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Wittgenstein and logic

Abstract

In his Tractatus Logico-Philosophicus Ludwig Wittgenstein (1889–1951) presents the concept of order in terms of a notational iteration that is completely logical but not part of logic. Logic for him is not the foundation of mathematical concepts but rather a purely formal way of reflecting the world that at the minimum adds absolutely no content. Order for him is not based on the concepts of logic but is instead revealed through an ideal notational series. He states that logic is “transcendental”. As such it requires an ideal that his philosophical method eventually forces him to reject. I argue that Wittgenstein’s philosophy is more dialectical than transcendental.

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References

  1. Bernays P. (1959). Comments on Ludwig Wittgenstein’s Remarks on the foundations of mathematics. Ratio 2: 1–22

  2. Carnap R. (1963). Intellectual autobiography. In: Hahn L.E., Schilpp P.A. (eds) The philosophy of Rudolf Carnap. Open Court, La Salle, pp 3–86

  3. Dedekind, R. (1888). Was sind und was sollen die Zahlen? Brunswick: F. Vieweg. Sixth edition in Essays on the theory of numbers (Trans: Beman, W.W.) (pp. 31–115). Reprinted (New York: Dover, 1963).

  4. Dreben B., Floyd J. (1991). Tautology: How not to use a word. Synthese 87:23–49

  5. Dummett M. (1959). Wittgenstein’s philosophy of mathematics. The Philosophical Review 68:324–348

  6. Floyd J., Putnam H. (2006). Bays, Steiner, and Wittgenstein’s ‘Notorious’ paragraph about the Gödel Theorem. The Journal of Philosophy 103:101–110

  7. Frege, G. (1879). Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. (Trans: van Heijenoort (1967a, pp. 1–82)). Halle.

  8. Frege G. (1892a). On sense and meaning, in Frege (1984, pp. 157–177) (Trans: Black, M.). From the original in Zeitschrift für Philosophie und philosophische Kritik, 100, 25–50.

  9. Frege, G. (1892b). On concept and object, in Frege (1984, pp. 182–194) (Trans: Geach, P.). From the original in Vierteljahrsschrift für wissenschaftliche Philosophie 16, 192–205.

  10. Frege, G. (1984). Collected papers on mathematics, logic, and philosophy (B. McGuinness, Ed.). Oxford and New York: Basil Blackwell.

  11. Goldfarb W. (1983). I want you to bring me a slab: Remarks on the opening sections of the Philosophical investigations. Synthese 56:265–282

  12. Hilbert, D. (1899). Grundlagen der Geometrie. Festschrift zur Feier der Enthüllung des Gauss-Weber Denkmals in Göttingen. Leipzig: Teubner. In P. Bernays (Ed.), Foundations of geometry (10th ed.) (Stuttgart: Teubner, 1968) (Trans: Unger, L.) (La Salle: Open Court, 1971).

  13. Hintikka J. (1968). On Kant’s notion of intuition (Anschauung). In: Penelhum T., MacIntosh J.J. (eds). The first critique: Reflections on Kant’s Critique of pure reason. Belmont, Wadsworth, pp. 38–53

  14. Hintikka J. (1984). Kant’s transcendental method and his theory of numbers. Topoi 3:99–108

  15. Kanamori A. (1996). The mathematical development of set theory from Cantor to Cohen. The Bulletin of Symbolic Logic 2:1–71

  16. Kant, I. (1787). Critique of pure reason (2nd ed.) (Trans: Guyer, P. & Wood, A.). Cambridge: Cambridge University Press, 1998 (First edition published in 1781).

  17. Kant, I. (1800). Logik: ein Handbuch zu Vorlesungen (2nd ed.) (G. B. Jäsche, Ed.). Königsberg: Friedrich Nicolovius.

  18. Kant, I. (1900). Kant’s gesammelte Schriften. (The Deutsche Akademie der Wissenschaften, Ed.). Berlin: Walter de Gruyter.

  19. Kreisel G. (1958). Wittgenstein’s Remarks on the foundations of mathematics. British Journal for the Philosophy of Science 9:135–158

  20. Kripke S. (1982). Wittgenstein on rules and private language. An elementary exposition. Cambridge, Harvard University Press

  21. Link, M. (2005). Wittgenstein and infinity. Ph.D. thesis. Boston University.

  22. Link, M. (2007). Wittgenstein and logical analysis. In A. Pichler, H. Hrachovec, & J. Wang (Eds.), Philosophie der Informationsgesellschaft. Kirchberg am Wechsel: Österreichische Ludwig Wittgenstein Gesellschaft: 131ff.

  23. Maddy P. (1986). Mathematical alchemy. British Journal for the Philosophy of Science 37:279–314

  24. Marion M. (1995). Wittgenstein and finitism. Synthese 105:141–176

  25. McDowell J. (1984). Wittgenstein on following a rule. Synthese 58:325–363

  26. Parsons C. (1984). Arithmetic and the categories. Topoi 3:109–121

  27. Ramsey, F. (1925). Foundations of mathematics, In Proceedings of the London Mathematical Society, s. 2, 25, 338–384.

  28. Russell, B. (1914). Our knowledge of the external world as a field for scientific method in philosophy. Open Court. Reprinted (London and New York: Routledge, 2005).

