more from Richard Dedekind

Single Idea 9189

[catalogued under 18. Thought / E. Abstraction / 3. Abstracta by Ignoring]

Full Idea

By applying the operation of abstraction to a system of objects isomorphic to the natural numbers, Dedekind believed that we obtained the abstract system of natural numbers, each member having only properties consequent upon its position.

Gist of Idea

Dedekind said numbers were abstracted from systems of objects, leaving only their position


report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by Michael Dummett - The Philosophy of Mathematics

Book Reference

'Philosophy 2: further through the subject', ed/tr. Grayling,A.C. [OUP 1998], p.146

A Reaction

Dummett is scornful of the abstractionism. He cites Benacerraf as a modern non-abstractionist follower of Dedekind's view. There seems to be a suspicion of circularity in it. How many objects will you abstract from to get seven?