Ideas from 'Counting and the Natural Numbers' by Jeffrey H. Sicha [1968], by Theme Structure

[found in 'Philosophy of Science' (ed/tr -) [- ,]].

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6. Mathematics / A. Nature of Mathematics / 3. Numbers / d. Natural numbers
The essence of natural numbers must reflect all the functions they perform
6. Mathematics / A. Nature of Mathematics / 3. Numbers / p. Counting
To know how many, you need a numerical quantifier, as well as equinumerosity
Counting puts an initial segment of a serial ordering 1-1 with some other entities