Identifying a name with the designated thing (in the context of Being)

Stranger: And yet he who identifies the name with the thing will be compelled to say that it is the name of nothing, or if he says that it is the name of something, even then the name will only be the name of a name, and of nothing else.

OP: "What is “identifying the name with the thing” even supposed to mean?"

Interpreting through modern ontology, Theaetetus and Stranger are debating whether being is a unitary principle or a multiplicity. Discriminated phenomena such as hot and cold are carved out from unconditioned reality—or 'being', or nameless totality—and given names which only have relevance to humans.

The unconditioned totality is not discriminated, is not observed, so does not itself appear. What is observed may be hot, which is a name of something discriminated: a part carved out from the unconditioned totality.

The discussion involves several puzzles about being vs not-being and one vs many: a sort of deconstruction of Presocratics main doctrines.

We have to record [ 240b ]: "Stranger And the not true is the opposite of the true? Theaetetus Of course. Stranger That which is like, then, you say does not really exist, if you say it is not true. Theaetetus But it does exist, in a way. Stranger But not truly, you mean."

Here the puzzle is about speaking of "the false", or about non-existent things: how can we predicate anything about something that does not exist?

Then follows a critique of Parmenides and other Presocratics's idea about the fundamental components or reality: [ 242c ]: "Stranger It seems to me that Parmenides and all who ever undertook a critical definition of the number and nature of realities have talked to us rather carelessly. Theaetetus How so? Stranger Every one of them seems to tell us a story, as if we were children. One says there are three principles, that some of them are sometimes waging a sort of war with each other, [...] And the Eleatic sect in our region, beginning with Xenophanes and even earlier, have their story that all things, as they are called, are really one. [...] [ 243b ] "Stranger When one of them says in his talk that many, or one, or two are, or have become, or are becoming, and again speaks of hot mingling with cold, and in some other part of his discourse suggests separations and combinations, for heaven's sake, Theaetetus, do you ever understand what they mean by any of these things?"

And then the discussione comes to the word "being" itself: [ 243d ]: "Theaetetus What do you mean? Or, obviously, do you mean that we must first investigate the term “being,” and see what those who use it think it signifies? Stranger [...] Come now, all you who say that hot and cold or any two such principles are the universe, what is this that you attribute to both of them when you say that both and each are? What are we to understand by this “being” (or “are”) of yours? [...] do you wish to call both of them together being? [...] But, friends, we will say, even in that way you would very clearly be saying that the two are one."

And here is another puzzle: if there is a plurality of beings, how is it possible to predicate "being" of both of them?

[ 244b ] Theaetetus It is rather ridiculous to assert that two names exist when you assert that nothing exists but unity. Stranger Then let them answer this question: Do you say that one only is? [...] Well then, do you give the name of being to anything? [...] Is it what you call “one,” using two names for the same thing, or how is this? [...] It is rather ridiculous to assert that two names exist when you assert that nothing exists but unity.

So, in the end, if there is no "real" plurality, but only one being ("the" one), a language that is fatithful to reality must use one name only for it.

And here is the last twist in the Stranger's argument: also names are, and thus, if we reject plurality we have to conclude that name and thing are one and the same.