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 language | English |
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Pages (from-to) | 680-704 |
Number of pages | 25 |
Journal | Review of Symbolic Logic |
Volume | 8 |
Issue number | 4 |
Early online date | 30 Apr 2015 |
DOIs | |
Publication status | Published - 1 Dec 2015 |
Structured keywords
- FSB
- Centre for Science and Philosophy