Two Kinds of Logical Impossibility

Abstract

In this paper, we argue that a distinction ought to be drawn between two ways in which a given world might be logically impossible. First, a world w might be impossible because the laws that hold at w are different from those that hold at some other world (say the actual world). Second, a world w might be impossible because the laws of logic that hold in some world (say the actual world) are violated at w. We develop a novel way of modelling logical possibility that makes room for both kinds of logical impossibility. Doing so has interesting implications for the relationship between logical possibility and other kinds of possibility (for example, metaphysical possibility) and implications for the necessity or contingency of the laws of logic.

Counterlogicals as Counterconventionals

“…This distinction is similar to the distinction due toSandgren and Tanaka (2019) between logically different worlds and worlds containing logical violations. We return to this point in §6.…”

“…This is due to an ambiguity in the notion of a "logically impossible" antecedent. To explain, we use a distinction due to Sandgren and Tanaka (2019), but phrased slightly differently: distinguish claims that are actually logically impossible, i.e., according to the logic we actually adopt, from sentences that are counterfactually logically impossible, i.e., according to a counterfactual logic. For example, the antecedent of (3) is actually logically impossible, i.e., impossible by our lights, though not counterfactually impossible, i.e., impossible by the lights of the counterfactual logic in question.…”

Counterpossibles

“…Perhaps the same goes for counteranalyticals, but matters are less clear for countermathematicals and counterconceptuals. It is also unclear whether one should put counter meta logicals in the same class as counterlogicals, especially since the former tend to be easier to interpret than the latter (Sandgren & Tanaka, 2020). Thus far, the literature on counterpossibles has tended to treat all counterpossibles the same.…”

Impossible Worlds, by Francesco Berto and Mark Jago

“…It is best to think of a world where the laws of logic are different as an Impossible Way rather than as a Logic Violator. (See Sandgren and Tanaka (2019) for more details.) For the reminder of this review, I will focus on the violation of logical laws rather than logical difference as the main issue with Berto and Jago's treatment of impossible worlds has to do with Logic Violator.…”