Epistemic modals have peculiar logical features that are challenging to account for in a broadly
classical framework. For instance, while a sentence of the form p∧♢¬p ('p, but it might be that
not p') appears to be a contradiction, ♢¬p does not entail ¬p, which would follow in classical logic.
Likewise, the classical laws of distributivity and disjunctive syllogism fail for epistemic modals. Existing
attempts to account for these facts generally either under- or over-correct. Some theories predict that
p∧♢¬p, a so-called epistemic contradiction, is a contradiction only in an etiolated sense, under a notion of
entailment that does not allow substitution of logical equivalents; these theories underpredict the infelicity
of embedded epistemic contradictions. Other theories savage classical logic, eliminating not just rules that
intuitively fail, like distributivity and disjunctive syllogism, but also rules like non-contradiction, excluded
middle, De Morgan's laws, and disjunction introduction, which intuitively remain valid for epistemic
modals. In this paper, we aim for a middle ground, developing a semantics and logic for epistemic
modals that makes epistemic contradictions genuine contradictions and that invalidates distributivity
and disjunctive syllogism but that otherwise preserves classical laws that intuitively remain valid. We
start with an algebraic semantics, based on ortholattices instead of Boolean algebras, and then propose a
more concrete possibility semantics, based on partial possibilities related by compatibility. Both semantics
yield the same consequence relation, which we axiomatize. Then we show how to extend our semantics
to explain parallel phenomena involving probabilities and conditionals. The goal throughout is to retain
what is desirable about classical logic while accounting for the non-classicality of epistemic vocabulary.
Chance, ability, and control
2023.
[abstract]
[archive]
-
A compelling, and popular, thought is that ability entails control: S's being able to ɸ entails that ɸ be, in some sense, in S's control. But this intuition is inconsistent with a different prima facie compelling thought: that S's succeeding in ɸ-ing entails that S is able to ɸ. In this paper, I introduce a new form of evidence to help adjudicate between these two theses: namely, probability judgments about ability ascriptions. I argue that these judgments provide evidence in favor of the intuition that success entails ability, and against the intuition that ability requires control. Moreover, I argue that these judgments support one particular analysis which vindicates the success intuition, namely, the analysis of ability in terms of conditionals.
Lecture notes
Notes from an ESSLLI course on conditionals taught with David Boylan.
Notes from an ESSLLI course on dynamic semantics taught with Daniel Rothschild.