Monthly Archives: November 2009

Gödel Without Tears — 5

Posted on November 6, 2009

Here now is the fifth episode on the idea of a primitive recursive function. The preamble explains why this matters and where this is going. [As always, I'll be very glad to hear about typos/thinkos.] The previous episodes are available: … Continue reading →

Posted in Gödel's theorems | Leave a comment

Ruse gets a beta minus.

Posted on November 4, 2009

Philosophers don’t get asked often enough to write for the newspapers and weeklies: so it is really annoying when an opportunity is wasted on second-rate maunderings. Michael Ruse writes in today’s Guardian on whether there is an “atheist schism”. And … Continue reading →

Posted in Rants, Religion | 7 Comments

The Autonomy of Mathematical Knowledge, §§2.3-2.5

Posted on November 4, 2009

To return for a moment the question we left hanging: what is the shape of Hilbert’s “naturalism” according to Franks? Well, Franks in §2.3 thinks that Hilbert’s position can be contrasted with a “Wittgensteinian” naturalism that forecloses global questions of … Continue reading →

Posted in Autonomy of Math Knowledge | Leave a comment

The Autonomy of Mathematical Knowledge, §§2.1-2.2

Posted on November 2, 2009

Hilbert in the 1920s seems pretty confident that classical analysis is in good order. “Mathematicians have pursued to the uttermost the modes of inference that rest on the concept of sets of numbers, and not even the shadow of an … Continue reading →

Posted in Autonomy of Math Knowledge | Leave a comment

Gödel Without Tears — 4

Posted on November 2, 2009

Here now is the fourth episode [slightly corrected] which tells you — for those who don’t know — what first-order Peano Arithmetic is (and also what Sigma_1/Pi_1 wffs are). A thrill a minute, really. Done in a bit of a … Continue reading →

Posted in Gödel's theorems | 2 Comments