more from Gottlob Frege

Single Idea 18256

[catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / c. Priority of numbers]

Full Idea

There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former.

Gist of Idea

Quantity is inconceivable without the idea of addition


Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit'

Book Reference

Dummett,Michael: 'Frege: philosophy of mathematics' [Duckworth 1991], p.279

A Reaction

Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree.

Related Idea

Idea 18255 Addition of quantities is prior to ordering, as shown in cyclic domains like angles [Dummett]