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All of the modal propositions I can think of are most reasonably analyzed as a modal operator applied to a proposition, and possibly other arguments. In the following examples, I'll write the arguments to the modal argument in parentheses:

  1. It is possible that (there are black swans).
  2. It has always been the case that (2+1=3).
  3. (Joe) believes that (all crows are black).

Note that the last one takes two arguments, an object (Joe) and a proposition (all crows are black). I can't think of any modal propositions that don't involve a modal operator that takes a proposition as one of the arguments, are there any? Are there any modal propositions that just look like a regular predicate applied to one or more regular, non-propositions objects?

Also, I imagine that by taking enough liberties, one could always express a modal proposition in this form, but are there any where it is natural to express the proposition as just a predicate applied to objects: p(x, y, z)?

What I mean by modal in this context is non-truth-functional. For example, if p(x,y,z) were a modal proposition, then some tautologies such as P->(Q->P) might not hold if P is p(x,y,z).

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  • "Philosophical zombies are possible, round squares are impossible". If you take the Meinongian view then existence and possibility become predicates (pace Kant), although, of course, there is always Russellian paraphrase to turn them into modal operators on descriptions, see SEP Nonexistent Objects and Possible Objects.
    – Conifold
    May 29 at 19:26
  • Would essentialism count as an example of what you are asking for? It is customary to distinguish modalities de dicto from de re. The former is a property of propositions only; the latter is a property of things and hence more naturally represented as a predicate, or an operator on predicates. Kripke holds that the identity relation is necessary, so it is an essential property of every thing that it is self-identical. David Lewis also allows for essential properties, though he expresses it differently, since he does not accept cross-world identity.
    – Bumble
    May 30 at 2:13
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    Small semantic clarification question - are sentences sufficiently distinct from propositions in the sense you mean? There’s something interesting to me in the distinction between the modal operator as a term in the language and the operator as a “second order” sentential metalanguage function!
    – Paul Ross
    May 30 at 7:08
  • @PaulRoss, I probably should have worded the question in terms of sentences or formulas to clarify that the question is about syntax. It is controversial whether propositions have the same structure as sentences.
    – David Gudeman
    May 30 at 11:28
  • @Bumble, essentialism might count if it interferes with tautologies. The test is whether there is a proposition for which some tautologies don't hold.
    – David Gudeman
    May 30 at 11:30

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