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]