Single Idea 10294

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

Full Idea

Full second-order logic has all the expressive power needed to do mathematics, but has an unworkable model theory.

Gist of Idea

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

Source

Stewart Shapiro (Higher-Order Logic [2001], 2.1)

Book Reference

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.34


A Reaction

[he credits Cowles for this remark] Having an unworkable model theory sounds pretty serious to me, as I'm not inclined to be interested in languages which don't produce models of some sort. Surely models are the whole point?