Van Heijenoort: Logic and Its History
in the Work and Writings of Jean van Heijenoort

Irving H. Anellis


[PREFACE] [vii]
         [30 May 1994]  
____  
xii  
   
ANALYTIC TABLE OF CONTENTS [xii]
   
[List of illustrations] [xiv]
   
CHAPTER 1. CURRICULUM VITAE 1
1.1     Early Education 1
1.2     With Trotsky in Exile and After 6
1.3     Graduate Education 9
1.4     Contributions to Differential Geometry and Topology 11
1.5     Teaching Career   21
1.6     The House on Kirkland Place   33
1.7     Van Heijenoort the Man      38
1.8     Acute Physical Suffering  44
   
CHAPTER 2. VAN HEIJENOORT AT BRANDEIS   49
2.1      Brandeis in its Heyday   49
2.2      Van Heijenoort in the Classroom — A Logic Course Sampler 52
2.3      Van Heijenoort and His Students 83
   
CHAPTER 3. VAN HEIJENOORT AS HISTORIAN OF LOGIC 89
3.1      From Geometry to Logic — Sketch of the History of Logic 89
3.2      Van Heijenoort’s Editorial Work   98
3.3      Van Heijenoort’s Work on the History of Logic     116
3.4      The Nature of Mathematical Logic — from Frege to Gödel 117
3.4A   Van Heijenoort on Frege’s Place in the History of Logic     123
3.4B   Van Heijenoort on Frege — A Closer Look   129
3.5      History of Quantification Theory and Proof Theory   136
3.5A   Outline of the History of Quantification Theory and Proof Theory 136
3.5B   Studies of Herbrand 142
3.5C   Paradoxes of Set Theory   149
3.5D   Gödel’s Incompleteness Theorems   154
3.6      Evaluating van Heijenoort as a Historian of Logic 157
   
CHAPTER 4. PHILOSOPHY AND FOUNDATIONS OF MATHEMATICS 160
4.1      Dialectical-Materialist Mathematics 160
4.2      Van Heijenoort’s Conception of Logic 172
4.3      Intuitionism 188
4.4      Van Heijenoort’s Influence on Philosophy of Mathematics 202
____  
xiii  
   
CHAPTER 5. VAN HEIJENOORT AS LOGICIAN — CONTRIBUTIONS TO PROOF THEORY 203
5.1      Van Heijenoort’s Research in Logic 203
5.2      From Semantic Tableaux to Smullyan Trees 205
5.2A    From Gentzen to Beth 206
5.2B    Hintikka and Smullyan’s Analytic Tableaux 211
5.3      Van Heijenoort’s Contributions to the Falsifiability Tree Method 222
5.4      Satisfiability Trees for Non-classical Logics 241
5.5      Some Applications of the Tree Method 248
5.6      Some New Developments in Tree Procedures 251
5.7      Van Heijenoort’s Proof of the “Semantic” Fundamental Theorem of Herbrand 256
   
CHAPTER 6. A FINAL WORD 258
            Facsimiles 262
   
APPENDICES  
   
            APPENDIX I. Syllabus, Second Semester Introduction to Logic (as taken from the notes of Marc Cohen) 266
   
            APPENDIX II. Review by John van Heijenoort of I. M. Bocheński. Spitzfindigkeit. (Thomas Drucker, translator) 269
   
BIBLIOGRAPHY 271
   
NAME INDEX 329
____  
xiv  
   
LIST OF ILLUSTRATIONS  
   
Figure 1: Examples of Convex Sets 13
Figure 2: Examples of Non‑convex Sets 13
Figure 3: Examples of Convex Bodies 14
Figure 4: Harvard Yard and Environs (including 4 Kirkland Place) 34
Figure 5: The House on 4 Kirkland Place 35

Figure 6: The Logical “Universe”

178
Figure 7: Falsifiability Tree of Type T 228
Facsimile 1: Lecture Announcement, University of Paris, 15 January 1968
“A Proof Procedure for the Predicate Calculus”		 263
Facsimile 2: Van Heijenoort letter to Anellis, 2 August 1978
(Van Heijenoort tentatively planning to attend Joint American Mathematical Society – Mathematical Association of America Meeting, Brown University Providence, Rhode Island, 8-12 August 1978) 		264
Facsimile 3: Obituary, Brandeis University “Justice,” 23 April 1986
(Courtesy of Department of Philosophy and History of Ideas, Brandeis University)

265

SOURCE: Anellis, Irving H. Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort. Ames, IA: Modern Logic Publishing, 1994. xiv, 341 p. ISBN 1-884905-00-5.

