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Editor’s Introduction to Jean van Heijenoort, Historical Development of Modern Logic

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Abstract

Van Heijenoort’s account of the historical development of modern logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.

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References

  1. Abeles, F.F.: Herbrand’s theorem and the beginning of logic programming. In: Tattersall, J.J. (ed.) Proceedings of the Canadian Society for History and Philosophy of Mathematics/Société Canadienne d’Histoire et de Philosophie des Mathématiques, vol. 5. Eighteenth annual meeting, University of Prince Edward Island, Charlottetown, PEI, May 28–29, 1992, pp. 38–45. Providence College, Providence, RI (1992)

  2. Abeles, F.F.: Herbrand’s fundamental theorem and the beginning of logic programming. Mod. Log. 4, 63–73 (1994). http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204835163

  3. Anellis, I.H.: Review of [115]. Cognit. Brain Theory 4(2, Spring), 191–193 (1981)

  4. Anellis I.H.: Bibliografía de Jean van Heijenoort. Mathesis 3, 85–88 (1987)

    MathSciNet  Google Scholar 

  5. Anellis, I.H.: Notes on a conversation with Gregory H. Moore, May 26–27, 1987 [re: van Heijenoort, etc.; manuscript (1987)]

  6. Anellis, I.H.: Jean van Heijenoort, the revolutionary, the scholar, and man (1912–1986). Stud. Sov. Thought 35, 147–178 (1988)

    Google Scholar 

  7. Anellis I.H.: La obra de Jean van Heijenoort en el campo de la lógica: sus aportaciones a la teoría de la demonstración. Mathesis 5, 353–370 (1989)

    MathSciNet  Google Scholar 

  8. Anellis, I.H.: From semantic tableaux to Smullyan trees: a history of the development of the falsifiability tree method. Mod. Log. 1, 36–69 (1990). http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204834539, http://project-euclid.org/DPubS/Re-pository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204902674

  9. Anellis, I.H.: Schröder material at the Russell archives. Mod. Log. 1, 237–247 (1990–1991). http://projecteuclid.org/DPubS/Repository/1.0/Disseminate?view=body&id=pdf_1&handle=euclid.rml/1204834617

  10. Anellis, I.H.: The Löwenheim-Skolem theorem, theories of quantification, and proof theory. In: Drucker, T. (ed.) Perspectives on the History of Mathematical Logic, pp. 71–83. Birkhäuser, Boston (1991)

  11. Anellis, I.H.: Jean van Heijenoort’s contributions to proof theory and its history. Mod. Log. 2, 312–335 (1992) (revised English version of 7)

  12. Anellis, I.H.: Van Heijenoort: Logic and Its History in the Work and Writings of Jean van Heijenoort. Modern Logic Publishing, Ames (1994)

  13. Anellis, I.H.: Peirce rustled, Russell pierced: How Charles Peirce and Bertrand Russell viewed each other’s work in logic, and an assessment of Russell’s accuracy and role in the historiography of logic. Mod. Log. 5, 270–328 (1995). http://www.cspeirce.com/menu/library/aboutcsp/anellis/csp&br.htm

  14. Anellis, I.H.: Review of 30, Transactions of the Charles S. Peirce Society 40, 349–359 (2004)

    Google Scholar 

  15. Anellis, I.H.: Some views of Russell and Russell’s logic by his early contemporaries. Rev. Mod. Log. 10(1/2) 67–97 (2004–2005). http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rml/1203432182; electronic version as: Some views of Russell and Russell’s logic by his contemporaries, with particular reference to Peirce, http://www.cspeirce.com/menu/library/aboutcsp/anellis/views.pdf

  16. Anellis, I.H.: Review of 41. Rev. Mod. Log. 10, 117–129 (2005). http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.rml/1203432-186

  17. Anellis, I.H.: Did the Principia Mathematica precipitate a “Fregean revolution”? Russell: Journal of Russell Studies 31, 131–150 (2011) [simultaneous published in: Griffin, N., Linsky, B., Blackwell, K. (eds.) Principia Mathematica at 100. The Bertrand Russell Research Centre, McMaster University, Hamilton, Ont., pp. 131–150 (2011)]

  18. Anellis, I.H., Houser, N.: The nineteenth century roots of universal algebra and algebraic logic: a critical-bibliographical guide for the contemporary logician. In: Andréka, H., Monk, J.D., Németi, I. (eds.) Colloquia Mathematica Societatis János Bolyai, vol. 54. Algebraic Logic, Budapest (Hungary), 1988, pp. 1–36. Elsevier Science, Amsterdam (1991)

  19. Badesa, C.: El teorema de Löwenheim en el marco de la teoría de relativos, Ph.D. thesis, University of Barcelona (1991) [published: Publicacións, Universitat de Barcelona, Barcelona (1991)]

  20. Badesa, C.: (Maudsley, M., trans.) The Birth of Model Theory: Löwenheim’s Theorem in the Frame of the Theory of Relatives. Princeton University Press, Princeton (2004)

  21. Beatty R.: Peirce’s development of quantifiers and of predicate logic. Notre Dame J. Form. Log. 10, 64–76 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  22. Bell, J., Machover, M.: A Course in Mathematical Logic. North-Holland, Amsterdam (1977)

  23. Bernays, P.: Über den Zusammenhang der Herbrand’schen Satzes mit den neueren Ergebnissen von Schütte und Stenius. In: Proceedings of the International Congress of Mathematicians, vol. 2, p. 397. Amsterdam, September 2 to September 9, 1954. Noordhoof, Groningen/North-Holland, Amsterdam (1956)

  24. Bernays, P.: Review of [143]. J. Philos. 67, 109–110 (1970)

    Google Scholar 

  25. Berry, G.D.W.: Peirce’s contributions to the logic of statements and quantifiers. In: Wiener, P.P., Young, F.H. (eds.) Studies in the Philosophy of Charles Sanders Peirce, pp. 153–165. Harvard University Press, Cambridge (1952)

  26. Beth, E.W.: Semantic entailment and formal derivability, Mededlingen van den Koninklijke Nederlandse Akademie van wetenschappen, afd. Letterkunde (n.s.) 18(13), 309–342 (1955)

    Google Scholar 

  27. Bibel, W.: Early history and perspectives of automated deduction. In: Hertzberg, J., Beetz, M., Englert, R. (eds.) KI 2007: Advances in Artificial Intelligence: 30th Annual German Conference on AI, KI 2007, Osnabrück, Germany, September 10–13, 2007: Proceedings. Springer-Verlag, Berlin, pp. 2–18 (2007)

  28. Boole, G.: The Mathematical Analysis of Logic. Macmillan, Cambridge (1847)

  29. Boole, G.: An Investigation into the Laws of Thought, on Which are Founded the Mathematical Theories of Logic and Probabilities. Walton and Maberly, London (1854)

  30. Brady, G.: From Peirce to Skolem: A Neglected Chapter in the History of Logic. Elsevier Science, Amsterdam (2000)

  31. Burnham, J.: Science and style: a reply to comrade Trotsky (February 1, 1940), Appendix to Trotsky. In: In Defense of Marxism (Against the Petty-Bourgeois Opposition), pp. 187–206. Pathfinder Press, New York (1970; reprinted 1973)

  32. Church, A.: A bibliography of symbolic logic. J. Symb. Log. 1, 121–218 (1666–1935)

  33. Church, A.: A bibliography of symbolic logic; additions and corrections. J. Symb. Log. 3, 178–212 (1936)

    Google Scholar 

  34. Church, A.: Review of [45,51,53,54,144,145], in: [143], pp. 1–82, 592–617, and [151], pp. 1–108, J. Symb. Log. 37, 405 (1972)

  35. Church, A.: Review of [46,119,146,147], in: [143], 124–128. J. Symb. Log. 39, 355 (1974)

  36. Church, A.: A Bibliography of Symbolic Logic (1666–1935), revised and expanded edition, American Mathematical Society/Journal of Symbolic Logic, Providence, RI (1984)

  37. Crouch J.B.: Between Frege and Peirce: Josiah Royce’s structural logicism. Trans. Charles S. Peirce Soc. 46, 155–177 (2011)

    Article  Google Scholar 

  38. De Morgan, A.: Formal Logic; or, The Calculus of Inference, Necessary and Probable. Taylor, London (1847)

  39. Dreben, B.S., van Heijenoort, J.: Introductory note to [49,50] and [52]. In: [55], pp. 44–59 (1986)

  40. Fang, J.: Hilbert. Paideia Press, Hauppauge, NY (1970)

  41. Feferman, A.B.: Politics, Logic, and Love: The Life of Jean van Heijenoort. A K Peters, Wellesley (1993) [reprinted as: From Trotsky to Gödel: The Life of Jean van Heijenoort. A K Peters, Natick (2001)]

