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Single Idea 13523

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

Full Idea

Existential Generalization (or 'proof by example'): From P(t), where t is an appropriate term, we may conclude ∃xP(x).

Gist of Idea

Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P

Source

Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3)

Book Ref

Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.20

A Reaction

It is amazing how often this vacuous-sounding principles finds itself being employed in discussions of ontology, but I don't quite understand why.

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]