This Thursday 12th of February at 15:00 hrs we will have a talk in our seminar’s sessions. This time, our PhD visitor Michael De will talk about “Negation as lack of evidence” (abstract follows). After the talk, further discussions about the topic and other dynamic business can take place with some drinks!
The meeting will take place in room 3.27 of the P building (Euclides).
If intuitionism is to be extended to empirical discourse (e.g. à la Dummett) then, on certain plausible assumptions about a theory of meaning, any coherent connective picked out by natural language expressions should be able to be conservatively added to intuitionistic logic. It is well-known that classical negation cannot be conservatively added to intuitionistic logic. Yet there is a negation in the vicinity that intuitionists must accept as coherent lest they justify intuitionistically invalid principles such as excluded middle, or end up in paradox as Williamson has argued. I show that such a negation can be conservatively extended to intuitionistic logic via Kripke semantics, and provide a sound and complete axiomatization of the resulting logic.