On a long walk in Princeton many years ago I asked David Lewis whether the distinction between what’s necessary and what’s contingent might be just an epistemic (based only on what we do and don’t, can and can’t know), rather than an ontic one: The things we regard as necessary are the ones that are either provably necessary, on pain of formal contradiction with our premises, such as the fact that 29 is prime or that “p or q” implies p, or are thought to be “nomologically necessary,” based on current causal theory and evidence, such as that apples fall earthward rather than skyward because of gravity. The things we regard as contingent are just the ones that are not provably necessary, nor thought to be nomologically necessary.
In other words, the necessary/contingent distinction could be metaphysical, but it could also be that everything that is and that happens is necessary (could not have been otherwise), either formally or nomologically, but we just don’t always know the proof, or the laws/evidence/reasons. Contingency and possibility are just symptoms of our ignorance.
The idea has its homologue in metatheory of probability: What look like possibilities only look that way because of our ignorance. Everything is determinate and necessary; just some of it (unproved and unprovable theorems, the answers to NP-complete questions, many-body problems, even quantum indeterminacy), is uncertain, unpredicatable, its formal or causal story unknown or even unknowable. (No, I don’t think QM’s hidden necessity would be committed to the truth of hidden-variable theory.)
What would become of the realist view of necessity if everything were necessary? (Those are, of course, epistimic “woulds” and “weres”.)
This would not solve the “hard” problem of consciousness either because it’s not enough to say that our brains must produce consciousness: We still want to know, as with everything else, how and why. The hard problem is an epistemic one, of causal explanation.
And of course there’s a lot more at stake in asking whether the laws of nature themselves could have been otherwise than in pondering whether or not the various incarnations of the Ship of Theseus are the same ship.
Formalists in mathematics would then be pragmatists, in John Burgess‘s sense, but the law of non-contradiction would be the underlying realist constraint.
Non-ontic contingency would of course have implications for “possible worlds” theory, “concepts,” and “free will.”
Footnotes:
“Uncomplemented Categories” (for which non-members do not exist) are admittedly problematic.
If everything were ontically determinate and necessary this would not only pose problems for free will but for ethics.