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Episode 42: Agustín Rayo discusses the construction of logical space

This month we’re joined by Agustín Rayo, Associate Professor of philosophy at MIT. Click here to listen to our conversation with him.

Many things are theoretically possible. In fact, just about anything you can imagine is possible in the broadest sense of the term. I might win the lottery, or win a tennis match, or travel to Mars. It isn’t likely that I’ll do any of these things, but it’s possible. A fiction author could come up with a story in which a series of extraordinary coincidences end up in my visiting the moon.

Philosophers call the set of all these possible circumstances logical space–the idea is that each possible circumstance is a point in logical space. (For a general introduction to the idea of logical space, see our post from last year.) In this episode, Agustín Rayo shows us how a number of traditional questions in logic, metaphysics, and the philosophy of mind can be thought of as questions about how many distinct possibilities there are in logical space. For example, is the possible situation where the number of dinosaurs is zero the same as the situation where there are no dinosaurs? Or are they different situations? If you think they’re different, then you think it’s possible to be in one situation but not the other: that there could be no dinosaurs while the number of dinosaurs somehow fails to be zero (or vice versa). If you find that idea strange, don’t worry–so does our guest!

Agustín Rayo argues that there is a trade-off between enriching your theory with extra possibilities and having more questions to answer. The more possibilities you allow into your theory, the more expressively powerful it is: the more distinctions it can capture. But working with additional possibilities also saddles you with additional questions to answer; and sometimes answering these questions is incredibly difficult, if not impossible!

Tune in to hear our guest’s thoughts on how to negotiate this trade-off!

Matt Teichman

Posted in Podcast.

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