論理学の歴史とは?

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論理学の歴史

出典: フリー百科事典『ウィキペディア(Wikipedia)』 (2019/08/07 23:42 UTC 版)

論理学の歴史では、妥当な推論を探求する学問の発展を取り扱う。形式論理学は古代の中国、インドギリシアで発展した。ギリシア論理学、中でもアリストテレス論理学は科学・数学に広く受容・応用されている。




  1. ^ a b Oxford Companion p. 498; Bochenski, Part I Introduction, passim
  2. ^ a b Oxford Companion p. 500
  3. ^ Kneale, p. 2
  4. ^ a b c d e Kneale, p. 3.
  5. ^ H. F. J. Horstmanshoff, Marten Stol, Cornelis Tilburg (2004), Magic and Rationality in Ancient Near Eastern and Graeco-Roman Medicine, p. 99, Brill Publishers, ISBN 90-04-13666-5.
  6. ^ D. Brown (2000), Mesopotamian Planetary Astronomy-Astrology , Styx Publications, ISBN 90-5693-036-2.
  7. ^ Heath, Mathematics in Aristotle, cited in Kneale, p. 5.
  8. ^ Kneale p. 15
  9. ^ Kneale, p. 16.
  10. ^ Kneale, p. 17.
  11. ^ "forming an opinion is talking, and opinion is speech that is held not with someone else or aloud but in silence with oneself" Theaetetus 189E–190A
  12. ^ Kneale, p. 20. For example, the proof given in the Meno that the square on the diagonal is double the area of the original square presumably involves the forms of the square and the triangle, and the necessary relation between them
  13. ^ Kneale p. 21
  14. ^ Zalta, Edward N. "Aristotle's Logic". Stanford University, 18 March 2000. Retrieved 13 March 2010.
  15. ^ See e.g. Aristotle's logic, Stanford Encyclopedia of Philosophy
  16. ^ Bochenski p. 63
  17. ^ "Throughout later antiquity two great schools of logic were distinguished, the Peripatetic which was derived from Aristotle, and the Stoic which was developed by Chrysippus from the teachings of the Megarians" – Kneale p. 113
  18. ^ Oxford Companion, article "Chrysippus", p. 134.
  19. ^ [1] Stanford Encyclopedia of Philosophy: Susanne Bobzien, Ancient Logic
  20. ^ K. Huelser, Die Fragmente zur Dialektik der Stoiker, 4 vols, Stuttgart 1986-7
  21. ^ Kneale, 117–158.
  22. ^ Metaphysics Eta 3, 1046b 29
  23. ^ Boethius, Commentary on the Perihermenias, Meiser p. 234.
  24. ^ Epictetus, Dissertationes ed. Schenkel ii. 19. I.
  25. ^ Alexander p. 177.
  26. ^ Sextus, Adv. Math. pp. viii, 113.
  27. ^ See e.g. Lukasiewicz, p. 21.
  28. ^ Sextus pp. viii., 11, 12.
  29. ^ Bochenski, p. 446.
  30. ^ S. C. Vidyabhusana (1971). A History of Indian Logic: Ancient, Mediaeval, and Modern Schools.
  31. ^ R. P. Kangle (1986). The Kautiliya Arthashastra (1.2.11). Motilal Banarsidass.
  32. ^ Bochenski p. 417 and passim
  33. ^ Bochenski pp. 431–7
  34. ^ Bochenski, p. 438.
  35. ^ Bochenksi, p. 441.
  36. ^ Kisor Kumar Chakrabarti (June 1976). “Some Comparisons Between Frege's Logic and Navya-Nyaya Logic”. Philosophy and Phenomenological Research (International Phenomenological Society) 36 (4): 554–563. doi:10.2307/2106873. JSTOR 2106873. "This paper consists of three parts. The first part deals with Frege's distinction between sense and reference of proper names and a similar distinction in Navya-Nyaya logic. In the second part we have compared Frege's definition of number to the Navya-Nyaya definition of number. In the third part we have shown how the study of the so-called 'restrictive conditions for universals' in Navya-Nyaya logic anticipated some of the developments of modern set theory." 
  37. ^ Boole, Mary Everest "Collected Works" eds E M Cobham and E S Dummer London, Daniel 1931. Letter also published in the Ceylon National Review in 1909, and published as a separate pamphlet "The Psychologic Aspect of Imperialism" in 1911.
  38. ^ Jonardon Ganeri (2001). Indian logic: a reader. Routledge. p. vii. ISBN 0-7007-1306-9 
  39. ^ Indian Thought and Western Science in the Nineteenth Century オンラインで公開されている当該書籍 (p. 9)
  40. ^ See e.g. Routledge Encyclopedia of Philosophy Online Version 2.0, article 'Islamic philosophy'
  41. ^ a b History of logic: Arabic logic, Encyclopædia Britannica.
