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Saul Kripke’s example is clear to me: I look at a star in the morning and call it(rigidly designate) Hesperus and I see a star in the evening and call it(rigidly designate) Phosphorus.

If I go out and find that they are the same object, it is necessarily so a posteriori. I do not disagree.

But what is interesting is his claim that if I go out and find out they’re two different stars, this wouldn’t be necessarily so a posteriori.

This seems to be inconsistent. Can someone explain what perhaps his justification is or a good justification for this?

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    There's no inconsistency here since the physical fact they're 2 different stars is contingent not necessary, and certainly it's posteriori... However, if you go Kripke's essentialism route, you have to be prepared to bear with some uncomfortable linguistic effect as it equivocates some intensions as pointed out by Stalnaker, Chalmers, et al using 2-dimensionalism... May 14 at 19:22
  • Can you quote where you think Kripke says this? P. 104 of Naming and Necessity seems to say the opposite, that while there might be another possible world where the names "Hesperus" and "Phosphorus" have a different meaning than what they mean in our world (under the assumptions they are rigid designators in both worlds), given what we mean by "Hesperus" and "Phosphorous", and given that they both refer to the same body in our world, it follows that "in no other possible world can they be different ... in any other possible world it will be true that Hesperus is Phosphorus".
    – Hypnosifl
    May 14 at 19:59

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Kripke is making clear that there are two different kinds of distinction here (or maybe more than two). There is a distinction between necessary and contingent on the one hand, and a distinction between a priori knowable and a posteriori knowable on the other. The first is a metaphysical distinction and is concerned with what could or could not have been otherwise, while the second is an epistemic distinction and is concerned with what is knowable by rational thought alone versus what is knowable only through empirical observation.

Earlier philosophers had always assumed that all necessary truths are knowable a priori and that anything knowable a priori is necessary. Hence the two categories of necessary and a priori were taken to be coextensive, as were contingent and a posteriori. Against this, Kripke argues that there can be truths that are necessary and a posteriori, and also truths that are contingent and a priori. He gives a number of arguments for this position in his book, Naming and Necessity, and this is not the place to rehearse them. Given that you agree with the necessity of "Hesperus is Phosphorus", you understand the distinction, and concur, at least in part, with Kripke's view of the matter.

On Kripke's account, Hesperus and Phosphorus are rigid designators, and so denote the same individual in all possible worlds. And since every individual is necessarily identical with itself, this identity is necessary. The corollary is that non-identity is also necessary. If two names a and b rigidly designate individuals in the actual world that are not identical, then this is also necessary. What remains is an illusion of contingency, whereby we could imagine circumstances in which qualitatively identical observations might lead to two distinct heavenly bodies being named Hesperus and Phosphorus, in which case "Hesperus is Phosphorus" would be false under those circumstances.

Kripke's views are highly influential, though I would say not amounting to a consensus. The nature of the necessity he speaks of can be thought of as resulting from a linguistic convention that chooses to treat names as rigid designators. In the case of necessary a posteriori truths, empirical facts make them true and linguistic conventions make them necessary. If one wished to argue against Kripke's position, one might object that modal language can be understood only in the context of some theory, and that there is no single theory that allows us to say unequivocally what is necessary and what is not. Rather, we are left with a piecemeal approach of identifying what is necessary or contingent relative to some given theory or set of presuppositions.

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    Re your "there is no single theory that allows us to say unequivocally what is necessary and what is not", I agree. But we may further judge unequivocally based on Kripke's own insight that for phenomenal concepts, there is no gap between reference-fixers and reference. So this potential alethic equivocation confusion doesn't occur in propositions unrelated to scientific/natural kinds, for example, in your own stated "necessity of identity" example such identification relation is unequivocally necessary in all conceivable theories complying with all logics except perhaps quantum logic... May 15 at 0:43
  • I'm inclined to say that the necessity of identity is just an example where the kind of modality in play is that of logical necessity and we are willing to treat the law of identity as a logical principle. It is not universal and unequivocal because for one thing logical necessity is just one kind of necessity, and also we don't have to treat identity this way: we could treat the identity predicate as an interpretable predicate, or we could dispense with the law of identity, as in Schrödinger logic.
    – Bumble
    May 15 at 9:15
  • Hmm, forget about the controversial and anyway not-popular Schrödinger (quantum) logic, isn't the entire alethic modal talk just about logic thus all necessity (if true at all) are implicitly logic necessity at least in most philosophical realm, maybe except in Kripke's Naming and Necessity since his rigid designator throwed a monkey wrench to this century-old philosophical problem with a linguistic twist. As Stalnaker pointed out some while ago, under PW semantics necessity implies a priority. Thus most like "non-identity is not (logic) necessary" as a corollary of "necessity of identity" May 16 at 4:35
  • Necessity can be of many kinds, and I don't think they are all reducible to logical necessity. A priority can be thought of as epistemic necessity. There are some clever ways of distinguishing necessity and a priority, such as the approach given by Weatherson in "Indicative and Subjunctive Conditionals", Philosophical Quarterly, 51 (2001), pp. 200-216. He picks up Davies and Humberstone's distinction between what necessarily holds at the actual world, and what holds at any world that might be substituted for the actual world.
    – Bumble
    May 16 at 11:32
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Kripke is confused. We cannot know that anything is so necessarily with empirical knowledge, it is all contingent and possibly over-rulable with further information we gain about the world.

