Table Of ContentNOMIC INFERENCE
NOMIC INFERENCE
AN INTRODUCTION TO THE LOGIC OF SCIENTIFIC INQUIRY
by
SALVATOR CANNAVO
•
MARTINUS NIJHOFF / THE HAGUE 1974
For my parents
Joseph and Francesca
© 1974 by Martinus Nijhof!, The Hague, Netherlands
All rights reserved, including the right to translate or
to reproduce this book or parts thereof in any form
ISBN 978-94-015-0266-5 ISBN 978-94-015-0788-2 (eBook)
DOl 10.1007/978-94-015-0788-2
TABLE OF CONTENTS
FOREWORD . IX
I. ANALYTICAL PmLOSOPHY OF SCIENCE
A. What is the Philosophy of Science? 1
B. Methods of Analytical Philosophy . 5
C. Methods of Analytical Philosophy of Science . 12
D. The Analytical Account of Science . 19
E. Philosophical Analysis of Science and a Theory of Science 22
II. WHAT SCIENCE IS : AN INTRODUCTORY CONSIDERATION
A. Science and Non-Science 26
B. Science and Common Sense . 40
C. Some Distinguishing Features of Science 42
D. Distinctive Aspects of Control on Scientific Inferences 57
E. Empiricist Background and Significance 69
III. AMPLIA TIVE SCIENCE
(I) DISCOVERY
A. Proposal and Acceptance 73
B. Discovery: An Old Question 75
C. The Idea of a Logic of Discovery 80
D. On the Possibility of a Logic of Discovery. 82
E. Patterns of Discovery 87
F. Reasons vs. Causes 95
VI TABLE OF CONTENTS
em
ACCEPTANCE
A. Confirmation 96
B. Does Discovery Differ from Acceptance in Some
Important Logical Respect? . 104
C. Summary . 106
N. SUBSUMPTIVE SCIENCE: SYSTEMIZATION
A. A Broad Distinction: Ampliative and Subsumptive
Inference 108
B. Nomic Inferences: Introductory Background 110
C. Nomic Inferences with Singular Conclusions 114
D. Explanation, a Species of Nomic Inference 125
E. A Detour: The Causal Relation 132
F. Back to Explanation Again . 147
G. Patterns of Nomic Inference 154
H. Summary 159
V. OTHER AsPECTS OF NOMIC INFERENCE
A. Are There non-Nomic Explanations? 161
B. Functional (Teleological) Accounts 167
C. Derivations : Nomic Inferences with Nomic Conclusions l72
..
D. Probabilistic Nomic Inference 180
E. Summary . 192
VI. NOMIC STATEMENTS (I) : SCIENTIFIC LAWS
A. Introduction: Necessary Truth, Logic and Factual
Science. 195
B. Universal Laws 202
C. Statistical Laws 222
D. Summary . 232
VII. NOMIC STATEMENTS (II): THEORIES, MODELS, ANALOGY
A. Theory and Observational Laws 234
B. The Formal Structuring of Theories 238
TABLE OF CONTENTS VII
C. Models. 256
D. Formalization and Scientific Theory 271
E. Analogical Content in Theories 280
F. Recapitulation: What is a Scientific Theory? . 286
VIII. GLIMPSES BEYOND
A. Overview . 290
B. Conventionalistic Trends 291
C. Incommensurability; Non-reduction and Non-accumu-
lation of Scientific Knowledge . 299
D. Non-methodism . 302
E. The History and Philosophy of Science 316
INDEX 320
FOREWORD
Those who speak of the philosophy of science do not all have the same
sort of study in mind. For some it is speculation about the overall nature
of the world. Others take it to be basic theory of knowledge and perception.
And for still others, it is a branch of philosophical analysis focused speci
fically on science. The present book is meant to be a study falling under
this last category. Generally, such a study has two aspects: one,
methodological, dealing with the logical structure of science, the other,
substantive, dealing with scientific concepts. Our concern here is primarily
methodological; and, where discussion veers at times towards substantive
matters, this will be largely for the purpose of illustrating underlying
methodological points. It should also be added that our considerations
will be of a general sort, intended to apply to all of science with no special
concern for any particular divisions. Except in an incidental manner,
therefore, we shall give no primary attention to special problems in the
methodology of the social sciences or in the philosophy of physics or of
biology. And if we draw the larger portion of our examples from the
physical rather than from the behavioral sciences, this is done merely for
simplicity, succinctness, and similar conveniences of exposition rather than
out of specialized concern for any particular area.
It is generally convenient in methodological discussion to distinguish
two major phases of all scientific inquiry, namely: the growth of science
and the systemization of results. The growth of science provides content
and includes both the discovery and acceptance of scientific hypotheses.
Systemization invests this content with logical order. It results, so to
speak, in the finished scientific report. The major portion of our discussion
concerns systemization (Chaps. IV-VII), although some consideration is
given to scientific growth in both the early and final portions of the text
(Chaps. III and VIII).
