Combining Philosophers

Ideas for Lycophron, Ofra Magidor and Michael Potter

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2 ideas

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic

17882	It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter]
	Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms).
	From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2)
	A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying.

6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / e. Caesar problem

17997	Some suggest that the Julius Caesar problem involves category mistakes [Magidor]
	Full Idea: Various authors have argued that identity statements arising in the context of the 'Julius Caesar' problem in philosophy of mathematics constitute category mistakes.
	From: Ofra Magidor (Category Mistakes [2013], 1.1 n1)
	A reaction: [She cites Benacerraf 1965 and Shapiro 1997:79]