I’m not a process theologian, but I like a lot about Charles Hartshorne (1897-2000, pronounced ‘hearts-horn’ by the way), an extremely brilliant philosopher. Recent conversations about the distinction between logical and ontological possibility have taken me back to Hartshorne’s view that ultimately logical and ontological possibility coincide and are one and the same. But philosophers today (exclusively of the analytic sort?) distinguish between these two modes of speaking and being. Logical possibility/necessity is strictly about the formal-logical consistency of the terms of a proposition. Do the semantics of some claim or description violate the axioms of logic (about which there is ongoing debate), which traditionally are the law of identity (A is A), the law of non-contradiction (A is not not-A), the law of excluded middle (between A and not-A there is no third option). Others (e.g., Schopenhauer) add the principle of sufficient reason (PSR) as a fourth which states that everything that exists has a reason sufficient to explain its existence. Some of these four are hotly debated today.
It is generally (as far as I can tell) held that logical possibility/necessity concerns itself with language and conceivability. It’s primarily about speaking. Something is logically possible just in case its definition doesn’t involve any violation of the rules of logic. Ontological (or metaphysical) possibility/necessity describes realities themselves. It’s about being.
The question then is, what is the relationship (if any) between logical and ontological possibility, between logical modalities and ontological modalities? One option is to conflate them, take them as coincident and say that whatever is logically possible is ontologically possible, or that whatever is ontologically impossible is logically impossible. Another option makes a hard distinction between them and holds that neither mode of possibility can be assumed from the other. What is logically possible may in fact be ontologically impossible. But to begin to expose the difficulty of positing too absolute a distinction between the two, I don’t know of any philosopher who argues that what is metaphysically possible may be logically impossible. That is, it must be logically coherent to say of what exists that it exists, or what may exist that it may exist. Additionally, and controversially, others (e.g., Hartshorne) argue that it is not coherent to conceive of what exists necessarily as not existing.
A clear example of how the two manners of speaking relate would be the existence of God. Take the proposition:
P1 “A necessary being of infinite intelligence and goodness exists.”
(Assume whatever apophatic qualifications you wish.) I don’t know of any atheist who argues this is logically impossible (i.e., the words generate one or more violation of the axioms of logic), although all atheists are committed (though very few recognize it) to the ontological-metaphysical impossibility of such a being, for the only way a proffered ‘necessary’ being fails to exist is if its existence is impossible. Contingent existence isn’t an option for the God folks debate. He either exists necessarily, or his existence is impossible.
However, many theists who hold to the truth of P1 agree that its contradiction (“No necessary being of infinite intelligence and goodness exists”) is logically possible. That is, the non-existence of God is ‘conceivable’, because it is thought that conceivability is purely about the formal-logical consistency of language. “God does not exist” does not generate any obvious logical contradiction, hence it’s logically possible (i.e., conceivable).
Charles Hartshorne took the rare view that ultimately logical and ontological possibility coincide and are one and the same. I’ve always gravitated toward this view. It doesn’t make sense to me that once committed to the necessity of God’s existence, one should concede the conceivability of the non-existence of God. Hartshorne felt the same thing. He expressed this on many occasions and the linked article here is one such instance.
No one who believes in the metaphysically necessity of God can find his non-existence conceivable, at least not if one’s understanding of God is that he is the ground and source of all being (as opposed to believing in “a” God, Zeus for example). We’re speaking about a necessary being here, so our options are either he exists necessarily or his existence is impossible. Hence, to the extent one grants the logical possibility of God, one is committed to his actual existence. When theoretical physicist Steven Weinberg, for example, grants that God’s existence is indeed logically possible but he doesn’t believe God exists, he’s being self-contradictory.
So what do we do with logical and ontological possibility? Well, since it isn’t immediately obvious what metaphysical necessities there are, we do require a consistent and predictable way to talk about candidates, and to this extent Hartshorne granted a distinction between logical and ontological possibility/necessity. The laws of identity, non-contradiction, etc., remain the immediate rules for meaningful discourse. But, as Hartshorne’s arguments revealed, once one had reasoned one’s way through to conclude the existence of a necessary God, one was justified in maintaining the inconceivability of God’s non-existence. And the rules of logic held one to this. The inconceivability in question had to be argued for, of course. Hartshorne didn’t think metaphysical (a priori) truth was always obvious, laying on the surface. And he granted that debate over the status of such truth would continue. But where the mind embraced the truth of God’s existence, it could not consistently concede the meaningfulness (conceivability) of his non-existence, even if to enter into conversation about God he admitted atheist claims for examination alongside his own rather than dismiss atheist claims as obviously incoherent, like “Married bachelors exist.” But he did maintain that there are legitimate grounds for affirming the logical impossibility of the metaphysically necessary. So long as one is up front and careful about one’s use of language, all is well. There’s no logical reason why one one’s formal-logical language game must in all cases remain unrelated to one’s metaphysical commitments. Metaphysical commitments carry logical implications.
I’m doing a poor job of describing it. Forgive me. Enjoy the Hartshorne piece.