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6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / d. Natural numbers

[the positive numbers used in counting]

6 ideas
Cantor presented the totality of natural numbers as finite, not infinite [Cantor, by Mayberry]
The essence of natural numbers must reflect all the functions they perform [Sicha]
There couldn't just be one number, such as 17 [Jubien]
Only higher-order languages can specify that 0,1,2,... are all the natural numbers that there are [Shapiro]
Numbers are identified by their main properties and relations, involving the successor function [MacBride]
The number series is primitive, not the result of some set theoretic axioms [Almog]