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A "non-prime world" is an abnormal world in modal logic where a disjunction can be true even if none of its disjuncts hold true. So they can be seen as a sort of "impossible" world. But this impossibility is not necessarily that of a direct threat of contradiction or explosion, it seems, like it wouldn't metaphysically destabilize a world to be non-prime, or even if it did, it wouldn't be to such an extent as in the so-called "trivial world."

Maybe that's just the impression that I get. But if not, if it's less drastic for a world to be non-prime than non-consistent, then maybe we can imagine worlds that are just partially non-prime, where some-but-not-all disjunctions satisfy the pertinent condition. If it is possible for there to be an "impossible" world of this kind,◊ even one that can be inhabited by real concrete beings, is this the kind of world that would be needed for hard free will to exist (there)? I ask because of the following from Berto[17] ("Impossible Worlds and the Logic of Imagination"):

However, to achieve [our goal] we do not need nonprime worlds such that [disjunctions are true apart from any of their disjuncts being so]. What does justice to under-determinacy in imagination is the plurality of worlds accessed via RA or fA : different worlds fill up the unspecified details in different ways. [emphasis added]

So we have that non-prime worlds can figure in a representation of "under-determinacy," and though this is not said to be relevant to imagination, yet insofar as imagination and will are not completely identical (though they be much involved, the one with the other), do we have that the "under-determinacy" involved in hard free will is related to the matter of non-prime worlds?

◊I wanted to think of "demi-possible" worlds, but per Conifold, if ◊ is idempotent, then d◊ = ◊, which means that possibility isn't properly demifiable. And on some reflection, I can conveniently acquiesce to the claim that ◊ is idempotent.

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  • A beautiful poetry describing the feeling rather than the meaning of the Matrix. Refusing to accept its own ineligibility, unfreedom and non-existence.
    – TheMatrix Equation-balance
    Commented Sep 28 at 2:06
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    SEP classifies "impossible" worlds by logical laws they violate. Non-bivalent logics do not have to violate LNC, so non-prime worlds can be consistent. Indeed, one of the standard ways out of logical fatalism, supervaluationism, produces "partially" non-prime worlds where future contingents are neither true nor false, but LEM and LNC both hold because connectives are not truth-functional. Other approaches reject LEM for future contingents but not LNC.
    – Conifold
    Commented Sep 28 at 3:59
  • Can you define free will so that it means something, first? I'd be happy to assume that you mean the ability of supernatural souls to exercise causal agency on nature in a manner contrary to the will of God, like the only people I've ever read who actually mean anything that means anything when they say "free will", but somehow I doubt that's your intent.
    – g s
    Commented Sep 28 at 6:59
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    @gs For the purposes of this question, nothing so exotic is needed and what the "hard free will" is makes little difference. All it is supposed to provide is indeterminism and the question concerns assigning truth values to statements about future events under indeterminism.
    – Conifold
    Commented Sep 28 at 8:35
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    I find supervaluationism to be the most intuitive resolution (and close to what Aristotle gets at with tomorrow's sea battle). A disjunction with indeterminate disjuncts is true ("supertrue") when it comes out classically true under any assignment of truth values to those disjuncts. This validates LEM even for truth gapped statements like future contingents. When it comes out true on some assignments and false on others then it is truth gapped itself.
    – Conifold
    Commented Sep 28 at 10:33

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Shadows in the cave - the simulated reality. It does not have to be consistent, it does not have to obey rules or logic. It can be as individual as a fleeting thought. But the shadows themselves are rigid slaves, they don't know freedom.

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    To It does not have to be consistent I would add ... rather its consistence lies outside its ken A classic allegory from Vedanta runs: In a room in complete darkness there are no shadows; likewise in bright sunshine there are none; But in flickering candlelight terrifying ghosts dance menacingly
    – Rushi
    Commented Sep 28 at 2:29

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