  42. Feferman A.B., Feferman S.: Alfred Tarski: Life and Logic. Cambridge University Press, Cambridge (2004)

    MATH  Google Scholar 

  43. Feferman, S.: Letter to I. H. Anellis, October 15, 1986 (1986) [quoted in: [12], pp. 98–99]

  44. Feferman, S.: Appendix: Jean van Heijenoort’s scholarly work, 1948–1986. In: [41], pp. 371–390 (1993)

  45. Frege, G., Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Verlag von Louis Nebert, Halle [English translation by S. Bauer-Mengelberg. In: [143], pp. 1–82 and [151], pp. 1–82]

  46. Frege, G.: Letter to Russell, 22 June 1902, English translation by Beverley Woodward. In: [143], pp. 127–128 (1902)

  47. Gentzen, G.: Untersuchungen über das logische Schliessen. Mathematische Zeitschrift 39, 176–210, 405–431 (1934)

    Google Scholar 

  48. Gillies, D.A.: The Fregean revolution in logic. In: Gillies, D.A. (ed.) Revolutions in Mathematics, pp. 265–305. Clarendon Press, Oxford (1992; paperback ed. 1995)

  49. Gödel, K.: Über die Vollständigkeit des Logikkalküls; Ph.D. thesis, University of Vienna (1929) [published with English translation on facing pages in [55], pp. 60–101]

  50. Gödel, K.: Die Vollständigkeit der Axiome des logischen Funktionenkalküls, Monatshefte für Mathematik und Physik 37, 349–360 (1930) [English translation by S. Bauer-Mengelberg: [143], pp. 582–591; reprinted with English translation on facing pages in [55], pp. 102–123]

  51. Gödel, K.: Einige metamathematische Resultate über Entscheidungsdefinitheit und Widersprunchsfreitheit, Anzeiger der Akademie der Wissenschaften in Wien, mathematisch-naturwissenschftliche Klasse 67, 214–215 (1930) [English translation by S. Bauer-Mengelberg: [143], pp. 595–596; [151], pp. 86–87; reprinted, with English tanslation on facing pages in [55], pp. 140–143]

  52. Gödel, K.: Über die Vollständigkeit des Logikkalküls, Die Naturwissenschaften 18, 1068 (1930) (reprinted with English translation on facing pages in [55], pp. 124–125 (1930))

  53. Gödel, K.: Über die formal unentscheidbare Sätze der Principia mathematica und verwandter Systeme, I, Monatshefte für Mathematik und Physik 38, 173–198 (1931) (English translation by J. van Heijenoort: [143], 596–616; [151], pp. 87–107; reprinted, with English translation, in [55], pp. 144–195)

  54. Gödel, K.: Über Vollständigkeit und Widerspruchsfreiheit (1931). Ergebnisse eines mathematischen Kolloquiums 3, 12–13 (1932) (English translation by J. van Heijenoort: [143], pp. 616–617; [151], pp. 107–108; reprinted with English translation on facing page: [55], pp. 234–237)

  55. Gödel, K.: In: Feferman, S., Dawson, Jr., J.W., Kleene, S.C., Moore, G.H., Solovay, R.M., van Heijenoort, J. (eds.) Collected Works, Vol. I. Publications 1929–1936. Oxford University Press, Oxford (1986)

  56. Gödel, K.: In: Feferman, S., Dawson, Jr., J.W., Kleene, S.C., Moore, G.H., Solovay, R.M., van Heijenoort, J. (eds.) Collected Works, vol. II. Publications 1938–1974, Oxford University Press, Oxford (1990)

  57. Goldfarb, W.D.: Logic in the twenties: the nature of the quantifier. J. Symb. Log. 44, 351–368 (1979). http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.jsl/1183740431

  58. Grattan-Guinness I.: Wiener on the logics of Russell and Schröder: an account of his doctoral thesis, and of his discussion of it with Russell. Ann. Sci. 32, 103–132 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  59. Herbrand, J.: Recherches sur la théorie de la démonstration, Doctoral thesis, University of Paris; published in Prace Towarzystwa Naukowego Warszawskigo, wydzial III(33) (1930) (reprinted in: [60], pp. 35–153; English version in: [61], pp. 44–202; English version of Chapter 5 in [143], 525–581)

  60. Herbrand, J.: In: van Heijenoort, J. (ed.) Écrits logiques. Presses Universitaires de France, Paris (1968)

  61. Herbrand, J.: (Goldfarb, W. D., trans.), Logical Writings. Harvard University Press, Cambridge (1971) (English translation of [60])

  62. Hilbert, D.: Grundlagen der Geometrie, Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, pp. 1–92. Teubner, Leipzig (1899)

