Abstract
In the previous chapter, we saw that Russell and Whitehead, like Frege, endorsed Applic, i.e. the principle according to which a good definition of a mathematical concept (rational and real numbers in the case in point) should account for its main applications. I emphasized that the way they implemented the constraint was different from Frege’s, but I have not yet explained why they endorsed Applic.
Applic seems to be composed of two distinct theses:
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1.
The recognition that there is a distinction between the mathematical content of a concept and its extra-mathematical uses.
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2.
The thesis that a good definition must relate the concept to its main extra-mathematical uses.
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© 2012 Sébastien Gandon
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Gandon, S. (2012). Application Constraint in Principia Mathematica. In: Russell’s Unknown Logicism. History of Analytic Philosophy. Palgrave Macmillan, London. https://doi.org/10.1057/9781137024657_7
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DOI: https://doi.org/10.1057/9781137024657_7
Publisher Name: Palgrave Macmillan, London
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