  42. ^ Feldman, Seymour (1964-11-26). “Rescher on Arabic Logic”. The Journal of Philosophy (Journal of Philosophy, Inc.) 61 (22): 724–734. doi:10.2307/2023632. ISSN 0022-362X. JSTOR 2023632.  [726]. Long, A. A.; D. N. Sedley (1987). The Hellenistic Philosophers. Vol 1: Translations of the principal sources with philosophical commentary. Cambridge: Cambridge University Press. ISBN 0-521-27556-3. 
  43. ^ Dag Nikolaus Hasse (2008年9月19日). “Influence of Arabic and Islamic Philosophy on the Latin West”. Stanford Encyclopedia of Philosophy. 2009年10月13日閲覧。
  44. ^ Richard F. Washell (1973), "Logic, Language, and Albert the Great", Journal of the History of Ideas 34 (3), pp. 445–450 [445].
  45. ^ a b Goodman, Lenn Evan (2003), Islamic Humanism, p. 155, Oxford University Press, ISBN 0-19-513580-6.
  46. ^ Goodman, Lenn Evan (1992); Avicenna, p. 188, Routledge, ISBN 0-415-01929-X.
  47. ^ Kneale p. 229
  48. ^ Kneale: p. 266; Ockham: Summa Logicae i. 14; Avicenna: Avicennae Opera Venice 1508 f87rb
  49. ^ a b Muhammad Iqbal, The Reconstruction of Religious Thought in Islam, "The Spirit of Muslim Culture" (cf. [2] and [3])
  50. ^ a b Tony Street (2008年7月23日). “Arabic and Islamic Philosophy of Language and Logic”. Stanford Encyclopedia of Philosophy. 2008年12月5日閲覧。
  51. ^ Dr. Lotfollah Nabavi, Sohrevardi's Theory of Decisive Necessity and kripke's QSS System, Journal of Faculty of Literature and Human Sciences.
  52. ^ Dr. Abu Shadi Al-Roubi (1982), "Ibn Al-Nafis as a philosopher", Symposium on Ibn al-Nafis, Second International Conference on Islamic Medicine: Islamic Medical Organization, Kuwait (cf. Ibn al-Nafis As a Philosopher, Encyclopedia of Islamic World).
  53. ^ See pp. 253–254 of Street, Tony (2005). “Logic”. In Peter Adamson and Richard C. Taylor (edd.). The Cambridge Companion to Arabic Philosophy. Cambridge University Press. pp. 247–265. ISBN 978-0-521-52069-0. 
  54. ^ Ruth Mas (1998). “Qiyas: A Study in Islamic Logic”. Folia Orientalia 34: 113–128. ISSN 0015-5675. http://www.colorado.edu/ReligiousStudies/faculty/mas/LOGIC.pdf. 
  55. ^ a b John F. Sowa; Arun K. Majumdar (2003). “Analogical reasoning”. Conceptual Structures for Knowledge Creation and Communication, Proceedings of ICCS 2003. Berlin: Springer-Verlag. http://www.jfsowa.com/pubs/analog.htm , pp. 16-36
  56. ^ Nicholas Rescher and Arnold vander Nat, "The Arabic Theory of Temporal Modal Syllogistic", in George Fadlo Hourani (1975), Essays on Islamic Philosophy and Science, pp. 189–221, State University of New York Press, ISBN 0-87395-224-3.
  57. ^ Boehner p. xiv
  58. ^ Kneale, p. 198.
  59. ^ Stephen Dumont, article "Peter Abelard" in Gracia and Noone, p. 492.
  60. ^ Kneale, pp. 202–3.
  61. ^ See e.g. Kneale, p. 225.
  62. ^ Boehner, p. 1.
  63. ^ Boehner, pp. 19–76.
  64. ^ Boehner, p. 29.
  65. ^ Boehner, p. 30.
  66. ^ Ebbesen 1981
  67. ^ Boehner, pp. 54–5.
  68. ^ Oxford Companion p. 504, article "Traditional logic"
  69. ^ a b Buroker xxiii
  70. ^ Farrington, 1964, 89
  71. ^ N. Abbagnano, "Psychologism" in P. Edwards (ed) The Encyclopaedia of Philosophy, MacMillan, 1967
  72. ^ Of the German literature in this period, Robert Adamson wrote "Logics swarm as bees in springtime..."; Robert Adamson, A Short History of Logic, Wm. Blackwood & Sons, 1911, page 242
  73. ^ Carl von Prantl (1855-1867), Geschichte von Logik in Abendland, Leipsig: S. Hirzl, anastatically reprinted in 1997, Hildesheim: Georg Olds.
  74. ^ See e.g. Psychologism, Stanford Encyclopedia of Philosophy
  75. ^ Wilhelm Wundt, Logik (1880–1883); quoted in Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, pp. 115–116.
  76. ^ Theodor Lipps, Grundzüge der Logik (1893); quoted in Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, p. 40
  77. ^ Christoph von Sigwart, Logik (1873–78); quoted in Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, p. 51
  78. ^ Benno Erdmann, Logik (1892); quoted in Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, p. 96
