Meta-Modal Conceivability

From the Archives: a challenge for conceivability-possibility inferences

[See my earlier posts in this series—Modal Rationalism intro and Chapter One: Kripke vs 2-D Semantics—for essential background.]

TL;DR: You might think that there are multiple ideally conceivable ways that the space of possibilities might turn out. For example, it might seem both conceivable that a necessary being (or God) exists, and conceivable that there are no such necessary beings. But if conceivability entails possibility, then this contradicts the S5 axiom of modal logic (which effectively states that the space of possibilities could not possibly be different). To rescue modal rationalism from this implication, I offer a principled case for a cross-modal variation on the S5 axiom—

(S5*): ◆□G -> ■G

—on which, for a necessary being to be coherently conceivable, it must be the case that the being exists in every scenario that can be conceived (a very difficult to satisfy requirement!). More generally, I suggest, our grasp of conceivable modal spaces should be built up from our grasp of conceivable worlds or scenarios.

Are there multiple ways that the space of possibilities could (conceivably) be?

§2.1 The Idea of “Strong Necessities”

We have seen that standard examples of the necessary a posteriori pose no threat to modal rationalism. They don’t involve any shrinking of modal space, and can be explained away as involving semantic rather than metaphysical ignorance. For all that has been said so far, it remains plausible that each coherent claim (i.e. that cannot be ruled out a priori) has a non-empty primary intension, or is verified by some possible world, in the sense that the claim is true of that world considered as actual. This may be understood as the central claim of modal rationalism: for every conceptually coherent scenario, there is a possible world to match.¹

This is the claim that must be denied by the opponent of modal rationalism. They must hold that there are not enough possible worlds to go around. This is what’s needed to break the link between apriority and indicative necessity. A claim could then be true of all possible worlds—whether considered as actual or counterfactual—without being a priori, because there is a coherent yet strictly impossible scenario that purports to falsify the claim. We may call a claim with these modal properties a strong necessity.²