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In Categories, Aristotle says that particulars can't be said of anything. But it seems possible to say of Socrates that he is the Athenian whose name is Socrates. Supposing there can be only one Athenian with that name, both the subject and the predicate are particulars, which seems to be an exception to the rule.

Is definition a different kind of operation than "saying of", and if so, how?

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For Aristotle, a predicate is an universal; particulars are individual. Thus, useing modern class terms, saying that "Socrates is Athenian" means that the (individual) Socrates belongs to the class of Athenians, which in this context is a class, irrespective of the fact that contains one or more memebers. –  Mauro ALLEGRANZA Jul 27 at 16:28

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As usual, as I was typing the answer, Mauro ruined it by giving it in simpler terms in the comments!

In Categories, Chapter 2, Aristotle divides things into two types: things that are said, and things that are. For these things that are, he gives a fourfold classification schema based on a fundamental distinction between two types of predicative relation:

  1. said of predication;
  2. present in predication.

This second type of predication has no straightforward analog in modern logic, so let's skip to (1), which is what your question is about. Said of predication is quite easy to understand. Here is a definition:

Definition. F is said of x    =df    F(x).

Purely extensionally, F is said of x just in case x is among the elements of the set F, i.e. iff x ∈ ext(F).

Let's apply this definition to your example.

  • The predicate F is "is an Athenian whose name is 'Socrates'";
  • the individual s of which you're predicating it is Socrates, the teacher of Plato and others.

To say F of Socrates, that is, to say that Socrates is an Athenian whose name is 'Socrates', you simply predicate F of him. F, extensionally speaking, is the set of all those Athenians whose name is 'Socrates'. Presumably Socrates was an Athenian named 'Socrates', so Socrates is a member of that set. That makes the predication F(s) true.

The further claim, namely that Socrates is the Athenian whose name is 'Socrates', requires that there be no other person who was an Athenian and was named 'Socrates'. I personally know a Greek person, now alive, who is called 'Socrates', so the set F contains at least two individuals: the famous philosopher and this Greek guy I know. That means that "Socrates is the Athenian whose name is 'Socrates'" is not a good definition; it's similar to defining 1 as the closest integer to 0 (not including 0).

The lesson is the following. Even if F was a singleton set containing Socrates the philosopher:

Lesson: there is a difference, between Socrates the individual and {Socrates} the set.

This resolves the worry you have about Aristotle's claim that particulars (e.g. Socrates) cannot be said of anything. Since {Socrates} is not a particular but a general term, it doesn't contradict Aristotle to say {Socrates} of Socrates (after all, Socrates ∈ {Socrates}).

                                                                     References

Ackrill, J.L. (1963) Aristotle's Categories and De Interpretatione, Clarendon, Oxford.

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