Pierre Menard does Berlitz

"The best method of acquiring the Spanish language is to establish oneself in a good casa de pupilos, to avoid English society and conversation, to read Don Quixote through and aloud before a master of a morning, and to be schooled by female tongues of an evening."

-- Richard Ford, A Handbook for Travellers in Spain, 3rd edn. (1855), part 1, p. 67.

Counterpossibles in popular culture

Jimi Hendrix's "If 6 Was 9" comes to mind. Any others?

A very sharp, and funny, review

Norman Kretzmann on Alexander Broadie's Introduction to Medieval Logic (Journal of Symbolic Logic 55 [1990]: 1320-22):

The sort of thing Broadie does in these chapters could have been very valuable, I think, as an exercise for advanced students who had learned some medieval and some contemporary logic and were set the task of assimilating some bits of the former to corresponding bits of the latter; but it cannot count as "a sketch of logic during the fourteenth century", or as an introduction to medieval logic. A better title for the book might be Fantasia and Variations on Familiar Themes Drawn From Medieval and Post-Medieval Scholastic Logic.

Gettier cases

Blindingly obvious once it's pointed out, but I never thought of it until I found this comment on a blog: The Importance of Being Earnest is a Gettier case.

Amusing discovery

The Columbia University formal ontologist Achille Varzi, co-author (with Roberto Casati) of Parts and Places and Holes and Other Superficialities, shares a name with (and, according to Wikipedia, is related to) the (seemingly rather famous) Italian racing driver Achille Varzi, winner of the 1933 Monaco Grand Prix, whose death during practice in 1948 led to the imposition of mandatory crash helmets in automobile racing.

Information-age idioms

A remarkable phrase encountered in Wikipedia: 'Turing porn farm'.

The hydra game

Andrej Bauer has a superb page on the hydra game, including a Java applet allowing you to play it. The hydra game is extraordinarily simple: the rules can be stated in a few sentences. A hydra is a finite tree: the object of the game is to cut off all of its nodes ("heads"). If you cut off a node at level 1, it does not grow back. If you cut off a node at level n > 1, the hydra grows new branches from the node two levels down -- duplicates of the subtree growing out of level n-1, the direct parent node, after the level-n node has been removed. The proof, in set theory, that every hydra can be killed, is beautiful and almost as short as this description -- the game is just Goodstein's theorem (1948) differently, and much more elegantly, phrased.

But that's not the remarkable thing. The remarkable thing, demonstrated in 1982 by Kirby and Paris, is that any proof of Goodstein's theorem requires transfinite induction up to epsilon-zero or its equivalent -- which is the consistency strength of Peano Arithmetic. So, by Gödel's second incompleteness theorem, it is impossible to prove in PA that the hydra game is always winnable.

I am astounded that a "mathematically natural" statement independent of PA (as opposed to a Gödel sentence tricked up for the purpose of proving incompleteness) is capable of such an exquisitely simple, intuitively appealing formulation.