Induction, Acceptance and Rational Belief

240 Pages·1969·13.82 MB·English

by  Marshall Swain (auth.)

INDUCTION, ACCEPTANCE, AND RATIONAL BELIEF
SYNTHESE LIBRARY
MONOGRAPHS ON EPISTEMOLOGY,
LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE,
SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE,
AND ON THE MATHEMATICAL METHODS OF
SOCIAL AND BEHAVIORAL SCIENCES
Editors:
DONALD DAVIDSON, Princeton University
J AAKKO HINTIKKA, University of Helsinki and Stanford University
GABRIEL NUCHELMANS, University of Leyden
WESLEY C. SALMON, Indiana University
INDUCTION, ACCEPTANCE,
AND RATIONAL BELIEF
Edited by
MARSHALL SWAIN
University of Pennsylvania
D. REIDEL PUBLISHING COMPANY / DORDRECHT-HOLLAND
ISBN-13: 978-94-010-3392-3 e-ISBN-13: 978-94-010-3390-9
DOl: 10.1007/978-94-0 I 0-3390-9
© 1970. D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover I st edition 1970
No part of this book may be reproduced in any form, by print, photoprint, microfilm,
or any other means, without written permission from the publisher
PREFACE
The papers collected in this volume were originally presented at a sym
posium held at the University of Pennsylvania in December of 1968.
Each of the papers has been revised in light of the discussions that took
place during this symposium. None of the papers has appeared in print
previously. The extensive bibliography that appears at the end of the
volume was originally distributed during the symposium and was revised
on the basis of many helpful suggestions made by those who participated.
The symposium was made possible by a grant from The National
Science Foundation and funds contributed by the Philosophy Depart
ment of the University of Pennsylvania. On behalf of the contributors to
this volume, I would like to express my thanks to these organizations for
their generous support.
In addition, I would like to express my gratitude to the members of the
Graduate Philosophy Students Organization at the University of Penn
sylvania for the considerable assistance they gave me during the sym
posium. My thanks, also, to Judith Sofranko and Lynn Luckett for their
very responsible efforts in the preparation of the manuscript. Finally,
I would like to thank Professor James Cornman for his invaluable
advice and encouragement.
M.S.
TABLE OF CONTENTS
PREFACE V
EDITOR'S INTRODUCTION 1
FREDERIC SCHICK / Three Logics of Belief 6
MARSHALL SWAIN / The Consistency of Rational Belief 27
HENRY E. KYBURG, JR. / Conjunctivitis 55
GILBER T H. HARMAN / Induction. A Discussion of the Relevance
of the Theory of Knowledge to the Theory of Induction (with a
Digression to the Effect that neither Deductive Logic nor the
Probability Calculus has Anything to Do with Inference) 83
KEITH LEHRER / Justification, Explanation, and Induction 100
ISAAC LEVI/Probability and Evidence 134
RICHARD C. JEFFREY / Dracula meets Wolfman: Acceptance vs.
Partial Belief 157
RALPH L. SLAGHT / Induction, Acceptance, and Rational Belief:
A Selected Bibliography 186
INDEX OF NAMES 228
INDEX OF SUBJECTS 229
EDITOR'S INTRODUCTION
The papers collected in this book are all devoted to the problem of the
role that induction plays in theories of knowledge and rational belief.
Nearly all of the papers are programmatic, and yet they contain many
specific and original suggestions toward solutions of isolated problems
in the area.
The volume opens with an essay by Frederic Schick in which he
delineates and compares three apparently competing theories about
the conditions under which we are obligated or entitled to believe
propositions. Schick calls these theories subjectivism, empiricism, and
pragmatism; he refers to the writings of H. E. Kyburg, Jr. as one source
of the subjectivist theory (not to be confused with the subjective theory
of probability!), to the work of J. Hintikka as an example of empiricism,
and to the work of I. Levi as an example of pragmatism. Schick argues
that each of these theories is operative only in the context of a certain
type of issue; empiricism and pragmatism provide principles relevant to
fundamentally different (indeed, incompatible) types of issues, and there
fore the results of these theories are not comparable. Consequently, the
theories are not incompatible. Moreover, Schick argues, subjectivism is
most plausibly interpreted in such a way that, depending on the issue, it
will yield the same results as the other two theories. He suggests that a
truly comprehensive theory of rational belief will incorporate all three of
these theories.
Schick also distinguishes the principles that individuate each of these
theories from certain other principles which the theories might have in
common; the latter are called 'overarching principles'. For example, the
principle that the set of propositions one believes ought (rationally) to
be deductively closed might be an overarching principle. The subject
of overarching principles is the topic of my paper, which follows Schick's
essay. In this paper, I construct a general theory of rational belief,
which is intended to provide, among other things, principles governing
the admissibility of propositions into sets of rationally believed proposi-
2 EDITOR'S INTRODUCTION
tions. A distinction is made between propositions one is obligated to
believe and propositions one is permitted to believe, from the point of
view of rationality. I argue that the principles governing obligatory belief
are quite different from those that govern permissible belief; this differ
ence is illustrated in a solution given to the lottery paradox. The theory
that I construct is intended to be 'overarching' in that it hopefully can
serve as a framework within which rules of rational acceptance can be
constructed. The theory is presented as an extension of Hintikka's logic
of knowledge and belief, although many of the basic concepts of his
system are considerably revised.
The problem of overarching principles is also the subject of the essay
by Henry E. Kyburg, Jr. Kyburg discusses several general principles that
have been adopted, either implicitly or explicitly, by a number of writers
on acceptance. He distinguishes 'weak' and 'strong' versions of principles
governing the consistency as well as the deductive closure of sets of
rationally accepted statements; in addition, he considers a principle of
conjunction, which stipulates that if statements Sl and S2 are rationally
accepted, then their conjunction ought to be accepted. After tracing a
number of connections that hold among these various principles, Kyburg
