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The Friedman-Sheard programme in intuitionistic logic

Published online by Cambridge University Press:  12 March 2014

Graham E. Leigh  and
Michael Rathjen
Graham E. Leigh
Affiliation:
Faculty of Philosophy, University of Oxford, Oxford OX1 4JJ, UK, E-mail: graham.leigh@philosophy.ox.ac.uk
Michael Rathjen
Affiliation:
School of Mathematics, University of Leeds, Leeds LS2 9JT, UK, E-mail: rathjen@maths.leeds.ac.uk
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Abstract

This paper compares the roles classical and intuitionistic logic play in restricting the free use of truth principles in arithmetic. We consider fifteen of the most commonly used axiomatic principles of truth and classify every subset of them as either consistent or inconsistent over a weak purely intuitionistic theory of truth.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 3 , September 2012 , pp. 777 - 806
Copyright
Copyright © Association for Symbolic Logic 2012

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References

REFERENCES

[1] Cantini, A., A theory of formal truth arithmetically equivalent to ID1 , this Journal, vol. 55 (1990), no. 1, pp. 244–259.Google Scholar
[2] Feferman, S., Toward useful type-free theories. I, this Journal, vol. 49 (1984), no. 1, pp. 75–111.Google Scholar
[3] Feferman, S., Reflecting on incompleteness, this Journal, vol. 56 (1991), no. 1, pp. 1–49.Google Scholar
[4] Friedman, H. and Sheard, M., An axiomatic approach to self-referential truth, Annals of Pure and Applied Logic, vol. 33 (1987), no. 1, pp. 1–21.Google Scholar
[5] Halbach, V., A system of complete and consistent truth, Notre Dame Journal of Formal Logic, vol. 35 (1994), no. 3, pp. 311–327.Google Scholar
[6] Kripke, S. A., Semantical considerations on modal logic, Acta Philosophica Fennica, vol. 16 (1963), pp. 83–94.Google Scholar
[7] Leigh, G. E., Proof-theoretic investigations into the Friedman-Sheard theories and other theories of truth, Ph.D. thesis, University of Leeds, 2010.Google Scholar
[8] Leigh, G. E. and Rathjen, M., An ordinal analysis for theories of self-referential truth, Archive for Mathematical Logic, vol. 49 (2010), no. 2, pp. 213–247.CrossRefGoogle Scholar
[9] McGee, V., How truthlike can a predicate bel A negative result, Journal of Philosophical Logic, vol. 14 (1985), no. 4, pp. 399–410.Google Scholar
[10] Troelstra, A. S. and van Dalen, D., Constructivism in mathematics. Vol. 1, Studies in Logic and the Foundations of Mathematics, vol. 121, North-Holland, Amsterdam, 1988.Google Scholar