Jonathan Mai

It is common in epistemic modal logic to model the epistemic states of agents via box operators in the normal logic S5. However, this ap proach treats agents as logically omniscient by requiring their knowl edge to be closed under classical logical consequence. A promising way of avoiding logical omniscience consists in extending epistemic models with impossible states, that is states, where complex formulas are not evaluated recursively. However, this approach faces the dual prob lem of logical ignorance by modeling agents as not even minimally logically competent. In this paper I will outline an epistemic logic that combines impossible states with dynamic realization modalities akin to the dynamic announcement operators from public announce ment logic (PAL). I will show that this epistemic logic avoids both the problem of logical omniscience and the problem of logical ignorance. Furthermore, I prove that so-called successful updates in my logic can be characterized in the same way as in PAL and that a similar logic due to Johan van Benthem can be simulated in my logic. Finally, I will compare my epistemic logic with a similar one, which has recently been advanced by JC Bjerring and Mattias Skipper.

English distinguishes between singular quantifiers like "a donkey" and plural quantifiers like "some donkeys". Pluralists hold that plural quantifiers range in an unusual, irreducibly plural, way over common objects, namely individuals from first-order domains and not over set-like objects. The favoured framework of pluralism is plural first-order logic, PFO, an interpreted first-order language that is capable of expressing plural quantification. Pluralists argue for their position by claiming that the standard formal theory based on PFO is both ontologically neutral and really logic. These properties are supposed to yield many important applications concerning second-order logic and set theory that alternative theories supposedly cannot deliver. I will show that there are serious reasons for rejecting at least the claim of ontological innocence. Doubt about innocence arises on account of the fact that, when properly spelled out, the PFO-semantics for plural quantifiers is committed to set-like objects. The correctness of my worries presupposes the principle that for every plurality there is a coextensive set. Pluralists might reply that this principle leads straight to paradox. However, as I will argue, the true culprit of the paradox is the assumption that every definite condition determines a plurality.