  63. Hilbert, D.: Axiomatisches Denken, Mathematische Annalen 78, 405–415 (1918)

  64. Hintikka, J.: Semantics: a revolt against Frege, In: Fløistad, G. (ed.) Contemporary Philosophy. Martinus Nijhoff, The Hague, vol. 1, pp. 57–82 (1981) (reprinted in: [66], 140–161)

  65. Hintikka, J.: On the development of the model-theoretic viewpoint in logical theory. Synthèse 77, 1–36 (1988) (reprinted in [66], 104–139)

    Google Scholar 

  66. Hintikka, J.: Lingua Universalis vs. Calculus Ratiocinator: An Ultimate Presupposition of Twentieth-Century Philosophy. Kluwer Academic Publishers, Dordrecht (1997)

  67. Hook, S.: Dialectics of nature, Marxist Quarterly 1, 253–284 (1937) (reprinted in: S. Hook, Reason, Social Myths and Democracy. The John Day Company, New York, pp. 183–226 (1940))

  68. Hook, S.: Out of Step: An Unquiet Life in the 20th Century. Harper and Row, New York (1987)

  69. Huntington, E.V.: Set of independent postulates for the algebra of logic. Trans. Am. Math. Soc. 5, 288–309 (1904)

    Google Scholar 

  70. Kenig, H.P.: Review of [143]. Rev. Metaphys. 21, 168–169 (1967)

  71. Ladd-Franklin, C.: Methods of. . .; unidentified manuscript, n.d. ca. 1913, re: Whitehead & Russell in Principia on Peirce & Schröder, from the Ladd-Franklin Papers of Rare Book and Manuscript Library, Columbia University (ca. 1913)

  72. Lenhard, J.: Axiomatics without foundations. On the model-theoretical viewpoint in modern axiomatics. Philosophia Scientiae 9(Cahier 2), 97–107 (2005)

    Google Scholar 

  73. Lewis, C.I.: A Survey of Symbolic Logic: The Classic Algebra of Logic, Outline of Its History, Its Content, Interpretations and Applications, and Relation of it to Late Developments in Symbolic Logic. University of California Press, Berkeley (1918)

  74. Linke, P.F.: (Schaub, E. L., trans.), The present state of logic and epistemology in Germany, The Monist 36, 222–255 (1926)

    Google Scholar 

  75. Linsky, B.: The Evolution of Principia Mathematica: Bertrand Russell’s Manuscripts and Notes for the Second Edition. Cambridge University Press, Cambridge (2011)

  76. Löwenheim, L.: Über Möglichkeiten im Relativkalkül, Mathematische Annalen 75, 447–470 (1915) (English translation in [143], pp. 228–251)

    Google Scholar 

  77. Lyndon, R.C.: Review of [143]. Math. Rev. 35, #15 (1968)

  78. Mitchell, O.H.: On a new algebra of logic. In: [96], pp. 72–106 (1883)

  79. Moore, G.H.: Review of [143, 2nd, corrected, printing]. Hist. Math. 4, 468–471 (1977) (Abstract of the same by Moore in Historia Mathematica 3, 505 (1976))

  80. Moore, G.H.: Beyond first-order logic; the historical interplay between mathematical logic and axiomatic set theory. Hist. Philos. Log. 1, 95–137 (1980)

  81. Moore, G.H.: A house divided against itself: the emergence of first-order logic as the basis for mathematics. In: Phillips, E.R., (ed.) Studies in the History of Mathematics, pp. 98–136. Mathematics Association of America, Washington, DC (1987)

  82. Moore, G.H.: Letter to I. H. Anellis, 30 June, 1987 (1987)

  83. Moore, G.H.: The emergence of first-order logic. In: Aspray, W., Kitcher, P. (eds.) History and Philosophy of Modern Mathematics, pp. 95–138. University of Minnesota Press, Minneapolis (1988)

  84. Moore, G.H.: Reflections on the interplay between mathematics and logic. Mod. Log. 2, 281–311 (1992)

    Google Scholar 

  85. Moore, G.H.: Hilbert and the emergence of modern mathematical logic. Theoria (Segunda Épocha) 12, 65–90 (1997)

  86. Mostowski, A.: Review of [143]. Synthèse 18, 302–305 (1968)

  87. Müller, G.H., Lenski, W.: Omega Bibliography of Mathematical Logic (in 6 Volumes). Springer-Verlag, New York (1987)

  88. Oppenheimer, P.E., Zalta, E.N.: Relations versus functions at the foundations of logic: type-theoretic considerations. J. Log. Comput. 21, 351–374 (2011)

