Research Group
in Analytic Philosophy

Abstract

Strong actualism involves the following two theses:

SA1: For any two different possible states of the world, there is some non-modal proposition that is true in one and false in the other.

SA2: For any two different modal hypotheses, there is some non-modal valuation that is possible according to one and impossible according to the other.

Weak actualism involves the following two theses:

WA1: For any two different possible states of the world, there is some proposition that is true in one and false in the other.

WA2: For any two different modal hypotheses, there is some valuation that is possible according to one and impossible according to the other.

SA1 entails:

Supervenience: For any two possible states of the world, if there is some modal proposition that is true in one and false in the other, then there is some non-modal proposition that is true in one and false in the other.

SA2 carries a commitment to:

Invariance: A modal proposition has the same truth value in every possible state of the world.

We might not want to treat Invariance and Supervenience as sematic truths, and then we won’t want to treat SA1 and SA2 as semantic truths either.

But we might still want to treat WA1 and WA2 as semantic truths.

However, the tools deployed by contemporary modal semantics to avoid treating SA1 and SA2 as semantic truths also fail to treat WA1 and WA2 as semantic truths.

This lends support to the following hypothesis:

If WA1 and WA2 are semantic truths, then the same goes for SA1 and SA2 (and hence for Supervenience and Invariance)

This hypothesis is false. It is possible to provide a semantics for modal propositional logic on which WA1 and WA2 come out as semantic truths but SA1 and SA2 don't.