Thursday, January 11, 2024

Actuality and the Actuality Operator

 There is a common, and generally overlooked, ambiguity with respect to 'actuality' in many discussions of modal metaphysics and philosophy of religion by analytic philosophers. The most common form it takes consists in talking about 'actualizing' possible worlds. Possibilities can perhaps in some sense be actualized, but possible worlds are logical objects; they are those logical objects associated with sets of truth-valued propositions. Thus they are not the kind of thing that is 'actualized' or not, but even setting that aside, the problem is that possible worlds as applied in any kind of modal metaphysics are always relative to what is already actual. In modal metaphysics, possible worlds are interepreted as 'ways the actual world can be'; thus they already describe the actual world. This is in fact their entire purpose in this context: to describe what is actual in terms of ways it can be. Actuality in this sense is presupposed by, and does not presuppose, possible worlds. 

An additional layer of confusion is created when we add to possible worlds what is often called the 'actuality operator', usually represented in notation as @. Philosophers often represent whatever they are calling 'actualization' with an actuality operator. But this sense of actuality cannot be the sense just mentioned, because this 'actuality' presupposes, and is not presupposed by, possible worlds. What the actuality operator actually does is privilege a given possible world as a reference-point possible world; it need not be interpreted as any kind of 'actuality' at all. But when we do interpret it as some kind of actuality, it has to be a 'posterior actuality', different from the 'prior actuality' that possible worlds as a whole describe, and to connect the two requires some sort of renormalization -- i.e., you are changing 'the actual world' and therefore have to reconfigure all of your possible worlds in light of the fact that you are now describing a different one. We don't, as far as I know, have any particular procedure for doing this.

Equivocation between the two would perhaps not be a serious problem, except that in modal metaphysics the whole point is to be accurate about actuality. And failing to distinguish the two can create serious problems -- e.g., if you conflate the two kinds of actuality, you often get a kind of necessitarianism in which actuality is simply identified with a single possible world (and thus a single way the actual world can be), allowing only one possibility. (This mistake is common when modal metaphysics is used to talk about God, and I've also seen it happen in discussions of free will.)