One of the main topics of the Leibniz-Arnauld correspondence is the question how, on Leibniz’s theory, it can be true that Arnauld might have had children and been a physician rather than being a celibate theologian (see Arnauld’s letter of May 13, 1686). One of the curious things that happens in this discussion is that both Leibniz and Arnauld start talking about the many Adams and many Judases and many Arnaulds in the various possible worlds, with Leibniz insisting that none of them is identical to the actual Adam/Judas/Arnauld. In that May 13 letter, Arnauld even speaks of ‘several mes’, pluralizing the first-person pronoun.
In my view, what’s going on here is that Leibniz holds that as long as we use ‘Arnauld’ as a genuine proper name, the sentence ‘Arnauld is a celibate theologian’ is in fact a necessary truth. This is because, when ‘Arnauld’ is used as a genuine proper name, it picks out the actual Arnauld by means of his Complete Individual Concept (CIC) which includes everything about him and, indeed, everything about the world he inhabits. Of course, we don’t actually possess such a concept (at least not consciously); only God does. But somehow or other, in Leibniz’s view, we manage to use the name ‘Arnauld’ in such a way that this concept is its meaning.
However, there are other, looser contexts in which we use ‘Arnauld’ in such a way that its meaning is given not by Arnauld’s CIC but rather by some concept we actually do possess. In this kind of case, ‘Arnauld’ could be seen as abbreviating some definite description which is sufficiently detailed to identify Arnauld uniquely among actual creatures, but not including all of his characteristics, and hence not uniquely identifying him among all possible creatures. For instance, the description might be, ‘the youngest child of Antoine and Catherine Arnauld, born February 8, 1612, assigned the given name “Antoine”, who went on to become a famous Jansenist theologian.’ When we talk about alternate possibilities (‘Arnauld might have been a married physician’) or evaluate counterfactuals (‘if Arnauld had been married, he would have become a physician rather than a theologian’) we are using ‘Arnauld’, not as a proper name, but as a common name standing for such a definite description. It is for this reason that we can pluralize ‘Arnauld’ in this usage and speak of the other Arnaulds, in other possible worlds, who are married physicians. These are merely possible creatures, distinct from the actual Arnauld, who nevertheless satisfy the description which, in this context, ‘Arnauld’ abbreviates.
Today, I came across some support for this interpretation from a surprising source. It turns out there is actually a discussion of the practice of pluralizing proper nouns in the Port-Royal Grammar which Arnauld co-wrote with Claude Lancelot:
if [proper nouns] are sometimes put in the plural, as when one says the Caesars, the Alexanders, the Platos, it is done figuratively by including in the proper name all the persons who resemble them, as one would speak of kings as brave as Alexander, of philosophers as wise as Plato, etc. (part 2, ch. 4, tr. Rieux and Rollin)
This, it seems to me, is good evidence that Arnauld understood Leibniz’s view in more or less the way I have described. Of course a more careful analysis of the correspondence would be required to show that Arnauld understood Leibniz correctly.
(Cross-posted at blog.kennypearce.net.)