### Single Idea 13844

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

Full Idea

Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification.

Gist of Idea

A limitation of first-order logic is that it cannot handle branching quantifiers

Source

Ian Hacking (What is Logic? [1979], §13)

Book Reference

'A Philosophical Companion to First-Order Logic', ed/tr. Hughes,R.I.G. [Hackett 1993], p.247

A Reaction

See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours.