Alessandro Zucchi

Stalnaker’s minimal change semantics for conditionals fails to support the import-export law, according to which (a) and (b) are logically equivalent:

(a) if A, then if B, then C

(b) if A and B, then C

However, natural language conditionals seem to abide by the law. McGee (1985) outlines a minimal change semantics for conditionals that supports it. I argue that, in fact, the equivalence between (a) and (b) does not hold unrestrictedly, and I suggest that the facts follow from the interaction between the semantics of conditionals and the ways suppositions may affect the context. I conclude by describing the consequences of my account for the issue of the validity of modus ponens.

Bjørn Jespersen

Circumstantialists already have a logical semantics for impossibilities. They expand their logical space of possible worlds by adding impossible worlds. These are impossible circumstances serving as indices of evaluation, at which impossibilities are true. A variant of circumstantialism, namely modal Meinongianism, adds impossible objects as well. The opposite of circumstantialism, namely structuralism, has some catching-up to do. What might a structuralist logical semantics without impossible worlds or impossible objects look like? This paper makes a structuralist counterproposal. I present a semantics based on a procedural interpretation of the typed l-calculus. The fundamental idea is that talk about impossibilities should be construed in terms of procedures yielding as their product a condition that could not possibly have a satisfier, or else failing to yield a product at all. Dispensing with a ‘bottom’ of impossibilia requires instead a ‘top’ consisting of structured hyperintensions, intensions, intensions defining other intensions, a typed universe, and dual predication. I explain how the theory works by going through a couple of cases.

Ulf Hlobil

The talk advocates a marriage of inferentialist bilateralism and truth-maker bilateralism. Inferentialist bilateralists like Restall and Ripley say that a collection of sentences, Y, follows from a collection of sentences, X, iff it is incoherent (or out-of-bounds) to assert all the sentences in X and, at the same time, deny all the sentences in Y. In Fine’s truth-maker theory, we have a partially ordered set of states that exactly verify and falsify sentences, and some of these states are impossible. We can think of making-true as the worldly analogue of asserting, of making-false as the worldly analogue of denying, and of impossibility as the worldly analogue of incoherence. This suggests that we may say that, in truth-maker theory, a collection of sentences, Y, follows (logically) from a collection of sentences, X, iff (in all models) any fusion of exact verifiers of the members of X and exact falsifiers of the member of Y is impossible. Under routine assumptions about truth-making, this yields classical logic. Relaxing one such assumption yields the non-transitive logic ST. Relaxing another assumption yields the non-reflexive logic TS. We can use known facts about the relation between ST, LP, and K3, to provide an interpretation of LP as the logic of falsifiers and K3 as the logic of verifiers. The resulting semantics for ST is more flexible than its usual three-valued semantics because it allows us, e.g., to reject monotonicity. We can also recover fine-grained logics, like Correia’s logic of factual equivalence.