various arguments in favor of invoking "hypothetical constructs" will be found in Feigl (21, pp. 38-41). Some aspects of the "semantic realism" concerning theoretical terms and sentences which Feigl presents in the same article are discussed in section 10 of the present essay. 83
This has been pointed out by
Camap
himself; see, for example, his (14)
91
.
Carl G. "See Campbell Feigl
Chapter VI). Important parts of
this
chapter are reprinted in
and Brodbeck (24).
"Campbell 85
(7,
Hempel
However,
(7, p. 122). this does not
show that there cannot
possibly be any necessary
sufficient condition in observational terms for the theoretical sentence: the
and
problem
of proving or disproving this latter claim is subject to difficulties analogous to those discussed in section 7 in regard to definability. M The intuitive notion of in interpretation, as well as the conception reflected Campbell's idea of an interpretative dictionary, would seem to call for the following
V
T as additional condition: (v) Each sentence of J contains essentially terms from well as terms from VB. However, this requirement introduces no further restriction of the of interpretative system; for any system J that meets conditions (i) to
concept can be stated in an equivalent form that satisfies (v) as well. To this end, it suffices to replace the member sentences of J by their conjunction; this yields a logi(iv)
cally equivalent interpretative satisfies 57 68
system which contains only one sentence, and which
(v) since } satisfies (iv).
Campbell (71, p. 43). Here, and on some subsequent occasions where there
is
no danger of misunder-
'H == O', for standings, logical connectives are used autonymously; the expression example, represents the sentence obtained by placing the triple-bar symbol (for 'if and only if) between the sentences of which 'H' and *O' are names. w Craig's paper (16) contains the first published account of this interesting theo-
A
less condensed and less technical presentation, with explicit though bnef references to applications such as the one here considered, is given in Craig (17) In application to the issue we are discussing, the result obtained by Craig may be ' T of primitive terms of T' and the set of briefly stated as follows: Let the set postulates of T' be specified effectively, i.e., in a manner allowing anyone, given any
rem.
.
V
a primitive expression, to decide in a finite number of steps whether the expression is term (or postulate) of T'. Let VT' be divided, by an effective criterion that may
V
otherwise be chosen at will, into two mutually exclusive vocabularies, VT and B Finally, let the rules of the logic used be such that there is an effective method of determining, for any given finite sequence of expressions, whether it is a valid deduc.
tion according to those rules. Then there exists a general method (i.e., a method applicable in all cases meeting the conditions just outlined) of effectively constructing (i.e., characterizing the postulates and the rules of inference of) a new system T'B whose set of primitives is VB; and whose theorems are exactly those theorems of T' which contain no extralogical constants other than those contained in VB. Note that the theorem permits us to draw the dividing line between T and VB wherever we please, as long as the cntenon used to effect the division permits us to decide in a finite number of steps to which of the two sets a given term belongs.
V
This condition
V
'
T will requirement of an effective characterization of example, if T is finite, and its member terms as well as those of VB and VT are specified simply by enumerating them individually. The further requirement of an effective characterization of the postulates and the rules of logic for T' are so liberal that no doubt any scientific theory that has yet been considered can be formalized in a manner that satisfies them as long as the connections between theoretical and observational expressions can be assumed to be expressible in the form of definite statements. The only important case I am aware of in which this condition would be violated is that of a theory for which no definite rules of interpretation are specified say, on the ground that the criteria of application for theoretical expressions always have to be left somewhat vague. A conception of this kind may have been intended, for example, by A. Wald's remark "In order to apply [a scientific] theory to real phenomena, we need some rules for establishing the cor-
be
as well as the
trivially satisfied, for
V
'
92
THE THEORETICIAN S DELEMMA respondence between the idealized objects of the theoiy and those of the real world. rules will always be somewhat vague and can never form a part of the theory
These
itself/'
Wald
(91, p. 1). conditions of Craig's theorem are satisfiable, however, referred to is reflected in definite rules. Thus, for example, the
The
if
the vagueness here
interpretative sentences
for a given theory might take the form of statistical probability statements (a possimentioned in Camap (14, section 5)), or perhaps of logical probability statements (each specifying the logical probability of some theoretical sentence relative to
bility
a specified sentence in observational terms, or vice versa). Either of these procedures would yield an interpretation of a more general kind than that characterized by the
an interpretative system given in section 8 of the present essay. Yet even which are interpreted in this wider sense, Craig's theorem can be applied. 60 Craig (17, p. 49) It may be well to note briefly two further points which were established by Craig, in the studies here referred to: (i) A theory T' may have a set of V B -consequences that cannot be axiomatized by means of a finite set of postulates expressible in terms of VB (ii) There is no general method that permits an effective decision, for every theory T', as to whether its VB -consequences can, or cannot, be axiomatized by means of a finite set of postulates. * Craig (17, p. 49). This fact does not detract in the least, of course, from the importance and interest of Craig's result as a theorem in logic. ** On this method, first used by von Neumann, see Camap (9, pp. 29-30 and p. 96), where further references to the literature are given. 63 This does not preclude the possibility of effecting the transition from the five data sentences to Tb' in a purely deductive fashion by means of a suitable modificadefinition of
to theories
.
.
T
tion of T'; in fact, just the addition, to Tx Vx Ex , of the statement '(x) ( (Gx Sx) Px)' would have the desired effect. But the modified theory thus obtained is clearly stronger than T'. 7
D
84
Ramsey (67, pp. 212-215, 231). SeeTaiski(85,p.350). On this point see, for example, MacCorquodale and Meehl (46); Lindzey (45); Feigl (21), (22); Hempel (31); Rozeboom (74). *
67
It is of interest to note here that if in addition to the conditions specified in section 8, an interpreted theory were also required to meet the criteria of significance for theoretical terms and sentences that have recently been proposed by Carnap in (14,
sections 6, 7, 8), the terms and the sentences of our be ruled out as nonsignificant.
mock
"learning theory"
would
68
More precisely, the assertion that there exist entities of the various kinds (such as hypothetical objects and events and their various qualitative and quantitative properties and relations) postulated by an interpreted theory T' is expressed by the Ramseysentence associated with T'. It is obtained by replacing all theoretical constants in the conjunction of the postulates of T' by variables and binding all these by existential quantifiers placed before the resulting expression. The sentence thus obtained is a logical consequence of the postulates of T'; but the converse does not hold; hence strictly speaking, the assertion of the existence of the various hypothetical entities assumed in a theory is logically weaker than the theory itself. For suggestive observations on the question of the reality of theoretical entities, example, Toulmin (89, pp. 134-139) and Smart (81). is used here in Quine's sense, according to which a theory is ontologically committed to those entities which must be included in the domains over which its bound variables range if the theory is to be true. Quine develops and defends this idea in several of the essays comprising his book (66) 70 This conception of laws or theories as inferential principles has been suggested, on different grounds, by several authors, such as Schlick (who says that he owes the idea to Wittgenstein; see Schlick, 79, p. 151 and p. 155); Ramsey (see 67, p. 241), see, for 80
The concept
.
93
Carl G.
Hempel
Ryle (see 78, especially pp. 120-125), and Toulmin (see 89, Chapters III and IV). (Toulmin remarks, however, that to think of laws of nature as rules or licenses "rediscussion flects only a part of their nature" (Joe. cit., p. 105).) See also Braithwaite's of the issue in (4, pp. 85-87). Finally, Popper's essay .(64) contains several critical and constructive comments that bear on this issue and on some of the other questions discussed in the present study.
REFERENCES 1.
Bergmann, Gustav. "The Logic
of
Psychological Concepts,"
Philosophy of
Science, 18:95-110 (1951). 2.
"Comments on Professor Hempers 'The Concept of CogniBergmann, Gustav. " tive Significance/ Proceedings of the American Academy of Arts and Sciences,
80(No.l):78-86 (1951). Reprinted in Gustav Bergmann, The Metaphysics of Logical Positivism. New York: Longmans, Green and Co., 1954. 3. Bergmann, Gustav, and Kenneth Spence. "Operationism and Theory in Psychology," Psychological Review, 48:1-14 (1941). Reprinted in Marx (50). 4. Braithwaite, R. B. Scientific Explanation. Cambridge, England: Cambridge Univ. Press, 1953. The Logic of Modem Physics. New York: Macmillan, 1927. 5. Bridgman, P. 6. Burks, Arthur W. "The Logic of Causal Propositions," Mind, 60:363-382
W.
(1951). Campbell, Norman R. Physics: The Elements. New York: Dover, 1920. 8. Camap, Rudolf. "Testability and Meaning," Philosophy of Science, 3:420-468 (1936); 4:1-40 (1937). Reprinted as a monograph by Whitlock's Inc., New Haven, Conn., 1950. Excerpts reprinted in Feigl and Brodbeck (24). 9. Camap, Rudolf. The Logical Syntax of Language. New York and London: Humanities, 1937. 10. Camap, Rudolf. Foundations of Logic and Mathematics. Chicago: Univ. of Chicago Press, 1939. 11. Camap, Rudolf. Logical Foundations of Probability. Chicago: Univ. of Chi7.
cago Press, 1950. Camap, Rudolf. "Meaning Postulates," Philosophical Studies, 3:65-73 (1952). 13. Camap, Rudolf. "Meaning and Synonymy in Natural Languages," Philosophical Studies, 6:33-47 (19 55). 14. Camap, Rudolf. "The Methodological Character of Theoretical Concepts," in H. Feigl, and M. Scnven (eds ), The Foundations of Science and the Concepts of Psychology and Psychoanalysis, pp. 38-76. Minneapolis: Univ. of Minnesota 12.
Press, 1956.
15.
16. 17. 18.
19.
Cohen, M. R., and E. Nagel. Introduction to Logic and Scientific Method. New York: Harcourt, Brace, 1934. Craig, William. "On Axiomatizability within a System," Journal, of Symbolic Logic, 18:30-32 (1953). Craig, William. "Replacement of Auxiliary Expressions," Philosophical Review, 65:38-55 (1956). Cram6r, Harald. Mathematical Methods of Statistics. Princeton: Princeton Univ. Press, 1946. Estes, W. K., S. Koch, K. MacCorquodale, P. E. Meehl, C. G. Mueller, W. S. Schoenfeld, and W. S. Verplanck. Modern Learning Theory. New York: Appleton-Century-Crofts, 1954.
"Some Remarks on the Meaning of Scientific Explanation," (A modified version of comments first published in Psychological Review,
20. Feigl, Herbert. slightly
52(1948) 21. Feigl,
),
in Feigl and Sellars (25, pp. 510-514). "Existential Hypotheses," Philosophy
Herbert.
(1950).
94
of Science,
17:35-62
THE THEORETICIAN
S
DILEMMA
22. Feigl, Herbert. "Logical Reconstruction, Realism, and Pure Semiotic," Philosophy of Science, 17:186-195 (1950). 23. Feigl, Herbert. "Principles and Problems of Theory Construction in Psychol-
ogy," in W. Dennis (ed.), Current Trends in Psychological Theory, pp. 179213. Pittsburgh: Univ. of Pittsburgh Press, 1951.' 24. Feigl, Herbert, and May Brodbeck (eds.). Readings in the Philosophy of Science. New York: Appleton-Century-Crofts, 1953.
and Wilfrid Sellars (eds.). Readings in Philosophical Analysis. York: Appleton-Century-Crofts, 1949. 26. Goodman, Nelson. "On Likeness of Meaning/* Analysis, 10:1-7 (1949). Re-
25. Feigl, Herbert,
New
pnnted
in a revised
form
Goodman, Nelson. The
27.
in Linsky (45). Structure of Appearance. Cambridge, Mass.: Harvard
Univ. Press, 1951. Goodman, Nelson. Fact, Fiction, and Forecast. Cambridge, Mass.: Harvard Univ. Press, 1955. 29. Gnce, H P., and P. F. Strawson. 'In Defense of a Dogma/' Philosophical Review, 65:141-158 (1956). 30. Hempel, Carl G. "Geometry and Empirical Science/* American Mathematical 28.
33.
Monthly, 52.7-17 (1945). Reprinted in Feigl and Sellars (25), in Wiener (97), and in James R. Newman (ed.), The World of Mathematics. New York: Simon and Schuster, 1956. Hempel, Carl G. "A Note on Semantic Realism," Philosophy of Science, 17: 169-173 (1950). Hempel, Carl G. "General System Theory and the Unity of Science/' Human Biology, 23:313-322 (1951). Hempel, Carl D. Fundamentals of Concept Formation in Empirical Science.
