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Single Idea 13900

[filed under theme 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 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.

The 4 ideas with the same theme [symbol showing a variable refers to 'at least one' object]:

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]