Monthly Archives: November 2009

Gödel Without Tears — 5

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

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Ruse gets a beta minus.

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

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

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The Autonomy of Mathematical Knowledge, §§2.1-2.2

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

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Gödel Without Tears — 4

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

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