34.
Hempel, Carl G. "Implications of Camap's
31. 32.
Chicago: Univ. of Chicago Press, 1952. Science/' in P. A. Schilpp
(ed.),
Work
The Philosophy
for
the Philosophy of
of Rudolf Carnap.
New
York: Tudor (forthcoming). 35. Hempel, Carl G. "The Concept of Cognitive Significance: A Reconsideration," Proceedings of the American Academy of Arts and Sciences, 80 (No. 1):61 77 (1951). 36. Hempel, Carl G., and Paul Oppenheim. "Studies in the Logic of Explanation/' Philosophy of Science, 15:135-175 (1948). Reprinted in part in Feigl and Brodbeck (24). 37. Hermes, H. "Erne Axiomatisierung der allgememen Mechanik," Forschungen zur LogiJc und Grundlegung der exaJcten Wissenschaften. Neue Folge, Heft 3. Leipzig, 1938. 38. Hull, C. L. "The Problem of Intervening Variables in Molar Behavior Theory," in Marx (50). Psychological Review, 50:273-291 (1943). Reprinted 39. Hull, C. L., C. I. Hovland, R. T. Ross, M. Hall, D. T. Perkins, and F. B. Fitch. Mathematico-Deductive Theory of Rote Learning. New Haven: Yale Univ. Press, 1940. 40. Hutten, Ernest H. The Language of Modern Physics: An Introduction to the Philosophv of Science. London and New York: Macmillan, 1956. 41 Kemeny, John G. Review of Camap, Logical Foundations of Probability. Jour-
42
"
nal of Symbolic Logic, 16:205-207 (1951). Kemeny, John G. "Extension of the Methods of Inductive Logic," Philosophical Studies,
43.
3:38-42 (1952).
Kemeny, John G., and Paul Oppenheim. "On Reduction/' Philosophical
Studies, 7-6-19 (1956). 44. Lindzey, Gardner. "Hypothetical Constructs, Conventional Constructs, and the Use of Physiological Data in Psychological Theory," Psychiatry, 16:27-33
(1953).
95
Carl G.
Hempel
45. Linsky, Leonard (ed.). Semantics and the Philosophy of Language. Urbana, 111.: Univ. of Illinois Press, 1952. 46. MacCorquodale, K., and P. Meehl. ''On a Distinction between Hypothetical Constructs and Intervening Variables/' Psychological Review, 55-95-107 (1948). in Marx (50) Reprinted Feigl and Brodbeck (24) and, with omissions, 47. MacCorquodale, K., and P. Meehl. "Edward C Tolman," in Estes et al (19),
m
pp. 177-266. 48. Margenau, Henry The Nature of Physical Reality. New York: McGra\vHill Book Co., 1950/ " 49. Martin, R. M. "On 'Analytic/ Philosophical Studies, 3:42-47 (1952). 50. Marx, Melvin H. (ed.). Psychological Theory. New York. Macmillan, 1951. 51. Mates, Benson. "Analytic Sentences/' Philosophical Review, 60 525-534 (1951). Foundations of 52. McKinsey, f C. C., A. Sugar, and P. Suppes "Axiomatic Classical Particle Mechanics/' Journal of Rational Mechanics and Analysis,
C
.
53.
2:253-272 (1953). McKinsey, J. C. C., and P. Suppes. "Transformations of Systems of Classical Particle Mechanics," Journal of Rational Mechanics and Analysis, 2-273289 (1953).
von. Positivism: A Study in Human Understanding. Cambridge, Mass.: Harvard Univ. Press, 1951 55. Nagel, Ernest. Principles of the Theory of Probability. Chicago: Univ of Chicago Press, 1939. Robert the Natural Sciences/' 56. Nagel, Ernest. "The Meaning of Reduction C. Stauffer (ed.), Science and Civilization. Madison, Wis.: Univ. of Wisconsin Wiener (97). Press, 1949. Reprinted 54. Mises, R.
m
m
m
Nagel, Ernest. "Mechanistic Explanation and Orgamsmic Biology," Philosophv and Phenomenological Research. 11-327-338 (1951). 58. Neumann, John von, and Oskar Morgenstern. Theorv of Games and Economic Behavior, 2d ed. Princeton- Princeton Univ Press, 1947 59. Northrop, F. S. C. The Logic of the Sciences and the Humanities. New York: Macmillan, 1947. 60. Pap, Arthur. "Reduction Sentences and Open Concepts," Methodos, 5-3-28
57
(1953). 61. Pap, Arthur Analvhsche Erkenntnistheone Wien. } Springer, 1955. 62. Popper, KarL LogiJc der Forschung. Wien- J Springer, 1935. G. Routledge 63. Popper, Karl The Open Society and its Enemies London
&
Sons, 1945.
H
64
D Lewis Popper, Karl. 'Three Views Concerning Human Knowledge," in (ed ), Contemporary British Philosophv: Personal Statements New York- Macmillan, 1956.
65
W. V. "Two Dogmas of Empiricism," Philosophical Review, 60:20-43 (1951). Reprinted in Qume (66). Ouine, W. V. From a Logical Point of View. Cambridge, Mass.: Harvard Univ. Press, 1953. Ramsey, Frank Plumpton. The Foundations of Mathematics and other Logical Essays. London and New York: Humanities, 1931. Reichenbach, Hans. AxiomatiJc der relativistischen Raum-Zeit-Lehre. Braunschweig: F Vieweg & Sohn, 1924. de Gruyter Reichenbach, Hans. Philosophic der Raum-Zeit-Lehre. Berlin. & Co., 1928. Reichenbach, Hans. Philosophic Foundations of Quantum Mechanics. Berkeley and Los Angeles: Univ. of California Press, 1944 Reichenbach, Hans. The Theory of Probability. Berkeley: Univ. of California Press, 1949.
66. 67.
68. 69.
70 71.
Qume,
W
96
THE THEORETICIAN
S
DILEMMA
72. Reichenbach, Hans. The Rise of Scientific Philosophy. Berkeley geles- Univ of California Press, 1951.
and Los An-
and Admissible Operations. AmNorth Holland Pub. Co 1954. 74 Rozeboom, William \V. "Mediation Variables in Scientific Theory/' Psy chological Review, 63 249-264 (1956). 75 Rubin, H., and P. Suppes. Transformations of System of Relativistic Particle Mechanics Technical Report No. 2. Prepared under contract for Office of 73. Reichenbach, Hans. iVomological Statements
sterdam
76 77
,
Naval Research Stanford University, Stanford, 1953 Introduction to Mathematical Philosophy. London and New York Macmillan, 1919. Russell, Bertrand. Mysticism and Logic. New York: W. Norton & Co., Russell, Bertrand
W
1929. 78. Ryle, Gilbert. The Concept of Mind. 79. Schhck, M. "Die Kausahtaet in der
80 81
London: Hutchmson's Univ. Libr., 1949. Die Nattirwfssen-
gegen\\aertigen Physik,"
schaften, 19:145-162 (1931). Skinner, B F. Science and Human Behavior New York: Macmillan, 1953 "The Reality of Theoretical Entities/' Australasian Journal of Smart, J. J.
C
Philosophy, 34:1-12 (1956) 82 Spence, Kenneth W. "The Nature of Theory Construction in Contemporary Psychology," Psychological Review, 51:47-68 (1944). Reprinted in Marx (50)'. 83. Tarski, Alfred. "Emge methodologische Untersuchungen uber die Definierbarkeit der Begnffe/' Erkenntms 5 80-100 (1935). English translation in Tarski (86). 84. Tarski, Alfred. Introduction to Logic and to the Methodology of Deductive Sciences. New York: Oxford University Press, 1941.
85
Tarski, Alfred "The Semantic Conception of Truth," Philosophy and Phenomenological Research. 4341-375 (1944) Repnnted in Feigl and Sellars
(25) and in Lmsky (45). 86. Tarski, Alfred. Logic, Semantics, ford- The Clarendon Press, 1956.
Metamathematics Tr by
J.
H. Woodger. Ox-
E C. "Operational Behaviorism and Current Trends in Psychology," Proceedings of the 25th Anniversary' Celebration of the Inauguration of Graduate Study, Los Angeles, 1936, pp. 89-103 Reprinted in Marx (50). 88. Tolman, E. C., B. F. Ritchie, and D. Kalish. "Studies in Spatial Learning. I. Orientation and the Short-Cut," Journal of Experimental Psychology, 36-
87.
Tolman,
89.
Toulmin, Stephen. The Philosophy of Science. London: Hutchmson's Univ.
13-24(1946). Libr., 1953.
Verplanck, W. S "Burrhus F. Skinner," in Estes et al. (19), pp. 267-316. Wald, A. On the Principles of Statistical Inference. Notre Dame: Univ. of Notre Dame Press, 1942. 92 Walker, A. G. "Foundations of Relativity: Parts I and II," Proceedings of the Royal Society of Edinburgh, 62 319-335' (1943-1949). 93. Walsh, W. H. An Introduction to Philosophy of History. London: Hutchmson's Univ. Libr., 1951.
90
91.
94.
Wang, Hao. "Notes on
the Analytic-Synthetic Distinction," Theoria, 21 158-
178 (1955).
White, Morton G. "The Analytic and the Synthetic. An Untenable Dualism," Hook (ed ), John Dewev: Philosopher of Science and of Freedom. New York: Dial Press, 1950. Repnnted in Linsky (45). 96. White, Morton G. Toward Reunion in Philosophy Cambridge, Mass.- Har-
95.
in S.
vard Univ. Press, 1956. 97. Wiener, Philip P. (ed.). Readings in Philosophy of Science. ner, 1953.
97
New
York- Scrib-
Carl G. 98.
H. The Axiomatic J. bridge Univ. Press, 1937.
99.
Woodger,
Woodger,
Chicago 100.
J.
Hempel
Method
H. The Technique
of
J.
Cambridge, England: Cam-
of Theory Construction. Chicago: Univ.
Press, 1939.
Woodger,
in Biology.
.
H. Biology and Language. Cambridge, England: Cambridge Univ.
Press, 1952.
98
MICHAEL SCRIVEN
Definitions, Explanations,
General Introduction.
and
Theories
The
ensuing account is not intended to be a full treatment of the topics referred to in the title. number of that have concerned recent on writers specific points logic and the 1
.
A
philosophy of science and which are related to these topics are discussed and an attempt is made to indicate how these are related. These points include a discussion of translation, rules, dispositions, theoretical concepts, correlational concepts, statistical explanation, incomplete explanations, 'bridge laws/ unobservable entities, implicit definition, etc.
But many other points would have to be dealt with, and those mentioned dealt with in more detail, in order to justify a claim of com1
pleteness.
It
is
not even supposed that the present topics are the
most important or the most controversial in any treatment of tions, explanations, and theories, nor that the treatment of these
defini-
topics
But it does represent a different approach from those which have been commonly supported. It is different in method is
of great originality.
from the approach of the
symbolic logicians whose work led
positivist
us to the major reconsideration of these topics which occurred in the earlier part of this century. And it is different in certain of its results
from the approach of the Wittgensteinian school of logicians whose
method 2.
it
shares.
Analytic Method. I shall call my interpretation of this method, the of context analysis, in order to focus attention on its comple-
method
mentarity with traditional and symbolic logic which might be called content analysis.
The
differences in approach,
patibility, arise
which in no way amount to incomin the success with which formaliza-
from the difference
1
1 have discussed many further points that arise in the analysis of one of these topics in "Explanations" (unpublished D. Phil, thesis, Oxford, 1956), especially pp 246-420; but others of equal importance I did not discuss at all.
99
Michael Scriven tion can
be employed
for these
two kinds
of analysis.
Context analysis
undertaken in the belief that the meaning of terms or concepts or if we include a logical problems can only be thoroughly understood is
meticulous examination of the circumstances in which they occur, rather
than relying on a
relatively rapidly extracted
thus stated has two important
formalization of their
The
context analyst's viewpoint as corollaries. First, it regards the rigor of
apparent internal logical features.
symbolic logic as partly spurious; for the problems of analysis with which we are faced concern already existing concepts and problems, and experi-
ence makes very clear that these are not governed by rigorous rules and definitions. This is not to deny that within symbolic logic, taken as a
branch of mathematics, the highest standards of rigor obtain; it is only to assert that this rigor is not the same thing as rigor in the analysis of
an ordinary
logical problem. views the utility of symbolic logic as partly illusory; the chief claim for symbolic logic that it provides a means of avoiding as
Second,
it
well as solving problems a language can in general of
it
is
held to rest on the mistaken belief that
be rich enough to perform the tasks required without containing the traps which produce the confusion or
puzzlement. Nevertheless, context analysis is frequently facilitated by limited formalization and in certain cases, for example, proof theory and dimension theory, regards a highly formal analysis as the best means for success.
such
But
common
it
should be noted that the latter cases do not include
topics as those
mentioned
in the title or introduction
or at the most refer to special instances of them. The context analyst employs a different tool; instead of formalization, he
to this paper
uses comparison.