When we establish empirical confidence in a model -- in this case the heliocentric model of planet orbits, one can make predictions using deductive reasoning based on that model. That is what Kripke is doing with the morning and evening star -- we have high confidence in the heliocentric model, use it to make deductive predictions about our phenomenal experiences we will have in the world, and therefore identify Phosphoros and Hesperus as almost certainty the same object.

BUT -- our models are always contingent. We may tomorrow discover that gravity changes in different regions of space, and if our galaxy enters that different region, our solar system orbits will change. Or we may discover that a subtle change in speed of light in a different region causes optical refraction to differ, and neither Phosphorus nor Hesperus would be visible anymore. Or he may be wrong about the orbit of Venus that night, and it isn't visible as Hesperus, and instead a newly arrived comet is close to the Sun, and he mistakenly identified it as Venus. '

None of these outcomes are "necessary" either. They are all contingent, as is the identity of Phosphorus and Hesperus.

Kripke is an analytic philosopher, and analytics NEEDS "rigid designates" to operate on, and for them to be certain (necessary). But our labels of objects in our world are tentative, soft-edged, and contingent. This is a problem for analytic philosophy -- one of the conclusions that Quine drew in "Two Dogmas of Empiricism" is that NO language is sufficiently precise to support validly doing logical analytics with it. This is also true of the objects one identifies thru empiricism. Kripke is ignoring Quine's argument, and is trying to simply assert, falsely, that both language and empiricism ARE definite and certain to the degree that analytics needs to be valid.

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    When you say "our models are always contingent" are you talking about models of physical reality? Kripke is giving an account of how some kinds of names work, he is not making any claims about physical facts. Basically, if we point at a light in the sky and say "whatever that thing is, let's agree to call it Hesperus", then any facts we later discover about that light will attach to the name Hesperus linguistically, and if there was a different possible world where they had done the same thing but found different later facts, we'd say their word "Hesperus" means something different from ours.
    – Hypnosifl
    May 14 at 16:47
  • @Hypnosifl -- Your example does not help Kripke. "Point at a light in the sky" presupposes contingent experience, which is post-processed unconsciously into speculative phenomena (speculative indirect realism is baked into our unconscious processing). IDENTIFYING that experience as a thing: "whatever that thing is, let's agree to call it Hesperus" is contingent and speculative, not necessary. And "facts we later discover about that light" are contingent, and cannot support any kind of necessary claims. Linguistic manipulation of designators of contingent speculations, are not necessary.
    – Dcleve
    May 14 at 18:16
  • "facts we later discover about that light" are contingent, and cannot support any kind of necessary claims. But there is no claim about any physical truths being necessary independent of this naming convention. It's like saying "bishops can only move diagonally according to the agreed-upon rules of chess"--no empirical evidence could falsify that, it follows from our conventions about what the rules of chess are. And saying this is necessarily true is no more problematic than saying it's necess. true that some deduction follows from some premises according to the rules of first-order logic.
    – Hypnosifl
    May 14 at 18:33
  • @Hypnosifl -- the question asker disagrees with you. He asserts that Kripke argues that facts about the light establish the necessary identity: "If I go out and find that they are the same object, it is necessarily so a posteriori." and he agrees with Kripke. I disagree with you that Kripke is NOT doing this. If all he is doing is just using deductive logic on contingent and loose inferences, then there is no need to try to establish some theoretic basis for "identity" or "necessity". Kripke is not a pragmatist, just doing pragmatic deduction on contingencies.
    – Dcleve
    May 14 at 19:01
  • How is that disagreeing with me? The convention is such that empirical facts about a thing named by a rigid designator determine what is necessarily true about that rigid designator, but this is still just a convention--it follows necessarily from the rules of how we define a "rigid designator" (specifically the rules concerning whether a name used in a different possible world qualifies as the 'same rigid designator' or not), just like the statement about the bishop follows necessarily from how we define "the rules of chess".
    – Hypnosifl
    May 14 at 19:33

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