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This is meant as a supplement to a modal ontological argument to show that God's existence is either logically impossible or necessary. Am I committing a fallacy or a logical error of some kind or does this logic hold up?

I am using "necessary" and "possible" in the classical modal logic sense. P is possible if and only if it P is not impossible. P is logically impossible if and only if P is self-contradictory. P is logically necessary if and only if not-P is impossible. I am assuming that God is an unlimited being.

If it is possible that God ceases to exist, then it is possible that God is caused to cease to exist or God happens to cease to exist. If it is possible that God is caused to cease to exist or God happens to cease to exist, then it is possible that God is a limited being. But God is not a limited being. Therefore, it is impossible that God ceases to exist.

If it is possible that God is caused to cease to exist or it is possible that God is caused to begin to exist, then God's existence is contingent. If God can neither cease nor begin to exist, then God happened to begin to exist or will happen to cease to exist, then God's existence is contingent.

Replace "ceases to exist" with "begins to exist" in the above argument for proof that it is impossible that God begins to exist. If God can neither cease nor begin to exist, then that makes it either impossible or necessary that God exists, right?

  • "then if it is possible that God exists, then it is necessary that God exists." Shouldn't this be "if it's possible god exists then it's necessary he continues to exist? – Cell Jan 1 at 19:19
  • @Cell That is the reasoning behind the premise, but being a modal argument, I expressed it using modal necessity (it is necessary that x -> it is impossible that x is false). – saltylight Jan 1 at 19:22
  • I do not see why ceasing/beginning to exist is relevant to possibility/necessity in the modal sense. Being necessary means holding in every possible world. A being that begins and ceases to exist can still be necessary in this sense, and a being that does not can still be contingent, i.e. be eternal in some worlds and non-existent in others. Your argument seems more relevant to Aquinas's notions of necessary/possible, which are very different, see What do necessity and possibility mean in Aquinas' Third Way argument for the existence of God? – Conifold Jan 1 at 20:59
  • @Conifold If a being cannot cease to exist or begin to exist, and that being exists in some possible world, then there is no possible world where that being does not exist because there is no way for that being not to exist. The opposite of being necessary is being contingent, and you cannot have a contingent being that always exists. – saltylight Jan 1 at 22:01
  • Why not? There is no logical relation between temporal duration and possible worlds. We can have two possible worlds, one with an eternal being and the other without. – Conifold Jan 1 at 22:05
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I think there are different kinds of necessity at play in your argument that should be kept separate. (I may be repeating some of what you said, and some of what you and Conifold discussed in chat.)

If a proposition is true at all moments in time, let's call that, let's call that proposition "eternally true".

If a proposition is true in some possible world, that proposition is called "metaphysically possible". If a proposition is true in all possible worlds, that proposition is called "metaphysically necessary".

If a proposition is free from contradiction, that proposition is called "logically possible". And if it's a contradiction to deny it, that proposition is "logically necessary".

Logical necessity implies metaphysical necessity, and metaphysical necessity implies being eternally true.

The reverse implications do not generally hold. A proposition may be true for all moments in time, without being true in all possible worlds. An example might be "the physical universe was caused by a big bang", or "nothing is travelling faster than the speed of light", or some law of physics. But, even though such propositions are always true in our world, it doesn't mean that they must be true in all possible worlds. In some worlds, there might not have been a big bang, or faster-than-light travel may occur.

There could be metaphysically necessary truths, such as "God exists" or "everything has a sufficient explanation" which are not logically necessary, since denying that God exists or asserting that there are brute facts doesn't seem to lead to explicit contradiction. And likewise, there may be some logical possibilities that may not be metaphysical possibilities. For example, Saul Kripke has argued that identity statements with rigid designators such as "water is H2O" are metaphysically necessary. If he's correct, then "water is not H2O" is not metaphysically possible, despite being free from contradiction (ie. logically possible). I think debates about abstract entities, causation, and the nature of time are like this too. Philosophers will leverage intuitions and possible-worlds talk to argue for metaphysical truths, even though the negation of such truths may not be explicitly contradictory.

Anyways, I understand your argument as trying to infer God's metaphysical necessity from God's eternity:

  1. If the proposition "God exists" is eternally true, then the proposition is metaphysically necessary.
  2. If the proposition "God exists" is eternally false, then the proposition is metaphysically impossible.
  3. "God exists" is either eternally true or eternally false (since God cannot come into being or cease to exist).
  4. Therefore, "God exists" is either metaphysically necessary or impossible.

It seems to me that we can't in general infer a being's metaphysical necessity from that being's eternal existence, for reasons that I gave above. Is so, then additional justification needs to be provided for 1. and 2.


It occurs to me after rereading your question, that maybe you're just trying to infer God's eternal existence or eternal non-existence from it being impossible for God to begin to exist or cease to exist. If this is the case, I think the talk of modal logic and logical necessity are somewhat distracting.

It also seems that your notion of metaphysical necessity is not truth in all possible worlds, but about what actual-world entities are able to cause (ie. to you, "possibly P" means that "actual-world entities can, by their causal powers, bring it about that P"). That's fine, but just remember that God's being necessary or impossible means just that there is no causal chain that can bring it about that God doesn't exist, or that he does exist. God's necessity (in this sense) is no longer about conceivability or logical possibility. I mention this because it seems like the next natural step in your argument is to say something like "God isn't impossible" since God is free from contradiction, so God must be necessary. But this isn't what your notion of necessity means any more.

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  • In the question, I was using 'possibility' and 'necessity' in their logical sense, which is equivalent to their metaphorical sense. What is the basis for your distinction between 'metaphysical possibility/necessity' and 'logical possibility/necessity'? – saltylight Jan 2 at 19:29
  • @saltylight It's not mine, but it is a commonly made distinction. The distinction is necessary (ha) if metaphysicians are doing more than just logical or conceptual analysis. You can see plato.stanford.edu/entries/modality-epistemology and plato.stanford.edu/entries/modality-varieties for a discussion. BTW I'm not defending the idea here, I just thought it was relevant since in your discussion with Conifold, you talked about causation as it was related to modality, and causation is not usually taken to be a purely logical relation. – Adam Sharpe Jan 2 at 19:53
  • As I understand it, "metaphysical possibility" is an interpretation of "logical possibility". I would agree that the distinction is necessary if metaphysicians are doing more than just logical or conceptual analysis. I would say that metaphysicians are doing just logical or conceptual analysis, so the distinction is not necessary. – saltylight Jan 2 at 19:57
  • @saltylight But then how do you justify statements such as "if something is contingent, then it is caused by something" by logic alone? I can imagine something coming into existence, uncaused, without explicit contradiction. It may be a truth of metaphysics that all contingent beings have a cause, but it shouldn't be a truth of logic. You could of course define "contingent" and "cause" in such a way as to make the statement 'true by definition', but these definitions would be additional axioms which are not purely logical (not tautologies). – Adam Sharpe Jan 2 at 20:38
  • @saltylight Metaphysicians (in my understanding anyways) see what they're doing as something not so different than what scientists do (though perhaps different in method). They're looking for rules that govern our world. The difference is that metaphysical laws are more general than physical laws, and so would hold in a larger set of worlds, but that aren't simply tautologies. The principle of sufficient reason, water=H2O, God exists, or some general laws of causation, would be possible examples. – Adam Sharpe Jan 2 at 20:38

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