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Full Idea
The so-called Comprehension Schema ∃X∀x(Xx ↔ φ(x)) says that there is a property which is had by just those things which satisfy the condition φ.
Gist of Idea
The Comprehension Schema says there is a property only had by things satisfying a condition
Source
Peter Smith (Intro to Gödel's Theorems [2007], 22.3)
Book Ref
Smith,Peter: 'An Introduction to Gödel's Theorems' [CUP 2007], p.190
3300 | Aristotle's logic is based on the subject/predicate distinction, which leads him to substances and properties [Aristotle, by Benardete,JA] |
3319 | Frege gives a functional account of predication so that we can dispense with predicates [Frege, by Benardete,JA] |
6076 | For Frege, predicates are names of functions that map objects onto the True and False [Frege, by McGinn] |
18894 | Predicates form a hierarchy, from the most general, down to names at the bottom [Sommers] |
10615 | The Comprehension Schema says there is a property only had by things satisfying a condition [Smith,P] |
15651 | Instead of saying x has a property, we can say a formula is true of x - as long as we have 'true' [Halbach] |