Séminaire Philmath : Walter Dean

Walter Dean (Philosophy, University of Warwick, UK) interviendra sur le sujet "Ultrafinitism, Feasibility, and the Sorities". La séance sera retransmise en direct à l'adresse : http://live.univ-paris1.fr:8080/IHPST.

This paper seeks to build a bridge between three subjects: the semantics of vague predicates in natural language, ultrafinitism in philosophy of mathematics, and the analysis of feasibility in computational complexity theory. These topics are linked by the need to provide a response to the sorites paradox — e.g. with respect to predicates like “bald” or “walking distance” in the first case, “practically constructible number” in the second, and “feasibly computable function” in the third. I will begin by arguing that several forms of the sorites implicitly rely on arithmetical assumptions, which are in turn related to concerns similar to those which motivate the formulation of theories of bounded arithmetic studied in complexity theory.  Although such connections were noted by Wang (1958), Yessenin-Volpin (1961/1970), Dummett (1975) and Boolos (1991), they have had little effect on subsequent theorizing about vagueness.  Once the connections are acknowledged, however, I will suggest that a semantical treatment of so-called almost consistent theories — as originally introduced by Parikh (1971) and subsequently studied by Carbone (1993/1996) — provides insight not only into soritical phenomena in natural language but also into our knowledge of arithmetic in light of the concerns raised by ultrafinitism.

It will be possible to follow the talk live at http://live.univ-paris1.fr:8080/IHPST.