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Abstraction and semantic presuppositions
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Abstract
According to the neo-Fregean abstractionism, numerical expressions of the form ‘the number of Fs’, introduced by Hume’s Principle, should be read as purportedly referential singular terms. I will explore the prospects of a version of abstractionism in which such expressions have presuppositional content, as in Strawson’s account. I will argue that the thesis that ‘the number of Fs’ semantically presupposes the existence of a number is inconsistent with the required ‘modest’ stipulative character of the truth of Hume’s Principle: since Hume’s Principle is true and provably presupposes that numbers exist, what it presupposes is also true; and so numbers exist. This, however, means that numbers are conjured into existence by a direct stipulation.
Title: Abstraction and semantic presuppositions
Description:
Abstract
According to the neo-Fregean abstractionism, numerical expressions of the form ‘the number of Fs’, introduced by Hume’s Principle, should be read as purportedly referential singular terms.
I will explore the prospects of a version of abstractionism in which such expressions have presuppositional content, as in Strawson’s account.
I will argue that the thesis that ‘the number of Fs’ semantically presupposes the existence of a number is inconsistent with the required ‘modest’ stipulative character of the truth of Hume’s Principle: since Hume’s Principle is true and provably presupposes that numbers exist, what it presupposes is also true; and so numbers exist.
This, however, means that numbers are conjured into existence by a direct stipulation.
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