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Leitgeb, Hannes (2012): From Type-Free Truth to Type-Free Probability. In: Restall, Greg; Russell, Gillian (Hrsg.): New Waves in Philosophical Logic. New Waves in Philosophy, Basingstoke: Palgrave Macmillan S. 84-94
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Abstract

Leitgeb [3] formulates a probabilistic theory of type-free truth that includes, amongst others, principles on the probabilities of sentences that speak about their own truth or falsity. In section 1 of the present paper we will recapitulate this theory. Section 2 is devoted to some new observations about that theory and to a set of open questions relating to it. Finally, section 3 takes this probabilistic approach to type-free truth one step further: we present two axiomatic theories of type-free probability which include, amongst others, principles on the probabilities of sentences that speak about their own probabilities. Such theories are stronger than theories for so-called second-order probability (see, e.g., Skyrms [5]) and are hoped to open up a whole new area of research in which all the expertise concerning type-free truth that has been accumulated in recent decades ends up being translated into theories of type-free probability and/or being extended to joint approaches to type-free truth and probability.