So, sabbatical is over, I’m back in Calgary, started to teach yesterday (history of analytic, and Gödel’s incompleteness theorem–from Peter‘s book). I saved so many posts in my reader over the summer that now there’s more saved posts than new posts every day. Let’s clean house.
- Graham Priest‘s Introduction to Non-classical Logic, 2nd edition, is out. Like Peter said: must buy, must read.
- Doug Patterson‘s New Essays on Tarski and Philosophy should be out soon. It’s got Etch‘s “Reflections on Logical Consequence” and Paolo‘s paper on the 1937 Congrès Descartes, among many others. (HT: Ole)
- Ole also linked the Arché’s extensive bibliographies on, among other things, philosophy of mathematics and logic.
- Kai pointed out a mystery novel based on the murder of Richard Montague, The Semantics of Murder, by Aifric Campbell.
- Alexandre Borovik posted a few quotes on the axiom of choice, to which furia_krucha added a comment linking to an article in by Jan Mycielski in the February 2006 Notices of the AMS, entitled “A System of Axioms for Set Theory for the Rationalists“. That’s a very interesting paper on the choice of axioms for set theory (“the 1% of mathematics where the philosophy of mathematics matters”, according to Mycielski). But the quote for which it was linked is particularly neat:
Tarski told me the following story. He tried to publish his theorem [If for all infinite sets X there exists a bijection of X to X × X, then the Axiom of Choice holds] in the Comptes Rendus Acad. Sci. Paris but Fréchet and Lebesgue refused to present it. Fréchet wrote that an implication between two well known propositions is not a new result. Lebesgue wrote that an implication between two false propositions is of no interest. And Tarski said that after this misadventure he never tried to publish in the Comptes Rendus. (p. 209)
I think there’s a paper just in mathematicians’ practice to show that this and that theorem are equivalent (usually, without any mention of what background theory they are equivalent over). I mean, why is it interesting to prove an implication between two (necessarily!) true propositions?
- Two more new entries in the SEP, on Naturalism in the Philosophy of Mathematics by Alexander Paseau, and one on Hans Reichenbach by Clark Glymour and Frederick Eberhardt.
- Henri Galinon of Theorème has an awesome collection of online tutorials and textbooks on logic, both introductory and advanced, at the Theorème Logic Toolbox. He also linked to Makkai’s notes on set and model theory, should be included in the list soon.
- Plurality of Words seems to be gone!? So sad. But Andreas Stokke did link to two YouTube videos of Kit Fine:
- Carrie Jenkins linked to a series of videos designed to help you visualize four dimensions.