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Single Idea 11020

[filed under theme 4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / c. Logical sets ]

Full Idea

Hard-headed realism tends to embrace the full Comprehension Principle, that every well-defined concept determines a set.

Gist of Idea

Realisms like the full Comprehension Principle, that all good concepts determine sets

Source

Stephen Read (Thinking About Logic [1995], Ch.8)

Book Ref

Read,Stephen: 'Thinking About Logic' [OUP 1995], p.214

A Reaction

This sort of thing gets you into trouble with Russell's paradox (though that is presumably meant to be excluded somehow by 'well-defined'). There are lots of diluted Comprehension Principles.

The 6 ideas with the same theme [sets whose membership is defined by a concept]:

9834 A class is, for Frege, the extension of a concept [Frege, by Dummett]
3328 Frege proposed a realist concept of a set, as the extension of a predicate or concept or function [Frege, by Benardete,JA]
21563 The 'no classes' theory says the propositions just refer to the members [Russell]
14461 Propositions about classes can be reduced to propositions about their defining functions [Russell]
11020 Realisms like the full Comprehension Principle, that all good concepts determine sets [Read]
15919 The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine]