Single Idea 13900

[catalogued under 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃]

Full Idea

It is a common mistake to render 'some Frenchmen are generous' by (∃x)(Fx→Gx) rather than the correct (∃x)(Fx&Gx). 'All Frenchmen are generous' is properly rendered by a conditional, and true if there are no Frenchmen.

Gist of Idea

'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional →

Source

E.J. Lemmon (Beginning Logic [1965], 3.1)

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.97


A Reaction

The existential quantifier implies the existence of an x, but the universal quantifier does not.