possible or not

Is it possible to swim the Atlantic?
An ex neighbor points out that if “possibly” doesn’t imply also “possibly not” then how is “possibly” different from necessity? Doesn’t “Life on Mars is possible” mean “It’s also possible that there’s no life on Mars”? And doesn’t it also mean “Life on Mars isn’t necessary”?
Grice gave an answer to this question, and I’ve written about it elsewhere in this blog, but I think there’s more to be said and I want to try to sort all of them out.
Suppose Goldbach’s postulate is possibly true. Suppose someone proves it. Now it’s necessarily true. Is it no longer possibly true?
My neighbor says no. I think Lukasciewicz agreed with him.
But suppose we have a set of conditions that fulfill the capacity to swim the Atlantic, and some person satisfies that set. Now it’s possible for someone to swim the Atlantic, and the question of whether it has been done is irrelevant.
One way to cash out the notion of truth is a saying of what is, and the notion of false, a saying of what is not. In this dichotomy, where does possibility lie?
One place is knowledge. There’s what we know exists, what we know doesn’t, and what we don’t know about is the possible.
But isn’t this Lukasiewicz trichotomy conflating knowledge with fact?
A lot depends on whether determinism holds — if every actuality is necessary, then everything that happens is necessary. But whether determinism is true is itself uncertain.
It seems to me that there are many meanings of “possible” besides “unsure.” There’s the abstract conditions of conceivability, “if someone were strong enough, someone could swim the Atlantic;” the actually satisfiable conditions of possibility, “there is someone strong enough, so it is possible,” and the actual itself, “she swam the Atlantic, proving that it is possible.”
If you choose a Lukasiewicz trichotomy, is there space for all these? It seems well suited to determinism, but not to modality. The classic Aristotelian four-way modality (possible+negation yielding possible, not possible, possibly not, not possibly not) along with the conjunction of “possible & possibly not” accommodates a distinction between actuality and necessity, where we can be agnostic about determinism and entertain possible worlds that will never be.

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