Table Of ContentLOCAL INDUCTION
SYNTHESE LIBRARY
MONOGRAPHS ON EPISTEMOLOGY,
LOGIC, METHODOLOGY, PHILOSOPHY OF SCIENCE,
SOCIOLOGY OF SCIENCE AND OF KNOWLEDGE,
AND ON THE MATHEMATICAL METHODS OF
SOCIAL AND BEHA VIORAL SCIENCES
Managing Editor:
J AAKKO HINTIKKA, Academy of Finland and Stanford University
Editors:
ROBERT S. COHEN, Boston University
DONALD DAVIDSON, The Rockefeller UniversityandPrinceton University
GABRIEL NUCHELMANS, University of Leyden
WESLEY C. SALMON, University of Arizona
VOLUME 93
LOCAL INDUCTION
Edited by
RADU J. BOGDAN
Stanford University
D. REIDEL PUBLISHING COMPANY
DORDRECHT-HOLLAND / BOSTON-U .S.A.
Library of Congress Cataloging in Publication Data
Main entry under title:
Local induction.
(Synthese library ; 93)
"A selected bibliography of local induction, by
Radu J. Bogdan" : p.
Includes indexes.
CONTENTS: Levi, I. Acceptance revisited.
Rosenkrantz, R. Cognitive decision theory. - Goosens, W. K.
A critique of epistemic utilities. [etc.]
1. Induction (Logic)-Addresses, essays, lectures. I.
Bogdan, Radu J.
BC91.L62 161 75-34922
ISBN 978-94-011-9801-1 ISBN 978-94-011-9799-1 (eBook)
DOl 10.10071978-94-011-9799-1
Published by D. Reidel Publishing Company,
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All Rights Reserved
Copyright © 1976 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of tile hardcover 1st edition 1976
No part of the material protected by this copyright notice may be reproduced or
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To Catalina
TABLE OF CONTENTS
PREFACE ~
ISAAC LEVI' Acceptance Revisited 1
ROGER ROSENKRANTZ' Cognitive Decision Theory 73
WILLIAM K. GOOSENS , A Critique of Epistemic Utilities 93
KEITH LEHRER' Induction, Consensus, and Catastrophe 115
JAMES H. FETZER' Elements of Induction 145
KLEMENS SZANIA WSKI , On Sequential Inference 171
GUNTER MENGES and E. KOFLER / Cognitive Decisions under
Partial Information 183
HENRY E. KYBURG, JR.' Local and Global Induction 191
RADU J. BOGDAN' Hume and the Problem of Local Induction 217
L. JONATHAN COHEN' A Conspectus of the Neo-Classical Theory
of Induction 235
ILKKA NIINILUOTO / Inquiries, Problems, and Questions: Re-
marks on Local Induction 263
HAKAN TORNEBOHM , On Piecemeal Knowledge-Formation 297
RAIMO TUOMELA' Confirmation, Explanation, and the Paradoxes
of Transitivity 319
RADU J. BOGDAN / A Selected Bibliography of Local Induction 329
INDEX OF NAMES 337
INDEX OF SUBJECTS 339
PREFACE
The local justification of beliefs and hypotheses has recently become a
major concern for epistemologists and philosophers of induction. As such,
the problem of local justification is not entirely new. Most pragmatists
had addressed themselves to it, and so did, to some extent, many classical
inductivists in the Bacon-Whewell-Mill tradition. In the last few decades,
however, the use of logic and semantics, probability calculus, statistical
methods, and decision-theoretic concepts in the reconstruction of in
ductive inference has revealed some important technical respects in
which inductive justification can be local: the choice of a language, with
its syntactic and semantic features, the relativity of probabilistic evalua
tions to an initial body of evidence or background knowledge and to an
agent's utilities and preferences, etc. Some paradoxes and difficulties
encountered by purely formal accounts of inductive justification, the
erosion of the once dominant empiricist position, which most approaches
to induction took for granted, and the increasing challenge of noninduc
tivist epistemolgies have underscored the need of accounting for the
methodological problems of applying inductive logic to real life contexts,
particularly in science. As a result, in the late fifties and sixties, several
related developments pointed to a new, local approach to inductive
justification. Among them: The Rudner-Levi-leffrey debate on scientists'
value judgments and the subsequent discussions of rules and criteria of
acceptance, Carnap's shift to a normative, decision-theoretic treatment
of inductive logic, Hempel's approach to epistemic utilities, the in
creasing influence of Popper's conception of the informational content
of scientific hypotheses, Hintikka's reconceptualization of logical proba
bility, information, and decision-theoretic rules of acceptance, etc. In his
1967 book Gambling with Truth, which has since become a classic of local
induction, Isaac Levi summed up the trend: "In science, justification of
belief is demanded only when the need for such justification arises in the
context of specific inquiries". The ensuing controversies notwithstanding,
x PREFACE
the increasing influence of this trend is undeniable. The present volume
attempts to offer a fair image of the present stage of research on local in
duction, characterized among other things by alternative approaches,
reformulations of earlier positions, conceptual innovations, more
attention paid to epistemological issues, and of course internal crit
icisms of specific proposals as well as external criticisms of the whole
enterprise.
The volume opens with Isaac Levi's essay on 'Acceptance Revisited'.
It is both a critical retrospect of his Gambling with Truth, and in several
respects a step forward. An important epistemological development is
Levi's treatment of the growth of knowledge as improvement or change.
