### Single Idea 13906

#### [catalogued under 4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / c. Derivations rules of PC]

Full Idea

If there are just three objects and each has F, then by an extension of &I we are sure everything has F. This is of no avail, however, if our universe is infinitely large or if not all objects have names. We need a new device, Universal Introduction, UI.

Clarification

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

Gist of Idea

With finite named objects, we can generalise with &-Intro, but otherwise we need ∀-Intro

Source

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

Book Reference

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.106