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While counting apples might be a useful example for teaching children, they're hardly the only thing there is to count. The putative abstraction isn't even in the number "one", the abstraction you're complaining about is in the chosen category of "apple". In other words, the fact that something can be comprised of many things does not change how many of that thing there are, nor does it reveal some deep unnaturalness of numbers. It at best casts doubt on our delimitation of objects.


Neat point, but I do think the abstraction of "one" fails us regularly.

Even in the supposedly simple idea of counting apples.

To continue to (ab)use the apple example, tell me how many apples this is [1].

Sure, there's a problem with the "apple" category/symbol (to your point) but similar exceptions and confounding examples are abundant throughout messy physical reality.

So I think my point stands, "one" is an imperfect model of reality. Useful, but inexact.

Given that "one" may be the most basic fundamental axiom of mathematics, as more abstractions are built upon it the accuracy with which those concepts reflect the physical world declines.

Hence the invention of fractions, etc...

[1] https://www.dailymail.co.uk/news/article-2433619/Siamese-app...


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