[FOM] A minor issue in modal logic

Michael Lee Finney michael.finney at metachaos.net
Sun Jul 4 11:40:51 EDT 2010

 It would seem to me that Np means that p is necessarily true without
 distinction of world, or that p is true in all possible worlds. In
 either case it would be true in the actual world because in one case
 the world was not distinguished and in the other case surely the
 actual world is possible. So you have Np => Np[a] no matter how you
 look at it.

 I do not see how the converse would hold, in general, no matter how
 you look at it. If you have Np[a], p may be necessarily true in the
 actual world, but I don't see how that ensures that p must be true in
 any possible world. There could be worlds which cannot be an actual
 world - perhaps they violate actual laws of physics and are made of
 half real matter and half anti-matter.

 For a believer we have g in the actual world, for an atheist we have
 ~g in the  actual world. For an agnostic we have g v ~g in the actual
 world and for the completely indifferent we don't even have g v ~g.
 That is entirely a matter of assumption and a biased assumption in the
 case of St. Anselm and others trying to prove the existence of god.
 If you want to prove the existence of god you cannot start with
 g, Ng[a] or Ng. I would even argue that P[g v ~g] cannot be assumed
 without biasing the argument.

 We could have a world ruled by the Norse gods and in that world ~g
 would hold. Given the possiblity of a world in which ~g holds, Ng
 cannot hold because Ng => ~P~g, and therefore by Modus Tollens you
 have P~g => ~Ng.

 I think the only real question is if it is possible to show a valid
 rule of inference in the arguments of those trying to prove the
 existence og god that doesn't depend on their assumptions of god and
 which would be different from current modal principles.

Michael Lee Finney

KBJ> All and sundry:  I have encountered an issue in modal logic
KBJ> that I haven't seen and don't know where to look for a resolution
KBJ> of, and my local philosophy department's members haven't been
KBJ> much help.  Perhaps FOMers can help.  

KBJ> The fundamental question, I think--I'll give its origin in
KBJ> a moment--is this:  For any proposition p, where "Np" means "It
KBJ> is necessarily true that p" and "Np[a]" means "p is necessarily
KBJ> true in the actual world," are Np and Np[a] equivalent--or, if
KBJ> not, does Np[a] at least entail Np?  

KBJ> Keith Brian Johnson


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