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Lately, I have been reading some of Quine's works on modality. I can't help but feel that many of his pronouncements on modality are wrong/misguided, although pinpointing exactly where is goes wrong is proving rather difficult. For instance, in The Problem of Interpreting Modal Logic and Reference and Modality, he seems to defines necessity as follows:

Where p is any proposition, "Necessarily, p" is true if and only if "p" is an analytic statement.

This way of viewing necessity seems to undergird many of the problems with, and objections to, modality that he identifies, particularly because he doesn't take kindly to the notion of analyticity. But defining necessity in terms of analyticity just seems plain wrong. I believe it is safe to say that every analytic statement is necessary, but I don't think the converse is true. I think I have a counterexample. "the morning star = the evening star" is true as a fact of astronomical discovery. According to Ruth Barcan, if "x=y" is true, then "necessarily x=y" is true. Thus "necessarily the morning star = the evening star" is true. But certainly the statement "the morning star = the evening star" is not analytic, which Frege realized long before Quine was even a philosopher.

Does this sound right? If so, why didn't Quine see such a simple counterexample? Would he not think it is a genuine counterexample? If so, how would he respond to the above argument.

Also: I am having trouble seeing the difference between saying "Necessarily, p" and " 'p' is necessarily true." . Quine seems to think there is a difference, which is most evident in his paper "Three Grades of Modal Involvement." He says of one (not sure which of the two) that it is a statement operator, while the other is a semantical predicate. However, I am having trouble seeing the difference between using necessarily in those two ways.

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    I think that Quine is reaching for the Kripke kind of necessity, where every conceivable possible world would force the fact to be true -- the kind of necessary Scholastic philosophers meant when they considered the first mover necessary. Your example certainly is not necessary in that sense, just because it happens to be scientifically provable. We could surely exist in a possible world where there were separate morning and evening stars.
    – user9166
    Oct 10, 2017 at 22:03
  • @jobermark How can that be right? Isn't this the very opposite of Kripke's view? Moreover, I never got the impression that Quine was hinting at possible world semantics. If "the morning star = the evening star" is true, then "the morning star" and "evening star" are co-referring terms, although they have different sense/meaning. If this the case, how could they fail to refer to the same thing? After all, this a theorem of logic which Ruth Marcus proved.
    – Eli Bashwinger
    Oct 10, 2017 at 22:28
  • Necessity as analyticity was Carnap's theory with which Quine originally argued. What you seem to have in mind is Kripke's "metaphysical necessity", a different notion, which Quine anticipated as an alternative and also rejected:"the way to do quantified modal logic if at all is to accept Aristotelian essentialism. To defend Aristotelian essentialism is not however part of my plan... And in conclusion I say as Carnap and Lewis have not: so much the worse for quantified modal logic." See modern modal logic on SEP
    – Conifold
    Oct 11, 2017 at 0:02
  • @Conifold I know he was suspicious of de re metaphysical necessity, as the quote you give shows, but did he have problems with de dicto metaphysical necessities?
    – Dennis
    Oct 11, 2017 at 11:38
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    @Dennis He made his peace with intensionality in Pursuit of Truth, but not necessity, of any sort:"there is less to be said for necessity than for the propositional attitudes... We modify a sentence with the adverb 'necessarily' when it is a sentence presumed acceptable to our interlocutor and stated only as a step toward the consideration of moot ones. Or we write 'necessarily' to identify something that follows from generalities already expounded, as over against new conjectures or hypotheses... The sublimity of necessary truth turns thus not quite to dust, but to pretty common clay".
    – Conifold
    Oct 11, 2017 at 19:25

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I. I do agree with Barcan and Kripke: if two things are actually one and the same, then they are necessarily one and the same. As far as my judgment can discern, this is just the statement that, for all possible worlds or scenarios, x exists if and only if x exists.

So when we say that "Hesperus is Phosphorus," or that "the morning star is the evening star," the state of affairs we are expressing is the same as when we say "Venus is Venus."

On the comments above, jobermark read the second of these sentences as de dicto, when the intended reading of you and Kripke is de re. To give a classic example of that distinction, consider what someone is stating when they say "Necessarily, the 44th president of the United States is Obama." The de re reading is that Obama is necessarily Obama: the object referred to by "the 44th PotUS" is what is being asserted some property (i.e. being necessarily identical to Obama). The de dicto reading is that whoever occupies the place of the 44th PotUS is necessarily identical with Obama: the description provided by "the 44th PotUS" is being asserted to always refer to something identical to Obama, which is false.

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II. Unlike you asserted, that A = A entails N(A = A) is not true for all of its instances because merely because it is a theorem of (some version of) modal logic, I think, but rather because the world (necessarily) is that way and that logic's axioms capture the way the world (necessarily) is.

Unlike Quine would have to assert if faced to your objection, A = A or N(A = A) is not true in all its instances because we have defined so, but rather because things in reality are such that something couldn't have been numerically distinct to itself. (I'm reading '=' as asserting numerical identity, of course. Reading '=' as asserting qualitative identity yields a contingent statement: the morning star now differs from what it itself was some time ago.)

Something makes it so Barcan's assertion is universally and necessarily true, and it's not our definitions or linguistic practices (I think — many would beg to differ), but rather because of something in reality, namely, everything, for everything is identical to itself. (Funnily enough, it was Quine that said that "A = A" is true because of the way reality is. I suppose he denied it to be necessary for any of its instances.)

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P.S. I don't see the difference between «N(P)» and «"P" is necessarily true». Perhaps the difference is that, in the second sentence, one is asserting that in all possible worlds the sentence-type "P" asserts something true. But this is false. "All female foxes are vixens" certainly expresses a necessary truth in our context of linguistic usage, because it expresses that all female foxes are vixens, which is necessarily true. But in some other context of usage, in the actual world or elsewhere, that very same sentence-type may express that some female foxes are NOT vixens, which is false. To fix that problem, we may instead state that «Necessarily, whenever "P" expresses that P, "P" is true» — which is very close to «N(P)», but pretty far away from our original sentence, for it does not involve what Quine dubs a semantic predicate.

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