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Main argument for a posteriori necessity uses these premises:

(P1) 'Hesperus' is a proper name that refers to the evening star. 'Phosphorus' is also a proper name and it refers to the morning star. But the evening star and the morning star are the same planetary body (Venus). So both names designate Venus.

(P2) If both names designate rigidly, they designate the same object (Venus) in every possible world. Therefore (by the definition of 'necessary') 'Hesperus = Phosphorus' is necessarily true. If it is the case that in all possible worlds the identity claim “Hesperus is Phosphorus” is true, the statement is necessary.

'Hesperus' and 'Phosphorus; are proper names that we give to the evening and morning stars in all possible worlds.There are a number of problems I see with this argument; for example:

1) The object (an eveing star/morning star) might not even exist in some possible world.

2) It is possible to have an evening as well as morning star but they could be different. It is only true in our world that evening and morning stars turned out to be the same planet. It doesn't follow they would be same in all possible worlds.

What is going on here?

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See Rigid Designators :

Kripke famously argues that because a rigid designator designates the same object in all possible worlds, an identity statement in which both designators are rigid must be necessarily true if it is true at all.

‘Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ‘Hesperus’ and ‘Phosphorus’ name in all possible worlds is Venus.

a rigid designator designates its designatum in every possible world containing the designatum and in other possible worlds the designator fails to designate. In places, Kripke suggests that this is his idea:

When I use the notion of a rigid designator, I do not imply that the object referred to necessarily exists. All I mean is that in any possible world where the object in question does exist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist (Kripke, “Identity and Necessity”, 1971, p. 146).

  • A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. Okay, this solves the first problem, but the second problem still persists. Hesperus and Phosphorus are rigid designators for an evening and morning stars respectively. It is an empirical fact about our world that both of them turn out to refer to the same object. I don't see why would they refer to the same object in all possible worlds. – Curious May 31 '18 at 6:23
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    @Curious - because in every possible world where there is Venus, there is only one Venus (in general, tehre is only one "copy" of every existing individual). – Mauro ALLEGRANZA May 31 '18 at 6:24
  • Yes but it is possible to have empirical evidence that the two stars are not Venus, we have evidence that it is true in our world. If by all possible worlds, you mean all possible worlds where the two stars are Venus, how is it different from a tautology? – Curious May 31 '18 at 6:26
  • I think you're missing the point here. the point is the idea of rigid designation , i.e. that there are proper names for things that pin to them in all possible worlds (where the thing exists at all). You're kind of doing the same thing by adding a third rigid designator "Venus". – virmaior May 31 '18 at 7:19
  • or to word it another way "morning star" and "evening star" might be things we could use as descriptors of "last object seen in sky in morning" and "first seen in evening", but that's not how Kripke is using the terms "hesperus" and "phosphorus". For him, those are rigid designators that always pick out the same thing whether we've discovered their empirical identity or not. The non-trivial non-tautological thing is to claim that names function as trans-world identifiers (compare this with Russell's treatment of names). – virmaior May 31 '18 at 7:21
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  • Regarding your first question, you are perfectly right: if N is a rigid designator of an entity a, which according to Kripke all proper names are, it refers to a at every world in which a exists. At the a-less worlds N doesn't refer.

  • An important point that applies to proper names only and not rigid designators in genera, but which needs to be kept in mind when thinking about "Hesperus": It is our N that doesn't refer. If speakers of an a-less world use a name that is, say, orthographically indistinguishable from N, that doesn't make it N. Names are not just strings of characters or sounds, but more like institutions, individuated by name-using practices. In typical cases, one can think of these practices as inaugurated by a baptism of sorts: a few first instances of use of N, with the intention to refer to a; and then a chain of speakers which pick up the name from previous links in the chain, and form the (tacit) intention to conform to whatever name-using practice the name belongs in.

    When thinking of these questions it is important to keep straight the difference between

    1. The names that we, speakers of the actual world, use to talk about states of affairs at the counterfactual worlds, and

    2. The names that they, speakers that inhabit the counterfactual worlds, use to describe the states of affairs at their world, which they consider as actual. Their names might be homophonic to our names but they are different names, because they correspond to wholly other name-using practices.

  • Regarding your second question, the whole idea of rigid designators is that they are not synonymous with any description---or any non-rigid description at least, which is the case with 'the first star visible in the morning'.

    In the case of 'Phosphorus', for example, the following sentence makes perfect sense, and is probably true:

    Phosphorus might not have been the first star visible in the morning.

    But, if 'Phosphorus' was synonymous with that description, this sentence would be a contradiction in terms. Mutatis mutandis for any other non-rigid description.

  • It seems to me that on this account, the definition of proper names change after observing some fact. For example, before observing Venus, by morning star we meant an object seen first in morning which could or could not be evening star. After observing Venus, we define morning star as an object which is necessarily evening star as well – Curious May 31 '18 at 8:09
  • You can understand "the morning star" as a bona fide description that will pock out whatever morning star there is in the situation at hand. But 'Phosphorus' is not (no longer, perhaps) such a definition. It's a proper name, and the semantics of proper names in not that of description, or so would Kripke (and the orthodoxy in contemporary philosophy of language) have it. – Schiphol May 31 '18 at 8:13
  • But we will be referring to distinct objects properties with the same name. In some possible world, morning star is evening star as well while in another world this is false. On this view, we will be referring to distinct objects with the same name. – Curious May 31 '18 at 8:18
  • I think you are perhaps confusing names as used in that possible world with the names we use to describe that possible world. They may well say correctly "Hesperus is not Phosphorus'" but that's because their idiolect (call it 'twin-English') lacks our names 'Hesperus' and 'Phosphorus' and has two homophones instead. We, on the other hand, cannot say with truth 'in that world Hesperus is not Phosphorus'. That would be tantamount to saying" Venus is not Venus". – Schiphol May 31 '18 at 8:23
  • I am using names that we use to describe the object in possible worlds. People in that possible world may assign a different name. I am saying we change the meaning of morning star after observing some evidence. Before observing evidence, by morning star we meant an object which could be an evening star as well. After observing the evidence, we use the name to refer to only those morning stars which are evening stars as well. – Curious May 31 '18 at 8:26

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