more from this thinker | more from this text
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 Ref
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.
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
13900 | 'Some Frenchmen are generous' is rendered by (∃x)(Fx→Gx), and not with the conditional → [Lemmon] |
13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |