Single Idea 10299

[catalogued under 5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic]

Full Idea

If the goal of logical study is to present a canon of inference, a calculus which codifies correct inference patterns, then second-order logic is a non-starter.

Gist of Idea

If the aim of logic is to codify inferences, second-order logic is useless

Source

Stewart Shapiro (Higher-Order Logic [2001], 2.4)

Book Reference

'Blackwell Guide to Philosophical Logic', ed/tr. Goble,Lou [Blackwell 2001], p.51


A Reaction

This seems to be because it is not 'complete'. However, moves like plural quantification seem aimed at capturing ordinary language inferences, so the difficulty is only that there isn't a precise 'calculus'.