Table Of ContentQUEBEC STUDIES IN THE PHILOSOPHY OF SCIENCE
PART I
BOSTON STUDIES IN THE PHILOSOPHY OF SCIENCE
Editor
ROBERT S. COHEN, Boston University
Editorial Advisory Board
THOMAS F. GLICK, Boston University
ADOLF GRUNBAUM, University of Pittsburgh
SAHOTRA SARKAR, McGill University
SYLVAN S. SCHWEBER, Brandeis University
JOHN J. STACHEL, Boston University
MARX W. WARTOFSKY, Baruch College of
the City University ofN ew York
VOLUME 177
HUGUESLEBLANC
Courtesy o/Virginia G. Leblanc
QUEBEC STUDIES IN THE
PHILOSOPHY OF SCIENCE
Part I: Logic, Mathematics, Physics
and History of Science
Essays in Honor ofH ugues Leblanc
Edited by
MATHIEU MARION
University of Ottawa
and
ROBERT S. COHEN
Boston University
KLUWER ACADEMIC PUBLISHERS
DORDRECHT I BOSTON I LONDON
Library of Congress Cataloging.in·Publication Data
Owebec studies in the philosophy of science I edited by Mathieu Marion
and Robert S. Cohen.
p. cm.
Contents: pt. I. LogiC, mathematics, physics, and history of
science
alk. paper)
1. SCience--Phllosophy--Congresses. 2. Logic--Congresses.
I. Marion, Mathieu, 1962- II. Cohen, R. S. (Robert Sonne)
0174.043 1996
501--dc20 95-17467
ISBN·13: 978·94·010·7204·5 e·ISBN·13: 978·94·009·1575·6
001: 10.1007/978·94·009·1575·6
Published by Kluwer Academic Publishers,
P.O. Box 17,3300 AA Dordrecht, The Netherlands.
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Printed on acid-free paper
All Rights Reserved
© 1995 Kluwer Academic Publishers
Softcover reprint of the hardcover 1st edition 1995
No part of the material protected by this copyright notice may be reproduced or
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TABLE OF CONTENTS
EDITORIAL PREFACE ix
LOGIC
HUGUES LEBLANC / On Axiomatizing Free Logic - And Inclusive
Logic in the Bargain 1
FRAN~OIS LEPAGE / Partial Propositional Logic 23
SERGE LAPIERRE / Generalized Quantifiers and Inferences 41
MARIE LA PALME REYES, JOHN MACNAMARA and GONZALO E.
REYES / A Category-Theoretic Approach to Aristotle's Term Logic,
with Special Reference to Syllogisms 57
JOACHIM LAMBEK / On the Nominalistic Interpretation of Natural
Languages 69
JEAN-PIERRE MARQUIS / If Not-True and Not Being True Are Not
Identical, Which One Is False? 79
DANIEL V ANDER VEKEN / A New Formulation of the Logic of
Propositions 95
YVON GAUTHIER / Internal Logic. A Radically Constructive Logic
for Mathematics and Physics 107
JUDY PELHAM / A Reconstruction of Russell's Substitution Theory 123
PHILOSOPHY OF MATHEMATICS
MICHAEL HALLETT / Hilbert and Logic 135
MATHIEU MARION / Kronecker's 'Safe Haven of Real Mathematics' 189
PHILOSOPHY OF PHYSICS
MARIO BUNGE / Hidden Variables, Separability, and Realism 217
STORRS McCALL / A Branched Interpretation of Quantum Mechanics
Which Differs from Everett's 229
MICHEL J. BLAIS / ... and Chaos Shall Set You Free. . . 243
vii
viii T ABLE OF CONTENTS
HISTORY AND PHILOSOPHY OF SCIENCE
PAUL M. PIETROSKI / Other Things Equal, The Chances Improve 259
DA VID DAVIES / The Model-Theoretic Argument Unlocked 275
JEAN LEROUX / Helmholtz and Modern Empiricism 287
WILLIAM R. SHEA / Technology and the Rise of the Mechanical
Philosophy 297
NOTES ON THE AUTHORS 309
NAME INDEX 315
EDITORIAL PREFACE
By North-American standards, philosophy is not new in Quebec: the first men
tion of philosophy lectures given by a Jesuit in the College de Quebec (founded
1635) dates from 1665, and the oldest logic manuscript dates from 1679. In
English-speaking universities such as McGill (founded 1829), philosophy
began to be taught later, during the second half of the 19th century. The major
influence on English-speaking philosophers was, at least initially, that of
Scottish Empiricism. On the other hand, the strong influence of the Catholic
Church on French-Canadian society meant that the staff of the facultes of the
French-speaking universities consisted, until recently, almost entirely of
Thomist philosophers. There was accordingly little or no work in modem
Formal Logic and Philosophy of Science and precious few contacts between the
philosophical communities. In the late forties, Hugues Leblanc was a young
student wanting to learn Formal Logic. He could not find anyone in Quebec
to teach him and he went to study at Harvard University under the supervision
of W. V. Quine. His best friend Maurice L' Abbe had left, a year earlier, for
Princeton to study with Alonzo Church.
