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SELF-REFERENCE IN ARITHMETIC II

Published online by Cambridge University Press:  07 October 2014

VOLKER HALBACH  and
ALBERT VISSER
VOLKER HALBACH*
Affiliation:
Oxford University
ALBERT VISSER*
Affiliation:
Utrecht University
*
*NEW COLLEGE OXFORD, OX1 3BN, ENGLAND E-mail: [email protected]
†PHILOSOPHY, FACULTY OF HUMANITIES UTRECHT UNIVERSITY JANSKERHOF 13 3512 BL UTRECHT, THE NETHERLANDS E-mail: [email protected]
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Abstract

In this sequel to Self-reference in arithmetic I we continue our discussion of the question: What does it mean for a sentence of arithmetic to ascribe to itself a property? We investigate how the properties of the supposedly self-referential sentences depend on the chosen coding, the formulae expressing the properties and the way a fixed point for the expressing formulae are obtained. In this second part we look at some further examples. In particular, we study sentences apparently expressing their Rosser-provability, their own ${\rm{\Sigma }}_n^0$-truth or their own ${\rm{\Pi }}_n^0$-truth. Finally we offer an assessment of the results of both papers.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 7 , Issue 4 , December 2014 , pp. 692 - 712
Copyright
Copyright © Association for Symbolic Logic 2014 

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