NEIL W. TENNANT

tennant.9@osu.edu

If you email me, please use the header PHIL 873: YOURNAME.

Professor
Department of Philosophy


Winter Term 2011

PHIL 873: Logicism

Research Seminar
University Hall, Room 353
Wednesdays 12:30-3:18 pm

Graduate students should note that this course can be used to satisfy a coursework distribution requirement either in LLS or in M&E.

Prerequisites: introductory logic, and some experience with conceptual analysis and the theory of meaning.

A useful link to research resources in Philosophy in the University Library

Aims and Topics. Logicism is the view that mathematics is a part of logic, or is somehow reducible to logic.

The logicist must accordingly specify exacly what conception of logic is involved, and whether the claim applies to all of mathematics, or just to some crucial and central parts of it (such as arithmetic and/or real analysis). In addition, one needs some explication of the notion of containment or reducibility that is involved.

This course will examine and explore arguments both for and against logicism as an overarching doctrine in (i) the theory of meaning (or truth-conditions), and (ii) the ontological commitments, of mathematical theorizing. We shall look into the historical roots of the modern form of the doctrine, beginning with early hints in Bolzano and Dedekind, and their culmination in the works of Frege and Russell. We shall examine the impact, on this doctrine, of the discovery of the set-theoretic paradoxes; of debates over potential v. completed infinities; and of independence results in both arithmetic and set theory.

If time permits, we shall look at some extensions of the methods of modern proof theory, and what they might be able to offer in the development of a view that might be called 'natural logicism'. This is a species of inferentialism (q.v.) concerning the meanings of statements in certain branches of mathematics.

This will be a course with a great deal of exploratory discussion. You will have the opportunity to express your own views and criticize the views of others.

Background reading (It will definitely not be assumed that you will have read these works by the beginning of term, or even that you will get round to reading them all in the course of the term! This list is provided for purposes of orientation only.)
  • Richard Dedekind, Continuity and Irrational Numbers, 1872
  • Gottlob Frege, Foundations of Arithmetic, 1884 (tr. 1959)
  • Richard Dedekind, Was sind und was sollen die Zahlen?, 1888
  • Bertrand Russell, The Principles of Mathematics, 1903
  • Rudolf Carnap, The Logical Syntax of Languge, tr. Amethe Smeaton, Routledge and Kegan Paul, London, 1937
  • tr. and ed. M. Szabo, The Collected Papers of Gerhard Gentzen, North Holland, Amsterdam
  • Dag Prawitz, Natural Deduction: A Proof-Theoretical Study, Almqvist and Wiksell, Stockhom, 1965
  • Michael Dummett, The Logical Basis of Metaphysics, Harvard University Press, 1991
  • Crispin Wright, Frege's Conception of Numbers as Objects, Aberdeen University Press, 1983
  • Neil Tennant, Anti-Realism and Logic, Oxford University Press, 1987
  • Neil Tennant, The Taming of The True, Oxford University Press, 1997
  • John Burgess, Fixing Frege, Princeton University Press, 2005

Canonical Reading List

Relevant articles by instructor

Assessment:
Item Date due Weight
Term paper Noon, Friday April 1, 2011 90%
Class participation Every session! 10%

Policy on attendance at classes

Plagiarism

Advice on writing essays