After receiving his Ph.D from Harvard in 1948, Leblanc started his profes
sional career at Bryn Mawr College, where he stayed until 1967. He then went
to Temple University, where he taught until his retirement in 1992, serving as
Chair of the Department of Philosophy from 1973 until 1979. His achievements
as a logician include seminal contributions to the development of Free Logic, in
particular with the ground breaking paper, written jointly with Theodore
Hailperin, 'Nondesignating Singular Terms' (Philosophical Review 68 (1959),
pp. 239-43). After initial results by Bas van Fraassen, using supervaluation,
Hugues Leblanc and Richmond Thomason obtained completeness results in
'Completeness Theorems for Some Presupposition-Free Logic' (Fundamenta
Mathematicae 62 (1968), pp. 125-64). More recently, Leblanc also made
seminal contributions to Truth-Value Semantics (cf. his Truth-Value Semantics,
Amsterdam, North-Holland, 1976) and, inspired by appendices to Karl Popper's
Logic of Scientific Discovery, to Probability Semantics and Probability Theory,
in his paper 'Probabilistic Semantics for First-Order Logic' (ZeitschriJt for
mathematische Logik und Grundlagen der Mathematik 25 (1979), pp. 498-
509). In all, Leblanc has written more than one hundred scientific papers, the
more recent of them in collaboration with Peter Roeper (Australian National
University), and four books, he collaborated on two books and edited or co
edited four. Many logic students will remember learning the subject from his
classic textbook, written with William A. Wisdom, Deductive Logic (3rd edn.,
Englewood Cliffs, Prentice Hall, 1993).
After a long and fruitful career in the United States, Hugues Leblanc is now
ix
x EDITORIAL PREFACE
back in Quebec, where the philosophical milieu has changed beyond recogni
tion since his student days. He came back to find studies in logic and in all
aspects of philosophy of science in a flourishing state. As a result of the revolu
tion tranquille which took place among the French-speaking society in the
sixties, philosophy in Quebec opened up to external influences such as, initially,
phenomenology and Marxism and, increasingly in the past twenty years, Anglo
American analytic philosophy. As a result, there is now a growing number of
French-speaking logicians and philosophers of science - although not all of
them work from the point of view of analytical philosophy. Conditions were set
for fruitful exchanges with the English-speaking philosophical community. (But
we should add here that the essential role of immigrants in the evolution of
the philosophical life in Quebec should not be overlooked. Contributors to the
present volumes come not only from other parts of Canada, but also from
Argentina, Australia, Belgium, Germany, Ireland, Switzerland, the United
Kingdom and the United States).
Such exchanges have led recently to the creation of research groups across
Quebec. These are now joined together under the name of Groupe de recherche
sur la representation, I' action et Ie langage or GRRAL. Our two volumes
of Quebec Studies in the Philosophy of Science comprise the first full-scale
collection of studies in the philosophy and history of science from French- and
English-speaking philosophers of Quebec to appear in English; they include in
particular most members of the GRRAL. As editors, we are happy to join the
contributors in dedicating these volumes to Hugues Leblanc, who is, among
philosophers, the first logicien quebecois.
In our first volume, which opens with a new essay on Free Logic by Hugues
Leblanc himself, we have collected together papers in logic, philosophy of
mathematics, philosophy of physics and in general philosophy and history of
science. This volume includes members of two of the research groups forming
the GRRAL, the group on Fondements de la logique et fondement du raison
nement (M. Hallett, F. Lepage, S. Lapierre, J.-P. Marquis, and, at the time of
writing, J. Pelham) and the group Actes du discours et grammaire universelle
(D. Vanderveken & Y. Gauthier).
The papers in the section on logic show the great variety of logical investiga
tions work done across Quebec. Both Franyois Lepage and Serge Lapierre
present their results, respectively, on partial functions in type theory and condi
tional quantifiers, within their more global context. The following three papers
reflect the fundamental research in category theory which has been taking place
in Montreal's various departments of mathematics. Marie La Palme Reyes, John
Macnamara and Gonzalo Reyes argue in their paper for the replacement of the
standard Boolean, class interpretation of syllogistic by a category-theoretical
approach. Jim Lambek argues for an extension of his nominalistic interpretation
of the language of mathematics, developed in collaboration with Jocelyne
Couture and Phil Scott, to natural languages, and Jean-Pierre Marquis studies
EDITORIAL PREFACE xi
the distinction between true, not-true and not being true within the perspective
of topos theory.
Further to his work on the logic of illocutionary forces, Daniel Vanderveken
presents in his paper a framework for a new logic of propositions. Yvon
Gauthier presents his own system of internal logic and system of finitist arith
metic, where the schema of complete induction is replacd by that of Fermat's
infinite descent. Finally, building on joint results with Alasdair Urquhart on
structured propositions, Judy Pelham presents in her paper a reconstruction of
Russell's substitution theory (circa 1905-6) that provides a resolution of the
paradoxes which originally caused Russell to abandon the theory in favour of
the ramified theory of types.
In the section on the philosophy of mathematics, Michael Hallett studies the
role of logic in Hilbert's approach to the foundations of mathematics, while
Mathieu Marion examines the relations between Kronecker's philosophy of
mathematics and the tradition of logical foundations. The section on philosophy
of physics comprises a paper by the distinguished philosopher of science Mario
Bunge, in which he argues that recent experiments which refuted hidden
variable theories were not a refutation of realism, a paper by Storrs McCall
presenting a new 'branched' interpretation of Quantum Mechanics and a paper
by Michel Blais on Chaos Theory.
The last section of the volume contains studies in general philosopy of
science and a study by the leading historian of science, William Shea. In his
paper, Paul Pietro sky presents an original conception of ceteris paribus laws
inspired by Ramsey's ideas about causation. Dave Davies argues that Putnam's
recent emphasis on conceptual relativity against metaphysical realism does
not vindicate critics of his model-theoretic argument, but actually clarifies
Putnam's objections to these very criticisms. Jean Leroux presents elements of
Helmholtz's epistemology which foreshadow modem forms of empiricism and
he argues for an anti-realist reading of his theory of science. Finally, Shea
studies the origin, in the development of new technologies from the medieval
ages onwards, of the mechanical philosophy which underlay modem science,
from Galileo to Newton.
We would like to thank Alain Voizard for his help in writing this preface, and
also the editor of the Brazilian Journal of Physics, formerly Revista Brasileira
de Fisica, for granting us permission to reprint Mario Bunge's essay 'Hidden
Variables, Separability and Realism' (volume especial os 70 anos de Mario
SchOnberg, 1984, pp. 150-168). We are especially grateful to Annie Kuipers for
her professional assistance on behalf of Kluwer Academic Publishers and for
her continued encouragement and patience.
Boston and Montreal MATHIEU MARION & ROBERT S. COHEN
April 1995
