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red75 comments on What's a "natural number"? - Less Wrong
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General brain's capability for (cross-domain) pattern matching? While studying objects of new formal system and their relations, it patternmatch them with already known formal and real objects and relations. Successful match results in insight (that can be formally wrong).
Pros: mathematics stems from observation of real world objects and their relations: countable objects, lines, etc.
Cons: too simple.