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If whatever is actual is possible, but not everything that is possible is also actual, and if everything that is necessary is actual (and hence possible), it looks like it might not make sense to talk of "merely necessary" things (things necessary but inactual and impossible, somehow). Or merely contingent, merely impossible, or merely actual things, for that matter. Maybe "merely contingent" still goes through, though, since this would be something that was not necessary and not impossible, i.e. it has a definition-by-absence, so to qualify it by "merely" so as to exclude other terms, would fail in its purpose (there being no positive terms to exclude, here). Or then merely impossible things might be, again, things referred to as "impossible" without the limiting qualifier. However, a merely actual thing would not be possible also, and if there were a necessary being that was merely actual otherwise, its actuality would not be a function of its necessity ("merely actual" and "merely necessary" conflict with each other, here; an object defined as both is being defined incoherently).

If nothing can be merely necessary, does this show that the concept of possibility is metaphysically prior to that of necessity, or rather does it show that the priority of the concept of necessity is a matter of modal/logical syntax (deduction theory as "the premises necessitate the conclusion"), but the priority of possibility is a matter of logical semantics (possible-worlds talk)?

Two corollary issues:

  1. Moreover, there are no necessarily merely possible things. If something is merely possible, it is not yet actual; if it must not be actual, then it is actually impossible.
  2. However, the option of merely possibly possible beings, and so on, also then is provided for us. Or, then, of possibly merely possible beings. The effect of the "merely" qualifier on the base operations, arguably should be had upon the iterated operations too, at least in such a way as to illustrate why (or why not) iterated modality is trivial/collapsible.
Kristian Berry
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  • According to Pruss's WPSR contrary to your claim 1, there exists necessarily merely possible things such as the ontological argument, due to the letter "W" there might possibly not exist God in this actual world, but there must necessarily be in some other non-empty PW due to the latter letters... – Double Knot Aug 14 '22 at 03:44
  • If God exists in some possible world, as in is actual in that world, He wouldn't be merely possible, would He? I was actually thinking this could be used as an argument against Lewisian realism, and later to too-strong multiversal set theories (ones without a principled filter on which "possible worlds" count as actual), that they would not allow for merely possible things (Lewis) or would include necessarily merely possible ones (unfiltered multiverses). – Kristian Berry Aug 14 '22 at 03:58
  • I think it is far simpler than syntax/semantics or metaphysical priority. "Merely A" relative to B refers exactly when the set difference A\B is non-empty, but that is equally reflected in syntax (inferentially) and semantics (extensionally). When A is a subset of B it does not refer, as with necessary and possible, but B being larger hardly makes it "metaphysically prior". And that is all that "merely" tracks, you can pick the dual adverb that favors supersets instead. The same goes for three or more sets, it is decided by extensional containments among them and the choice of adverb. – Conifold Aug 14 '22 at 04:53
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    Pruss also has a further WWPSR saying possibly for any contingent truth p it's possible that p has an explanation, whose iterated modality cannot be collapsed, otherwise its meaning is distorted and cannot prove that with S5 frame of WWPSR God exists necessarily in every world and thus explains all contingent truths at all accessible PWs! Please note in most modal logics once a proposition p is possible it cannot be merely possible since by its elim-rule there must be some PW found to apply p. And conversely it's not the case for necessity operator... – Double Knot Aug 14 '22 at 05:07
  • As for principle/ultrafilter of all multiverses that's related to orders and you have to introduce order relation of all PWs in additional to Kripke's accessibility relation, and in most popular frames such as S5 every PW is kind of like in the same "order" with each other... – Double Knot Aug 14 '22 at 05:21
  • @DoubleKnot, the filter I meant was not a set-theoretic filter, but something that differentiates between merely possible and actual worlds. If set-theoretic universes are mere possibilities, and nothing sets some apart as actual, then they are necessarily merely possible. But this violates the concepts of actual possibility and possible actuality, so there must be a way to filter out "nonactual" set universes (something orthogonal to forcing, say). – Kristian Berry Aug 14 '22 at 05:43
  • There is no such thing as necessary but not possible or actual. – David Gudeman Aug 14 '22 at 06:24
  • PW semantics implicitly allows mere necessity but not mere possibility as I hinted from their difference of elim-rules above, mere necessity is best seen in deontic logic where ought p doesn't imply p is already the norm, while mere possibility cannot hold since for anything possible or permissible p by definition you can always find an accessible PW where p is the case, otherwise why bother with PW semantics in the first place. And only in this sense possibility may be said to be prior to necessity... – Double Knot Aug 14 '22 at 06:24
  • @DoubleKnot, I don't have in mind the whole ensemble over modalized worlds, but only those in terms of alethic modality. If something is necessary by being true in all possible worlds, how could it be true in all possible worlds but not true in any specific possible world, AKA how could it be merely necessarily true without being possibly true (and actually true, somewhere)? – Kristian Berry Aug 14 '22 at 06:51
  • By default in modal logic we're talking about the most general K, I didn't see you mentioned alethic in your question. As for mere alethic possibility it's still the same case as non-alethic one, at least in PW semantics you can always find a (actual) PW where its operand holds. But then there's no hint implying its ontic priority, per ontological argument it seems quite the opposite... – Double Knot Aug 14 '22 at 07:03
  • Necessity holds where it holds in all accessible possible worlds. A proposition might be necessarily true at a world but not true in all worlds, i.e. including inaccessible ones. Perhaps one might understand mere necessity to mean that a proposition is true in all accessible worlds, but is only contingently true at some of those worlds. Similarly, a proposition may be possibly possible, but not possible. Of course, for this to work, you must eschew axioms 4 and 5, and this imposes some restrictions on the natural semantics of your logic. – Bumble Aug 14 '22 at 17:00
  • @DoubleKnot, when people talk about necessity, they usually don't mean deontic logic, especially if they are also using the words "possible" and "impossible" rather than "permissible" and "impermissible'. – David Gudeman Aug 15 '22 at 04:36

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