Logic Colloquium 2008
Hannes Leitgeb On Truth and Probability
We will give an overview of how probability theory can be studied from a logical point of view. On the probabilistic side, this leads us to an investigation of (unary) absolute probability measures and (binary) conditional probability measures on propositional or first-order languages. In particular, we will show (i) how the standard axioms of probability may be justified in terms of ``closeness to the truth'', (ii) how logical truth can be pinned down by purely probabilistic means, (iii) how conditional probability measures on formulas may be represented as limits of ratios of absolute probability measures on formulas, (iv) what a probabilistic semantics for conditional logic looks like, (v) how a probabilistic theory of truth for semantically closed languages can be developed, and finally (vi) how models for higher-order probabilities, probabilistic reflection principles, and type-free probability can be constructed. (Most parts of this talk will be based on unpublished or forthcoming material.)