considers acceptance rules proposed by Hempel, Hintikka and Hilpinen,
Levi, and Lehrer, all of which satisfy the conjunction principle and some
or all of the other principles as well. Kyburg argues that each of these
systems has flaws, and that many of the flaws are most plausibly attribut
able to the fact that they satisfy the conjunction principle. He points out
that his own system of rational belief, developed in earlier writings,
abandons the conjunction principle and is consequently able to avoid
many of the problems that the other systems face. Although his primary
concern is to cast doubt on the conjunction principle, Kyburg also presents
us with lucid expositions of the above theories and discusses many of
their interesting aspects.
Overarching principles of the type discussed above have an obvious
relevance to the problem of constructing an adequate acceptance rule.
Once these principles have been agreed upon, they can be used to formu
late a partial criterion of adequacy for acceptance rules; any adequate
acceptance rule must at least satisfy the demands of the overarching
principles. In his contribution to this collection, Gilbert Harman introduces
another kind of consideration that is relevant to the adequacy of accept-
EDITOR'S INTRODUCTION 3
ance rules; namely, the connection between inferences warranted by such
rules and the analysis of knowledge. Harman suggests that one partial
test of adequacy for a proposed acceptance rule is whether inferences in
accordance with that rule could provide one with knowledge. He discusses
the causal theory of knowing developed by Alvin Goldman, and points
out that this theory suggests a theory of inductive inference; namely, that
inductive inference is inference to the best of competing causal statements.
That theory has defects, however, and Harman proposes that we replace
it with the theory that inductive inference is inference to the best of
competing explanatory statements, a view that he has developed in pre
vious writings. In the present paper, Harman expands and clarifies this
interesting doctrine.
The relation between explanation and justified belief is also the subject
of the highly original essay by Keith Lehrer. Lehrer suggests that a belief
is justified either because of what it explains or because of what explains it;
he dubs this theory of justification expJanationism. Warranted inductive
inference is viewed by Lehrer as one source of justified belief; if a hypo
thesis h is inducible from one's background knowledge, then h is explained
by that knowledge, and given the theory of explanationism, it follows
that h is justified by that background knowledge. Lehrer provides us with
a number of overarching principles governing the explanation of a hypo
thesis or set of hypotheses relative to given background knowledge, and
constructs an inductive acceptance rule such that inductive inferences
warranted by that rule satisfy the demands of these overarching principles.
Lehrer then argues that hypotheses inducible in accordance with this rule
are also explained by the background knowledge from which they are
induced. Consequently, he argues, his rule satisfies the demands of ex
planationism; that is, a hypothesis is justified by inductive inference in
accordance with his rule only if it is explained by the background know
ledge. In the course of his discussion, Lehrer sheds new light on many
interesting problems; for example, he discusses the problem of self
justified (but fallible) beliefs within the context of explanationism.
The papers discussed thus far have been directed primarily at problems
surrounding the concept of rational acceptance, or rational belief. It is
often supposed that a theory which assumes that there is such a thing as
acceptance is fundamentally opposed to theories which instead speak of
(rational) degrees of belief, or degrees of credence. In his important essay,
4 EDITOR'S INTRODUCTION
Isaac Levi argues that this is not necessarily so. He points out that a
theory of rational probability judgement will consist of conditions that
determine rational degrees of credence at a given time as well as rational
revision of degrees of credence over time. He rejects the Carnapian image
of such conditions as a set of norms for an ideally rational man on
the grounds that such a view has untoward consequences. He suggests,
instead, that the conditions for rational probability judgement be viewed
as necessary conditions for a state of 'equilibrium', analogously to a
comparative static theory of consumer demand. In order to avoid
subjectivism, Levi argues that the conditions for rational probability
judgement must ground such judgements empirically, and he suggests a
way in which this can be done. The resulting theory, he points out,
presupposes that it is legitimate for one to accept some statements as
evidence, contrary to a proposal made by Richard Jeffrey that rational
credence judgements can be empirically grounded even though no state
ments are accepted as evidence. Levi concludes that an adequate empir
icistic theory of rational probability judgement must allow for the accept
ance of statements as evidence; and, in turn, an adequate theory of
acceptance will presuppose a theory of problem solving, which utilizes
rational probability judgement. Thus, rather than being incompatible, the
theory of rational credence judgement and the theory of acceptance are
mutually dependent.
Isaac Levi is to the theory of acceptance as Richard Jeffrey is to the
theory of partial belief. In his contribution to this collection, Jeffrey offers
a defense of his approach to the problem of rational belief; he is concerned
especially to answer some standard criticisms of his approach (some of
which have been raised by Levi). The Bayesian theory espoused by Jeffrey
is, he points out, a pragmatic theory intended to provide a framework
for rational deliberation which issues in action. The theory uses the
term 'degree of belief' as a technical term which refers to an attribute of
ones' attitude toward risks; the ordinary sense of belief, which seems to
be used by those who speak of acceptance, is only vestigially present in
this concept. One of the conditions that a set of partial beliefs must
satisfy if it is to be rational is conformity to the laws of the elementary
probability calculus. The theory is often criticised on the grounds that
if this is sufficient for rationality, then any coherent set of partial beliefs
will do in a given situation. But, Jeffrey argues, this is a misunderstanding;