George (the person) is “this man” - a primary substance, a this “something”, a “tode ti” (in Aristotelian Greek).
Harry (the person) is the “same man”.
Therefore, George is the “same” as “Harry” (a=c, b=c, then a=b).
But George is not the “same” as Harry.
So this is indeed a slightly more complex issue. It seems to me that you’re imagining the scenario where one person has two names. So you are saying someone’s name can be George and Harry (i.e. not George) at the same time.
This is a subtle abuse of language. Specifically, it assumes something untrue about George, which is that he only has one name. That assumption is inherent in the statement “His (one) name is…”
Now, lets suppose there is actually a criteria for a “one true name.” In that case, only one of George and Harry would qualify as the “one true name” and there would be no difficulty. On the other hand, we could correct our single-name assumption and say that “one of George’s names is George” and “one of George’s names is not George.” Here there is also no contradiction, because “one of George’s names” isn’t a
particular name. That is, there is no single name that is simultaneously George and not George.
Now perhaps your phrasing was deliberate, and we want to flip the order. That is to say, instead of thinking of a person “having” a name, we want to think of a name as referring to a person.
Then it is the case that George refers to some person, and that Harry refers to the same person. In that case, no one would ever assert that George and Harry (the names) are the same thing as the person they refer to. And so here the law of non-contradiction doesn’t apply because George and Harry (the names) are the same
with respect to what they refer to but are different
with respect to how they are spelled.
Now lets return to the case of God.
I have already quoted Feser’s explanation of the trinitarian requirements. So let us apply our shorthand to them and once again consider the case of the The Father (F), the The Son (S), and God (G). According to Feser:
- F is G.
- S is G.
- F is not S
- There is exactly one G.
When Feser says “F is G” what does he actually mean? It seems to me that he could
either mean “F is identical to G
in every respect”
or he could mean “F is identical to G
in some particular respect that I have in mind.”
When Feser says “S is G” what does he actually mean? It seems to me that he could
either mean “S is identical to G
in every respect”
or he could mean “S is identical to G
in some particular respect that I have in mind.”
When Feser says “F is not S” what does he actually mean? It seems to me that he could
only mean “I have in mind some respect in which F and S are different.”
Now what? Clearly if Feser means “F/S are identical to G
in every respect” then we’ve got ourselves a logical contradiction when he says F is not S. It is also clear that we have ourselves a logical contradiction if the respect Feser has in mind is the same for all three assertions. So the only way to
avoid the contradiction is to claim that Feser equivocated on “is” by having different respects in mind between assertions 1, 2, and 4.