Continuing on René Descartes's Rules for Direction of the Mind (1628), covering rules 7 through the first part of the lengthy rule 12. We try to figure out what he means by "enumeration"; the faculties of imagination, sense, and memory; the virtues of perspicacity and sagacity; his psychology of the senses, the "common sense" where all sense data comes together, and the Continue Reading …
Ep. 229: Descartes’s Rules for Thinking (Part One)
On René Descartes's Rules for Direction of the Mind (1628). Is there a careful way to approach problems that will ensure that you'll always be right? What if you're just really careful to never assert anything you can't be sure of? This is Descartes's strategy, modeled on mathematics. This early, incomplete work lays out 21 rules for careful thinking (out of a planned 36) Continue Reading …
Ep. 229: Descartes’s Rules for Thinking (Citizen Edition)
On René Descartes's Rules for Direction of the Mind (1628). Is there a careful way to approach problems that will ensure that you'll always be right? What if you're just really careful to never assert anything you can't be sure of? This is Descartes's strategy, modeled on mathematics. This early, incomplete work lays out 21 rules for careful thinking (out of a planned 36) 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 …
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 …
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 to a couple articles on 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 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 …
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 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 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 space ("knowledge 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, properties, etc. -- Continue Reading …