As regards general methodological outlook, we admit, straight away, to
some heresy in at least two matters : First, we depart from the main line
x FOREWORD
of tradition by siding with the minority OpInIOn that there can be a
measure of "logic" or method in discovery, and that therefore - besides
falling under history, psychology, or sociology - the study of scientific
discovery can also make the agenda of philosophy of science.
We also depart from another tradition, this time concerning scientific
explanation. Except for a few recent dissenters, philosophers since Aristotle
have traditionally regarded explanation as central to the structure of
systemized science. Our quarrel with this tradition is that the centrality
view is wrong. We shall contend that explanation, construed as an answer
to the question, "why"?, fails to represent the structure of large and im
portant portions of modern science. We propose, therefore, to speak more
generally of subsumptive or nomic inference, and to regard explanation as
merely a species of such inferences. When this modification is granted,
explanation and prediction come out as overlapping rather than as
mutually exclusive forms of nomic inference. Moreover, on this analysis,
several mixed subsumptive patterns come to light which we take the
liberty to baptize with new hybrid labels.
Nomic inferences are the structural units of subsumptive science. They
are the logical means for the basic task of showing how given matters of
fact may be regarded as special cases of others that are more general.
The structure of nomic inference is our principal concern in Chapters IV
and V where two modes of such inference are distinguished: deductive and
probabilistic. The aim· of discussion is to trace out various patterns of
nomic inference. But the distinctions are drawn in such a manner as to
apply equally to both deductive and probabilistic nomic inferences. This
manner of exposition seems to be an advance over more usual approaches
to the subject, which tend to put great stress on the. primacy and
fundamentality of deductive sUbsumption and to neglect notable .aspects
of isomorphism with the probabilistic form. More particularized discussion
of nomic inferences relating specifically to the derivation of laws and to
probabilistic nomic inference is left to Chapter V where we also consider
two special topics pertaining to nomic inference - namely, the question of
whether there are non-nomic explanations and the status of functional or
teleological accounts. At this point, having examined the structure of
nomic inference, it seems natural to go on to a consideration of the law
like statements which serve as premises of nomic inferences.· Thus, in
Chapters VI and VII we take up the structure of laws, theories, and
related nomic forms.
Our opening chapter offers a discussion of philosophic method for the
purpose of orienting the reader to philosophy of science as an analytic
FOREWORD XI
discipline. But the reader who prefers to forgo it, may easily do so
without loss of coherence by beginning instead with Chapter II which
serves as an introduction to the main body of discussion.
Chapter VIII concludes our considerations with a brief perspectiva on
relatively recent trends in methodology, not developed in the main text.
The aim is to round off discussion with a short presentation of these
developments, along with some attempt to say how they relate to the more
traditional body of methodological opinion. As it happens, the currents
of thought which we touch on have bearing on the growth ("ampliative
phase") of science. And, though there are some implications also for
subsumptive systemization, these closing reflections represent a shift of
attention from our more central concern - a shift which, it is hoped, can
serve to enhance perspectival balance for the overall study.
It is a hard and frustrating fact of our culture that positive science - a
great product of culture - cannot be reached by most students of culture.
Nor does science readily unveil its broader delineaments to the casual
visitor even when he can read its cant. Popularized science helps little in
this respect; for, at its best, it tends to highlight factual content rather
than logical structure. Some burden of duty, therefore, may well fall on
the philosophy of science which, like any account about a precisely
formulated system of discourse, can (and in fact usually does) proceed in
language that is far less exact and artificial than that of the discourse
under study.
With considerations of this sort in mind I have presupposed, in the
main body of discussion, no special knowledge of logic or mathematics,
the discussion proceeding, therefore, with relatively little use of formal
symbolic devices. But where technical details seem desirable, they are
placed in the footnotes, so they may be easily bypassed without loss of
continuity or coherence. I hope to have done this in such a manner as to
invite the participation of the more generally oriented reader without
disinvolving the professional student of philosophy.
In the way of acknowledgments, I should express, first, my indebtedness
to the teachers, colleagues, students and friends who immeasurably
influenced the growth and direction of my interests. In particular, I must
mention Professors Sidney Hook, A. J. Ayer and Albert Hofstadter to
whom I owe my first real lessons in philosophical analysis. I also recall
with much pleasure my earlier teachers at Fine Hall and at the Palmer
Physical Laboratory. Among these, I am especially grateful to Professors
V. Bargmann and J. M. Jauch for the breadth and depth of their lectures
in mathematical physics and its foundations.
XII FOREWORD
The late R. Carnap, N. R. Hanson and H. Reichenbach, together with
Professors Carl G. Hempel, Ernest Nagel and my friends, Adolf Grtinbaum
and John Hospers, have not been formally my teachers, but my debt to
them will no doubt be obvious.
My thanks to Brooklyn College for supporting preliminary research
with a six-month, paid leave in 1968 and to the University of Southern
California for an enriching semester of specialized teaching and research
in the methodologies of the physical sciences, 1970. Finally, I wish to
thank my dear wife, Gaetana, and daughter, Francesca, without whose
help and understanding this book could not have been.
New York, 1973 S.C.