The purpose
of these comparisons
is
to elicit the less
apparent significance of the concept (etc.) which is under analysis. It is thought that the process of exhaustive comparison with cases where the meaning of the concepts is clear is the best way of discovering the function of the expression (s) being considered. The function is not
the meaning but is a guide to the meaning just as the manifest form is not itself the meaning but is a guide to the meaning. So the
itself
two approaches could
and formal
alternatively
be described
as functional analysis
2
analysis.
a
The importance of context is a central theme of P. F. Strawson's Introduction to Logical Theoiy, especially pp. 187, 213-217. London: Methuen, 1952. The role of comparison in philosophical method is excellently expressed by F. Waismann in 100
DEFINITIONS, EXPLANATIONS, It is as sis is
well to
largely
remember
AND THEORIES
that the context analyst's claim about analy-
an empirical one;
it is
the claim that most logical problems
3
can be solved only by reference to detailed and varied examples described with considerable care. If the logical problem is to give an analysis
of the concept of a theory, then
some thoroughness
it
will
be necessary to examine with
various aspects of various theories
their suscepti-
by observation, the extent to which they
bility to discontinuation
volve reference to unobservable entities, etc.
Now
in-
a position which can hardly be said to rest on a naive error as to the nature of logic or the infallibility of common sense; in fact it is hard to see how could be denied at
this
is
The
functional analyst, however, sees his posiby that of a formal analyst who puts up a and neat model of what he takes to be the essential simple symbolic features of a theory and argues for the reform of so as to use
it
all.
tion as implicitly rejected
language the term "theory" only for things that are represented by this model. In this the programmatic aspect of their activities the representative of the formal approach is normally called a reconstructionist. For want of a better term,
I
would describe the context
analyst's alternative as
The actual continuity of the two positions should The context analyst should indeed be entirely amen-
that of the repairist.
now be apparent. able to the formal analyst's solution if two points can be substantiated: first, that the model embodies the essential features of a theory (i.e.,
the identifying criteria), and second, that redefining the original term or introducing a new one will produce a substantial improvement. His general view will tend to be that if there are very few essential charac-
we do not need anything that could be approformal model or a revision of language; while a as described priately if there are very many^ the formal model will not be sufficiently less
teristics of a theory,
complex than the original and adoption worthwhile.4 cases
where the gains
"How
I
will
logical structure to It is
make
obvious that there
outweigh the
losses;
and
its
comprehension
may be
intermediate
in such cases the
two
See Philosophy," in H. D. Lewis (ed.), Contemporary British Philosophy, London: Allen & Unwin, 1956. which I mean such problems as giving an analysis of meaning, inference, and
pp. 445-490. 3
By
necessity. *
think the most important argument for context analysis depends on the vast of information about the meaning of a term that is implicit in a welldescribed example of its use over and above that which can be summarized in any manageable form by a definition or set of definitions. The present paper in part endeavors to illustrate the truth of this remark. I
amount
101
Michael Scriven and often do agree. It is therefore essential not to suppose an irreconcilable difference between the procedures of the two
analysts will
there
is
schools of analysis. In fact, we can readily see that when their positions are so stated that such a difference exists, one of them is actually at fault. For a
formal analyst to propose an analysis of theories which he could not
support by showing that
what we
of
be
it
refers to
and illuminates important examples as irresponsible as it would
would be
usually call "theories"
for a context analyst to insist that precisification or
enlargement of
our logical vocabulary is always superfluous. Despite the impossibility of defending either position when stated in a way that makes it sharply distinguishable from the other, there is certainly a considerable difference (even visually) teristic results
of an investigation
In fact
nearly as
it
is
common
between the charac-
by representatives of the two for context analysts
schools. 5
to regard their
method as illuminating, precise, and indeed responsible for a new revolution in philosophy, as it is for content analysts and non-analytical philosophers to regard
it as
an
insidious, corrupting, decadent, faddish,
pointless perversion of the great traditions. It is worth addthat the Minnesota Center for Philosophy of Science has found the ing interaction of the two viewpoints a source of great stimulation and sloppy,
and
hybrid vigor and has until allegiance
is
3. Definitions:
They
will all
now
always had
staff
members whose primary
to different schools.
Introduction.
be necessary.
We begin with
some
very simple points. that a definition
We may start by assuming
supposed to give the meaning of a term or terms. These terms already been in use or they may have been coined for a special purpose by the proposer of the definition. There are many ways in which the meaning of a term can be given, some of them rather strikgives or
is
may have
ingly different
generated by
from
others. Let us consider
some
of the particular types
these alternatives.
Dictionary Definitions. In a traditionally pre-eminent position there the explicit linguistic definition of a word in current use, such as the
4. is
New Collegiate Dictionary (1953). Introduced from a foreign country; extraneous; foreign
following example from Webster's exotic.
.
.
.
(4.1)
"For example, compare this paper or Strawson's paper with the one by Pap in volume or the one by Camap in the first volume of Minnesota Studies in the
this
102
DEFINITIONS, EXPLANATIONS,
How
AND THEORIES
does this give the meaning of a term?
We
who
understand
the conventions of the dictionary interpret the line of type as expressing the interchangeability, i.e., sameness of meaning, of the term
and any of the three words or phrases, separated by the semiwhich follow it. If we understand some of the latter, then by colons, "exotic"
virtue of this definition
we understand
arrangement of words (which
this
is
the term
we looked
not a sentence)
meaning of the term. There are some complications, however.
Is
this
still
up.
Hence
gives us the
a definition
if
we do not understand
the words separated by semicolons? It can perfectly well still give the meaning of "exotic" although we would not understand what that was. But this is so only if these terms, mysterious
to us, actually have meaning. If they are meaningless, this would not a be proper definition of the term "exotic", for it would not give it
any meaning. So we must distinguish between understanding a definition and deciding whether it is a definition at all; the second requires
more 5.
investigation.
Erroneous Definitions.
make
Now
could such a definition be in
error;
never be in error? Although the line of type 4.1 does not a it nevertheless in the context of the dictionarysentence, up
or could
it
expresses a claim. Similarly a string of flags may have meaning. This claim or assertion is about the meaning of "exotic", and, in the case
of the dictionary chosen, this claim
is
in error. "Exotic" does not
now
mean
"foreign" or "extraneous"; in fact the entailment holds in neither direction. Hence dictionary definitions can be in error in so far as they do not correctly represent the meaning of the terms they contain.
We
can decide whether they err only in cases where we understand both the term defined, and the terms used in the definition, or have indirect evidence about their meaning. 6 The recognition of error in a definition does not require that we be capable of giving a better definition, any Philosophy of Science. The paper by Sellars in this volume affords an excellent example of a synthesis of the two approaches. * This does not mean that whenever we understand all the terms involved we can always tell whether a dictionary definition is at fault; for there may be senses of the term given or not given about which we are ignorant. However to understand the term requires at least that we understand one sense of it (usually the main sense, and usually several other senses as is certainly the case with, e.g. "but"), so when we understand all the terms in a definition we can sometimes say that it is definitely incorrect, sometimes that it is definitely incomplete, and in the remaining cases that it is
correct with respect to the senses
it
does discuss.
103
Michael Scriven
more than the on one's to
do
so.
ability to recognize one's
ability to describe
The
from the
him
ability to use a
dog in a canine lineup depends which would enable another
in terms
term correctly
ability to correctly formulate
its
is
so enormously different
use that the context analyst
(which we know how to identify if we know how to speak the language) whenever a great deal hinges on the meaning of a word. It would be unfair to criticize the definition quoted by pointing out
always
relies
on the
that "extraneous"
the
literal
is
meaning
understood, do
erly lent,
first
not (and probably never was) synonymous with
of ''foreign". For the dictionary conventions, propnot imply that the alternatives are exactly equiva-
but rather that in certain contexts each will be a near-synonym for
and these contexts may
the term defined tive reader picks
up some
of the flavor
The perceprefinements of
differ slightly.
of the term
its
Of course, unless the meaning by studying the range of its synonyms. contexts are specified in which each substitution is permissible, the definition will not
be
and
fully adequate;
it
is
chiefly for this reason
that the Oxford English Dictionary runs to eleven volumes it actually of the terms by means of quotations, gives contexts for the different uses i.e.,
by giving examples of the proper
use.
Encyclopedias. There is clearly a certain vagueness about dictionary definitions, and indeed there are very marked differences between those proposed in one dictionary and those proposed 6. Dictionaries versus
another dictionary, so one cannot place very much reliance on every definition in every dictionary; a considerable amount of research beyond the dictionaries is often required in order to obtain even a limited in
of understanding of the meaning of a term. Conversely, a good deal is not a which information is contained in strictly part of dictionary the meaning of terms at all, e.g., the family relationships of biblical figures
And
and the
there
is
fact that mistletoe
clearly great difficulty
is
the state
emblem
of
Oklahoma.
about drawing a line between
formation about a defined class and the definition of that
class.
in-
Is it
part of the definition of "Iroquois" that this Indian confederacy was centered in New York State or that it admitted the Tuscarora in 1722?
as
m
Webster, but such facts can't all be dismissed irrelevant to a proper definition, because the distinguishing part of
These
facts are given
definition consists only of such facts.
that the term
is
Of
course,
we might conclude
not definable other than as "an Indian tribe"; yet some104
DEFINITIONS, EXPLANATIONS,
one who reads the
'definition' in
Webster
AND THEORIES will actually
be
in nearly as
he understands the meaning good anyone of the term. Moreover, a confederacy with different members, admitted at different times, centered in Oklahoma rather than New York would a position as
else to say that
not be the Iroquois at all, but the so-called Five Civilized Tribes; so such facts are not wholly independent of the meaning of the term "Iroquois". One doesn't have to know some Iroquois by sight in order to use their tribe's
vidual's
name
properly;
and the same
is
true of any indi-
name.
7. Definitions
as Substitution Rules.
Now
the usual decision pro-
cedure advocated in logic textbooks amounts to taking definitions as giving substitution rules (elimination rules); in deciding whether the property P is part of the definition of the term X, one asks "Could there be any meaning in the description of something as 'an that isn't P7" If the answer is "Yes," then P cannot be part of the defini-
X
tion of
X
since
the description would be self-contradictory. Un-
if it is,
fortunately, as the Iroquois
away
example shows, this approach would whittle which could possibly be part of the mean-
virtually every property
ing, leaving us
with the alternatives of saying the term has no
tory definition or that
some other
criterion
for definition
satisfac-
must be
employed. It may be thought that proper names could well be said to have no definition in the sense of a substitution rule (i.e., to have no -intralinguistic equivalent).
for
which substitution
such;
its
But "Iroquois" is not a proper name of the kind rules cannot be given, if indeed there are any
capitalization
German. To make
is
logically as
irrelevant as that of
nouns
in
a decisive point against the decision procedure of
last paragraph, however, we need only show its inapplicability to other important kinds of terms. The term "lemon" as the name of a fruit is defined by Webster as
the
"The
acid fruit of a tree (citrus limonia) related to the orange." Supis a way of identifying the tree without looking at its
pose that there fruit.
lemon
We if
can it
now
ask whether something could possibly
still
be a
grew on
quinces. Supposing taste, color, etc.
a special variety of quince tree in place of the that it is exactly the same in every respect shape,
surprised but we would surely might call it a 'quince-grown lemon'
we would indeed be
We
not deny that it was a lemon. but the justification for this kind of description 105
(cf.
