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 | |||||||||
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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 |
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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 |
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Date: | 2018 | |||||||||
URI: | https://philsci-archive.pitt.edu/id/eprint/15096 |
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