### Single Idea 10704

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

Full Idea

In second-order logic only the formation rules are completely formalizable, not the inference rules.

Gist of Idea

We can formalize second-order formation rules, but not inference rules

Source

Michael Potter (Set Theory and Its Philosophy [2004], 01.2)

Book Reference

Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.13

A Reaction

He cites Gödel's First Incompleteness theorem for this.