ETD

• counterpossibles
• formal semantics
• non-vacuism
• psychology of reasoning

Counterpossibles – counterfactual conditionals with impossible antecedents – constitute a boundary case for the semantics of counterfactuals. On the standard possible-worlds account, developed by Stalnaker (1968) and Lewis (1973), counterpossibles are treated as vacuously true: since the antecedent is impossible, it holds at no possible world; the consequent is therefore vacuously true at all of them. This position, known as vacuism, clashes with persistent and structured intuitions that some counterpossibles are non-trivially true or false. For instance, while “If Hobbes had secretly squared the circle, sick children in the mountains of South America at the time would not have cared” seems true, its opposite – “If Hobbes had secretly squared the circle, sick children in the mountains of South America at the time would have cared” – seems false (Nolan 1997). Such contrasts motivate the non-vacuist alternative, according to which any adequate semantics must capture the difference between true and false counterpossibles.
Counterpossibles thus mark a methodological divide. Vacuists prioritize simplicity and theoretical clarity, even at the cost of counterintuitive results, whereas non-vacuists develop more fine-grained semantics to reflect our counterpossible judgments. Both sides acknowledge the phenomenon but diverge on how it should be treated: as a genuine semantic fact to be represented in theory, or as a by-product that falls outside its scope. To support the vacuist stance, Williamson (2018) appeals to a heuristic, which recommends rejecting “If p, ¬q” whenever “If p, q” seems true. This principle works well when p is possible, but, Williamson argues, it breaks down once the antecedent is impossible.
This thesis challenges the vacuist interpretation by drawing on recent empirical work in the psychology of reasoning, particularly Byrne’s (2024) experimental study on counterpossibles. Byrne’s data reveal systematic patterns in how people judge the truth of conditionals with impossible antecedents. Crucially, participants often judge both a counterpossible and its opposite to be false (for unrelated content), or even both to be true (for unknown or concept-combination content). These results undermine Williamson’s heuristic explanation, as they show that human judgments about counterpossibles do not merely follow a binary heuristic but are instead sensitive to content, relevance, and inferential structure.
Building on these findings, I argue for a non-vacuist, hyperintensional semantics of counterpossibles. In particular, I explore the evidential conditional developed by Crupi and Iacona (2022), which evaluates conditionals based on the degree of incompatibility between the antecedent and the negation of the consequent. This framework successfully captures the role of evidential support and inferential relevance, accounting for why conditionals like “If people were made of steel, they would not bruise easily” are judged true, while their opposites are judged false – even when their antecedents are impossible. However, challenges arise when moving toward a technical formulation of incompatibility. Crupi and Iacona propose a probabilistic measure, which, while conceptually robust, struggles to account for cases where the antecedent has zero probability – precisely the case with counterpossibles. A natural next step is to investigate whether the evidential conditional can be extended into a hyperintensional framework capable of handling such cases while preserving its explanatory power.