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Ideas for 'Abstract Objects: a Case Study', 'The Theory of Communicative Action' and 'Structuralism Reconsidered'

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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

8923	Numbers are identified by their main properties and relations, involving the successor function [MacBride]
	Full Idea: The mathematically significant properties and relations of natural numbers arise from the successor function that orders them; the natural numbers are identified simply as the objects that answer to this basic function.
	From: Fraser MacBride (Structuralism Reconsidered [2007], §1)
	A reaction: So Julius Caesar would be a number if he was the successor of Pompey the Great? I would have thought that counting should be mentioned - cardinality as well as ordinality. Presumably Peano's Axioms are being referred to.