Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-19T05:44:13.372Z Has data issue: false hasContentIssue false

Tait's conservative extension theorem revisited

Published online by Cambridge University Press:  12 March 2014

Ryota Akiyoshi*
Affiliation:
Department of Philosophy, Keio University, Tokyo, Mita 2-15-45, Japan, E-mail: [email protected]

Abstract

This paper aims to give a correct proof of Tait's conservative extension theorem. Tait's own proof is flawed in the sense that there are some invalid steps in his argument, and there is a counterexample to the main theorem from which the conservative extension theorem is supposed to follow. However, an analysis of Tait's basic idea suggests a correct proof of the conservative extension theorem and a corrected version of the main theorem.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] Martin-Löf, Per, An intuitionistic theory of types, Twenty-five years of constructive type theory, Oxford University Press, 1998, pp. 221224.Google Scholar
[2] Tait, William W., Against intuitionism: Constructive mathematics is part of classical mathematics, Journal of Philosophical Logic, vol. 12 (1983), pp. 173195.Google Scholar
[3] Tait, William W., Theplatonism of mathematics, Synthese, vol. 69 (1986), pp. 341370.Google Scholar
[4] Tait, William W., The law of excluded middle and the axiom of choice, Mathematics and mind (George, Alexander, editor), Oxford University Press, 1994, reprinted in [6], pp. 4570.Google Scholar
[5] Tait, William W., The completeness of Hey ting first-order logic, this Journal, vol. 68 (2003), pp. 751763.Google Scholar
[6] Tait, William W., The provenance of pure reason: Essays in the philosophy of mathematics and its history, Oxford University Press, 2005.Google Scholar