Skip to main content

The Tractatus System of Arithmetic

Abstract

The philosophy of arithmetic of Wittgenstein's Tractatus is outlined and the central role played in it by the general notion of operation is pointed out. Following which, the language, the axioms and the rules of a formal theory of operations, extracted from the Tractatus, are presented and a theorem of interpretability of the equational fragment of Peano's Arithmetic into such a formal theory is proven.

This is a preview of subscription content, access via your institution.

REFERENCES

  • Anscombe, G. E. M.: 1959, An Introduction to Wittgenstein's Tractatus, Hutchinson University Library, London.

    Google Scholar 

  • Frascolla, P.: 1994, Wittgenstein's Philosophy of Mathematics, Routledge, London–New York.

    Google Scholar 

  • Hintikka, M. B. and Hintikka, J.: 1986, Investigating Wittgenstein, Blackwell, Oxford–New York.

    Google Scholar 

  • Lewy, C.: 1967, 'A Note on the Text of the Tractatus', Mind XXVI, 416–23.

    Google Scholar 

  • Ramsey, F. P.: 1931, The Foundations of Mathematics and Other Logical Essays, Routledge & Kegan Paul, London

    Google Scholar 

  • Russell, B.: 1922, Introduction, in L. Wittgenstein (1922).

  • Wittgenstein, L.: 1922, Tractatus Logico-Philosophicus, Kegan Paul-Trench-Trubner, London (quotations are from the Routledge & Kegan Paul edition, London 1969, translation from the German text by D. F. Pears and B. F. McGuiness).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Frascolla, P. The Tractatus System of Arithmetic. Synthese 112, 353–378 (1997). https://doi.org/10.1023/A:1004952810156

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1004952810156

Keywords

  • Formal Theory
  • General Notion
  • Equational Fragment