Ojea: Evaluation Games for Many Valued Logics

Evaluation Games for many valued logics
Ignacio Ojea (Columbia University)
4:15 PM, March 28th, 2014
Room 3305, CUNY Graduate Center

Abstract.  Evaluation Games for classical logic are well known. Following early applications of games in model theory, by Ehrenfeucht and Fraisse, Hintikka and Parikh independently proposed a game-theoretic approach as a way of defining the classical semantics. A great deal of the game theoretic approach has been more recently studied by van Bentham. The original idea was to define the truth-value of a wff, in a given model, in terms of the existence of a strategy for one of the players (the “Verifier” and “Falsifier”) in a certain two-person game. These games can be also viewed in terms of pay-offs. Recently I suggested a natural extension of these games to the case of many valued logics, where the notion of a Nash equilibrium plays a crucial role.

Rescorla: Is Computation Formal?

Is Computation Formal?
Michael Rescorla (University of California, Santa Barbara)
4:10 PM – 6:00 PM, Thursday, October 31, 2013
Philosophy Hall 716, Columbia University
Reception to follow

Tamar Lando: The topology of gunk

The topology of gunk
Tamar Lando (Columbia University)
Monday, May 13th, 4 to 6 PM
2nd floor seminar room, Philosophy Department, NYU (5 Washington Place).

Abstract. Space as we typically conceive of it in mathematics and physics is composed of dimensionless points. Over the years, however, some have denied that points, or point-sized parts are genuine parts of space. Space, on an alternative view, is ‘gunky’: every part of space has a strictly smaller subpart. If this thesis is true, how should we model space mathematically? The traditional answer to this question is most famously associated with A.N. Whitehead, who developed a mathematics of pointless geometry that Tarski later modeled in regular open algebras. More recently, however, Whiteheadian space has come under attack, because it does not allow us to talk about the size or measure of regions in a nice way. A newer approach to the mathematics of gunk, advanced by F. Arntzenius, J. Hawthorne, and J.S. Russell, models space via the Lebesgue measure algebra, or algebra of (Lebesgue) measurable subsets of Euclidean space modulo sets of measure zero. But problems arise on this approach when it comes to doing topology. According to Arntzenius, the standard topological distinction between ‘open’ and ‘closed’ regions “is exactly the kind of distinction that we do not believe exists if reality is pointless.” I argue that the turn to non-standard topology in the measure-theoretic setting rests on a mistake. Once this is pointed out, the newer approach to gunk can claim two important advantages: it allows the gunk lover to talk about size and topology—both in perfectly standard ways.

Hellman: On Resolving the Set-Theoretic and Semantic Paradoxes

On Resolving the Set-Theoretic and Semantic Paradoxes
Geoff Hellman (University of Minnesota)
4-6pm, Monday, April 22nd
2nd floor seminar room, NYU (5 Washington Place)

Abstract. Our main goals are, first, to describe how modal structuralism resolves the set-theoretic paradoxes, concentrating on the Burali-Forti paradox, and then to note a close connection to recent proposals (due to Cook and Schlenker, independently) for resolving semantic paradoxes, especially the Liar.