Category Archives: Modality

Modal Alternate Possibilities

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.

Modal Possibility and Necessity

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.