more from this thinker     |     more from this text

Single Idea 13502

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

Full Idea

When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier.

Gist of Idea

∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...'

Source

William D. Hart (The Evolution of Logic [2010], 4)

Book Ref

Hart,W.D.: 'The Evolution of Logic' [CUP 2010], p.96

A Reaction

The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier.

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]