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Single Idea 3328

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

Full Idea

Contrary to Dedekind's anti-realism, Frege proposed a realist definition of a set as the extension of a predicate (or concept, or function).

Clarification

The 'extension' of the set is the actual things which the set contains (e.g. trees); hence he must accept real trees

Gist of Idea

Frege proposed a realist concept of a set, as the extension of a predicate or concept or function

Source

report of Gottlob Frege (works [1890]) by José A. Benardete - Metaphysics: the logical approach Ch.13

Book Ref

Benardete,José A.: 'Metaphysics: The Logical Approach' [OUP 1989], p.91

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]