Quote: a number is the number of some class, i.e., the class of those classes that are similar to it; discovered by Frege

Quotation

Two classes are said to be "similar" when there is a one-one relation which correlates the terms of the one class each with one term of the other class, in the same manner in which the relation of [monogamous] marriage correlates husbands with wives. ... [p. 18] The number of a class is the class of all those classes that are similar to it. Thus the number of a couple will be the class of all couples. In fact, the class of all couples will be the number 2, according to our definition. ... A number will be a set of classes such as that any two are similar to each other, and none outside the set are similar to any inside the set. ... [p. 19] A number is anything which is the number of some class. [p. 11. Discovered by Frege, Grundlagen der Arithmetik 1884, but not noticed. Rediscovered by Russell in 1901.]   Google-1   Google-2

Published before 1923

Additional Titles

Quote: two classes are similar when there is a one-one relation between them

Related Topics

Topic: number as the extension of a class of equinumerous classes (23 items)