Handbook of the History of Logic. Volume 03: The Rise of Modern Logic: From Leibniz to Frege

781 Pages·2004·44.32 MB·English

by  Dov M. Gabbay

Handbook of the History of Logic
Volume 3
The Rise of Modern Logic"
Fro m Leib niz to Fre ge
Handbook of the History of Logic
Volume 3
The Rise of Modern Logic"
From Le ib niz to Fre ge
ELSEVIER
NORTH
HOLLAND
Handbook of the History of l~ogic
Volume 3
The Rise of Modern Logic"
From Leibniz to Frege
Edited by
Dov M. Gabbay
Department of Computer Science
King's College London
Strand, London, WC2R 2LS, UK
and
John Woods
Philosophy Department
University of British Columbia
Vancouver, BC Canada, V6T 1Z 1
and
Department of Computer Science
King's College London
Strand, London, WC2R 2LS, UK
2004
ELSEVIER
NORTH
HOLLAND
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CONTENTS
Preface vii
Dov M. Gabbay and John Woods
List of Contributors ix
Leibniz's Logic
Wolfgang Lenzen
Kant: From General to Transcendental Logic 85
Mary Tiles
Hegel's Logic 131
John W. Burbidge
Bolzano as Logician 177
Paul Rusnock and Rolf George
Husserl's Logic 207
Richard Tieszen
Algebraical Logic 1685-1900 323
Theodore Hailperin
The Algebra of Logic 389
Victor Sanchez Valencia
The Mathematical Turn in Logic
545
Ivor Grattan-Guinness
Schr6der's Logic 557
Volker Peckhaus
Peirce's Logic 611
Risto Hilpinen
Frege's Logic
659
Peter M. Sullivan
Index 751
This Page Intentionally Left Blank
PREFACE
With the publication of the present volume, the Handbook of the History of Logic turns
its attention to the rise of modern logic. The period covered is 1685-1900, with this vol-
ume carving out the territory from Leibniz to Frege. What is striking about this period
is the earliness and persistence of what could be called 'the mathematical turn in logic'.
Virtually every working logician is aware that, after a centuries-long run, the logic that
originated in antiquity came to be displaced by a new approach with a dominantly math-
ematical character. It is, however, a substantial error to suppose that the mathematization
of logic was, in all essentials, Frege's accomplishment or, if not his alone, a development
ensuing from the second half of the nineteenth century. The mathematical turn in logic, al-
though given considerable torque by events of the nineteenth century, can with assurance
be dated from the final quarter of the seventeenth century in the impressively prescient
work of Leibniz. It is true that, in the three hundred year run-up to the Begriffsschrifi, one
does not see a smoothly continuous evolution of the mathematical turn, but the idea that
logic is mathematics, albeit perhaps only the most general part of mathematics, is one that
attracted some degree of support throughout the entire period in question. Still, as Alfred
North Whitehead once noted, the relationship between mathematics and symbolic logic
has been an "uneasy" one, as is the present-day association of mathematics with com-
puting. Some of this unease has a philosophical texture. For example, those who equate
mathematics and logic sometimes disagree about the directionality of the purported iden-
tity. Frege and Russell made themselves famous by insisting (though for different reasons)
that logic was the senior partner. Indeed logicism is the view that mathematics can be re-
expressed without relevant loss in a suitably framed symbolic logic. But for a number of
thinkers who took an algebraic approach to logic, the dependency relation was reversed,
with mathematics in some form emerging as the senior partner. This was the precursor
of the modern view that, in its four main precincts (set theory, proof theory, model theory
and recursion theory), logic is indeed a branch of pure mathematics. It would be a mistake
to leave the impression that the mathematization of logic (or the logicization of mathe-
matics) was the sole concern of the history of logic between 1665 and 1900. There are,
in this long interval, aspects of the modern unfolding of logic that bear no stamp of the
imperial designs of mathematicians, as the chapters on Kant and Hegel make clear. Of the
two, Hegel's influence on logic is arguably the greater, serving as a spur to the unfolding
of an idealist tradition in logic m a development that will be covered in a further volume,
British Logic in the Nineteenth Century.
The story of logic's modernisation in the twentieth century is taken up in another com-
panion volume Logic from Russell to GOdel, also in preparation.
The Editors wish to record their considerable debt to this volume's able authors. Thanks
are also due, and happily rendered, to the following individuals: Professor Mohan Matthen,
viii
Head of the Philosophy Department, and Professor Nancy Gallini, Dean of the Faculty of
Arts, at the University of British Columbia; Professor Bryson Brown, Chair of the Philos-
ophy Department, and Professor Christopher Nicol, Dean of the Faculty of Arts and Sci-
ence, at the University of Lethbridge; Professor Alan Gibbons, Head of the Department of
Computer Science at King's College London; Jane Spurr, Publications Administrator in
London; Dawn Collins and Carol Woods, Production Associates in Lethbridge and Van-
couver, respectively; and our colleagues at Elsevier, Senior Publisher, Arjen Sevenster,
and Production Associate, Andy Deelen.
Dov M. Gabbay
King's College London
John Woods
University of British Columbia
and
King's College London
CONTRIBUTORS
John W. Burbidge
Department of Philosophy, Trent University, 379 Stewart Street, Peterborough, ON K9H
4A9, Canada
j ohn.burbidge @s ympatico.ca
Dov M. Gabbay
Department of Computer Science, King's College London, Strand, London WC2R 2LS,
UK
[email protected]
Rolf George
Department of Philosophy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
rgeorge @w atserv 1. uwaterloo.ca
Ivor Grattan-Guinness
Middlesex University at Enfield, Middlesex EN3 4SF, UK
eggigg @ghcom.net
Theodore Hailperin
175 W. North St. Apt. 234C, Nazareth, PA 18064 USA
thailperin @fast.net
Risto Hilpinen
Department of Philosophy, University of Miami, PO Box 248054, Coral Gables, FL
33124-4670, USA
hilpinen @m iami.edu
Wolfgang Lenzen
Department of Philosophy, Universit~it Osnabrtick, PO Box 4469 49069 Osnabrueck, Ger-
many
[email protected]
Volker Peckhaus
Universit~it Paderborn, Kulturwissenschaftliche Fakult~it, Fach Philosophie, Warburger
Str. 100, D-33098 Paderborn, Germany
peckhaus @h rz.upb.de
Paul Rusnock
Department of Philosophy, University of Ottawa, Arts Hall, 70 Laurier Avenue East, Ot-
tawa, Ontario, KIN 6N5, Canada
prusnock @u ottawa.ca