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Ideas for 'New Scientist articles', 'Higher-Order Logic' and 'Frege's Theory of Numbers'

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6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure

17447

Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]

6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order

10294

Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]