  29. Sheffer H.M. (1926). Review of Whitehead and Russell (1925). Isis 8:226–231

  30. van Heijenoort J. (ed) (1967a). From Frege to Gödel. A source book in mathematical logic, 1879–1931. Cambridge and London, Harvard University Press

  31. van Heijenoort J. (1967b). Logic as calculus and logic as language. Boston Studies in the Philosophy of Science 3:440–446

  32. von Wright, G. H. (1993). The Wittgenstein papers. In L. Wittgenstein, Philosophical occasions. 1912–1951 (J. C. Klagge, & A. Nordmann, Eds.) (pp. 480–510). Indianapolis: Hackett.

  33. Wang, H. (1958). Eighty years of foundational studies. Dialectica, 12, 466–497. Reprinted as the second chapter of A Survey of Mathematical Logic (Peking: Science Press, 1962).

  34. Whitehead A.N., Russell B. (1910). Principia Mathematica (Vol. 1). Cambridge, Cambridge University Press

  35. Whitehead A.N., Russell B. (1912). Principia Mathematica (Vol. 2). Cambridge, Cambridge University Press

  36. Whitehead A.N., Russell B. (1925). Principia Mathematica (Vol. 1, Second edition of Whitehead and Russell (1910) with new introduction). Cambridge, Cambridge University Press

  37. Wittgenstein, L. (1921). Logisch-philosophische Abhandlung. Annalen der Naturphilosophie, In Wilhelm Ostwald (Ed.), Band XIV, Heft 3/4.

  38. Wittgenstein, L. (1922). Tractatus Logico-Philosophicus. International library of psychology and scientific method (Trans: Ogden, C. K. with the assistance of F.P. Ramsey, with original German of Wittgenstein (1921) included). London: Routledge and Kegan Paul. Corrected edition (New York and London: 1933) reprinted (Trowbridge: Redwood Burn, 1988).

  39. Wittgenstein, L. (1929). Some remarks on logical form. In Proceedings of the Aristotelian Society, s.v. 9, pp. 162–171.

  40. Wittgenstein, L. (1953). Philosophical investigations (G. E. M. Anscombe, Trans. with the original German text included). Oxford: Basil Blackwell; New York: Macmillan. (Second edition (Oxford: Basil Blackwell and Mott; New York: acmillan, 1958)).

  41. Wittgenstein, L. (1956). Remarks on the foundations of mathematics (G. H. von Wright, R. Rhees, & G. E. M. Anscombe, Eds., G. E. M. Anscombe, Trans.). Oxford: Blackwell.

  42. Wittgenstein, L. (1974). Philosophical grammar (R. Rhees, Ed., A. Kenny, Trans.). Oxford: Basil Blackwell; Berkeley and Los Angeles: University of California Press.

  43. Wittgenstein, L. (1975). Philosophical remarks (R. Rhees, Ed., R. Hargreaves & R. White, Trans.). Chicago: University of Chicago Press.

  44. Wittgenstein, L. (1976). Lectures on the foundations of mathematics, 1939 (C. Diamond, Ed.). Ithaca: Cornell University Press. Reprinted (Chicago and London: University of Chicago Press, 1989).

  45. Wittgenstein L. (1978). Revised edition of Wittgenstein (1956). Cambridge, MIT Press

  46. Wittgenstein, L. (1979). Notebooks 1914–1916 (2nd ed.) (G. H. von Wright & G. E. M. Anscombe, Eds., G. E. M. Anscombe, Trans.). Chicago: University of Chicago Press.

  47. Wittgenstein, L. (1982). Last writings on the philosophy of psychology (Vol. 1). Preliminary studies for part II of philosophical investigations (G. H. von Wright & H. Nyman, Eds., C. G. Luckhardt & M. A. E. Aue, Trans.). Chicago: University of Chicago Press. Midway reprint (1990).

  48. Wittgenstein, L. (1992). Last writings on the philosophy of psychology (Vol. 2). The inner and the outer. (G. H. von Wright, & H. Nyman, Eds., C.G. Luckhardt, & M. A. E. Aue, Trans.). Oxford and Cambridge: Blackwell.

  49. Wittgenstein, L. (1995). Cambridge letters. Correspondence with Russell, Keynes, Moore, Ramsey, and Sraffa (B. McGuinness & G. H. von Wright, Eds.). Oxford and Cambridge: Blackwell.

  50. Wright C. (1982). Strict finitism. Synthese 51:203–282

  51. Wrigley M. (1977). Wittgenstein’s philosophy of mathematics. Philosophical Quarterly 27:50–59

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Correspondence to Montgomery Link.

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Link, M. Wittgenstein and logic. Synthese 166, 41–54 (2009). https://doi.org/10.1007/s11229-007-9256-8

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Keywords

  • Wittgenstein
  • Logic
  • Order
  • Thought
  • McDowell
  • Operation
  • Number
  • Rule