Vallicella has a good post here about why he rejects individual concepts (aka singular concepts, haecceity concepts, singular meanings etc.).
His argument is that an individual concept, if there is such a thing, is either pure, or not. A pure concept C “involves no specific individual and can be grasped without reference to any specific individual”. If there such a concept C, or not. If there is, it is either pure or not. But every pure concept, no matter how specific, is possibly such as to have two or more instances. So C is not pure. But then it must involve an individual - the very individual of which it is the individual concept, and no individual can be grasped as such, and so C is not pure either. Thus there can be no such C.
I reply: the definition of “pure concept” is ambiguous, for the verb ‘involves’ is ambiguous between being logically transitive and logically intransitive. I discussed this idea back in March. A logically intransitive verb is one which has a grammatical accusative but no ‘logical’ accusative, i.e. such that ‘aRb’ can be true, without ‘Ex x=b’ being true. ‘Refers to’ is such a verb. Thus
(1) ‘Frodo’ refers to Frodo.
is true. And so is
(2) ‘Frodo’ refers to someone.
(3) Someone is such that ‘Frodo’ refers to them.
is not. If the verbs ‘involves’ and ‘grasps’ of Vallicella’s definition are logically intransitive, then the minor premiss of his argument – that we cannot grasp an individual – is questionable. For then you can grasp the concept of Frodo without any real relation to any existing individual.
To clarify, I hold that you can only grasp the concept of Frodo if you have read ‘Lord of the Rings’ (or some other book or text or body of information that references Frodo). It is analogous to ‘the former’ and ‘the latter’. These are descriptions which appear to be first-level, and to qualify the individuals referred to, but really, as it were, qualify the text itself (or the information received).
Borgesque thought-experiment: a Chinese author, who has never read Lord of the Rings, writes a very similar or identical work. I say that when people read this work and talk about the characters – say the one corresponding to Frodo – then they are not talking about Frodo. The right kind of causal connection to the work is not available. By contrast, if I read a sequel to LOTR in which Frodo appears as a character, and if I make it explicit the reference to Tolkien’s text, then I am referring to Frodo, and people who talk about my character are referring to him also. Thus, by the right kind of causal connection to a particular text (or mass-produced copies of it) we acquire individual concepts – in this case, individual concepts corresponding to things that do not exist.
The case of real history (e.g. Julius Caesar) is no different. There is no semantic connection between my individual concept of Caesar, and Caesar himself. But there is a connection between this concept and the historical texts I learned at school, or from books I read. It is this specific connection to items of information, texts etc. that guarantees the acquisition of individual concepts by different people, and their successful use to make individuating reference. What guarantees that we are thinking about Julius Caesar is the right kind of relation to a certain set of texts – not a relation to any existing person, which is irrelevant. What guarantees that we are all thinking about Frodo is exactly the same kind of relation. The existence of the individual referred to, and even their causal relation to the text, is irrelevant.