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Publication - Dr Catrin Campbell-Moore

    How to Express Self-Referential Probability. A Kripkean Proposal


    Campbell-Moore, C, 2015, ‘How to Express Self-Referential Probability. A Kripkean Proposal’. Review of Symbolic Logic, vol 8., pp. 680-704


    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.

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