Tom Griffiths

I mean, I think there are things that we can point to, like Bayes' rule as a general principle of probability theory that allows us to describe how it is that we should go about making inductive inferences.

And you could think about that as something that's a candidate kind of law.

And then logic, there's sort of analogous things like modus ponens, a particular form of argument, right?

if P then Q, P therefore Q, right?

That's a sort of description of a kind of inference that it's valid to make in any circumstance where you can substitute in your P's and Q's, right?

And so those are things that are sort of appropriately law-like, but it's more that we have these mathematical systems that allow us to characterize what it is, you know, thinking should look like in these different circumstances.

Really, the place where the book starts is with Aristotle trying to figure out what makes a good argument.

Aristotle did that by thinking about syllogisms, these simple arguments where you'd have two premises and a conclusion,

where they're about sets of things like all A's are B's, all B's are C's, therefore all A's are C's.

That's a classic syllogism.

He did some theorizing about, first of all, trying to identify what are good syllogisms, and then second, trying to say, what's the theory of what makes a good syllogism?

What are the properties that we can use to look at these

good syllogisms and say what it is that they have in common.

And that's why I was saying he was maybe the first person to really try and develop a little bit more of a theory of what good argument or maybe even good thinking might look like.

And the reason why that was important is that for both Leibniz and Boole, who were the next people who tried to actually formalize thought,

What they were trying to do was formalize Aristotle.

Their way of saying, oh, I've succeeded in coming up with a mathematical theory of thought, the proof of that was going to be that they could reproduce the conclusions that Aristotle had produced about what made something a good syllogism or not.

They set out to do that each in slightly different ways.

Leibniz had this idea that arithmetic was going to be enough.

That was what he had as math and he knew