Full Idea
One pair of boots may be the same visible and tangible phenomenon as two boots. This is a difference in number to which no physical difference corresponds; for 'two' and 'one pair' are by no means the same thing.
Gist of Idea
There is no physical difference between two boots and one pair of boots
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §25)
Book Reference
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.33
A Reaction
He is attacking Mill. Those of us who are seeking an empirical account of arithmetic have certainly got to face up to this example. Not insurmountable, I think.
Related Idea
Idea 17861 Two men do not make one thing, as well as themselves [Aristotle]