The Maverick philosopher has a comment on my earlier question about the necessity of identity. Can we get from ‘a=b’ to ‘necessarily a=b’ in a simple step? He thinks we can.
Now if ‘H’ and ‘P’ designate one and the same entity, then what appears to be of the form a = b, reduces to the form a = a. Clearly, if a = a, then necessarily a = a. The assumption that the identity of H and P is contingent entails the absurdity that a thing is distinct from itself. Therefore the relation denoted by ‘=’ holds necessarily in every case in which it holds. Q. E. D.
The problem is the claim that ‘H’ (‘Hesperus’) and ‘P’ (‘Phosphorus’) designate one and the same entity. How do we get there, given only that H is the same object as P? Suppose we grant that H and P are this ‘one and the same entity’. We are saying that there is some entity, call it ‘V’ (i.e. Venus), such that H is identical with V and P is identical with V. Fair enough. But how do we get from there to the claim that the names designate this one and the same entity, i.e. that ‘H’ designates V and ‘P’ designates V? I.e. what validates the move from 2 to 3 in the following argument?
2. ‘H’ designates H
3. Therefore ‘H’ designates V.
You need the principle of substitutivity, the principle that if a=b and Fa, then infer Fb. For example, let F be the function ‘‘H’ designates –’. Then we agree that F(H), because we assumed that ‘H’ designates H. And we posit that H=V. Given substitutivity, it follow that F(V). But only given that substitutivity is valid in this case, which is not at all obvious, at least to me.
I think we pass over this covert assumption because of the particular example chosen. Everyone knows about the planet Venus, so we all know what ‘Venus’ designates. Not so many people know about Hesperus and Phosphorus, and that’s because the names are introduced via the philosophical discussion itself. As an aside, I don’t know when these names got introduced to philosophical debate. Frege uses the names ‘Abendstern’ and ‘Morgenstern’ and it may have been he who introduced the example. Ruth Barcan Marcus (‘Modalities and intensional languages, Synthese 13 (4):303-322 (1961) discusses the same example, using the terms ‘evening star’ and ‘morning star’. But where did the names ‘Hesperus’ and ‘Phosphorus’ come from? They are transliterated from the Greek, and there is a story that the Greeks believed they were different objects, indeed that they weren’t a planet at all but a god. Certainly the Babylonians knew that the object visible in the morning and the one in the evening were the same, as the Venus tablet of Ammisaduqa attests. As for the name ‘Venus’, we know the Romans also called the planet by that name, (Quem Venus ante alios astrorum diligit ignes, Vergil Aeneid viii. 590), probably after the Greek goddess Aphrodite, whose name was also given to the planet. Diodorus Siculus claims that the Greeks borrowed the name from the Chaldeans, but enough of that. My point is that Kripke starts with an example where the designations of ‘Hesperus’, ‘Phosphorus’ and ‘Venus’ are presumed. Moreover, the object designated is one that is now visible to us and so can be the object of demonstrative reference. So it is completely obvious, starting with that background, that the three names designate one and the same object. It’s rather like the situation he remarks on elsewhere, that there a conventional, and community-wide connotation of the names ‘Holland’ and ‘the Netherlands’, and that these names are effectively synonymous. So if the names ‘Hesperus’ and ‘Phosphorus’ are synonyms, and if they are rigid designators, it is plain as day that necessarily Hesperus is identical with Phosphorus, just as it is necessary that Holland is the Netherlands!
Once we turn to an example where there is no community-wide connotation, it becomes less obvious. My favourite examples are the name ‘Nebo-Sarsekim’, which designates the man mentioned in Jeremiah 39:3, a chief officer who took a seat at the middle gate of Jerusalem after Nebuchadnezzar laid siege to it, and ‘Nabu-sharrussu-ukin’, which designates a man mentioned in a Babylonian clay tablet dated to around 595 BC by the British Museum. It reads
[Regarding] 1.5 minas (0.75 kg) of gold, the property of Nabu-sharrussu-ukin, the chief eunuch, which he sent via Arad-Banitu the eunuch to [the temple] Esangila: Arad-Banitu has delivered [it] to Esangila. In the presence of Bel-usat, son of Alpaya, the royal bodyguard, [and of] Nadin, son of Marduk-zer-ibni. Month XI, day 18, year 10 [of] Nebuchadnezzar, king of Babylon.
The two names plainly do not designate the same person. ‘Nebo-Sarsekim’ means or designates the man mentioned by Jeremiah. ‘Nabu-sharrussu-ukin’ means or designates the man mentioned by the clay tablet. And unlike the case of Hesperus and Phosphorus, we don’t have a third name like ‘Venus’ which we can use to designate a single object identical with the object designated by each of the other two names. We just have the two names. So what if Nebo-Sarsekim was in fact the same person as Nabu-sharrussu-ukin? Does it follow that there is a single person who we shall designate by a new name ‘Nebo-Nabu’, such that this name, and the other two names, designate Nebo-Nabu in every possible world, so that it is necessary that Nebo-Nabu is identical with Nebo-Sarsekim, and with Nabu-sharrussu-ukin? Only if we buy the following argument:
1. Nebo-Sarsekim = Nebo-Nabu
2. ‘Nebo-Sarsekim’ designates Nebo-Sarsekim
3. Therefore ‘Nebo-Sarsekim’ designates Nebo-Nabu
But why should we buy the move to (3)? It’s not at all obvious to me.