'corn-fed beef)
Michael Scriven in some difference in quality of the end product which in not present, ex hypothesi. It would simply be a lemon with an odd history. Moreover, if we were able to produce them in a hydro-
usually
lies
this case
is
ponic farm from a chemical pulp
itself
organic mixture, they would surely
no
of
tree.
produce a
what we now
synthesized from a purely inbe lemons, though the fruit
by selective crossbreeding of lemon trees we could which w as in every respect except taste identical with if
Again, fruit
still
r
call a
not sweet but not
lemon, but had a curious pungent flavor of
really acid either,
the term "lemon" for
it
we would
we abandon
than
surely
its own, no more abandon
the term "grapefruit" for the
sweeter, pink-fleshed products of the lower Rio Grande Valley. Then can clearly divide and conquer any what sort of fruit is a lemon?
We
m
the same way; and concomitance of physical or genetic characteristics yet the term clearly has no distinct meaning over and above such characteristics.
most
The answer must be
of these properties,
one of these properties decision procedure
fails
that a
lemon
is
something with some or
those given by Webster, but that no individually necessary. Hence, the usual
e.g., is
again.
The
formal analyst will about this stage propose that such sloppy terms could well be smartened up by adopting an exact definition; and we could then concentrate on the important work for science, which
and prediction and control of functional analyst will raise his two crucial questions:
research into the nature of the world
is
its
future.
What
The
we adopt, and what advantages would The theme of this paper is that no exact
'exact definition' could
there really
be
in doing this?
definition could
be adopted which would exhibit
significant advantages not only for commonplace terms "lemon" but even more certainly for the crucial terms of theoreti-
over the present Vague' definitions like cal
and observational
science.
Yet
I still
wish to maintain an intensional
account of definition; my aim is to retain the notions of synonymy but to recognize their limitations.
The good
points so far
made should
lead us to
definition contains only terms each of
abandon the idea that which
nected with the term being defined. (Of course, to
deny that
some
sister".) I said at
etc.,
I
is
a
necessarily con-
do not at
definitions are like this, e.g., "sibling"
all
wish
= "brother
the beginning of this section that this idea
or
is
equivalent to regarding definitions as substitution rules. For two terms to be intersubstitutable,
it is
both necessary and 106
sufficient that
the decision
DEFINITIONS, EXPLANATIONS,
AND THEORIES
procedure we have just examined should be applicable. If the rule applies, then all the properties PI which pass the test must be present
when
X
present and vice versa. (Using the rule in reverse we ascerjointly sufficient as well as severally or the set P! occurs will necessary.) Hence any sentence where either
tain
is
whether the conditions are
X
be unchanged in meaning if the other is substituted. Conversely, if X and the set PI can be substituted for each other without loss of meanit cannot be the case that one of the PI, say P n> fails to pass the decision procedure since such a failure would have made the substitution impossible in any context where the compound description "X but " not P n occurs (this would be a self-contradiction if the set PI is sub-
ing,
stituted for
X, but
is
not a contradiction as
In consequence of these considerations,
it
stands, ex hypothesi)
we may
wish to
.
restrict
the
term "definition" to substitution rules at the expense of saying that large numbers of common words are undefinable. Before doing this
examine a few other examples of dictionary definitions. The price may turn out to be higher than we can pay, to be in fact an error strictly
let us
comparable to the idea that good definitions must capture the 'real from which all other properties could be deduced.
essence' of a concept
In both cases, as
we
shall see,
the only respectable candidates come is a poor ideal for a logical analysis
from mathematics, and mathematics of the factual sciences since
its
truths are mostly analytic
and
its cri-
teria for existence 8.
mostly conceptual. 'Undefinable' Terms. In the first place
it is
completely mistaken to
suppose that scientific vocabularies do not contain words with the systematic evasiveness of the examples considered above. Not only do the relatively undeveloped sciences such as meteorology and psychology contain innumerable words with the same logical properties, but even
the highly developed sciences such as physics exhibit them, though often in a disguised form. The commonest indication of their r.eal nature is
change in the operational criteria. Such terms as "acid" and "temperature" have certainly changed their operational meaning over
a history of
the
last
reveals
few centuries, and that
no complete
this indicates
analysis of their
what
careful study clearly
meaning can be given
in
P each
ly necessarily connected with their application in the sense explained above. However, it is quite unnecessary for us to complicate our task by dealing with such concepts over whose defini-
terms of a set
tions a
good many disputes have raged and 107
still arise.
We
shall find it
Michael Scriven easier to deal
with everyday terms and easy to
justify the application very few special properties dealt with specifically, e.g. the reference to un-
of our conclusions to scientific terms. of the latter will
be
The
observed entities.
Before coming to that stage of the argument, however, I want to lay the foundations for a constructive account of definition by examination of
some other
for the logical types of dictionary definition,
moment
continuing to use the term 'definition' in the wider sense indicated at the beginning of section 3.
Language is put together with conjunctions, prepositions, and pronouns which for the lexicographer present in part a similar and in part a different problem from that of defining nouns and adjectives. It is clear that they have meaning, and it is fairly clearas we shall see
that this
be given by an intra-linguistic contexts. This raises the problem
usually cannot
meaning
equivalent that is satisfactory for all of selecting the proper interpretation of an
lem common enough
ambiguous term, a prob-
In the definition of any grammatical "but" as a conjunction connecting coordinate elements (it is defined for
class.
grammatical categories) there are still two alternative meanings given, viz. "with this exception" and "on the contrary; yet; are unable to formulate a single substitution notwithstanding." in eleven other
We
rule
which takes account of
this residual ambiguity; for the rule can-
not be a satisfactory substitution rule if it includes both (since they are different in meaning), and it cannot be adequate if it leaves out
We
either. can only formulate two rules and select one rather than the other depending on the context. And we cannot do that unless we understand the context so well that we can make some quite subtle discriminations. Not only can no single rule be given here, as is the
ambiguous terms, but the actual rule given is not an exact substitution rule. Webster gives as an example of the first use the case with all
all
but he had fled" and one cannot substitute "with
this exception" for
"but" in this context and retain the grammatical
phrase "whence
proprieties. (In this context "except"
produces nonsense.) This incompleteness
is
would do, but in others "except"
not accidental or the result of inefficiency but
typical of the approximative process of conveying tions.
The
exact rules,
meaning by definiwhat he takes to be the ideal situation where unambiguous forms, and necessary connections are the only
formalist sees
108
DEFINITIONS, EXPLANATIONS,
AND THEORIES
ones allowed, and hastens to reform language in that direction; the functionalist hesitates pending further consideration, dubious whether
such a pervasive feature can be legislated out of existence, suspicious that if the new language was used to do the tasks for which language is required it might immediately acquire these features. If so, there has been no gain in redefining terms and a great loss of time and energy. It may be better to recognize from the beginning that there are certain
limits of precision
usually cannot go.
beyond which
We
definitions in
shall argue that
the same
an applied language is
true of laws
and
explanations in science.
The
reconstructionist might concede the possibility of such a situaone does not progress by sitting still in the face of
tion but argue that
the possibility that we are incapable of movement. But the repairist has Not only has the reconstructionist been trying for many decades
a reply.
to produce definitions and rules which will eliminate our difficulties, without he argues any noticeable success (the pragmatic counterargument), but there are some strong reasons for suspecting that success
impossible and not merely frustrated by apathy (the logical counterargument) These reasons arise from a consideration of the function is
.
of language.
We
may
T expect, the functionalist argues, that a noun, X,
used to refer to something, PI, which always in fact occurs together with P 2 will soon come to be applied upon the appearance of P 2 in the expectation that PI will also be present. In the course of time we ,
discover that P 2 is one of a family of predicates which provides a than does PI'S family. Eventubetter basis for classifying things like X. Or we may never ally, we shall adopt P 2 as the primary meaning of
may
X
quite decide. In either event there will be a long intermediate stage meant PI during which it would be quite incorrect to assert that
X
Yet during that time the term X is no less useful or less comprehensible than before. Hence the substitution type of definition would hardly apply at all to what may be a
alone or that
it
meant P2
alone.
apply only when we can categorithe accidental properties of X. cally distinguish the essential from To this the formalist's standard reply is that we must distinguish the central scientific term, since
it
will
context of discovery from the context of justification and analysis. Imthe rough-and-ready needs of the frontier precise terms may suffice for 7
The symbols
are here
well as words, since there
and on some other occasions used no danger of confusion.
is
109
as
names
of
words
as
Michael Scriven
when we wish to say what we have discovered as opposed what we have defined, then we must be able to distinguish definitions from empirical statements. The functionalist counters by saying that it
of research; but to
dubious whether anyone except the historian, i.e., the student of the context of discovery, needs to be able to distinguish discovery from definition to the degree of precision which the formalist is seeking; and
is
what we know and what evidence we have for it, and also to explain what terms mean ('define' them, in the usual sense) without having to make any but the most elementary disfor the rest, it
tinctions
P/s.
quite easy to say
is
between necessarily-connected Pi's and empirically-connected to assert that conservative physicist would not permit one
Thus the
systems were discovered to obey the conservation laws or that canal rays were defined as having a positive charge. But he does not have to answer the question whether it's a matter of fact or definition that neon has
the atomic weight 20.2; the relative unimportance of this question is a central tenet of this paper. One's logical reflexes make one fight against this conclusion.
But
if
the distinction
is
an
artificial
one,
why
should
one suppose that answers are not also artificial, i.e., do not reflect a real difference? I think the answer must be "The distinction does not apply here": there are truths by definition and empirical truths and there are also truths that are a compound like "Men are less than 120 feet
So the functionalist argues that there is a certain class of examples where a predicate can be said to be part of the meaning of a term and yet can also be said to tell us something empirical when it is applied tall/'
to the term.
ing
how
And
the more one reflects on the difference between know-
and knowing how to formulate
to use a language
its
rules cor-
rectly (or identify correct formulations of its rules), the more odd it would Seem to insist that there must be a yes-or-no answer to the ques-
tion "Is 'X
is
P' true
by
definition?"
Compare
"Is
it
a matter of con-
vention (rather than free choice) that the clan gathers every Easter?" and "Is it by rational consideration (rather than unreasoning acceptance) that a
Communist adopts
the
This, then, would be the
Moscow
of the noun-adjective type of term. called connectives,
i.e.,
line'?"
functionalist position argued
words
The
on the
basis
particular interest of the so-
like "but", "and", "or",
and "therefore",
throughout a language; regardless of the boundaries between theory and observation, between scientific terms and the terms of everyday speech. do not have a scientific definilies
in their pervasiveness
We
110
DEFINITIONS, EXPLANATIONS, tion of "but", as opposed to
AND THEORIES
an ordinary definition of
it.
Moreover, the
and argument depends almost entirely on these terms the content analyst would say entirely. What we talk about varies from the laboratory to the kitchen, but what follows from what we say
structure of assertion
is
dependent almost
solely
on the
location
and meaning
of the connec-
our statements. Inference, proof, and argument, then, in science in common experience depend on these words. This should suggest
tives in
as
discovered to the precision with which these terms can be defined have little if any practical effect on the preto us that the limitations
we
cision of descriptions arid proofs involving
them.
It is a
misunderstand-
attainment depends clarity to suppose their the possibility of formulating exact substitution rules for the terms Indeed it is not clear that these goals would even be ren-
ing of linguistic accuracy
on
and
employed. dered easier of general attainment were such rules available, because the the language (here it would price of such rules is a loss in the utility of a loss in the range of applicability of the connective) Notice that a similar argument does not apply to quantitatively vague terms: one cannot achieve certain kinds of linguistic precision without
be
.
of "many", using non-vague terms such as numerical predicates instead of indeterkinds all that conclusion "large", "'heavy", etc. The natural
minateness are handicaps to precise expression of scientific data and because his hypotheses is that challenged by the functional analyst, study discovers the necessity
for,
and advantages
of,
certain kinds of
8
the terms "many", 'indeterminacy' of definable meaning. Of course, not are and useful are etc. wholly replaced but are immensely "large",
supplemented when
we
extend the language to include numerical predicates. With respect to certain terms, however, no such useful addition can be made according to the functional analyst because their very function cist can't
form. The physialready best served by their indeterminate use a definition of "force" which makes Newton's first law
is
of motion
simply one either;
any
negative. 8
because it isn't simply definitional or simply empirical mean that it's a queer mixture, more than the number is a queer mixture of positive and
9
or the other. This doesn't
One
could say
it's
positive because
it's
not negative and vice
is a reflection of indeterminacy vagueness; for the latter to exact definition is somegeneral property of non-susceptibility as a limitation of the procedures of definition best else, regarded in^a perhaps thing follow there is an associated vague concept, e.g., "but". given language; it does not 8 constant velocity with moves no forces under body
Not
the same
of the concept.
as actual
The
A
in
Michael Scriven but
versa,
this
a property in
is
needless paradox.
only a
It is
little
better to say
has
common
with positive numbers and a property in common with negative numbers. So one could say that the first law is definitional because it could very properly be included in or entailed by an
adequate explanation of the meaning of the term "force", and it is 10 in a Galilean world (where the empirical because it would be false motion of particles under no forces is ultimately circular). But "being definitional"
and "being empirical" are uneasy bedfellows no
"positive" and "negative"; one should rather admit they
less
than
are not true
contradictories. 9.
