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HOW TO EXPRESS SELF-REFERENTIAL PROBABILITY. A KRIPKEAN PROPOSAL

Published online by Cambridge University Press:  30 April 2015

CATRIN CAMPBELL-MOORE
CATRIN CAMPBELL-MOORE*
Affiliation:
Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität München
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN E-mail:[email protected]
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Abstract

We present a semantics for a language that includes sentences that can talk about their own probabilities. This semantics applies a fixed point construction to possible world style structures. One feature of the construction is that some sentences only have their probability given as a range of values. We develop a corresponding axiomatic theory and show by a canonical model construction that it is complete in the presence of the ω-rule. By considering this semantics we argue that principles such as introspection, which lead to paradoxical contradictions if naively formulated, should be expressed by using a truth predicate to do the job of quotation and disquotation and observe that in the case of introspection the principle is then consistent.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 8 , Issue 4 , December 2015 , pp. 680 - 704
Copyright
Copyright © Association for Symbolic Logic 2015 

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