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