Essential Bibliography

Anellis, Irving H. Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort. Ames, IA: Modern Logic Publishing, 1994.

Feferman, Anita Burdman. Politics, Logic, and Love: the Life of Jean van Heijenoort. Boston: Jones and Bartlett, 1993.

Van Heijenoort, Jean. Introduction à la sémantique des logiques non-classiques. Paris: J. Van Heijenoort, 1979.

Van Heijenoort, Jean. Selected Essays. Napoli: Bibliopolis; Atlantic Highlands, NJ: Distributed in the U.S.A. by Humanities Press, 1985.

CONTENTS  
Foreword 9
Logic as calculus and logic as language (1967a) 11
Subject and predicate in Western logic (1973) 17
On the number of planets (1974) 35
On Kripke’s puzzle (1974a) 37
W. V. Quine: Letter to van Heijenoort (Quine 1974) 39
Letter to W. V. Quine (1974b) 41
Set-theoretic semantics (1976) 43
Sense in Frege (1977) 55
Frege on sense identity (1977a) 65
Ostension and vagueness (1979) 71
Absolutism and relativism in logic (1979a) 75
Frege and vagueness (1985) 85
Jacques Herbrand’s work in logic and its historical context (1985a) 99
Friedrich Engels and mathematics (1948) 123
References 153

Van Heijenoort, Jean, ed. Frege and Gödel: Two Fundamental Texts in Mathematical Logic. Cambridge, MA: Harvard University Press, 1970.

Van Heijenoort, Jean, ed. From Frege to Gödel: a Source Book in Mathematical Logic, 1879-1931. Cambridge, MA: Harvard University Press, 1967.

Van Heijenoort, Jean. With Trotsky in Exile: from Prinkipo to Coyoacán. Cambridge, MA: Harvard University Press, 1978.

Note: Van Heijenoort edited or contributed to other books on Trotsky, Trotskyism, logic, and mathematics, and of course there are numerous journal articles, and the contents of archives. Here I list the most essential books.

“What is the Relationship Between Logic and Reality?”
by R. Dumain

Martin Gardner, Mathematical Games, & the Fourth Dimension
(web guide & bibliography)

Nicolas Calas — Surrealist & Trotskyist:
A Bibliographical Introduction

Marx and Marxism Web Guide

Offsite:

Van Heijenoort @ archive.org

Jean van Heijenoort Internet Archive
includes:

Bio-bibliography of Jean van Heijenoort

“Science”, the style of Burnham
by Jarvis Gerland (pseudonym of Jean van Heijenoort)

The Algebra of Revolution
by Jarvis Gerland (pseudonym of Jean van Heijenoort)

Friedrich Engels and Mathematics (1948)
by Jean van Heijenoort

Nicolas Calas: The Trotskyist Time Forgot
by Alan Wald
(Against the Current #196, September-October 2018)
[NB: van Heijenoort & diamat]

Anellis links:

Irving Anellis - Wikipedia

Irving Anellis's Home Page
(defective links corrected below)

Irving's Favorites

Dr. Irving Anellis's Curriculum Vitae

Bibliography of Irving H. Anellis

An Annotated Bibliography of Western-Language (Mainly English)
Sources on the History of Formal Logic in Russia [no working link]

Review of Logic and its History in the Work and Writings of Jean van Heijenoort
by Jean-Yves Beziau
(Modern Logic, vol. 8, no. 1/2, January 1998 - April 2000, pp. 105-117)

academia.edu:

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