Drawing from the distinctions in possibility and necessity I drew previously, I would like to sketch three distinct types of alternate possibilities (in order to nuance the traditional Principle of Alternate Possibilities): “[actual] alternate possibilities” (or “actual AP”), “metaphysical AP”, and “logical AP”.
Propositions that are logically necessary do not have alternate logical possibilities (“logical AP”) and therefore do not have metaphysical or [actual] AP either. Propositions that are metaphysically necessary do not have metaphysical AP (or [actual] AP, though they may or may not have logical AP). And propositions that are [actually] necessary do not have [actual] AP (though they may or may not have metaphysical AP, etc.).
Thus, what I once called the “freedom sense” of alternate possibilities maps onto what I am now calling “metaphysical” alternate possibilities (though my designs for the “freedom sense” of AP included the implication that the free agent in question supplies the final conditions sufficient to determine the truth value of the proposition in question — more on this in a future post). And what I at one time called the “matter of fact” sense of alternate possibilities maps onto what I am now calling “actual AP”.
These categories strike me as easy to believe, if subtly difficult to grasp. For all they do is point out that just because something doesn’t contradict the rules of logic doesn’t mean it’s metaphysically possible (much less actual). And just because something is metaphysically possible doesn’t mean it is actual.
And the reverse: just because something is actual, doesn’t mean it is the only metaphysical possibility. And even if a thing is metaphysically necessary, it does not follow there are no other logical alternatives.
The broadest type of possibility is “logical”. A proposition is logically possible if it is not self-contradictory and if it does not otherwise violate a rule of logic. Inside this ring of possibility is “metaphysical possibility”. A proposition is metaphysically possible if it is logically possible and it [does not violate the rules of metaphysics, of which the best way we have come up with to discern is through conceivability experiments]. Inside this latter ring of possibility is “
epistemic [actual] possibility”. A proposition is epistemically [actually] possible if it is logically and metaphysically possible, and also possible in the actual world. If a proposition is epistemically [actually] possible, it is possibly actual, whereas a metaphysically possible proposition might be known not to be actual, and a logically possible proposition might be obviously inconceivable (and thus metaphysically impossible).
For senses of “necessity” these three concentric circles get inverted such that the broadest ring of necessity is “actual”. A proposition is actually necessary if it [happens to be true in the actual world]. But the fact that Apple exists (which I happen to know is true), though actually necessary, is not metaphysically necessary. That is, I can conceive of a world in which Apple doesn’t exist. Moreover, it is certainly not logically necessary! There is nothing about the rules of logic which make it such that Apple exists. Thus, “metaphysical necessity” lies inside of “actual necessity” and encircles “logical necessity”.
This paradigm sheds new light on this issue for me. For, P → P makes P necessarily true, but only actually, and certainly not metaphysically or logically. That is, since we know that P, we know that P, necessarily. But actual necessity is trivial. It is an actual necessity that I am typing on this computer right now and it is similarly necessary that the cars outside are driving by, given that I see them driving by. But there are possible worlds in which I am not typing on this computer and the cars outside are not driving by.