The semantic paradoxes have drawn much attention throughout the history of philosophy. There is something deeply puzzling about them. Something is going wrong; there is a dissonance/tension in what we philosophically uphold. Firstly, this is very interesting, and secondly, this needs to be dealt with. The first motivates, and the second requires before anything else a comprehensive analysis of the semantic paradoxes, i.e. an overview of their realm. This analysis consists of at least understanding when semantic paradoxes appear (characterise), what kinds of them there are (classify), what is causing them, and any (philosophical) implications thereof. It is overhasty to jump the gun and block the semantic paradoxes at first sight; and it is misguided to do nothing about them.
In this talk, I will explore an attempt to understand the semantic paradoxes by means of a possible-worlds semantics for modal predicates. Specifically, I will make a start at characterising them. In modal logic, there are two main ways of formalising the notion of ‘modality'. The prominent approach is that of viewing modality as a sentential operator. In this approach there are no paradoxes that are like the semantic paradoxes. However, an alternative approach is that of viewing modality as a predicate in some syntax theory, such as PA. Usually, such a syntax theory proves some version of the diagonal lemma. Hence, in this second approach we do get such ‘semantic-like' paradoxes, by diagonalising in exactly the same way as with the semantic paradoxes. Examples include the Liar Paradox and the Knower Paradox/Montague's Paradox, and more subtle paradoxes involving the interactions of multiple distinct modal predicates. Moreover, if we introduce a possible-worlds semantics for the predicate approach, I claim that we can intuitively characterise (and classify) the semantic-like paradoxes, and hence the semantic paradoxes, according to their frames; I will give a partial proof of a characterisation theorem which states that a frame admits a model if the frame is converse well-founded. This seems to suggest that converse ill-foundedness lies at the heart of the semantic paradoxes, as opposed to only circularity as some logicians think.
The talk will be in person, but if you require a Teams link then please email firstname.lastname@example.org or email@example.com.
See the DPhil Seminar website for details.
DPhil Seminar Convenor: Mariona Miyata - Sturm