more from Henri Poincaré

### Single Idea 10180

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism]

Full Idea

Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.

Gist of Idea

Mathematicians do not study objects, but relations between objects

Source

Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6

A Reaction

This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.