Week 8, 18 November 2014 (16:00-18:00 Watson R17/18)

Walter Dean (Warwick)

Title : Induction, feasability, and the sorites

Abstract: This paper seeks to build a bridge between three subjects: the study of vague predicates in philosophy of language, strict finitism 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 case, and “feasibly computable function” in the third. I will begin by arguing that several forms of the sorites implicitly rely on arithmetical premises such as the universal applicability of mathematical induction or the necessity of using compact notations to denote large numbers. Such a connection between vagueness and arithmetic was discussed by Yessenin-Volpin (1961/1970) and Dummett (1975), but has been largely ignored by subsequent theorists. Once this relationship is acknowledged, I will propose that a semantical treatment of so-called almost consistent theories (as originally introduced by Parikh (1971)) provides insight into how we might model soritical phenomena in natural language in a manner which bears on the contemporary discussion of epistemicism and supervaluationism.

About the seminar

The Midlands Logic Seminar was founded in 2011 and aims to cover all areas of mathematical logic, as well as related areas of theoretical computer science and philosophy of mathematics.

Study group

Our topic for Term 1 of 2014-2015 is the use of induction and heuristics in mathematical problem solving. We will be working through George Polya's book Induction and Analogy in Mathematics .


All meetings for Term 1 2014-15 will be Tuesday from 16:00-18:00 (study group 16:00-17:00, research talks 17:00-18:00) in room 310 of Watson Building (TBC) on the campus of the University of Birmingham.
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    To get to campus, take the train from Birmingham New Street to the University stop (7 minutes).


    Dr Richard Kaye
    School of Mathematics
    University of Birmingham


    Dr Walter Dean
    Department of Philosophy
    University of Warwick