Ideas from 'Structuralism Reconsidered' by Fraser MacBride [2007], by Theme Structure

[found in 'Oxf Handbk of Philosophy of Maths and Logic' (ed/tr Shapiro,Stewart) [OUP 2007,978-0-19-532592-8]].

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / d. Natural numbers
Numbers are identified by their main properties and relations, involving the successor function
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
For mathematical objects to be positions, positions themselves must exist first