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Is Hume's Principle Analytic?

Darnell, Eamon and Thomas-Bolduc, Aaron (2018) Is Hume's Principle Analytic? [Preprint]

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Abstract

The question of the analyticity of Hume's Principle (HP) is central to the neo-logicist project. We take on this question with respect to Frege's definition of analyticity, which entails that a sentence cannot be analytic if it can be consistently denied within the sphere of a special science. We show that HP can be denied within non-standard analysis and argue that if HP is taken to depend on Frege's definition of number, it isn't analytic, and if HP is taken to be primitive there is only a very narrow range of circumstances where it might be taken to be analytic.The latter discussion also sheds some light on the connections between the Bad Company and Caesar objections.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Darnell, Eamoneamon.darnell@mail.toronto.ca
Thomas-Bolduc, Aaronathomasb@ucalgary.ca0000-0001-9955-2371
Additional Information: Forthcoming in Synthese.
Keywords: Neo-logicism, Frege, Hume's Principle, Non-standard Analysis, Analyticity
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics
Depositing User: Aaron Thomas-Bolduc
Date Deposited: 09 Oct 2018 19:59
Last Modified: 09 Oct 2018 19:59
Item ID: 15096
Subjects: Specific Sciences > Mathematics > Epistemology
Specific Sciences > Mathematics > History of Philosophy
Specific Sciences > Mathematics > Logic
Specific Sciences > Mathematics
Date: 2018
URI: http://philsci-archive.pitt.edu/id/eprint/15096

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