They
Now the definitions we have so far from the dictionary exhibit at least one common logical feature. provide words that, precisely or imprecisely, necessarily or emtell us about the meaning of a term by providing alternative
Inter-categorical Definitions.
solicited all
pirically,
words that would not be completely out of place if substituted for the term definedthough we might have to do a little grammatical trim-
ming If
as in the case
where "but" was defined
they have not been exact substitution
possible substitution rules,
i.e.,
as
"with
this exception".
they were nevertheless they offered a translation in the same rules,
grammatical category as the original. I wish now to mention some strikingly different cases. Taking another connective of an even more fundamental nature, we find that "and" is
Webster in the following terms: "a particle expressing the of connection or addition, used to relation general conjoin word with defined by
word, phrase with phrase, clause with clause." Now this is a grammatical account of the role of the word, not a possible substitute for it. It does not appear to express an equivalence which have enabled us to
first
it tells
us
might employ the term when we learned the language as a native, something about the word from the viewpoint of the gram-
marian.
It does this partly because there is no alternative. One can produce synonyms for "but" if one is prepared to separate out enough contexts. "And" is too fundamental. So Webster abandons the search for
synonyms completely and instead talks about function. two things about this definition. First, it seems
I
want
to say
remotely possible that
there are circumstances in which
it
standing of the meaning of a term, 10
This
is
would e.g.,
give
someone complete under-
a foreigner with an understand-
something of an oversimplification since there are some possible though from the mentioned disproof.
unlikely escapes
112
DEFINITIONS, EXPLANATIONS,
AND THEORIES 7
ing of the grammatical vocabulary and the terms "with", "of , "or", etc. which occur in the definition. Second, there are clearly better ways of
explaining the
meaning of the term than this, e.g. in the context of a questions and answers about the properties of a single object where one can conjoin the answers into one statement and indicate series of
the equivalence of this statement to the set of separate answers. (This is neither a standard case of ostensive definition nor of contextual defini-
tionif
it
were the ktter,
which contains many such
it
would
certainly occur in the dictionary,
cases.)
The
Definition of "Definition". Again we must decide whether to draw the line at calling this a definition or not. Webster would allow 10.
it
not only in practice but in theory ("a formulation of the meaning
or meanings of a word;
as,
dictionary definitions") unless
we
object to
the term "meaning" in the same way. But his product contains many examples which make his own definition too narrow, e.g. definitions of phrases such as "definite article" (the adjacent entry to "definition"), and translations of sentences in foreign languages, e.g., "Le roi est mort, vive le roi." The formalists are well behind us by this time, and only
Robinsonwith an
Richard
occasional disciple
is
objections to a restriction of the term "definition"
the above definition of "and" are, to repeat, that is
indefinable,
out in front, 11
we must then
say "and"
which makes rather mysterious the fact that it what it means, and that no more restrictive
easy to explain
appears to hold
up under
careful scrutiny
The
which would exclude
perfect
synonymy
is
quite
analysis
in natural
languages being virtually imaginary. The objection to the wider interpretation offered by Robinson is that a flash of (telepathic or other) inthe sight is an odd-looking definition. But there is a way of meeting objections to a narrower view of definition.
We
examine with care
the difference between indefinability and incomprehensibility, taking "indefinable" to mean simply "such that no explicit definition of it
can be formulated" rather than "such that no explanation of its meanin ing can be given". Then we abandon the ideal of exact synonymy favor of the realistic, fully satisfactory concept of practical or conditional synonymy (discussed at length later in this paper). (This is perfectly
u
".
.
.
any process, whether verbal or otherwise, by which any individual, whether
God or angel or man or beast, brings any individual, whether know the meaning of any elementary symbol, whether a word tion, p. 27. Oxford: The Clarendon Press, 1950. 113
himself or another, to or other
.
.
." Defini-
Michael Scriven compatible with the rejection of some definitions of a given term as inferior to others on the grounds that they are less adequate formulations of intralinguistic equivalents, If
we adopt
i.e.
synonymous terms.) which a definition expresses conditions and with a workable
this position, according to
a substitution possibility under certain
degree of accuracy,
it
appears that
we would
still
be able to
reject the
have said above, "a particle expressing the general relation of connection or addition, etc." cannot be used as a substitute for "and", any more than "a noun made proffered 'definition' of "and".
up of the
three letters
substitute for "ink".
T
The
V
For
and
surely, as I
Tc'
in that order" can
be used
clues in a crossword puzzle are
as a
not always
synonyms for the missing words though they are usually unambiguous but obscurereferences to them. Similarly there are many ways in which we can unambiguously and not obscurely convey the meaning of a term to someone other than by giving a synonymous term or conjunction of terms. definition of
We
might add to this reason for differentiating Webster's "and" from his definition of most common nouns, the
further reason that the latter alone can
be regarded
as reflecting the
meaning the terms originally have for us. The definition of a term, it might be said, is the one which serves correctly to introduce it to the language-user previously unfamiliar with it. Robinson is right in stressing the connection of definition with bringing someone to understand a word, and right in stressing that definition refers only to elementary terms. 12
We
do not
talk of the definition of a sentence.
a definition has a preferred status
among
But
it
also
seems that
possible explanations of
mean-
ing which in part depends on its role as the proper formulation of the meaning of the term for the language-learner. A particular language has a structure of a particular kind according to about the meaning of terms are definitions
which some expressions and some are not, even
all could be used for bringing someone to know the of a term. in a natural meaning Certainly, language there are usually several slightly different formulas which are all acceptable as expressing
though almost
'the' definition
of a given term; but they are distinguishable from the
"Robinson's elementary terms are (my interpretation) terms which contain no proper parts such that the meaning of the term as a whole can be inferred by the usual rules from the meaning of the proper parts. Thus, the term "book end" has proper parts with meaning but its own meaning could not be inferred from their meaning by the usual rules (which would give it a meaning analogous to that of "rope end").
114
DEFINITIONS, EXPLANATIONS,
AND THEORIES
other true and complete statements about the meaning which the sophisticated user of the language can produce, and these other
many
statements are such that the individual learning the language could (virtually) never extend his vocabulary by learning them. They would include such analyses as the grammatically slanted one of "and", as well as others which involve 'circularity' or more difficult terms than the
one being defined.
The implied functional (or genetic) character of definition I have here been proposing is not the same as the forma] one of requiring substitutability. It is possible for a substitution rule to fail the functional requirement in point, as 13
sibling."
Dr. Johnson's celebrated 'definition' of "net" is a case the definition of "sibling" as "male sibling or female
is
And
conversely, a functionally satisfactory definition
may
ignoring ostensive 'definition' for the moment of an example mention the 'recursive definitions' of
not be a substitution rule
we may by way number theory. 14
If this functional
condition
is
allowed,
we
see a further reason for
our disquiet about the definition of "and". Even though there are conceivable circumstances in which it might be used to introduce someone
meaning of the term, they are so queer as almost to evade description: how could someone have understood the quite sophisticated grammatical vocabulary and the meaning of "with", "or", "connection", and "addition" without understanding the word "and"? If some doubts to the
whether the functional condition is allowable, then they be may allayed by asking whether it would be perfectly satisfactory if all definitions were couched in terms more abstract and complicated than that which is being defined? Or again if they were all circular, are entertained
directly or at first or
second remove?
It
seems
clear that part of the
function of definitions is the explanation of the meaning of the terms defined, in the language as it stands; and this is not possible or is extremely difficult if they are substitution rules of a kind in which the 18
If one alters the substitution-rule requirement to an elimination-rule requirement the (and the distinction is not usually made, though its importance is here apparent) For to require eliminability is genetic condition is satisfied more or less adequately. to require that none of the defining terms be such that they could only be understood via an understanding of the defined term, i.e. it is almost the genetic condition. w See, e.g. R. L. Wilder, Introduction to the Foundations of Mathematics, p. 253. New York: Wiley, 1952. A simpler example than the one he gives would be the definition of the square of a positive integer by the two assertions (a) the square of 1 is 1; of (n 4- 1) is greater than the square of n by (2n 1). (b) the square
+
115
Michael Scriven is harder to understand than, or impossible to understand without understanding, the defined term. 11. The Misleading Analogy with Mathematical Definition; The
proffered substitute
Actual Limitations on Redefinition. Before exploring the further consequences of this analysis of definition for certain traditional beliefs
important to examine one possible objection. It might be said that an elementary understanding of formal systems reveals the possibility of defining terms in a large number of different
about definition,
it is
ways, providing that corresponding changes are made in the status (but not the statement) of other definitions and propositions. To use the example given above we may define the square of an integer in terms
and subtraction in the recursive fashion indicated; in which case we will be able to prove that the square is equal to the self-product of addition
of the integer. Or, alternatively, we may define the square as the selfproduct; in which case we can readily prove that the differences between successive squares are the successive odd numbers (the formula is based). In either case, it would be all in the set of true propositions about is no at there argued, change numbers, in which we are to believe. Hence the functional condition,
on which the recursive definition
which would the other,
is
single out
one of these
as a correct definition
and
reject
too restrictive.
But the functional condition would not have this consequence. It only requires that in a given formalization we be consistent about our descriptions of the various formulas. The ones which are used to express theorems are not usable to express definitions in the same system because one can't give proofs for definitions and one has to be able to give
them
for theorems. Mathematicians are very used to dealing
alternative formalizations
with
and the comment that we can define the
function "square of an integer" recursively as indicated does not mean that we can (in the ordinary way) assert that this is the definition of that function. It
is
not, since the accepted formalization introduces
as the self-product. But,
of arbitrariness
which
is
and here
it
the crucial point, even the degree permissible in the formalization of a deducis
not generally possible for a highly interpreted language. Essentially this is because the sentences expressing laws in one formalization which would be adopted as definitions in another are empirically tive system,
true,
is
not necessarily true
must add the
as are
most mathematical propositions. (One
qualification "most" in view of the Axiom of Choice,
116
etc.)
DEFINITIONS, EXPLANATIONS, In the
first
place, of course,
scientific extensions,
tions
hence
one cannot
AND THEORIES 'reformalize' English plus its
present structure places definite limitadefinition. Second, in spite of the limitations
on what can be a
its
on the program of formalizing Cantorian mathematics imposed by the Skolem paradox, truth-in-all-normal-interpretations remains an important criterion for judging the desirability of a mathematical axiom, it counts against an axiom for a formalization of a physical
whereas
theory (though some with this property are permissible). Hence a switch from one definition to another which was previously a law involves a risk
which does not
^generally) arise in mathematics, viz. discovery that this world is one in which the assumed interpretation does not give true statements. Since there are many cases (it would be
wrong
to say all)
where the meaning of a term
impervious to
is
new
discoveries, this indicates that such a reforaiilization involves a
change meaning. For example, the traits 'dominant' and 'autonomous' correlate very highly but to incorporate this correlation into the meanin the
ing of the terms by a 'reformalization' would because the terms have other commitments of in determining their
be a
plain error, roughly
much
meaning which require that
greater importance this
connection be
dispensable by the facts in certain circumstances. This point is elementary enough, but its significance has been ob-
scured by the long search for extensional analyses (i.e., analyses in which necessity is nothing more than truth without existing exceptions) in the positivist logical tradition, since on an extensional analysis the distinction cannot
be
Thus Hempel
is prone to saying ". the imagine theory-plus-interpretation at hand to be thrown into the form of a deductive system in which (7.5) be-
if
we
wish,
comes a
sustained.
.
.
we may then
definitional truth,
empirical statements
.
.
."
and
assumes the character of a set of
(7.3)
(p.
56,
"The
Theoretician's
Dilemma").
could be done only at the According to what I am now expense of giving the terms in (7.5) a new meaning. The remark then becomes somewhat unexciting since it then expresses the fact that we saying, this
can always adopt a
new meaning
for a given symbol.
be adopted as a definition (presumably Hempers without change of meaning) is derived from his extensional requirements for a definition, viz. a set of empirically necessary and sufficient idea that a law can
conditions for the application of a term. This is unsatisfactory accordIt is not a formally ing to both the formal and the functional criteria.
