Table Of ContentEXACT PHILOSOPHY
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, The Rockefeller University and Princeton University
J AAKKO HINTIKKA, Academy of Finland and Stanford University
GABRIEL NUCHELMANS, University of Leyden
WESLEY C. SALMON, Indiana University
EXACT PHILOSOPHY
Problenls, Tools, and Goals
Edited by
MARIO BUNGE
Foundations and Philosophy of Science Unit, McGill University, Montreal
D. REIDEL PUBLISHING COMPANY
I
DORDRECHT-HOLLAND BOSTON-U.S.A.
Library of Congress Catalog Card Number 72-77872
ISBN-13: 978-94-010-2518-8 e-ISBN-13: 978-94-010-2516-4
001: 10.1007/978-94-010-2516-4
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All Rights Reserved
Copyright © 1973 by D. Reidel Publishing Company, Dordrecht, Holland
Softcover reprint of the hardcover 1s t edition 1973
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FOREWORD
The papers that follow were read and discussed at the first Symposium
on Exact Philosophy. This conference was held at Montreal on November
4th and 5th, 1971, to celebrate the sesquicentennial of McGill University
and establish the Society for Exact Philosophy.
The expression 'exact philosophy' is taken to signify mathematical phi
losophy, i.e., philosophy done with the explicit help of mathematical logic
and mathematics. So far the expression denotes an attitude rather than a
fully blown discipline: it intends to convey the intention to try and pro
ceed in as exact a manner as we can in formulating and discussing phi
losophical problems and theories. The kind of philosophy we wish to
practice and promote is disciplined rather than wild, systematic rather
than disconnected, and capable of being argued over rather than oracular.
We believe that even metaphysics, notoriously riotous, can be subjected
to the control of logic and mathematics. Even the history of philosophy,
notoriously unsystematic, can benefit from an exact reconstruction of
some classical ideas.
Exactness, though desirable, should not be taken for an end: it is a
means for enhancing clarity and systemicity, hence control. Exactness,
whether in philosophy or in science, does not guarantee certainty: it
eases the discovery of error and its correction. Nor does exactness ensure
depth, hence interest: it warrants the possibility of rational scrutiny. The
ideal is, of course, to tackle genuine and deep problems in an exact
manner. But before we can solve any deep problems in exact philosophy
we must accumulate a stock of modest yet exact theories. I submit then
that our immediate task is to build well circumscribed theories in exact
philosophy: in semantics, epistemology, metaphysics, value theory, ethics,
legal logic, etc. The big systems will emerge, if at all, from the fusion of
such modest but exact theories.
The style of research in exact philosophy is the one familiar from ma
thematics and theoretical science: Finding or inventing a problem / For
mulating the problem in a reasonably precise way / Trying possible solu-
VI FOREWORD
tions within available theories or in theories built ad hoc I Checking the
possible solutions against the body of relevant knowledge / Choosing and
weighing a solution / Revising the rest of the relevant knowledge in the
light of the previous result. The initial problem may be internal to an
existing theory or it may consist in building a new theory. While the form
er situation is common in the advanced area of exact philosophy, namely
logic (whether ordinary or not, truth functional or not), in other areas we
are usually faced with the much harder task of building new theories.
Some of these theories will formalize (perhaps in alternative ways) phi
losophical insights inherited from inexact philosophy, while others may
have no roots in the past although they may settle questions handed down
by traditional philosophy. In either case we should not regard our solu
tions as perfect: it will be enough if they are perfectible.
The name 'exact philosophy' seems to be new. It was born, or at least
revived, in typical Viennese fashion, namely at a restaurant table. To be
exact, the birth took place at the Vienna Rathauskeller on the evening of
September 6th, 1968, during the XIVth International Congress of Philoso
phy. The name was proposed by the late mathematician and philosopher
Richard Montague (1930-1971), whose untimely death prevented him
from reading a paper at our Symposium. However, the denotatum of
'exact philosophy' is not new: it has been going on for quite a while, so
that we can now exhibit a number of results in exact philosophy. To be
gin with there are both the standard and the noncanonical systems of
mathematical logic, as well as the semantics of logics and of mathematics,
which belong to both mathematics and philosophy. We also have a sprin
kling of results in the philosophy of science, in metaphysics, in ethics, and
in legal logic, that qualify as members of exact philosophy. But we should
acknowledge that most of the exact work in semantics, epistemology,
metaphysics, value theory, and ethics, remains to be done. We should
take some of the problems inherited from traditional philosophy, as well
as the totality of philosophical problems posed by mathematics and sci
ence, and should approach them in an exact fashion. Ifwe succeed in handl
ing in an exact way some of the deep problems in these areas we shall
be entitled to talk of a new revolution in philosophy.
This Symposium marks the coming of age of the Bertrand Russell Col
loquium in Exact Philosophy, launched in February 1970 by our Foun
dations and Philosophy of Science Unit. I take this opportunity to thank
FOREWORD VII
the Canada Council for a generous Killam award that has kept this Unit
alive, as well as for funding this Symposium. We are also indebted to the
International Union of History and Philosophy of Science (Division of
Logic, Methodology and Philosophy of Science) for another generous
grant in support of our conference.
MARIO BUNGE
Foundations and Philosophy of Science Unit,
McGill University,
Montreal
CONTENTS
FOREWORD v
PART I: LOGIC
HUGUES LEBLANC I Matters of Relevance 3
BRIAN F. CHELLAS I Notions of Relevance. Comments on
Leblanc's Paper 21
PART II: SEMANTICS
LARS SVENONIUS I Translation and Reduction 31
MARIO BUNGE I A Program for the Semantics of Science 51
PART Ill: EROTETICS
NUEL D. BELNAP, Jr. I S-P Interrogatives 65
PART IV; PHILOSOPHY OF MATHEMATICS
WILLIAM S. HATCHER I Foundations as a Branch of Mathematics 83
CHARLES CASTONGUAY I Naturalism in Mathematics. Comments
on Hatcher's Paper 93
PART V: PHILOSOPHY OF SCIENCE
RAIMO TUOMELA I Deductive Explanation of Scientific Laws 103
PART VI: METAPHYSICS
PETER KIRSCHENMANN I Concepts of Randomness 129
PART VII: ETHICS
BAS C. VAN FRAASSEN I The Logic of Conditional Obligation 151
x CONTENTS
HARRY BEATTY / On Evaluating Deontic Logics. Comments on
van Fraassen's Paper 173
PART VIII: LEGAL PHILOSOPHY
CARLOS E. ALCHOURR6N / The Intuitive Background of Norma-
tive Legal Discourse and Its Formalization 181
PART IX: HISTORY OF PHILOSOPHY
HECTOR-NERI CASTANEDA / Plato's Phaedo Theory of Relations 201
PARTI
LOGIC