    Google Scholar 

  89. Pave, M.: Trotsky files are unveiled. In: Boston “Globe”, January 3, 1980, pp. 1–2 (1980)

  90. Pave, M.: His travels with Trotsky were always exciting, Boston “Globe”, January 6, 1980 (1980)

  91. Peckhaus, V.: Calculus ratiocinator vs. characteristica Universalis? the two traditions in logic, revisited (preprint, 16 May 2003). http://www.uni-paderborn.de/fileadmin/kw/institute/Philosophie/Personal/Peckhaus/Texte_zum_Down-load/two-traditions.pdf

  92. Peckhaus, V.: Calculus ratiocinator vs. characteristica universalis? the two traditions in logic, revisted, History and Philosophy of Logic 25, 3–14 (2004) (reprinted: Beaney, M., Reck, E. H. (eds.), Gottlob Frege. Critical Assessments of Leading Philosophers, Bd. 1: Frege’s Philosophy in Context. London/New York, Routledge, pp. 176–190 (2005))

  93. Peirce, C.S.: On an improvement in Boole’s calculus of logic (Paper read on 12 March 1867). In: Proceedings of the American Academy of Arts and Sciences, vol. 7, pp. 250–261 (1868) (reprinted in: [101], pp. 12–23)

  94. Peirce, C.S.: Description of a notation for the logic of relatives, resulting from an amplification of the conceptions of Boole’s calculus of logic. Mem. Am. Acad. 9, 317–378 (1870) (reprinted in: [101], pp. 359–429)

  95. Peirce, C.S.: On the algebra of logic. Am. J. Math. 3, 15–57 (1880) (reprinted in: [102], pp. 163–209)

  96. Peirce, C.S. (ed.): Studies in Logic by the Members of the Johns Hopkins University. Little, Brown & Co., Boston (1883) (reprinted, with an introduction by M. H. Fisch and a preface by A. Eschbach. John Benjamins Publishing Co., Amsterdam (1983))

  97. Peirce, C.S.: The logic of relatives. In: [96], pp. 187–203 (1883) (reprinted in: [99], pp. 195–210 and [102], pp. 453–466)

  98. Peirce, C.S.: On the algebra of logic: a contribution to the philosophy of notation. Am. J. Math. 7, 180–202 (1885) (reprinted in: [100], pp. 359–403 and [103], pp. 162–190)

  99. Peirce, C.S.: In: Hartshorne, C., Weiss, P. (eds.) Collected Papers of Charles Sanders Peirce, vol. III. Exact Logic (Published Papers). Harvard University Press, Cambridge (1933; 2nd edn., 1960)

  100. Peirce, C.S.: In: Hartshorne, C., Weiss, P. (eds.) Collected Papers of Charles Sanders Peirce, vol. IV: The Simplest Mathematics. Harvard University Press, Cambridge (1933; 2nd edn., 1961)

  101. Peirce, C.S.: In: Moore, E.C. (ed.) Writings of Charles S. Peirce: A Chronological Edition, vol. 2, pp. 1867–1871. Indiana University Press, Bloomington (1984)

  102. Peirce, C.S.: In: Kloesel, C.J.W. (ed.) Writings of Charles S. Peirce: A Chronological Edition, vol. 4, pp. 1879–1884. Indiana University Press, Bloomington (1989)

  103. Peirce, C.S.: In: Kloesel, C.J.W. (ed.) Writings of Charles S. Peirce: A Chronological Edition, vol. 5, pp. 1884–1886. Indiana University Press, Bloomington (1993)

  104. Prawitz D.: An improved proof procedure. Theoria 26, 102–139 (1960)

    Article  MathSciNet  MATH  Google Scholar 

  105. Putnam H.: Peirce the logician. Hist. Math. 8, 290–301 (1982)

    Article  MathSciNet  Google Scholar 

  106. Quine, W.V.: Methods of Logic. Holt, Rinehart, and Winston, New York (1950) (Routledge and Kegan Paul, London, 2nd edn. (1962))

  107. Quine, W.V.: In the logical vestibule, Times Literary Supplement, July 12, 1985, p. 767 (1985) (reprinted as MacHale on Boole, in [109], pp. 251–257)

  108. Quine, W.V.: Letter to Irving H. Anellis, 2 January 1988, manuscript (1988)

  109. Quine, W.V.: Selected Logic Papers. Harvard University Press, Cambridge (1995)

  110. Quine, W.V.: Peirce’s logic. In: Ketner, K.L. (ed.) Peirce and Contemporary Thought: Philosophical Inquiries. Fordham University Press, pp. 23–31 (1995) (an abbreviated version appears in [109], 258–265)