117
Michael Scriven satisfactory substitution rule since
it
makes nonsense out of many
per-
fectly sensible subjunctive statements; and it is not functionally satisfactory because it elevates any accidental but exceptionless concomitants
of a given condition or entity to the status of defining characteristics, i.e. characteristics which could be used to introduce and adequately express the meaning of the term. The further errors into which it seems to me this leads him in connection with, e.g., the hypotheses of reduci-
be considered below; for the moment, let us spell out the two simple reasons mentioned against the extensional account of defi-
bility will
nition.
Suppose
all
faculty
members
at Harvard live in a special city hous-
ing project, the Bainbridge Development. They do this by free choice, because they prefer the company of their colleagues and the rents are paid by the estate of Jonathan Bainbridge ('03); the city gave them first refusal on the space and no one else lives there. Clearly this will continue to be the case! Then this residence characteristic is an empiri-
cally necessary
and
member
sufficient condition for
at Harvard". If
the application of the term
we
regard this as a justification for in that the conditional statement, "If they increase way, defining the size of the faculty by another 850, some faculty members at Harvard "faculty
it
not be living in Bainbridge Development," (S) becomes self-contradictory. Now consider Hempers suggestion about the possibility of will
We
adopt the residence predicate as rearranging the deductive system. of member" "Harvard and we observe the empirical definitory faculty fact that all
Harvard faculty members have jobs on the teaching
at the largest private university in Massachusetts.
mathematics appears to hold in the sense that the same two
ments about the Harvard faculty are held to be
staff
The analogy with state-
true, although true for
different reasons. Is this not a perfectly satisfactory alternative
method
of defining the term? faculty member" of in the city of Camwholly independent possible housing shortages the and second formulation it makes bridge, Massachusetts, wholly It
is
not, since the
meaning of the term "Harvard
is
dependent on this. The corresponding situation cannot arise empirically or even logically in mathematics because no future contingency will falsify
the theorem which
fonnalization. It
member"
is
an
we adopt
as a definition in
essential part of the
the second
meaning of "Harvard
faculty that sentences such as S are sensible rather than nonsensical,
118
DEFINITIONS, EXPLANATIONS, that
we can
group
AND THEORIES
use the term to describe changes in the residence of the it refers, just as it is an essential part of the meaning
which
to
of "resident of the Bainbridge
Development" that
whom
it
be independent
applies. In fifty years, it may be a radioactive slum where a few dying Martians live; the term will not have altered its meaning in the literal sense, even if the associations
of the occupation of those to
may have often
is
soured for those
a literal
it
who know what for a term,
has happened. Hence there a shifting boundary beyond
meaning which only misuse and metaphor lie. Similarly, and in this case consequently, we should be doing a poor service to the language-learner were we to suggest that "Harvard faculty member" could be defined as "one who lives in the Bainbridge Dei.e.
velopment" since he would then suppose,
for example, that
when the
Bainbridge Development is wiped out by a cobalt bomb, the term no longer has any application which would simply be an error in his understanding of its meaning. An error of a different kind would result
when he claimed
to have discovered the occupational similarity
of
Harvard faculty members. It is therefore not possible to reformalize interpreted languages and theories without changing the meaning in the only useful sense of certain of the terms, a point to
which
I shall
make
further reference in
the later parts of this paper. The special features of mathematics make it a dangerous ideal for the logician concerned with the analysis of theoretical language, but we observed that it is even true in mathematics that the functional requirement applies to a given formalization.
A
Constants in Symbolic Logic. nice exof the borderland arises in connection with the definability of
12. Definitions of Logical
ample
the logical constants' in terms of each other. There is an understandable sense in which we can say that "and" (as a statement connective, only!)
is
definable in terms of "not"
p and
q: It is
and "or" according
to the rule
not the case or q
is not the case that; either p is not the case or neither p nor q are the
case.
the formal requirement (the exceptions make it poor but not an absurd definition), but one can see the improbability of supposing that it could satisfy the genetic requirement in any ordinary
This almost
satisfies
a
language used for the usual purposes. But let that point go and examine
119
Michael Scrfven the claimed possibility of defining "not" in terms of the Sheffer stroke function which we introduce according to the rule
p/q: either p or q
The
p
is
that
is
suggestion
is
we
not the
case.
use the definition
not the case: p/p.
This clearly violates the functional condition since the notion being defined is not only linguistically prior to that doing the defining in terms of feasible language training, but
is
directly involved in
hence could not conceivably be learnt from not unless
it
is
possible to acquire the apparently
This
is
it
(At
and
least,
compound notion
acquiring that of a neganot a problem of experimental psychology; for it can be
of a disjunction of negations without tion.
this definition.
first
answered by and only answered by a logical analysis which provides an account of what it would be like for someone to do this, (In formal terms this amounts to giving a model of a behavior-descriptive system
which
is
and can be shown
(1) adequate for ordinary language-using situations
(2) in
to be in question is true.) If it the point I am making would have to be modified,
which the description logically possible,
without any necessity for research into what is physically possible for the human organism.) This point is well put by Strawson in the following words:
"The
stroke-formula has an especial
charm
in that
it
illus-
with peculiar clarity the remoteness of the conception of definition within a formal system from the ordinary conception of verbal elucidatrates
tion of meaning."
15
The
actual account of definition that Strawson
16 equivalent to the straight synonym approach. It is important not to forget that even the mathematical concept of definition is tied to the functional criterion within the system; if we
adopts, however,
is
define f(xi) as g(Xi) -h(xi),
This
is
because
we
we cannot
also define g(xi)
h(xt) as f(x 4 ).
normally wish our definitions to serve as elimination
not merely substitution rules, i.e., the substitution has a particular point. The condition which ensures that this point is attainable is the rules,
functional condition, the requirement that the series of definitions should be such that the terms used in each definition are comprehen-
independently of the term being defined. The special peculiarity of defining the negation of a proposition in terms of the stroke operasible
16
M Op.
cit, p. 97.
Ibid, p. 9.
120
DEFINITIONS, EXPLANATIONS, tor
is
that
it
violates the functional condition in interpretation
in the uninterpreted calculus.
term
in
AND THEORIES but not
How can one be said to understand a When one can give its permissible
an uninterpreted calculus?
equivalences and transformations, etc. Thus, there
is nothing at all with the stroke defined an wrong using by uninterpreted operator, truth table to define the uninterpreted "~p". But one cannot define
the logical concept of negation in terms of the logical concept of double negation, in the ordinary sense of definition, because one cannot intro-
duce the
without using and understanding the former; and if one and understand it, one is operating according to some kind
latter
has to use
it
of a definition already. This might of course be something unformalizable and not a definition in the usual sense; but in the prepositional calculus
it is
in fact formalizable, e.g. in truth table form. Hence, the
definition does not serve to introduce the concept; crucially, it
cannot serve to eliminate
it.
of a definition as an elimination rule
is
and hence, more
So the mathematician's
ideal
attained only formally
(the
can be eliminated) but not semantically (the concept of monadic negation is not eliminated) This is different from the situa-
"~p"
sign
.
tion in
a calculus where we define "and"
in terms of "not"
and "or".
17 Apart from the literal weaknesses of the truth-functional formalization, semantic elimination is in this case perfectly possible, since the concept
of conjunction does not enter into the concept of negation and disjunction. I think this is a reason for preferring the axiomatization of Prin-
Mathematica or Hilbert and Ackermann to the hyper-formalized 18 performances by, e.g., Church in Introduction to Mathematical Logic,
cipia
unless systemic elegance
is
regarded as
more important than
interpret-
able logical analysis. Of course, after all the connectives have been introduced, there is no difference between the systems; but their means of introducing the connectives makes one of them a reasonable analysis of
the connectives
we use
in non-formal logic, while the other is not. To say that a definition of a term already
13. Definitions as Analyses.
in use should
be an
another way of asserting the are appraising a formal system supposed to
analysis
functional condition. If
we
is,
I think,
we regard it as a defect if they are represent the usual connectives, terms of concepts which are incomprehensible in as defined represented 17
18
Strawson, op.
cit.,
pp. 78-79.
Alonzo Church, Introduction
to
Mathematical Logic. Princeton: Princeton Univ.
Press, 1956.
121
Michael Scriven comprehension of the defined term, partly because they cannot be an analysis of what is meant by the defined term. Certainly Moore had something like this in mind when he said "we cannot define
prior to the
19 which he later elucidates by saying anything except by an analysis," that a concept has been analysed when "nobody can know that the analysandum applies to an object without knowing that the analysans
20 This applies to it."
would eliminate such
definitions as "brother"
"male sibling" and would not eliminate "sibling"
would eliminate the grammatical
it
definition of
~ "a brother or sister"; "and" and the stroke-
operator definition of "not"; but allow the definition of the statement connective "and" in terms of "not" and "or", etc. It is well not to
suppose that Moore imagines that someone who knows the analysandum can properly be applied in a certain case, thereby knows what the analysis of
ft is.
Robinson misinterprets Moore
talking of his 21 ." obvious. it,
".
.
.
in this
way and
peculiar view that analysis
He knows
criticizes
is
him
for
always easy and
someone produces it; but he has not necessarily got it in mind as the analysis. In somewhat the same way, the man who knows how to swim an eight-beat crawl knows how to coordinate his arm and leg movements in the ratio of one cycle to eight cycles; but he may not even be aware that this is what he is doing in the sense of being able to produce this fact. However, he can very readily be brought to see that this is what he knows how to do .
.
that
it
applies, if
(slow-motion in photography, etc.). 14. Definability and Reducibility. There is a type of putative definition of considerable importance closely related to the Moorean type
of analytical definition
on the one hand, and to the
intercategorical
definition, e.g., the grammatical definition of "and", on the other. This is exemplified by the definition of "(visual) light" as "electromagnetic
waves from such-and-such a frequency range", and by the definition of "thirst" as "the state of an organism, after such-and-such a period of deprivation, terns". It
know
is
which has
a tendency to emit such-and-such response patnot the case that someone using the defined term must
the defining terms apply in the same range of cases, hence not a Moorean analysis and does not satisfy the functional condition. Nor, on the other hand, would its use as a substitution rule thai!
this is
19
G. E. Moore, * P. A.
Principia Ethica, p. 10. Cambridge: Cambridge Univ. Press, 1903. The Philosophy of G. E. Moore, p. 663. New York: Tudor,
Schilpp (ed.),
1952. Quoted in Robinson. a Ibid, p. 175.
122
DEFINITIONS, EXPLANATIONS,
produce a nonsensical
The
result, so it
reductionists are those
who
AND THEORIES
not an inter-categorical definition. have supported programs which in-
is
volve 'reducing' optics and chemistry to the physics of waves, fields and particles, or psychology to the study of observable behavior, or biology to chemistry, or history and ethics to psychology, or ethics to decision theory, etc.
22
As Hempel
"one component of
this
problem is the question whether the terms of the first discipline can be defined by means of those of the latter" (this volume, p. 56). The preceding discussion should alert us to the possibility of two different interpretations of this question.
or does
it
observes,
Does
mean "can be
it
mean "can be
defined" in this
defined" in this
way
in
some
way now,
future recon-
structioning of our language? I think most discussions of reduction have been inconclusive due to a failure to specify which of these alternatives 23 If the first, we shall certainly have to abandon is under consideration.
the functional condition on definition and even
as
we shall
see
modify
the formal condition, which makes a definition possible only in a peripheral sense. If the second, then the issue becomes either trivial
way one likes or involves meaning of the redefined term different from not be too the must original meaning of the term; in which case the first alternative question must be answered. since one can always introduce a term in any
a hidden condition to the effect that the
shall assert that
I
definability less,
and
is
the reductionist
untenable, in so far as
thesis,
it
in so far as
it
involves redefinability
in so far as it involves anything else
amounts to the
involves is
point-
assertion
that there's an explanation for everything. First, then, to answer the question whether one can properly define the term to be reduced in terms of the reduction base, we notice im-
mediately that the functional condition has to be abandoned since with respect to the English language as it now stands (which is all we can consider under the first alternative), we can certainly understand "light" without in any way understanding or recognizing the correctness of an analysis in terms of "electromagnetic". There may well
be a technical usage of the term according to which it defined in terms of "electromagnetic"; but to consider that alone
be
said to
33
The
it are,
in
reduction of mathematics to logic
important part,
is
is is
another instance; but the objections to
different.