Thus, a large part of the paper is devoted to an examination of the con
ditions and criteria according to which the basic modifications in a corpus
of knowledge, i.e. expansion or contraction, are contextually and yet
rationally justified. In the process some problems dealt with in Gambling
with Truth such as the criterion of maximizing expected utility, the multi
plicity of epistemic desiderata, finite versus infinite partitions, interval
versus point estimation, the bookkeeping problem, etc., are reexamined,
and many objections are answered. The next two papers are directly
concerned with Levi's view of local induction. Roger Rosenkrantz
analyzes the cognitive decision-theoretic approach to inductive justifica
tion, particularly Levi's. According to Rosenkrantz, the major short
comings of such an approach are the SUbjectivity of the criteria of
acceptance and evaluation, and the undesirable multiplicity of epistemic
utilities taken as formally independent objectives. These shortcomings
can be avoided by adopting a bayesian theory of evidential support,
based on the concepts of likelihood and sample coverage, and capable
of handling any significant epistemic utility such as content, simplicity,
accuracy, etc., as ingredients of support. William Goosens' paper takes
the critique of epistemic utilities into the field of inductive evaluations
based on generating-evidence experiments. Goosens maintains that there
is "an integral connection between evaluation and experimentation"
which poses a major challenge to an epistemic utility approach such as
Levi's. In particular, he proves that the latter allows for a perfect experi
ment having lower expected utility than an imperfect experiment, thus
leading to unreasonable preferences.
The papers by Keith Lehrer and James Fetzer indicate that the decision-
PREFACE XI
theoretic and epistemic utility reconstruction of local induction is far
from being monolithic. Keith Lehrer holds that local inductive methods
can satisfy the basic objective of maxiverificity, i.e. acceptance of all and
only those statements of a language which are true, and promote inter
personal agreement or consensus. The quest for maxiverificity in a certain
context of inquiry is shown to be relative to an epistemic field in which
it is reasonable to accept a maximally consistent set of statements which
is more probable than any of its competitors. The rule of acceptance is
set up in terms of utilities, qua costs and benefits of acceptance, and prob
abilities, qua consensual probabilities derivable from personal assign
ments made by members of a group. According to Lehrer, this approach
can also account for major shifts in what a scientific group accepts as
evidence and hypotheses. Like Lehrer, James Fetzer relates his theory of
epistemic utility to a definite context of knowledge characterized as a
minimally rational set of beliefs accepted by an individual at a given
time in a certain language. The general inductive strategy of maximizing
estimated epistemic utility is accounted for on a two-level basis. First, the
notion of estimated epistemic utility of a hypothesis relative to a knowl
edge context is explicated as the product of the epistemic probability
of that hypothesis on the relevant data and its epistemic utility. Second,
the epistemic probability itself is explicated as a product of the degree
of confidence in the given data and the likelihood of the hypothesis on
that data; while the epistemic utility is explicated as the product of the
logical scope of the hypothesis and its systematic power.
Two more papers, by Kl. Szaniawski, and G. Menges and E. Kofler,
respectively, can also be included in the above category, although
their treatment of cognitive decisions and utilities is closer to the
working statistician's viewpoint. Starting from A. Wald's definition of
sequential inference, Szaniawski discusses two rules of inference based
on likelihoods and epistemic utilities, respectively. Then he introduces a
third approach which interprets sequential inference as a search for in
formation. The three construals are compared, and their merits and ranges
of application are assessed. The problem of cognitive decisions under
partial information is the subject of the paper by Menges and Kofler. The
authors' view is that the notion of partial or local information should be
analyzed relative to Cournot's concept of a priori probability (and not
Laplace's), and also relative to the distinction between prior and posterior
XII PREFACE
probabilities. The formal framework of such an analysis is briefly formu
lated and explored.
The following two papers consider local induction relative to global
approaches and their philosophical motivation. The paper by Henry E.
Kyburg, Jr. is a detailed comparative analysis of several alternative
treatments of local induction with respect to the use and interpretation
of probability. Kyburg's own account of the latter, as epistemological
probability, is proposed as being better equipped to handle some specific
problems of local induction. It is argued, however, that no matter what
technical improvements are introduced, local induction still faces a gener
al challenge, namely the adjudication of disagreements caused by initially
different data or bodies of background knowledge. Kyburg claims that
local induction cannot meet this challenge unless the very contexts of
justification it relies upon are suitably broadened. But such a move will
inevitably require a global theory of justification. The global inductivism
my paper is concerned with is that of Hume. Local induction is viewed
as an epistemologically motivated attempt to avoid the basic failure of
Hume's approach, namely his atheoretical view of knowledge and induc
tion. I try to find the logical and epistemological sources of this concep
tion in the context of its opposition to rationalism. I then argue that in
duction should be relativized to a theoretical context of knowledge, and
explicated as a relation of relevance between evidence and the ontological
claims made by a theory.
The remaining papers offer alternative frameworks for local induction
and suggest specific solutions to some local inductive problems. L. Jona
than Cohen's essay is a synthesis of his neo-classical and nonprobabilistic
theory of induction. The basic issues Cohen deals with are the nature of
inductive evidence, the syntax of inductive reliability, the justifiability of
induction, inductive reasoning versus probability, and the epistemology
of neo-classical induction. Unlike most approaches to local induction,
Cohen's is more concerned with scientific experimentation. The induc
tive conclusions reached in the latter's context are accounted for by his
method of relevant variables and evaluated within a modal, nonprobabi
listic, formalism. Ilkka Niiniluoto's paper is an attempt to explicate the
theory of local inductive acceptance in terms of the question-making
and answer-providing strategies used in scientific inquiries. The types of
questions relevant to such inquiries are regarded as requests for informa-
