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HOW TO EXPRESS SELF-REFERENTIAL PROBABILITY. A KRIPKEAN PROPOSAL

  • CATRIN CAMPBELL-MOORE (a1)

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.

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*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LUDWIG-MAXIMILIANS-UNIVERSITÄT MÜNCHEN E-mail:catrin@ccampbell-moore.com

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HOW TO EXPRESS SELF-REFERENTIAL PROBABILITY. A KRIPKEAN PROPOSAL

  • CATRIN CAMPBELL-MOORE (a1)

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