Discussing Russell's Introduction to Mathematical Philosophy (1919), ch. 1-3 and 13-18.
This is a 33-minute preview of our vintage 1 hr, 31-minute episode which you can buy at partiallyexaminedlife.com/store or get for free with PEL Citizenship (see partiallyexaminedlife.com/membership). You can also purchase the full episode in the iTunes Store: Search for "Partially Examined Russell" and look under "Albums."
How do mathematical concepts like number relate to the real world? Russell wants to derive math from logic, and identifies a number as a set of similar sets of objects, e.g. "3" just IS the set of all trios. Hilarity then ensues.
This book is a shortened and much easier to read version of Russell and Whitehead's much more famous Principia Mathematica, and given that we can't exactly walk through the specific steps of lots of proofs on a purely audio podcast (nor would we want to put you through that), we spend some of the discussion comparing analytic (with its tendency to over-logicize) and continental (with its tendency towards obscurity) philosophy.
Featuring guest podcaster and number guy Josh Pelton, filling in for Seth.