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To err is humeant

Philosophia Mathematica 7 (3):247-257 (1999)

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  1. On the Origin and Status of our Conception of Number.William Demopoulos - 2000 - Notre Dame Journal of Formal Logic 41 (3):210-226.
    This paper concerns the epistemic status of "Hume's principle"--the assertion that for any concepts and , the number of s is the same as the number of s just in case the s and the s are in one-one correspondence. I oppose the view that Hume's principle is a stipulation governing the introduction of a new concept with the thesis that it represents the correct analysis of a concept in use. Frege's derivation of the basic laws of arithmetic from Hume's (...)
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  • The caesar problem in its historical context: Mathematical background.Jamie Tappenden - 2005 - Dialectica 59 (2):237–264.
    The issues surrounding the Caesar problem are assumed to be inert as far as ongoing mathematics is concerned. This paper aims to correct this impression by spelling out the ways that, in their historical context, Frege's remarks would have had considerable resonance with work that other mathematicians such as Riemann and Dedekind were doing. The search for presentation‐independent characterizations of objects and global definitions was seen as bound up with fundamental methodological questions in complex analysis and number theory.
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