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Single Idea 13903

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

Full Idea

The elimination rule for the universal quantifier concerns the use of a universal proposition as a premiss to establish some conclusion, whilst the introduction rule concerns what is required by way of a premiss for a universal proposition as conclusion.

Gist of Idea

Universal elimination if you start with the universal, introduction if you want to end with it

Source

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

Book Ref

Lemmon,E.J.: 'Beginning Logic' [Nelson 1979], p.104

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A Reaction

So if you start with the universal, you need to eliminate it, and if you start without it you need to introduce it.

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The 6 ideas with the same theme [normal rules used in predicate logic reasoning]:

13907

If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon]

13901

Predicate logic uses propositional connectives and variables, plus new introduction and elimination rules [Lemmon]

13903

Universal elimination if you start with the universal, introduction if you want to end with it [Lemmon]

13904

Universal Elimination (UE) lets us infer that an object has F, from all things having F [Lemmon]

13906

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

13908

UE all-to-one; UI one-to-all; EI arbitrary-to-one; EE proof-to-one [Lemmon]