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Single Idea 10615

[filed under theme 5. Theory of Logic / E. Structures of Logic / 7. Predicates in Logic ]

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

The 6 ideas with the same theme [assigning predicates to objects in formulae]:

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]