On Kurt Gödel's essays, “Some Basic Theorems on the Foundations of Mathematics and their Implications” (1951) and “The Modern Development of the Foundations of Mathematics in Light of Philosophy” (1961). Gödel is famous for some "incompleteness theorems" of direct interest only to those trying to axiomatize mathematics. What are the implications for the rest of philosophy? Continue Reading …
Episode 95: Gödel on Math
On Kurt Gödel's essays, “Some Basic Theorems on the Foundations of Mathematics and their Implications” (1951) and “The Modern Development of the Foundations of Mathematics in Light of Philosophy” (1961). Gödel is famous for some "incompleteness theorems" of direct interest only to those trying to axiomatize mathematics. What are the implications for the rest of philosophy? Continue Reading …
Precognition of Ep. 95: Gödel
Guest Adi Habbu lays out Kurt Gödel's famous incompleteness theorems and describes some highlights from "Some Basic Theorems on the Foundations of Mathematics and their Implications" (1951) and "The Modern Development of the Foundations of Mathematics in Light of Philosophy" (1961). Read about the topic. Listen to the full episode. Continue Reading …
Precognition of Ep. 95: Gödel
Adi Habbu lays out Kurt Gödel's incompleteness theorems and describes "Some Basic Theorems on the Foundations of Mathematics and their Implications" (1951) and "The Modern Development of the Foundations of Mathematics in Light of Philosophy" (1961). Read about the topic. Listen to the full episode. Continue Reading …
Topic for #95: Godel on Math
Listen to guest Adi Habbu lay out Gödel's incompleteness theorems and introduce the readings. Kurt Gödel is of course best known as a mathematician, and some of the mechanics involved with the proof of his first incompleteness theorem had a direct influence on Alan Turing's development of modern computing. But what does this have to do with philosophy? Well, most Continue Reading …
Episode 38: Bertrand Russell on Math and Logic (Citizens Only)
Discussing Russell's Introduction to Mathematical Philosophy (1919), ch. 1-3 and 13-18. 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 Continue Reading …
PREVIEW-Episode 38: Bertrand Russell on Math and Logic
This is a 33-minute preview of a 1 hr, 31-minute episode. Buy Now Purchase this episode for $2.99. Or become a PEL Citizen for $5 a month, and get access to this and all other paywalled episodes, including 68 back catalogue episodes; exclusive Part 2's for episodes published after September, 2020; and our after-show Nightcap, where the guys respond to listener email and chat Continue Reading …