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Single Idea 13521

[filed under theme 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀ ]

Full Idea

Universal Specification: from ∀xP(x) we may conclude P(t), where t is an appropriate term. If something is true for all members of a domain, then it is true for some particular one that we specify.

Gist of Idea

Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance

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

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The 4 ideas with the same theme [symbol showing a variable refers to 'all' objects]:

17745

For Frege, 'All A's are B's' means that the concept A implies the concept B [Frege, by Walicki]

13905

If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon]

13522

Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS]

13521

Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS]