On two unpublished essays considering the implications of Godel’s incompleteness theorems and asserting mathematical realism. With guest Adi Habbu.

## Episode 95: Gödel on Math

On two unpublished essays considering the implications of Godel’s incompleteness theorems and asserting mathematical realism. With guest Adi Habbu. Learn more.

End song: “Axiomatic” from Mark Lint & the Simulacra. Read about it.

## 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).

## 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).

## Topic for #95: Godel on Math

Kurt Gödel is 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?

## Math Mutation Podcast on “New Math” and Russell

In the Russell episode, I brought up “new math,” whereby young people were taught set theory. The podcast I was referring to was Math Mutation Podcast #145: “Why Johnny Couldn’t Add.” Given how short the episodes are, it appears as if the author (Eric Seligman) has actually posted transcripts. Here’s the one on new math (and he provides unannotated links Continue Reading …

## Bertrand Russell’s Very Short Introduction to His Ontology

Watch in YouTube For those who can’t get enough Bertrand Russell, here’s an introduction to logical analysis from his History of Western Philosophy. In this concluding chapter, Russell explains his own philosophy, as inspired by Frege, so even critics of Russell-as-historian shouldn’t object. I was particularly taken with Russell’s ontology, via Einstein. Russell succinctly and I think fairly summarizes a 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.

End song: “Words and Numbers,” by Mark Lint & the Madison Lint Ensemble. Read about it.

## PREVIEW-Episode 38: Bertrand Russell on Math and Logic

Discussing Russell’s *Introduction to Mathematical Philosophy *(1919), ch. 1-3 and 13-18. With guest Josh Pelton.

## Topic for #38: Russell on Math and Logic

What is a number? Is it some Platonic entity floating outside of space and time that we somehow come into communion with? We’ll be following up our foray into analytical philosophy with Frege with some Bertrand Russell: specifically his Introduction to Mathematical Philosophy (1919), which is the much shortened, non-technical version of his famous Principia Mathematica(written with Whitehead). Frege and Continue Reading …

## Logicomix!

In the recent Frege episode, Mark related the famous anecdote of how Bertrand Russell, the man who “discovered” Frege, later confounded him by pointing out a paradox apparent within his logical system. As Wes recounted, Russell’s own attempt to ground mathematics in logic was also later frustrated by a young Kurt Gödel, whose early incompleteness theorems crippled the central purpose of Principia Continue Reading …

## Schopenhauer on Euclid’s Geometry

One point on our Schopenhauer episode that we didn’t take much time to get into was his attitude towards geometric demonstration, which was of course the model for all philosophy for thinkers like Descartes. Here’s a short selection from section 39 of the Fourfold Root, which illustrates his idea that our knowledge of geometry is founded on our intuition of Continue Reading …

## Goodman and Quine’s Nominalism

I referred on the podcast to Goodman’s 1947 article “Steps Toward a Constructive Nominalism.” You can look at it here. The philosophical content is in the first couple of chapters; in fact, I’ll just give you the first half of the first chapter here: We do not believe in abstract entities. No one supposes that abstract entities — classes, relations, Continue Reading …