Nancy Day 2 was a quiet as far as the official program went. Talks were scheduled in the morning leaving the afternoon free. Michael Lynch and I took in the Musée des Beaux-Arts and talked philosophy and much else with Peter van Inwagen, Scott Shalkowski and others into the evening and late in the night.
The morning featured a well-put-together talk by Jonathan Lowe on the contrast between his robust essentialism and conceptualism. For Jonathan, conceptualism collapses into a global anti-realism because it really requires a kind of essentialism about concepts and agents themselves.
I also attended a helpful presentation by Mathieu Marion on game semantics for logic. (For an introduction to game semantics, try the Stanford Encyclopedia entry by Wilfrid Hodges.) Mathieu contrasted the agonistic conception of game semantics according to which the two players (proponent and opponent, or Abelard and Eloise) are competing against one another. He proposed a cooperative understanding in which the players are building something together, like a proof. This strikes me as plausible. The devil, however, is in the detail. The distinctive feature of game semantics is that the proof is not a play of a game, or something you can look back on as having constructed. A proof corresponds to a winning strategy for the proponent, and a refutation corresponds to a winning strategy for the opponent. (Parenthetical remark: Compare this to my comments a few weeks ago on the duality between proofs and counterexamples. Game semantics is an account of proofs and counterexamples. It seems to be interestingly self-dual. I should think more about this… End parenthetical remark.) The issue I find with thinking of game semantics as a cooperative construction of a proof or a refutation is that you don’t get a proof or refutation through a play of the game. You construct a proof (or a refutation) through repeated plays of the game where the opponent (or proponent) tries all possible options and the proponent (or opponent) deals with them all.
That will bear more thinking, and I’ll attempt to do some of that thinking.
For now however, I’ll attend to Day 3. The report on Day 3 will hopefully come today or tomorrow.