Kant's Philosophy of Mathematics, Volume I: The Critical Philosophy and Its Roots

332 Pages·2020·2.917 MB·English

by  Carl Posy, Ofra Rechter

KANT’S PHILOSOPHY OF MATHEMATICS
Volume I: The Critical Philosophy and Its Roots
The late s saw the emergence of new philosophical interest in
Kant’s philosophy of mathematics, and since then this interest has
developed into a major and dynamic field of study. In this state-of-
the-art survey of contemporary scholarship on Kant’s mathematical
thinking, Carl Posy and Ofra Rechter gather leading authors who
approachitfrommultipleperspectives,engagingwithtopicsinclud-
ing geometry, arithmetic, logic, and metaphysics. Their essays offer
fine-grained analysis of Kant’s philosophy of mathematics in the
context of his Critical philosophy, and also show sensitivity to its
historical background. The volume will be important for readers
seeking a comprehensive picture of the current scholarship about
the development of Kant’s philosophy of mathematics, its place in
his overall philosophy, and the Kantian themes that influenced
mathematicsand itsphilosophy after Kant.
  is Professor Emeritus of Philosophy at the Hebrew
University of Jerusalem. He is editor of Kant’s Philosophy of Math-
ematics: Modern Essays () and has written extensively on the
philosophy of mathematicsas well as on Kant.
  is a member of the philosophy department at Tel
AvivUniversity.HerworkfocusesonKantwithinthephilosophyof
mathematics and its history, and she has published a number of
papers onKant’sphilosophy ofarithmetic.
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KANT’S PHILOSOPHY OF
MATHEMATICS
Volume I: The Critical Philosophy and Its Roots
 
CARL POSY
HebrewUniversityofJerusalem
OFRA RECHTER
TelAvivUniversity
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Jaakko Hintikka (–) founded the modern study of Kant’s
philosophy of mathematics. His early papers spurred the revival of the
field as we know it. His work inspired us all; his interest and generosity
encouraged us all. He was active in the field until his very last days. We
are privileged that the present volume includes his last publication on
our topic. We dedicate this volume to his memory.
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Contents
List of Contributors page ix
Acknowledgements x
Introduction 
   
 Kant and Mendelssohn on the Use of Signs in Mathematics 
Katherine Dunlop
 Of Griffins and Horses: Mathematics, Metaphysics, and
Kant’s Critical Turn 
Carl Posy
 Kant on Mathematics and the Metaphysics of
Corporeal Nature: The Role of the Infinitesimal 
Daniel Warren
     
 Kant’s Theory of Mathematics: What Theory of
What Mathematics? 
Jaakko Hintikka
 Singular Terms and Intuitions in Kant: A Reappraisal 
Mirella Capozzi
 Kant and the Character of Mathematical Inference 
Desmond Hogan
vii
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viii Contents
     
 Kant on Parallel Lines: Definitions, Postulates, and Axioms 
Jeremy Heis
 Continuity, Constructibility, and Intuitivity 
Gordon Brittan
 Space and Geometry in the B Deduction 
MichaelFriedman
     
 Arithmetic and the Conditions of Possible Experience 
Emily Carson
 Kant’s Philosophy of Arithmetic: An Outline of a
New Approach 
Daniel Sutherland
 Kant on ‘Number’ 
W. W. Tait
References to Works by Kant 
Bibliography 
Index 
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Contributors
 ,DepartmentofPhilosophy,MontanaStateUniversity
 , Department of Philosophy, University of Rome “La
Sapienza”
 , Department of Philosophy, McGill University
 , Department of Philosophy, University of Texas at
Austin
 , Department of Philosophy, Stanford University
 ,DepartmentofLogicandPhilosophyofScience,University
of California at Irvine
 , Late of the Departments of Philosophy at the Uni-
versity of Helsinki, Boston University, and of the Academy of Finland
 , Department of Philosophy, Princeton University
 , Department of Philosophy, the Hebrew University of
Jerusalem
 , Department of Philosophy, University of Illinois
at Chicago
. . , Department of Philosophy, University of Chicago
 ,DepartmentofPhilosophy,theUniversityofCalifornia
at Berkeley
ix
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Acknowledgements
A conference in March of  brought together a lively group of
researchers on Kant’s philosophy of mathematics. Discussions at that
conference planted the idea of producing this two-volume collection.
The Israel Science Foundation, the van Leer Jerusalem Institute, and the
EinsteinCenter attheHebrewUniversityco-sponsoredtheconference.It
tookplaceoverthecourseoffourdaysatthevanLeerJerusalemInstitute.
All the essays collected here were composed especially for this volume.
Some authors submitted their contributions early on in the editorial
process andsomelater.We aregrateful to alltheauthors fortheircooper-
ation throughout this process.
JaakkoHintikkawasthefirstto submithiscontribution,andhe kept a
lively andencouraging interest in the project.We are grateful to Professor
Ghita Holmström-Hintikka for permission to publish posthumously the
essay he so cared about in this volume, as he wished.
Grant #/ of the Israel Science Foundation supported Carl Posy
during the editing of this volume and the writing of the “Introduction”.
TheUniversitätbibliothekLeipziggenerouslygavethepermissiontouse
imagesofKant’shandwrittenlettertoAugustRehebrg()thatappear
on the cover of this volume. We are grateful to Steffen Hoffmann for
finding the original manuscript in the library’s Bereich Sondersammlun-
gen, and to Susanne Dietel for dealing with the digital images and
handling the copyright.
TheeditorswouldliketothankHilaryGaskinofCambridgeUniversity
Pressforhersupportandguidancethroughtheproductionofthisvolume.
WeoweaspecialdebtofthankstoDavidKashtanforhisvaluablehelpin
editing it.
x
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