Logic, Epistemology and Metaphysics Seminar

Logic, Epistemology and Metaphysics Seminar
19 February 2019, 5.30pm - 7.30pm
Room 243, Second Floor, Senate House, Malet Street, London WC1E 7HU

Speaker: Andrzej Indrzejczak (Lodz)

Title: How to Provide a Decent Proof System for Definite Descriptions

Abstract: Definite descriptions and proof theory rarely come together. The former are more often discussed in the framework of the philosophy of language. In logic very often Russell's reductionist perspective is taken as the last word on this question. Moreover, even serious logical research on definite descriptions (as developed for example in the area of free logics), usually is carried out by means of semantical methods. Modern proof theoretic apparatus, in particular sequent calculus, has rarely been applied in this field so far. However, it seems that the application of proof theory to this important philosophical problem is advantageous for both sides. On the one hand, competing theories of definite descriptions may be shown in the new light. On the other, the behaviour of definite descriptions needs subtle syntactical analysis enriching a toolkit of proof theory. After a brief summary of the problems with definite descriptions and several approaches to their solution we focus on proof theoretic features. Several problems with their application to the description-operator as an additional constant will be characterised. In particular, we address the problem of cut admissibility for such extended logic. The application of sequent calculus to definite descriptions will be examined on three different theories due to Hilbert and Bernays (and developed by Stenlund), Frege (developed by Kalish and Montague) and Lambert (as developed by Thomason and Garson).

The Centre for Logic and Language hosts a regular seminar series - the Logic, Epistemology and Metaphysics Forum (LEM). The forum generally meets fortnightly in term time.


Institute of Philsophy
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