  111. Reid, C.: Hilbert—Courant. Springer-Verlag, New York (1986)

  112. Resnik, M.D.: Review of [143]. Philos. Sci. 35, 72 (1968)

  113. Robinson, J.A.: Theorem-proving on the computer. J. Assoc. Comput. Mach. 10, 163–174 (1963)

    Google Scholar 

  114. Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. Assoc. Comput. Mach. 12, 23–41 (1965)

    Google Scholar 

  115. Robinson, J.A.: Logic: Form and Function, the Mechanization of Deductive Reasoning. Elsevier, New York (1979)

  116. Robinson, J.A.: Computational logic: memories of the past and challenges for the future. In: Proceedings of Computational Logic–CL 2000, First International Conference, London, UK, 24–28 July, 2000. Lecture Notes in Computer Science, vol. 1861, pp. 1–24. Springer (2000). http://www.computational-logic.org/iccl/downloads/Robinson-CL2000.pdf

  117. Russell, B.: Notes on Peirce 1880 [95] and Peirce 1885 [98], manuscript, Russell Archives (ca. 1900–1901)

  118. Russell, B.: Notes on Schröder 1890–1900 [122–125], manuscript, RA file #230:030460 (1901)

  119. Russell, B.: Letter to G. Frege, 16 June 1902. In: [143], pp. 124–125 (1902)

  120. Russell, B.: The Principles of Mathematics. Cambridge University Press, Cambridge (1903)

  121. Russell, B.: Comments on the MIT version of [185], October 1913; manuscript, unpublished Russell Archives (1913)

  122. Schröder, E.: Vorlesungen über die Algebra der Logik (exacte Logik). Bd. I. Teubner, Leipzig (1890)

  123. Schröder, E.: Vorlesungen über die Algebra der Logik (exacte Logik). Bd. II, Th. 1, Teubner, Leipzig (1891)

  124. Schröder, E.: Vorlesungen über die Algebra der Logik (exacte Logik). Bd. III, Th. 1: Alegebra und Logik der Relative. Teubner, Leipzig (1895)

  125. Schröder, E.: Vorlesungen über die Algebra der Logik (exacte Logik). Vorlesungen über die Algebra der Logik. Exacte Logik, Bde. III. Teubner, Leipzig (1900)

  126. Shields, P.B.: Charles S. Peirce on the Logic of Number, Ph.D. Thesis, Fordham University (1981)

  127. Sluga, H.: Frege against the Booleans. Notre Dame J. Form. Log. 28, 80–98 (1987). http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ndjfl/109363-6848

  128. Smullyan, R.M.: A unifying principle in quantification theory. In: Proceedings of the National Academy of Sciences (June), vol. 49, 828–832 (1963)

  129. Smullyan, R.M.: Analytic natural deduction. J. Symb. Log. 30, 123–139 (1965)

    Google Scholar 

  130. Smullyan, R. M.: A unifying principle in quantification theory (1965). In: Addison, J.W., Henkin, L., Tarski, A. (eds.) The Theory of Models, pp. 433–434. North-Holland, Amsterdam (1973)

  131. Smullyan, R.M.: Trees and nest structures. J. Symb. Log. 31, 303–321 (1966)

    Google Scholar 

  132. Smullyan, R.M.: Finite nest structures and propositional logic. J. Symb. Log. 31, 322–324 (1966)

    Google Scholar 

  133. Smullyan, R.M.: First-order logic. Springer-Verlag, Berlin (1968) (corrected republication: Dover Publications, New York (1995))

  134. Smullyan, R.M.: Uniform Gentzen systems. J. Symb. Log. 33, 549–559 (1968)

    Google Scholar 

  135. Smullyan, R.M.: Analytic cut. J. Symb. Log. 33, 560–564 (1968)

  136. Smullyan, R.M.: The tableau method in quantification theory (1969); unpublished: was to have appeared in Transactions of the New York Academy of Sciences

  137. Smullyan, R.M.: Abstract quantification theory. In: Kino, A., Myhill, J.R., Vesey, R.E. (eds.) Intuitionism and Proof Theory: Proceedings of the Summer Conference at Buffalo, New York, 1968. North-Holland, Amsterdam/London, pp. 79–91 (1970) [To have originally been published in Transactions of the New York Academy of Sciences (1969)]

  138. Tarski, A.: (Woodger, J.H., ed. and trans.), Logic, Semantics, Metamathematics: Papers from 1923 to 1938, Clarendon Press, Oxford (1956)

  139. Thiel, C.: Leben und Werk Leopold Löwenheim (1878–1957). Jahresbericht der Deutschen Mathematiker-Vereinigung 77, 1–9 (1975)

  140. Thiel, C.: Leopold Löwenheim, life, work and early influence. In: Gandy, R.O., Hyland, J.M.E. (eds.) Logic Colloquium ‘76, pp. 235–252. North-Holland, Amsterdam (1977)

  141. van Heijenoort, J.: Jean Van Heijenoort Papers, 1946–1988, Archives of American Mathematics, Dolph Briscoe Center for American History, University of Texas at Austin (1946–1988)

  142. van Heijenoort, J.: Interpretations, satisfiability, validity; typescript. In: [141] Box 3.8/86-33/1 (1966)

  143. van Heijenoort, J. (ed.): From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Harvard University Press, Cambridge (1967)

  144. van Heijenoort, J.: Introductory note to [45]. In: [143], pp. 1–5 (1967) (reprinted: [151], pp. 1–5 (1970))

  145. van Heijenoort, J.: Introductory note to [51,53,54]. In: [143], pp. 592–595 (1967) (reprinted: [151], pp. 83–86 (1970))

  146. van Heijenoort, J.: Introductory note to [119]. In: [143], p. 124 (1967)

  147. van Heijenoort, J: Introductory note to [46], pp. 126–127 (1967)

  148. van Heijenoort, J: Logic as calculus and logic as language, Synthèse 17, 324–330; reprinted in: Cohen, R.S., Wartofsky, M.W. (eds.) Boston Studies in the Philosophy of Science 3: Proceedings of the Boston Colloquium Philosophy of Science 1964/1965. Reidel, Dordrecht, pp. 440–446 (1967); reprinted in [172], pp. 11–16 and [66], pp. 233–239

  149. van Heijenoort, J.: Préface to [60], pp. 1–12 (1968)

  150. van Heijenoort, J.: On the relation between the falsifiability tree method and the Herbrand method in quantification theory; typescript, 20 November 1968. In: [141], Box 3.8/86-33/1 (1968)

  151. van Heijenoort (ed.): Frege and Gödel: Two Fundamental Texts in Mathematical Logic. Harvard University Press, Cambridge (1970)

  152. van Heijenoort, J.: On the relation between the falsifiability tree method and the Herbrand method in quantification theory; abstract. J. Symb. Log. 35, 358 (1970)

    Google Scholar 

  153. van Heijenoort, J.: Notes on the tree method; typescript, 15 October 1971. In: [141], Box 3.8/86-33/1 (1971)

  154. van Heijenoort, J.: Proof of the completeness of the method of Beth sentential tableaux; manuscript, 1 March 1972. In: [141], Box 3.8/86-33/1 (1972)

  155. van Heijenoort, J.: Falsifiability trees; unpublished typescript, 15 March 1972. In: [141], Box 3.8/86-33/1 (1972)

  156. van Heijenoort, J.: The tableau method for Grzegorczyk quantification theory; manuscript, 18 March 1972. In: [141], Box 3.8/86-33/1 (1972)

  157. van Heijenoort, J.: The falsifiability-tree method for the simple theory of types with extensionality; draft typescript, 23 July 1972. In: [141], Box 3.8/86-33/1 (1972)

  158. van Heijenoort, J.: Comparison between the falsifiability-tree method and the Gentzen system; typescript (numbered pp. 25–33), 3 May 1973. In: [141], Box 3.8/86-33/1 (1973)

  159. van Heijenoort, J.: Soundness and completeness of the falsifiability-tree method for sentential logic; manuscript, 23 September 1973. In: [141], Box 3.8/86-33/1 (1973)

  160. van Heijenoort, J.: Subject and predicate in Western logic, Philosophy East and West 24, 253–268 (1974) (reprinted in: [172], pp. 17–34)

  161. van Heijenoort, J.: Falsifiability trees; typescript, revised version of 150; 30 September 1974. In: [141], Box 3.8/86-33/1 (1974)

  162. van Heijenoort, J.: Historical development of modern logic, in [141], Box 3.8/86-33/1 (1974); first published: [177]; reprinted: this issue

  163. van Heijenoort, J.: The tree method for intuitionistic sentential logic; manuscript, 5 May 1975; in Anellis archives (1975)

  164. van Heijenoort, J.: The tree method for intuitionistic quantification theory; manuscript, 9 May 1975. In: [141], Box 3.8/86-33/1 (1975)

  165. van Heijenoort, J.: Herbrand; typescript; 18 May 1975. In: [141], Box 3.8/86-33/1 (1975)

