more from this thinker     |     more from this text


Single Idea 9834

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

Full Idea

A class is, for Frege, the extension of a concept.

Gist of Idea

A class is, for Frege, the extension of a concept

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by Michael Dummett - Frege philosophy of mathematics Ch.8

Book Ref

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.91


A Reaction

This simple idea was the source of all his troubles, because there are concepts which can't have an extension, because of contradiction. ...And yet all intuition says Frege is right..


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

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