How to Express Self-Referential Probability. A Kripkean Proposal

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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.
Original languageEnglish
Pages (from-to)680-704
Number of pages25
JournalReview of Symbolic Logic
Volume8
Issue number4
Early online date30 Apr 2015
DOIs
Publication statusPublished - 1 Dec 2015

Structured keywords

  • FSB
  • Centre for Science and Philosophy

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