Interview with Robinson Erhardt

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I've just appeared as a guest on Robinson Erhardt's philosophy podcast! We chat about learning languages, Islamic philosophy, etc.
Andrew Maclaren on 4 January 2023

Different sized infinities

At around 1:24:40-55, you mentioned how that in an eternal universe juiper would have revolved around the earth an infinite amount of times, and that would mean the moon would have as well x 30, which would be absurd since that would mean that one infinity is bigger than another, with Robinson making a joke that they haven't read Cantor. Multiplying any positive number by infinity would actually just be infinity, not a bigger one. This wouldn't actually be related to Cantor.

Aside from clearing that up, this makes me wonder about two questions. 1. How would this mathematical fact effect their reasoning? Would it just simply solve the absurdity objection? 2. Cantor discovering that there are different sized infinities makes me wonder (if at all) how it would effect typical philosophical arguments and theories about infinity in classical/medieval philosophy in general? Or would we just avoid the issue by saying mathematical infinity is different than philosophical infinity?

In reply to by Andrew Maclaren

Peter Adamson on 5 January 2023


Thanks for checking out the interview! Just to start with your last point, there is definitely an open question (which people often forget) about whether everything mathematicians say about infinity can just be transferred to the kind of debate that was had in antiquity and the middle ages. For instance paradoxes might arise with infinitely large bodies that don't do so with infinitely large sets. Still, I think that the modern notion(s) of infinity would at the very least make the medievals less quick to take certain things as obviously absurd, like that point about the impossibility of doubling infinity: if this is impossible, then it is not obviously so, at least.

In reply to by Peter Adamson

Karl Young on 6 January 2023

Yes, I guess the medievals…

Yes, I guess the medievals didn’t have the opportunity to check in to Hilbert’s hotel.

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