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4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀

[symbol showing a variable refers to 'all' objects]

4 ideas
For Frege, 'All A's are B's' means that the concept A implies the concept B [Walicki on Frege]
If there is a finite domain and all objects have names, complex conjunctions can replace universal quantifiers [Lemmon]
Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS]
Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS]