Logic and Language

Bahram Assadian (Birbeck, University of London): Abstraction Principles: Freedom, Arrogance and Presuppositions

Speaker: Bahram Assadian (Birbeck, University of London)
Title: Abstraction Principles: Freedom, Arrogance and Presuppositions
Time: 16:00 - 17:30
Location: ILLC seminar room F1.15

In the abstractionist philosophy of mathematics, Hume's Principle tells us that the number of Fs is identical to the number of Gs if and only if the Fs and the Gs are one-to-one correlated. But what is the semantic function of 'The number of Fs'? Following Frege, the abstractionists Bob Hale and Crispin Wright argue that such numerals must be taken as genuinely singular terms effecting reference to particular objects. I will explore the prospects of two different semantic interpretations of 'The number of Fs' in the abstractionist setting: in terms of the Russellian quantificational account of definite descriptions in which the numeral asserts the existence and uniqueness of an object, and in terms of the Strawsonian presuppositional account in which the numeral triggers a presupposition to the effect that there exists a unique individual that satisfies the descriptive content.