Tom Griffiths

So the third thread here is this idea of thinking about thought in terms of points in space and using the math that we use for thinking about spaces.

And that was an idea that developed in the 20th century.

So I said, we had Newell and Simon and Chomsky demonstrating that things like logic were really effective for giving us ways of expressing theories about how something like thought or language might work.

But then that was the big idea of the 1950s and carried forward from there.

And then in the 1970s, psychologists started to realize that there are some gaps in this.

And so this is where we get to, okay, what happens when you take these mathematical theories like logic and then start comparing them rigorously against human behavior?

And when you start to do that, you start to turn up

know these sort of meaningful discrepancies um and so one of these sets of discrepancies came from the work of eleanor rush who was a psychologist who uh explored how people think about categories right um if you think about categories from the perspective of logic you're looking for a rule that characterizes that category you're looking for sort of like a definition that tells you you know exactly what it is to be a member of that category you know you have to have these properties you have to not have these properties whatever it is that's that's the rule that tells you you know what it is to belong to category

And Roche showed that it really seems like very few human categories have that kind of structure.

So if you look at our intuitions about what makes something a piece of furniture or what makes something a vehicle,

there aren't definitions that you can find that characterize those in the way that the logician would want you to have.

And instead, it seems like they're characterized by a much more fuzzy structure, where you can say certain things are definitely pieces of furniture, like an armchair, and other things are maybe pieces of furniture, like a rug.

And there's a sort of gradients that was hard to capture from that logical perspective.

Um, and so it seemed like you needed a different kind of theory to be able to capture that.

Um, and psychologists started to think about, well, maybe if you think about objects as points in space, then how close things are in space as a way of characterizing, you know, their, the extent to, you know, if you think about the, your, you have another point that characterizes your category of furniture.

And so now an armchair is close to that point and a rug is further away from that point.

And maybe that gives us a way of capturing that sort of gradients.

But then you end up with a new problem, which is if concepts are points in space, then how do you do something like computation?

So with logic, that translated into the ideas behind digital computers, Turing machines, all of these things.

We had a way of thinking about what thought was because we could say, OK, if you represent something logically, then fulfilling that idea of lightness, we can then make a machine that executes our rules and tells us what the consequences are.