* An excellent paper, "The Meaning exception must be made of Professor Nagel's of Reduction in the Natural Sciences," reprinted in P. Wiener (ed.), Readings in York: Scribner, 1953. Philosophy of Science, pp. 531-559. New 123
Michael Scriven comparable to considering a language in which the term has been redefined in that way, i.e., amounts to considering the second alternative.
Of
course, the functional condition, although implicitly accepted
most
logicians
have seen
who
actually propose only the formal
by conditionas we
may be abandoned
a sense of definition
is
experimentally in order to see left for the reductionist.
how
strong
Unfortunately, the formal condition cannot survive either. For suppose that what we might call a temporal Doppler shift is discovered to be operating, i.e., the wave lengths of visible light are steadily changing,
but without any only that
we
effect
on the ordinary phenomena of vision. by what was previously
find ourselves able to see
as ultraviolet light according to its
(It
is
not
identified
wave length and unable to see what
was previously in the wave band of red light; the same objects at the same temperature and under the same conditions still have the same but the measured wave length of what we see as yellow light has increased quite noticeably and gives every appearance of reaching the point where it would have been called red prior to the visual appearance,
beginning of the
shift.)
Suppose also that no biological explanation
any (independent) support to the claim that our retinal have altered, and that the wave length of the sodium lines,
gives ties
changes.
Then we would have
sensitivi-
etc. also
the sort of situation which produces
fundamental changes in theoretical physics; but it would certainly not produce any change, fundamental or otherwise, in our ordinary use of the term "light". Why should it? The same things have the same colors, the same devices shed light, darkness comes at the same time, etc. Yet the proposed 'definition' of light no longer applies, i.e. the description just given is nonsensical. Hence it cannot be a substitution rule; hence, the formal criterion is violated. "Light" does not mean what the defini-
Nor is this case like the definition of "lemon" where we might be able to say that an approximately correct substitution rule has been proposed (a move which has its own serious difficultiesit will be discussed later); for there is every that the tion asserted
it
does mean.
possibility
present definition will be as far
This conclusion leaves tionist position the
mediate candidate cient conditions/
wrong
as
we
care to specify, given time.
the only possibility for saving the reducadoption of a weaker sense of definition. The im-
is
as
Hempel's
But
'set
of empirically necessary
and
suffi-
the crucial difficulty of failing to distinguish between an empirically well-confirmed correlation and what we this has
124
DEFINITIONS, EXPLANATIONS,
AND THEORIES
would now regard as a definitional connection, as a basis for definition, a point made above in terms of the description "Harvard faculty member". It eliminates forever the question, "Is this true by definition or is it a matter of fact?" a question which it is indeed mistaken to suppose can always be usefully asked or answered (see section 8 above), but equally mistaken to suppose need never be answered. as meaningless the consideration of certain hypotheses
It eliminates
and conditional
statements which are of great importance in the discussions of theoretical physics. It should be clear that if we can only support the definability aspect of
reductionism by using such a weak account of definition, then the definability thesis had better be called something else since all it now amounts to is the that the requirement original term be in the cases same as the 'reduction' of applicable it, assuming our beliefs
remain the same, and regardless of differences of meaning such
as
those between "featherless, tailless biped" and "human". that "human" can be defined in such a way is to
To suppose suppose that the
meaning of the term makes it perfectly applicable to a plucked chicken, and this is simply to display ignorance of its meaning. important to make two extensions of the above remarks. In the place, it is entirely incidental that the example chosen the defini-
It is first
We
tion of "light" happens to be of a term in ordinary language. could have equally well chosen a chemical term such as "aqua regia" or a psychological term such as "drive", and the corresponding reductions in terms of atomic physics
and neurophysiology respectively. In the second place, even in the Hempelian sense of "definable", the thesis does not hold owing to the imprecision of the terms involved. That is, no exact set of necessary and sufficient conditions in the reduction vocabulary could be specified for the important terms from the discipline which is to be reduced. It may seem odd that such a seem-
be thought
to really count against an abstract logical thesis. But the limitation is not one of careless practice; it is rather an essential feature of theoretical terms that they are not
ingly practical limitation should
reducible by definition or empirical correlation to an observation base and a fortiori not reducible to the theoretical terms of another discipline.
This point and
its
effect
on the 'deductive
ideal' for explanations will
be further examined below.
We
should
now
turn to the second alternative, that of interpreting
the definability thesis as applying to a possible, not an actual language.
125
Michael Scriven
Of
say that it can be done only at the expense of the of the applicability language. The reason is very simple; the fact that a term is introduced by means of a certain definition does not guarantee this I
want to
that the term will always be correctly defined in that way. Thus, if we construct a new language within which the usual terms of chemistry are replaced
by
their 'reduction' in terms of
atomic physics,
I
am
sug-
if the language gesting that the terms will not retain these meanings If it is so laboratories. in chemical chemists for is used as a language
used, I
am
suggesting that the terms would quickly
metamorphose
in
such a way as to reacquire their original unreduced meanings. This has nothing to do with the linguistic habits of chemists making them recalcitrant
about altering their theoretical vocabulary:
it reflects
the
logi-
cal point that the observation vocabulary and procedures of chemistry differ from those of atomic physics. Not that theoretical terms are explicitly definable in
terms of the observational vocabulary; but with-
out doubt their meaning is in part or wholly a function of their relation to the observation language. Chemists use, not bubble chambers and bevatrons, but flame tests
and litmus
solutions; psychologists use,
not
neurone probes and electroencephalographs, but T-mazes and Skinner boxes; naturalists use binoculars and counting devices rather than the electron microscope, etc.24 Naturally the reductionist believes that even the observation base of
chemistry can be described in terms of the reduction base of atomic physics. But the description is one which depends upon the correctness of atomic physics whereas the meaning of chemical terms does not in general. The example of the definition of "light", discussed at some
length above, shows the way in which a redefinition in terms of the reduction base gives new hostages to fortune in a way which greatly reduces the utility of the redefined term and the viability of theories
phrased in terms of
it.
Such a handicap
is
offset
by no apparent
gain.
The
unity of science can be exhibited in other ways; the utility of terms whose meaning is directly related to the observable phenomena is far greater than
if
some other domain must be consulted before
definite
u Of
course, there are physical chemists, neuropsychologists like Hebb, and laboratory biologists. But the existence of shades of grey does not lessen the difference between black and white. I shall in fact argue for the necessity of shades of grey below; here I argue for the necessity of black and white (differences of meaning between the
terms used by those whose observational vocabularies are different). Different semantic rules
imply different concepts.
126
DEFINITIONS, EXPLANATIONS,
AND THEORIES
proof of their applicability can be obtained. In short, the precision bought at the expense of the utility.
is
The Concept
of 'Completed Science/ The formalist at this stage is likely to resuscitate the 'context of discovery vs. context of justifica7 tion distinction; to suggest that for 'completed science' the redefinition 15.
will
be advantageous.
in a yet
To do
this
is
to interpret the definability thesis
more Utopian way. The
very notion of 'completed science' rea misunderstanding of the context of scientific research; it depends on the metaphysical supposition of a determinate list of possible questions within a given field. There is no such list. Not only are there an flects
number of logically distinguishable questions which would not in itself preclude the possibility of answering them all but there is an infinite number of possible new of and there is at least
infinite
types
question,
one type of question which permits no end to its answers. These points can even be made at the observation level. There
is
no
such thing as a 'complete description' of the contents of a laboratory. Not because there are an infinite number of atoms in the room, but
an indefinite number of things in the room 25 and an indefinite number of relations between them and always an indefinite
because there
is
number of answers to the question, "What is the Of course, in any given context we can often talk
best description?" of a complete de-
scription, e.g., for the police
files, for the public health records, for the bank's inventory, for the interior decorator, for the time-and-motion investigator, and for the biologist. In the same way we can come to
the end of a particular type of enquiry in a scientific field; and in certain cases, we can even define the field in terms of a type of enquiry rather than a type of subject matter. But physics, chemistry, astronomy, and
psychology are
fields
which are not
restricted
by the
interests of
type of enquirer, e.g., the man using only optical instruments interested in finding linear relations. So,
first,
one
and only
the idea of the 'completed science' is a myth; but second, the most of its little remaining point in
redefinability thesis seems to lose
If all the questions have been answered, then we the relation of the concepts in the sciences at both levels, already and this relation is already formalized. What virtue is there in con-
such circumstances.
know
verting these empirical relations into matters of definition? One disadvantage \yould be the impossibility of teaching the history of science 25
1
owe
this point to Stuart
Hampshire.
127
Michael Scriven without the most appalling confusion since all the terms used in the contemporary science would have meanings different from that used in history, and every conceptual problem would have to be radically and confusingly reformulated. Another would be a development of my last point: even if the science is complete, it is presumably not com-
pletely dead,
i.e.,
it is still
new
least to situations
applied,
to those
if
not to
'really
new' situations at
who confront them. In that case the come to supplant the reduction-base
criteria of application will rapidly criteria, as before,
because the theory
is still
supposed to be an account
of the original field for the worker in that field, not for the worker in the reduction-base field. One can redefine the chemical vocabulary in
terms of atomic physics, but as long as people are dealing with the kind of practical problems the applied chemist deals with, e.g. making analy-
long will the terms he uses have their meaning connected with the reactions of his samples to chemical tests, rather than ses of samples, so
to atomic physics.
Perhaps, however, one should go even further and ask whether the chemist as such might not become superfluous to the atomic physicist armed with a computer and various devices for producing beams of test
The answer
that one can hardly deny it as a logical possibility though for both theoretical and economic reasons it is highly improbable. But such an event would not save the definability thesis particles.
to this
is
of reductionism. It would merely show that the chemist's problems can be solved by means of atomic physics better than by specifically chemical techniques.
Remembering
that the chemist's problems are often
solvable with the help of a balance, a gas flame and a few dollars worth of reagents and glassware, rather than computers and beam analyzers,
one can see the economic improbability of
this occurrence.
Remember-
ing that the synthesis of organic compounds for specific purposes shows a terminable process since, for one reason, the list of signs of
no
being]
purposes comes from fields as diverse as agriculture and zoology and can always include as desiderata previously uncatalogued properties, one can see the theoretical improbability of the occurrence. There is also the sense in which the completeness of one science
16.
me in
is
impossible before
sciences are complete.
all
The Acceptable Aspects
to be
of Reductionism. Finally, there seem to to the definability thesis
two further insuperable objections
any form. In the
first
place
it is
unnecessary for the reductionist posi-
128
DEFINITIONS, EXPLANATIONS, tion
and
in the
second place
it
AND THEORIES
involves an unjustifiable assumption about
the logical form of concepts.
shall
I
beyond a few paragraphs, since
not elaborate these points here be expanded in the
their substance will
later parts of this paper.
The
reductionist position contains a certain element of truth which,
as far as I
truth
can
see,
we
does not carry over to the definability thesis. This
committed to explaining macro-phenomena in terms of micro-phenomena and thus must believe that the truths of the macrois
that
are
level
(whether observations or statements about theoretical entities) can be accounted for in micro-terms.20 The levels are not independent; they bear the relationship of explaining level to phenomena level, just as within each level there is also a distinction to be made between the
observed
phenomena and the phenomena
postulated to explain them. Chemical reactions per se are not part of the observed phenomena of atomic physics which would include, e.g., tracks on photographic plates
exposed at high altitudes but they consist in (can be described in terms of) atomic phenomena and hence must be explicable in atomic terms.
Why?
Because the atomic level
explanation of
what we accept
the periodic table.
If
is
the level to which
as basic data at the
we cannot
we
turn for an
chemical
find an account there,
we
level, e.g.,
take that
be a deficiency of the micro-theory; it may be remediable there or we may have to invoke a new micro-theory, or we may have to invoke a micro-micro-level, the nuclear level. This procedure is what the search to
amounts to, in our world, with science as it no means inconceivable that we shall have to accept by
for explanations chiefly
now
stands. It
is
limits to this procedure
we have
ics
and
already done
it is
so.
often argued that in quantum mechanoutside such areas, we
At the moment,
have the very best inductive reasons for persevering in many such cases. In others, such as the reduction of psychology to the behavior level, we
need to be very clear in what we consider the subject matter to consist; since only in one interpretation can even this form of the reductionist view be maintained. 27 28
As I understand him, Nagel (loc. cit.) does not agree with this. To say that we committed to the existence of a micro-account is by no means to say that we are not sometimes likely to find, or committed to finding non-micro-accounts. There is
are
nothing very mysterious about the former claim; it is mostly an analytic consequence of the identification of a particular level as the micro-level with respect to another. 27 See "A Study of Radical Behaviorism" in Volume I of Minnesota Studies in the Philosophy of Science.
