Three things to read …

The death was announced a few days ago of W.W. Tait, whose work I have much admired over the years. His early technical work was on proof theory, and then he wrote with great knowledge and insight on the philosophy of mathematics and its history. His collection of papers The Provenance of Pure Reason is a must-read, and more excellent papers can be found on his otherwise minimalist website here. One piece of Tait’s which I can’t remember reading before and which will surely be of interest to anyone reading this blog is his piece contributing to Philosophy of Mathematics: 5 Questions: you can read it here.

Brian Leiter’s blog linked yesterday to a piece by a one-time colleague of mine, Leif Wenar, lambasting the pretentions of the “effective altruism” cult. I laughed out loud at his (surely just) comment that “To anyone who knows even a little about aid, it’s like [Will] MacAskill has tattooed “Not Serious” on his forehead.”. But this is serious stuff, and well worth a read here.

For some hard-core logical reading, here is another one-time colleague in action. Tim Button has just posted on the arXiv a forthcoming JSL paper “Wand/Set Theories: A realization of Conway’s mathematicians’ liberation movement, with an application to Church’s set theory with a universal set”. Tim describes a template for introducing mathematical objects which prima facie is much more liberal than standard set theory provides. Indeed it seems to very nicely encapsulate Conway’s liberation movement, allowing that (in Conway’s words)

(i) “Objects may be created from earlier objects in any reasonably constructive fashion.

(ii) Equality among the created objects can be any desired equivalence relation.”

Note, though, that Conway expected that any theory whose objects are so created in such a “reasonably constructive” fashion can be embedded within (some extension of) ZF. Tim aims to prove a stronger theorem: all loosely constructive implementations of the Wand/Set Template are not merely embeddable in (some extension of) ZF, but synonymous with a ZF-like theory. Which seems a surprise.

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