The following propositions demonstrate how a priori works in the actual world and how it doesn’t work in the possible world scenario. First, if ‘Hesperus = Hesperus’, H=H is a true statement because Hesperus is identical to itself, thus necessarily a priori. If O designates the same object in all possible worlds, but P designates different objects in all possible worlds, there could be at least one possible world in which O=P which is not possible. Therefore, this statement may not be true in all possible worlds.
Kripke’s response is that this is not a world in which Hesperus isn’t Phosphorus. Rather, it’s a world in which we might have used one of the names ‘Hesperus’ or ‘Phosphorus’ to name a different object from the one we actually use it to name. So although ‘Nothing but Hesperus could have been Hesperus; but something other than Hesperus could have been named ‘Hesperus’. So, given our usage of the names ‘Hesperus’ and ‘Phosphorus’, there is no possible world in which Hesperus is not Phosphorus — for there’s no possible world in which Hesperus is not itself.
It appears that it is only contingently true that Hesperus is Phosphorus due to a conflation of epistemic with metaphysical possibility. What many philosophers agree upon is that the names which should be considered in all possible worlds are not rigid but flaccid. A “flaccid” designator is not required to designate an object in all possible worlds (La Porte). An example of this type of semantic argument might be “The chef on television cut her hand while preparing a chicken.” While the chef might have been Julia Childs in our world, in another world perhaps “Julia Childs” was not herself but was actually Dan Aykroyd imitating Julia Childs. Therefore, while the name remains, it does not specify the same object in all possible worlds and thus remains flaccid.
One argument against a posteriori necessary truth is seen in the writings of Soames. He states that Hesperus = Phosphorus and Hesperus = Hesperus and each of these propositions are equally a priori even though superficially they appear to be different (Source Soames 2002, pp. 240, 243) I believe Soames over simplifies the discussion simply because he felt it to be trivial.
In addition, Wong states one of the other issues with a posteriori truth is that there remains the question whether or not there is only one single a posteriori truth in the above propositions about Hesperus and Phosphorus (Wong 9). For this reason, the claim that rigidity presents propositions that are necessarily true and a posteriori is often disputed. Although Kripke believes names to be rigid designators, it is my opinion that it does not matter whether it is a name, an identity statement, or a natural kind which is referred. Let us state simply that this does not mean that different nouns (e.g. Hesperus, Phosphorus, Venus) cannot denote the same object or only single objects.
Indeed, it becomes apparent that his theory on epistemically justified a posteriori knowledge of names is most likely feasible, but it also becomes obvious that it is not necessary that names are rigid in all possible worlds. Rather, names are only possible in all possible worlds. The reasoning behind this stems from Kripke’s own example of Hesperus and Phosphorus. The first thing one notices is that he is referring to two separate names and upon first glance appear to identify two separate objects. But it is possible that the names refer to the same star, thus Hesperus could possibly be Phosphorus and therefore contingently true a priori. But the names Hesperus and Phosphorus can only be shown to be necessarily true ex post facto through empiricism. So while the Greeks may have already understood that Hesperus was Phosphorus, it wasn’t until Galileo’s empirical studies that the path of the star was confirmed to be the same star. Kripke clearly understood that if the names, albeit different, referred to a single star, then the statement Hesperus = Phosphorus was not a contingent truth but necessary truth (Kripke 125). That would therefore make the modal statement epistemically justifiable, ergo, necessarily a posteriori.
However, what is not mentioned by Kripke is the fact that while his comments on the identity of Hesperus and Phosphorus make sense, he does not actually explain that the one thing that keeps the identity of the two entities separate are their names (Doyle 378), and thus, what remains rigid is the object being nominated differently, not the names themselves. In fact, if we were to speak of Nixon as possibly not the President in another possible world, even if the name remained the same, the object would be different, the necessity that Nixon was Nixon would change, because it could stand to be the case that Nixon was not Nixon in another world. Kripke’s idea of a possible world is that it is the same individual, differing only in the property of losing the election. All of Kripke’s possible worlds are different ways our actual world might have been, thus it could have been the case that Nixon, the President in 1968 was not the President in 1968 in another world.