129
Michael Scriven But the claim that the macro-facts can be given does not at
a micro-explanation involve the claim that the macro-terms can be defined
all
by micro-terms. In
fact, reflection indicates
how
unlikely this will
be
Chinese have a perfectly adequate language for ordinary the case that we can give descriptive purposes, but it is far from being in terms of the English character explicit definitions of each Chinese to an vocabulary. Certainly we can (a) often give good approximations
in general: the
(or simple contextual) definition, and (b) always explain need not eventually what the character means, in English. Even this explicit
be possible
as
between macro- and micro-languages; but supposing
which
it is
it is,
not thereby supported except in the sense in indistinguishable from the thesis that a micro-explanation
the definability thesis
is
We
have seen that in this can be given of any macro-phenomena. the of sense a matter of fact, not definability thesis is very meaning misleadingly titled. As a particular application of the above remarks, that an identity thesis
For
if it
merely
on the mind-body problem
is
asserts extensional coexistence, it
it
should be noted
a case of reduction. is
not a solution of
the mind-body problem but an assertion about the goings on in the world; whereas if it asserts an intensional identity, it runs onto the logi
noble analysis think shows, the possibility of a channel
(But Professor
cal reefs partially charted above.
in this
volume
suggests,
through the reefs.) There remains for
and
I
many people
Feigl's
the intuitive feeling that
possible to construct, in the micro-language, a concept
it
must be
which would
have the same role
as any given macro-concept, if the micro-theory is be capable of making the 'same' predictions and giving the 'same* explanations, etc. as the macro-theory. This view I shall call the isomorphism thesis, a name suggested by Paul Meehl. It seems to
going to
me
to rest
upon
a very strong assumption about the ways in which terms It is quite common in certain branches of applied
may be given meaning.
chemistry and zoology for a distinction to be made between substances on the basis of their origin or history even when this does not coincide
with any intrinsic physical differences. To take an example from gemmology, the stones known as Cape emeralds (from their origin and color) are physically identical with the hydrated calcium-aluminum silicate usually called "prehnite"
and Connecticut.
Now we
and found
in the Hautes Alpes region this distinction to mani-
would not expect 130
DEFINITIONS, EXPLANATIONS, fest itself at
the micro-level, nor would
affect the success of predictions
AND THEORIES
its failure
to
do so
in
any way about the behavior of the stone under
conditions of heating, scratching, illuminating, etc. The isomorphist might say that gemmology is partly geography or economics and that this part is not reducible. This move is dangerous since
immediately leads to the question why, e.g^ variations in the strength of gravity between Cape Province and Connecticut are not it
also questions of geography.
be defined
in terms of
What we
undertake to reduce must not
what we can achieve. But
it
might be
said,
by
the isomorphist, that his language does contain an isomorphic element for each of the terms "Cape emerald" and "prehnite", viz. the physico-
chemical description of the mineral, qualified by a geographical description of the origin. That is, he imports the geography into the microlanguage. Then what does the isomorphist position amount to? It looks very much like "If you can't beat them, hire them": it does not provide us with a further characteristic of a micro-language over and above its
explanatory ability with respect to the macro-phenomena. Certainly it is a requirement of a micro-theory that it be able to
answer the question,
"What do
X's consist of?" for every name, "X", 7 if the s figure in macro-laws,
of a macro-state or macro-entity; and
X
then their micro-equivalent must figure in formally similar laws or else we cannot be said to have correctly given the micro-equivalent of X.
But our example shows that one cannot always give a purely microaccount of some X's, e.g., when they are distinguished from Y's by something which has no micro-reduction. If these examples do not count against isomorphism, then it is no more than a reiteration of the defining condition of any micro-account, that
it
explain macro-
phenomena by
analysing macro-concepts. question naturally arising from these criticisms of the reductionprogram concerns the extent to which similar criticisms can be made
The ist
of the proposals to reduce theoretical terms to the observation vocabucriticisms can be made; but it will repay us lary. I think very similar first
to pursue
somewhat
further our study of the
many
curious ways
of defining which even the limitations of the dictionary encompass. There is a somewhat crude form of the latter program embodied in the its characteristic interpretations), operationist criterion of meaning (in to which the objections can readily be extrapolated from the above
account.
131
Michael Scriven 17. Definitions in
Terms
explicit identification
cussed in the earlier
of Linguistic Function.
The
limitations of
with synonyms as a means of definition were dispart of the paper, and it is now time to examine
some of its relatives on the other side of the family from those that abandon the formal requirement of meaning equivalence (intensional truth equivalence equivalence) in favor of the empirical requirement of intensional retain (extensional equivalence) The cases to be examined .
equivalence but abandon the explicit form; or compromise with both,
but in
way from Hempers candidates. be recalled that the definition of "but" was given
a different
It will
as a set of
synonym sets, the major divisions being according to grammatical cateillustrated by gories and the minor according to context, this being examples. erence to
The
definition of
"and" consisted primarily in a direct
ref-
used to conjoin its grammatical function, "a particle word with word, etc.", although the context where it could so serve .
by reference
indicated
is
tion.
.
.
meaning It is
."
to the
".
meaning
.
.
.
.
connection or addi-
This definition thus reverses the methods of context and
specification
employed in the definition of "but".
not hard to find further cases in which some reference to the
function of a word
involved in giving its definition. In fact the conventions of the dictionary disguise the fact that every word which is is
both a noun and an adjective or verb,
etc.,
e,g.,
"board" and "hand"
various definitions distinguished by reference to these grammatical criteria. In what sense is this a defect? It is a defect in the sense
has
its
that
it
involves
abandonment of the formal
criterion since
one
certainly
does not find the part-of-speech label in the context of the uncomprehended term. It
may not
violate the functional criterion since, even
if
the labels
not understood, the mere displaying of various alternative definitions may provide enough assistance for the reader to select the appropriate one, given the context in which the term occurs. But to give
are
several definitions
conclusion
I
want
is
hardly to give the definition of a term and the is that in many cases there is no way of
to insist on
giving the definition of a term in a particular context unless some labeling according to function is allowed. What is the definition of "board"? it depends on the context. If we know from the context what its grammatical function is, we may then be able to give the definition. Again, we may not be able to do this, because the term may still be
Well,
132
DEFINITIONS, EXPLANATIONS,
ambiguous, no matter whether case, a
it is
AND THEORIES
a verb, an adjective,
or, as in this
noun.
The
sign 1/4/57 in the top right-hand corner of a business letter be read by an American as January 4, and by an Englishman as April 1, without either having a suspicion that it is ambiguous. The context that decides will here consist in data about the nationality and will
residence of the author, the addressee, etc.
In view of such cases, why shouldn't it be allowable to use some other clues in order to identify its relevant sense, such as a reference to the type of situation of those who used the term? Certainly a dictionary does this, with its descriptions "colloquial", "slang", "geometry", "classical", "obsolete", "Old Persian", etc. These are not, as is commonly thought, merely further information of an etymological nature, though indeed for someone who already or otherwise understands the word in question, they serve this purpose. They are also aids to selecting one sense of the word from the others. Yet they could form no
part of the "definition" in the sense of
And on the text to
these devices
"synonymous terms".
they commonly do, we have to rely we are able to abstract from the meaning original conthe distinguish among remaining alternatives. So the definition
if
fail us, as
partial
gives us sets of possible translations, but only incomplete rules of selection. Nor should it be that these difficulties afflict am-
thought biguous terms. For, in the first place, it is a great problem to decide is ambiguous. Is the word "rational" (or "certain") there are important differences between
what
it
only
when
a term
ambiguous because takes to be rational/cer-
tain in different situations, e.g. observing the standards of deductive versus inductive logic? Is the word "ground" ambiguous to the extent
of having 23 different definitions as in Webster, or is the smaller number given in other dictionaries a more accurate analysis? Whereas philosophers often proliferate 'senses' of words the dictionary defines quite simply, e.g., "rational", the reverse is even more common. To some ex-
because the term "ambiguous"
tent, this
is
reference;
what senses
itself involves
some context
are distinguishable depends upon what is to count differences are significant for the current discussion.
a sense, i.e. what But there remain many cases where it is possible to argue as strongly for regarding a term as ambiguous as against it; and in such cases, it seems a little absurd always to suppose that one point of view is really
as
133
Michael Scriven and the other incorrect. ("Number" is unambiguous because means "the basic arithmetical concept"; ambiguous because it includes integers, fractions, imaginary numbers, etc.) Hence a real difficulty re-
correct, it
mains for the lexicographer with respect to terms referring to linguistic function. If he can see a difference in linguistic function he is very inclined to distinguish meanings: how could a noun and a verb have the same meaning? But couldn't a conjunction connecting co-ordinate elements have the same meaning as a conjunction introducing a sub-
And
ordinate clause?
exactly
what
is
the difference in
meaning between
"board" in "room and board" (noun use) as opposed to "You may board here" (verb use) except function? Different synonyms may be relevant because of the different function; but could one really under-
stand one meaning and not be able to understand the other? If not, the ambiguity here is unlike that between "board" meaning "plank"
and "board" meaning "group of directors". I want to suggest that distinguishing meanings (and hence defining terms) commonly involves, is
facilitated by,
and sometimes
necessitates reference to linguistic func-
tion.
In the second place, there are of a term
may
must involve
many
occasions
reference to linguistic
prefer to say the term
is
indefinable.
I
when any
definition
functionalthough we
have in mind such cases
"him", "today", "this", as well as more complex cases such Oxford English Dictionary (but not the Webster) definition of
as "here", as the
"good" in terms of not include for the
its
commendation.
role in the procedure of
moment
I
do
the other standard 'indefinables' such as
"red", "itch", "cold", etc. because they are at least further 'ideal' cases of triangles and squares.
away from
the
Now
"here" can be defined, and
but then
we
is
by Webster,
as "in this place";
word referring parwhat is present or near in place, time. ." So the linguistic function comes in at one remove. It could be avoided even then, at find "this" defined as "a demonstrative
ticularly to
.
.
the cost of complete circularity; but the dictionary is intended to serve the purpose of explaining meanings not merely providing synonyms, and
hence it
it,
like a logical system, adopts the functional criterion as far as
can.
Once more, of a
as
with the word "and",
dilemma because, unlike
we
find ourselves in something
'definitions' of "red", "cold", etc. these
definitions in terms of linguistic function are
134
(a)
complete and cor-
DEFINITIONS, EXPLANATIONS,
AND THEORIES
admittedly in odd circumstances; (c) possibly analytic; and (d) about the meaning of the words. Thus we hesitate about sayrect; (b) usable,
ing the terms are indefinable. I wish to bring out the difficulty of a decision here in order to bring out the continuity of these definitions
with 'contextual definitions' and 'implicit definitions' as well as with 'ostensive definitions/ But I think there are considerable dangers in overlooking the differences, so the fact that in this paper I use the term "definition" in all these cases is not to be regarded as evidence that I
them
take
all
to
be
essentially the same. Certainly I
wish to retain a
between "defining a term" and "explaining the meaning of and hence do not agree with Robinson's account. Since (a),
distinction
a term" (b),
and (d) have already been discussed or do not need add a few comments on (c).
discussing,
I shall
J8.
The
Function.
Analyticiry of Definitions It
would normally be
and Statements about Linguistic
said that the definition of "this" just
quoted was a metalinguistic statement, and that the dictionary slips these in among the translation rules because its conventions do not provide for a distinction between use and mention. The term to be defined occurs in heavy type and the definition may say something about it or give a synonym for it.
There is an alternative interpretation. Since the grammatical classification also occurs, along with various etymological facts, etc., it might be better to say that the material given is always about the term and that sometimes it contains other terms which the conventions entitle one to regard as jointly or separately synonymous, while at other times no such terms are given. as being asserted to be synonyms the demonstrative definition as the properties of "this" are just by it is the Hence definition. asserted by always the case that dictionary
These synonyms should be regarded
about meaning, linguistic function, supported by the extent to which other material is included; Robinson cites as examples judgments on the success of theories (definition of "phlogiston" as "the supposed cause of fire"),
definitions ar