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Reflecting in epistemic arithmetic

Published online by Cambridge University Press:  12 March 2014

Leon Horsten
Leon Horsten*
Affiliation:
Center for Logic, Philosophy of Science and Philosophy of Language, Institute of Philosophy, Katholieke Universiteit Leuven, Kardinaal Mercierplein 2, 3000 Leuven, Belgium, E-mail: Leon.Horsten@hiw.kuleuven.ac.be
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Abstract

An epistemic formalization of arithmetic is constructed in which certain non-trivial metatheoretical inferences about the system itself can be made. These inferences involve the notion of provability in principle, and cannot be made in any consistent extensions of Stewart Shapiro's system of epistemic arithmetic. The system constructed in the paper can be given a modal-structural interpretation

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 3 , September 1996 , pp. 788 - 801
Copyright
Copyright © Association for Symbolic Logic 1996

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References

REFERENCES

[1]Barwise, J. (editor), Handbook of mathematical logic, North-Holland, 1977.Google Scholar
[2]Boolos, G., The unprovability of consistency. An essay in modal logic, Cambridge University Press, North-Holland, 1979.Google Scholar
[3]Boolos, G. and Jeffrey, R., Computability and logic, third ed., Cambridge University Press, North-Holland, 1989.Google Scholar
[4]Flagg, R., Integrating classical and intuitionistic type theory, Annals of Pure and Applied Logic, vol. 32 (1986), pp. 27–51.CrossRefGoogle Scholar
[5]Hellman, G., Mathematics without numbers. Towards a modal-structural interpretation, Clarendon Press, North-Holland, 1989.Google Scholar
[6]Horsten, L., On modal-epistemic variants of Shapiro's system of epistemic arithmetic, Notre Dame Journal of Formal Logic, vol. 35 (1994), pp. 284–291.CrossRefGoogle Scholar
[7]Myhill, J., Some remarks on the notion of proof, Journal of Philosophy, vol. 57 (1960), pp. 463–471.CrossRefGoogle Scholar
[8]Odifreddi, P., Classical recursion theory, North-Holland, 1989.Google Scholar
[9]Owings, J., Diagonalization and the recursion theorem., Notre Dame Journal of Formal Logic, vol. 14 (1973), pp. 95–99.CrossRefGoogle Scholar
[10]Putnam, H., Mathematics without foundations, reprinted in: Putnam, H., Mathematics, matter and method, Philosophical Papers. Volume I, Cambridge University Press, 1975, pp. 43–59.Google Scholar
[11]Scedrov, A., Extending Gödel's modal interpretation to type theory and set theory, Intensional mathematics (Shapiro, S., editor), North-Holland, 1985, pp. 81–119.CrossRefGoogle Scholar
[12]Shapiro, S., Epistemic and intuitionistic formal systems, Intensional mathematics (Shapiro, S., editor), North-Holland, 1985, pp. 11–47.CrossRefGoogle Scholar
[13]Shapiro, S. (editor), Intensional mathematics, North-Holland, 1985.Google Scholar
[14]Smorynski, C., The incompleteness theorems, Handbook of mathematical logic (Barwise, J., editor), North-Holland, 1977, pp. 821–865.CrossRefGoogle Scholar
[15]Smorynski, C., Self-reference and modal logic, Springer, 1985.CrossRefGoogle Scholar
[16]Smorynski, C., Review of Shapiro, S. (ed): Intensional mathematics, this Journal, vol. 56 (1991), pp. 1496–1499.Google Scholar