Using this logic with the example of the evening star, if Hesperus was rigid, in another possible world it might not denote the evening star, it would denote something else…perhaps a quasar, a tree, or a frog. If I am interpreting Kripke correctly, even though Hesperus was dubbed Hesperus and there is a long line of Hesperian followers who were present when someone exclaimed, “I shall call that evening star Hesperus!”, in another world it may not be Hesperus the star. Therefore, this situation begs the question: Is the name irrelevant when one needs to describe who or what the name refers to?
Simply because we know something a posteriori (and therefore it must be necessary in all possible worlds) somehow doesn’t hold with the actual meaning of “possible.” Possible means “that may exist or happen, but that is not certain or probable” (Possible). A posteriori necessary truth exists in our actual world when we can prove that it exists. It may not exist in another world at all, and certainly (at this point in time anyway) there is no way for us to prove the existence of possible worlds other than just thinking about them. What needs to happen is the semantics of how we present the information needs to change. Therefore, in our actual world it was learned that:
At first, Hesperus appeared similar to Phosphorus which appeared similar to Hesperus. We have learned through empirical investigation that the names actually refer to the same star in our actual world. However, their names do not appear rigid because they are not the same names, and possibly the names or the star itself may or may not exist in another possible world. Therefore, Hesperus and Phosphorus are known to be necessarily a posteriori the same star, even though the names are different, and it could be possible or not be possible that either the star or its various names exist in other possible worlds.

It should be mentioned that it is said that the substitution of contingent empirical facts that are not true in all possible worlds (when it relates to concepts that are necessarily true) is what causes substitution failure (Information). However, with this type of linguistic presentation, the names and their single referent are understood to be necessarily a posteriori, but it still returns us to the idea that names (nouns) must remain necessarily flaccid a posteriori because of the uncertainty of what may or may not be in a possible world; and synonomy and substitutivity can only occur after empirical validation in our actual world.
An argument against a posteriori necessary truth is seen in the writings of Soames. He states that Hesperus = Phosphorus and Hesperus = Hesperus are actually the same thing even though superficially they appear to express different propositions (Source Soames 2002, pp. 240, 243) According to him, Hesperus = Hesperus is as a priori as Hesperus = Phosphorus. However, I argue that at the point the names were shown to identify one object through empirical investigation, we cannot refer to them as a priori simply because “now we know.” In fact, the actual definition of a priori is “relating to or denoting reasoning or knowledge which proceeds from theoretical deduction rather than from observation or experience” (a priori). Therefore, the only statement that can be a priori in this case is Hesperus=Hesperus.
According to Leibniz, “truth in all possible worlds” is limited to logically possible and non-contradictory statements (Source). It thus justified the logic behind it and justified the epistemological need to identify that possible propositions are true in some possible world (Menzel 29).
Kripke uses a definition of “possible worlds” which is not metaphysically accurate in order to prove his theory of rigid designation of names. He states that we give names to objects and use those names in our world; therefore, we ought to rigidly refer to those objects by those names across all possible worlds (Kripke 77). Perhaps the rationale behind theorizing about maintaining names is comforting, or at least allows us to believe in free will and the importance of mans’ existence outside of our actual world. In my opinion, I see Kripke’s responses as trying to return from the rejection of private language by Wittgenstein and return to the Deweyan sense that language occurs between people (Source? Quine 142). This behaviorism approach seems appropriate in that language is a construct of man in his attempt to better understand his world. However, Kripke seems convinced that human identity vis-à-vis names must be held rigidly across all possible worlds and does not realize that in other possible worlds man may not even exist, let alone his names. Indeed, I posit that Kripke’s concept of what could be in possible worlds creates metaphysical and epistemological issues with his theories and results in him disproving much about which he has theorized. Having said that, perhaps what we can say for certain is that we can acknowledge that things exist in our world both necessarily a priori (bachelors are unmarried men) and contingently a priori (Hesperus=Phosphorus) once the empirical knowledge is acquired, but that the existence in other possible worlds remains both contingently a priori and a posteriori in that we must still acquire empirical validity, and until now do not have this knowledge. One thing is certain, though: In maintaining the rigidity of the name in our actual world, Kripke’s interest in celebrating the Causal-Historical link is respected.

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