Tom Griffiths

So you could tell from the word for fish and the word for cat that fish and cats were not the same things.

So you could never say a fish is a cat just because the symbols that you use or the sounds that you would make corresponded to sort of it told you the location of this object within a taxonomy.

And so there was this idea that you could sort of systematize language in such a way that then the truth of things would become self-evident.

And for Leibniz, he wanted to take that one step further and do that through math.

And so what he did was take your Aristotelian syllogisms and then with each syllogism,

term within those syllogisms or each set of things, you wanted to associate some numbers.

We could credit him with inventing the vector embedding because he had this idea that there was a string of numbers that you would associate with each thing.

In one version of this, there's just two numbers.

Sorry, the vector embedding is what is used in large language models to- Yeah, that's right.

It's the idea that you can represent a word as a vector of numbers.

Yeah.

And so he had this idea then, okay, so maybe if you have these numbers for this set and then these numbers for this set, if the second set of numbers divides the first set of numbers, then we can say that the second set is contained within the first.

And so, you know, that sort of gave him a way of thinking about how you could use arithmetic and sort of doing things with prime numbers and trying to figure out how to make this work.

And then he does this and he sort of like assigns values to various terms and then runs an argument.

He's like, okay, it works.

Then he goes on to the next one in Aristotle and he's like, oh no, it doesn't work.

The notes stop, right?

And then the next note, a little bit later, you know, he gets another argument to work and so on, but he never quite gets the whole thing to work out.

Yeah.

But he was also, I think, visionary in recognizing that if he could get this to work out as arithmetic, then thought would be something that we could get machines to do for us.