Single Idea 8639

[catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique]

Full Idea

Patterns can be completely different while the number of their elements remains the same, so that here we would have different distinct fives, sixes and so forth.

Gist of Idea

If numbers are supposed to be patterns, each number can have many patterns

Source

Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §41)

Book Reference

Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.53


A Reaction

A blow to my enthusiasm for Michael Resnik's account of maths as patterns. See, for example, Ideas 6296 and 6301. We are clearly set up to spot patterns long before we arrive at the abstract concepts of numbers. We see the same number in two patterns.

Related Ideas

Idea 6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]

Idea 6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]