Full Idea
Universal Generalization: If we can prove P(x), only assuming what sort of object x is, we may conclude ∀xP(x) for the same x.
Gist of Idea
Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x)
Source
Robert S. Wolf (A Tour through Mathematical Logic [2005], 1.3)
Book Reference
Wolf,Robert S.: 'A Tour Through Mathematical Logic' [Carus Maths Monographs 2005], p.20
A Reaction
This principle needs watching closely. If you pick one person in London, with no presuppositions, and it happens to be a woman, can you conclude that all the people in London are women? Fine in logic and mathematics, suspect in life.