Let’s back up here for a minute and take stock of where we are. We’ve been trying to find a handle on the issue of whether a piece of software understands language. That seems like a simple enough question. Isn’t it just a bit odd, then, that to answer it, you now find yourself having to reconsider the metaphysics of the entire universe? That whether a piece of software (or we, for that matter) actually understands text should determine that the world as such is, at the bottom, just relata-less relation, all the way down? Doesn’t that seem kind of unbalanced?
Personally, whenever I find myself wanting to overthrow centuries of metaphysical thought and question the foundations of the universe just to determine what some piece of code oodles of layers away from anything remotely fundamental does, I think it’s a good idea to take a long look in the mirror and ask myself if I haven’t just maybe taken a wrong turn somewhere. But anyhow.
That’s not what I meant. The issue is that no matter if the world is, at bottom, matter-points, events, relations or bundles of properties, at the relevant level, we clearly can think about it in terms of things standing in certain relations. And that’s what ChatGPT gets to work with: its input consists of sentences, and a sentence is a particular relation over its terms (recall sentence diagramming?). That’s where it gets its structure from: a set of terms with a particular relation to be abstracted away from the text inputs.
It doesn’t get its input in terms of pure relation. I mean, what would that even look like? What form does the relation embodied by a sentence take, if you take away the terms? So the OSR-manoeuvre just doesn’t apply: we don’t have to wonder whether there are, ultimately, deep down at some very, very deep bottom, just pure relations. The quotidian world is a world of things, and those things stand in relations, and the terms referring to those things stand in (roughly) conforming relations, and that’s that.
Consider ChatGPT getting its input instead in terms of colored pebbles variously arranged. The arrangement of the pebbles yields a structure, but it’s the pebbles that supply the structure by being arranged thus. You can’t claim that there’s only the relation the pebbles stand in, and the pebbles don’t exist, because without the pebbles, there wouldn’t be any relation. Whatever the pebbles may be, deep down, there is no arrangement of pebbles without them! It’s like you can say that Alice is taller than Bob by virtue of Alice being 1,78m and Bob being 1,74m, but saying that there’s some ‘tallerness’ without there being Alice and Bob is just meaningless.
Alice and Bob may, themselves, be just a particular relation over cells, which are just a particular relation over elementary particles, which are just a particular relation over spacetime events, and so on. And perhaps there’s just relations, that never bottom out into any relata (I don’t see how there could be, but I don’t have to understand everything). But that question is wholly immaterial to the fact that Alice and Bob are two concrete relata standing in some relation regarding their size.
‘There aren’t any relata’ only works (if it does) at some deep, deep bottom of the world, where we’re concerned with the fundamental substrate of reality. It doesn’t work at the everyday level of things being related every whichwise.
So. ChatGPT is given certain tokens, instantiating a certain relation. If this relation were enough to settle the things the tokens refer to, and the relation they stand in, then ChatGPT could learn to understand language from just that data. But the Newman argument says that there’s nothing there to fix any particular relation over the things in the world. Any given permutation of those things can have an appropriate structure ‘pushed through’.
There’s an explicit example in this book, which concerns the three terms ‘Ajax’, ‘Betty’, and ‘Chad’, as well as the one-place relation ‘is a cat’. The ‘text corpus’ of the example is given by the sentences ‘Ajax is a cat’, ‘Betty is a cat’, and ‘Chad is not a cat’.
So, in the above notation, we’d have our domain D = {Ajax, Betty, Chad}, and relation R = {<Ajax>, <Betty>}. (Of course, the ‘ordered tuple’ notation is redundant, but I’m using it for consistency.) If ChatGPT understands language, then the only model for that should be the one where ‘Ajax’ refers to Ajax, and ‘Betty’ refers to Betty, and Ajax and Betty are both cats, and ‘Chad’ refers to Chad, not a cat.
But using push-through, we can construct an equivalent model using a permutation h on D such that h(Ajax) = Betty, h(Betty) = Chad, and h(Chad) = Ajax. Then, we have the relation h(R) = {<Betty>, <Chad>}. This model makes the same sentences true as before. The sentence ‘Betty is a cat’, that in D refers to Betty, which is in the extension of the relation R, and is a cat, in h(D) refers to Chad, which is in the extension of the relation h(R). But Chad is not a cat. So while the relation R does pick out cats, the relation h(R) fails to. But we (and ChatGPT) have no grounds on which to say that R is the right relation, and h(R) isn’t.
As it’s put in the book:
The issue generalises rapidly. By Pushing-Through, we can see that any name could be taken to refer to anything, that any one-place predicate could be taken to pick out any collection of things (provided only that there are enough of them), and similarly for all the other expressions of our language. We will stare into the abyss of radical referential indeterminacy, where every word refers equally to everything, which is just to say that nothing refers at all.
This is the world of ChatGPT. It can produce the sentence ‘Betty is a cat’, but it simply has no way to anchor it to the right structure that makes it mean that Betty is, in fact, a cat (and not, for instance, that Chad is whatever sort of thing is picked out by h(R)).