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.
Item Type: | Book Section |
---|---|
Faculties: | Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) Philosophy, Philosophy of Science and Religious Science > Munich Center for Mathematical Philosophy (MCMP) > Logic |
Subjects: | 100 Philosophy and Psychology > 100 Philosophy 100 Philosophy and Psychology > 160 Logic |
ISBN: | 9780230251731 |
Place of Publication: | Basingstoke |
Language: | English |
Item ID: | 20723 |
Date Deposited: | 28. May 2014, 06:56 |
Last Modified: | 15. Dec 2020, 09:13 |