Episode 42: Agustin Rayo discusses the construction of logical space
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Hello and welcome to Elucidations, a philosophy podcast recorded at the University of Chicago. I'm Matt Teichman. And with me today is Augustine Real, Associate Professor of Philosophy at the Massachusetts Institute of Technology. And he is here to talk with me about the construction of logical space. Augustine Raya. Welcome.
Thank you, thank you. I'm delighted to be here.
Um okay, logical space. That's a term that's guaranteed to sound a little puzzling to a lot of people, I think, because usually we think of space as like something like physical space. Here is a table and here's another table to the right of it, and there they are in sort of physical, geometrical space. But uh but what's logical space? That seems a little weird.
It's the space of possibility. So a point in logical space is a way for the world to be. And uh the whole of logical space is the collection of every possible way the world could be. And it's a very useful way for thinking about inquiry, for trying to understand how it is that we learn things about the world. Because you could think that to learn things about the world we need to do two things. First we identify logical space. First we decide which are the different ways the world could be. And secondly, we try to decide of those ways the world could be. Which is the way the world is, or at least uh identify some ways the world is not, reducing the candidates for truth.
So for example, if I say Professor Rayo is in the library, then what I'm doing is I'm drawing a line between all the different places that Professor Rayo could be and all the places where he isn't. So namely I'm saying that the actual world, the world we live in, is sort of within that boundary. So he might be near the entrance, he might be on the fourth floor, he might be wherever, but wherever he is, he's in the library. He's not down the street drinking coffee or anywhere else. Exactly.
Now, those are the easy cases because everyone agrees that it's at least logically possible that I be at a cafe or in the library or whatnot. But there are certain cases where it's just not clear, it's not obvious whether we really have a possibility. So let me give you an example.
What is logical space and why does it matter for philosophy?
There are some logicians who think that there is a gap between a statement of the form not not P and the statement P itself. So maybe it's the case that it's not the case that it's not the case that snow is white, but we're not immediately entitled to conclude that snow is white. So here's a question. Do we want to admit a possibility of Where we have the double negation, but not the claim itself. That's a big philosophical discussion. And in order to decide what conception of logical space to work with, we need to figure out whether to treat such difficult cases as genuine possibilities or not. And part of the what the book is about is to try to find criteria to help us decide those difficult cases.
Okay, right. So the idea is that there are different possible situations that we might be in. There are different ways the world might be And we want to ask the question given to specifications of a possible situation. Are those the same possible situation or are they a different possible situation? So, you know, is the situation where Matt is not not happy the same situation as the situation where Matt is happy?
Exactly. And When we were talking about possible questions for this interview, you came up with an example which I think is really interesting and a really good way of illustrating this kind of thing. So consider the sentence there is a table in the room and the sentence there are some things arranged table wise in the room. Do we want to say that those two statements say the same thing, or do we want to say that they say different things? If we think they say different things, then we might have a possibility where we have one but not the other.
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