### Single Idea 13905

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

Full Idea

If all objects in a given universe had names which we knew and there were only finitely many of them, then we could always replace a universal proposition about that universe by a complex conjunction.

Clarification

A 'universe' is usually now called a 'domain'

Gist of Idea

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

Source

E.J. Lemmon (Beginning Logic [1965], 3.2)

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.105