  79. ^ Dermot Moran, "Introduction"; Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, p. xxi
  80. ^ Michael Dummett, "Preface"; Edmund Husserl, Logical Investigations, translated J.N. Findlay, Routledge, 2008, Volume 1, p. xvii
  81. ^ Josiah Royce, "Recent Logical Enquiries and their Psychological Bearings" (1902) in John J. McDermott (ed) The Basic Writings of Josiah Royce Volume 2, Fordham University Press, 2005, p. 661
  82. ^ Bochenski, p. 266
  83. ^ Peirce 1896
  84. ^ Bochenski, ibidem
  85. ^ See Bochenski p. 269
  86. ^ Oxford Companion p. 499
  87. ^ Edith Sylla (1999), "Oxford Calculators", in The Cambridge Dictionary of Philosophy, Cambridge, Cambridgeshire: Cambridge.
  88. ^ El. philos. sect. I de corp 1.1.2.
  89. ^ Bochenski p. 274
  90. ^ Rutherford, Donald, 1995, "Philosophy and language" in Jolley, N., ed., The Cambridge Companion to Leibniz. Cambridge Univ. Press.
  91. ^ Wiener, Philip, 1951. Leibniz: Selections. Scribner.
  92. ^ Essai de dialectique rationelle, 211n, quoted in Bochenski p. 277.
  93. ^ Wissenschaftslehre II 198ff, quoted in Bochenski 280; see Oxford 'Companion p. 498.
  94. ^ See e.g. Bochenski p. 296 and passim
  95. ^ Before publishing, he wrote to De Morgan, who was just finishing his work Formal Logic. De Morgan suggested they should publish first, and thus the two books appeared at the same time, possibly even reaching the bookshops on the same day. cf. Kneale p. 404
  96. ^ Kneale p. 404
  97. ^ a b c Kneale p. 407
  98. ^ Boole (1847) p. 16
  99. ^ Boole 1847 pp. 58–9
  100. ^ Beaney p. 11
  101. ^ Kneale p. 422
  102. ^ Peirce, "A Boolean Algebra with One Constant", 1880 MS, Collected Papers v. 4, paragraphs 12–20, reprinted Writings v. 4, pp. 218-21. Google Preview.
  103. ^ Trans. Amer. Math. Soc., xiv (1913), pp. 481–8. This is now known as the Sheffer stroke
  104. ^ Bochenski 296
  105. ^ See CP III
  106. ^ a b Kneale p. 435
  107. ^ Jevons, The Principles of Science, London 1879, p. 156, quoted in Grundlagen 15
  108. ^ Beaney p. 10 – the completeness of Frege's system was eventually proved by Jan Łukasiewicz in 1934
  109. ^ See for example the argument by the medieval logician William of Ockham that singular propositions are universal, in Summa Logicae III. 8 (??)
  110. ^ "On concept and object" p. 198; Geach p. 48
  111. ^ BLC p. 14, quoted in Beaney p. 12
  112. ^ See e.g. The Internet Encyclopedia of Philosophy, article "Frege"
  113. ^ See e.g. Potter 2004
  114. ^ Zermelo 1908
  115. ^ Feferman 1999 p. 1
  116. ^ Girard, Jean-Yves; Paul Taylor, Yves Lafont (1990) [1989]. Proofs and Types. Cambridge University Press (Cambridge Tracts in Theoretical Computer Science, 7). ISBN 0-521-37181-3. http://www.paultaylor.eu/stable/Proofs%2BTypes.html. 
  117. ^ Alex Sakharov. "Cut Elimination Theorem". MathWorld(英語).
  118. ^ Feferman and Feferman 2004, p. 122, discussing "The Impact of Tarski's Theory of Truth".
  119. ^ Feferman 1999, p. 1
  120. ^ See e.g. Barwise, Handbook of Mathematical Logic
  121. ^ The Independence of the Continuum Hypothesis, II Paul J. Cohen Proceedings of the National Academy of Sciences of the United States of America, Vol. 51, No. 1. (Jan. 15, 1964), pp. 105-110.
  122. ^ Many of the foundational papers are collected in The Undecidable (1965) edited by Martin Davis
  123. ^ Jerry Fodor, "Water's water everywhere", London Review of Books, 21 October 2004
  124. ^ See Philosophical Analysis in the Twentieth Century: Volume 2: The Age of Meaning, Scott Soames: "Naming and Necessity is among the most important works ever, ranking with the classical work of Frege in the late nineteenth century, and of Russell, Tarski and Wittgenstein in the first half of the twentieth century". Cited in Byrne, Alex and Hall, Ned. 2004. 'Necessary Truths'. Boston Review October/November 2004




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