Classical Counterpossibles

Abstract

We present four classical theories of counterpossibles that combine modalities and counterfactuals. Two theories are anti-vacuist and forbid vacuously true counterfactuals, two are quasi-vacuist and allow counterfactuals to be vacuously true when their antecedent is not only impossible, but also inconceivable. The theories vary on how they restrict the interaction of modalities and counterfactuals. We provide a logical cartography with precise acceptable boundaries, illustrating to what extent nonvacuism about counterpossibles can be reconciled with classical logic.

Counterlogicals as Counterconventionals

“…Our presentation of this semantics roughly follows that of Berto et al 2018 with some minor changes. See also French et al 2020. and every w P P, if I, w , i Γ, then I, w , i φ. This guarantees that ( i obeys all of the laws of classical logic (in fact, S5).…”

“…See French et al 2020 for details. While they assume impossible worlds are logically consistent and maximal, at least these correspondence results carry over to our more general setting.…”

Counterpossibles

“…In the impossible worlds framework, this corresponds to the following principle (French et al., 2020) 11 : Some nonvacuists endorse this constraint (Jago, 2014; Kment, 2014; Krakauer, 2012; Mares, 1997). 12 Others reject it (Bernstein, 2016; Clarke‐Doane, 2017; Nolan, 1997, 2017; Vander Laan, 2004).…”

“…Also, while French et al. (2020) ignore logically impossible worlds in their models, the correspondence result holds even if one includes them.…”

“…The latter corresponds to the constraint that if is possible, then the closest ‐worlds include some possible worlds (what French et al. [2020] call the “MCP” condition). One could maintain this, but deny that if is possible, then the closest ‐worlds are all possible.…”