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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. |