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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
Affiliation:
Munich Center for Mathematical Philosophy, Ludwig-Maximilians-Universität München
Corresponding

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
Copyright
Copyright © Association for Symbolic Logic 2015 

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HOW TO EXPRESS SELF-REFERENTIAL PROBABILITY. A KRIPKEAN PROPOSAL
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