  166. van Heijenoort, J.: El desarrollo de la teoría de la cuantificación. Universidad Nacional Autónoma de México, Instituto de Investigaciones filosóficas, Mexico City (1976)

  167. van Heijenoort, J.: Set-theoretic semantics. In: Gandy, R.O., Hyland, J.M.E. (eds.) Logic Colloquium ‘76, Proceedings of a Conference Held in Oxford in July 1976. North-Holland, Amsterdam, pp. 183–190 (1977) (reprinted in: [172], pp. 43–53)

  168. van Heijenoort, J.: With Trotsky in Exile, from Prinkipo to Coyoacán. Harvard University Press, Cambridge (1978)

  169. van Heijenoort, J.: Introduction à à la sémantique des logiques non-classique. Collection de l’École Normale Supérieur des Jeunes Filles, no. 16, École Normale Supérieur des Jeunes Filles, Paris (1979)

  170. van Heijenoort, J.: The history of Trotsky’s papers, Harvard Library Bulletin 28(3), 291–298 (1980); Italian translation: Il Ponte 36(11/12), 1493–1499 (1980)

  171. van Heijenoort, J.: L’oeuvre logique de Jacques Herbrand et son contexte historique. In: Stern, J. (ed.) Proceedings of the Herbrand Symposium, Logic Colloquium ‘81, Marseilles, France, July 1981. North-Holland, Amsterdam, pp. 57–85 (1982); English translation in: [172], pp. 99–121

  172. van Heijenoort, J.: Selected Essays. Bibliopolis, Naples (1985)

  173. van Heijenoort, J: Jacques Herbrand’s work in logic and its historical context. In: [172], pp. 99–121 (1985)

  174. van Heijenoort, J.: Absolutism and relativism in logic (1979). In: [172], pp. 75–83 (1985)

  175. van Heijenoort, J.: Système et métasystème chez Russell; abstract. J. Symb. Log. 52, 298 (1987)

    Google Scholar 

  176. van Heijenoort, J.: Système et métasystème chez Russell. In: The Paris Logic Group (eds.), Logic Colloquium ‘85. Amsterdam, pp. 111–122 (1987)

  177. van Heijenoort, J.: Historical development of modern logic (edited, with an introduction by I. H. Anellis). Mod. Log. 2, 242–245 (1992) (reprinted, this issue)

  178. Weyl, H.: David Hilbert and his mathematical work. Bull. Am. Math. Soc. (1) 50, 612–654 (1944)

    Google Scholar 

  179. Whitehead A.N.: A Treatise of Universal Algebra. Cambridge University Press, Cambridge (1898)

    Google Scholar 

  180. Whitehead, A.N.: Memoir on the algebra of symbolic logic. Am. J. Math. 23, 139–165, 253–316 (1901)

    Google Scholar 

  181. Whitehead, A.N., Russell, B.: Principia Mathematica, vol. 1. Cambridge University Press, Cambridge (1910)

  182. Whitehead, A.N., Russell, B.: Principia Mathematica, vol. 2. Cambridge University Press, Cambridge (1912)

  183. Whitehead, A.N., Russell, B.: Principia Mathematica, vol. 3. Cambridge University Press, Cambridge (1913)

  184. Whitehead, A.N., Russell, B.: Principia Mathematica, 3 vols, 2nd edn. Cambridge University Press, Cambridge (1925–1927)

  185. Wiener, N.: A Comparison between the Treatment of the Algebra of Relatives by Schroeder and that by Whitehead and Russell. Ph.D. Thesis, Harvard University (Harvard transcript and MIT transcript) (1913) (Partial publication as Appendix 8 of the introduction and last chapter in [30, pp. 429–444])

  186. Wiener, N.: A simplification of the logic of relations. In: Proceedings of the Cambridge Philosophical Society, vol. 17, pp. 387–390 (1914); reprinted in: [143], pp. 224–227

  187. Wittgenstein, L.: Tractatus Logico-philosophicus (with an introduction by B. Russell). Routledge and Kegan Paul, London (1922)

  188. Wittgenstein, L.: (Anscombe, G. E. M., trans.), Philosophical Investigations. Blackwell, Oxford (1953)

  189. Zermelo, E.: Beweis, dass jede Menge wohlgeordnet werden kann, Mathematische Annalen 59, 514–516 (1904); English translation in [143], pp. 139–141

    Google Scholar 

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Anellis, I.H. Editor’s Introduction to Jean van Heijenoort, Historical Development of Modern Logic. Log. Univers. 6, 301–326 (2012). https://doi.org/10.1007/s11787-012-0063-8

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