Single Idea 14776

[catalogued under 6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism]

Full Idea

To say that 'if' there are two persons and each person has two eyes there 'will be' four eyes is not a statement of fact, but a statement about the system of numbers which is our own creation.

Gist of Idea

That two two-eyed people must have four eyes is a statement about numbers, not a fact

Source

Charles Sanders Peirce (Scientific Attitude and Fallibilism [1899], II)

Book Reference

Peirce,Charles Sanders: 'Philosophical Writings of Peirce', ed/tr. Buchler,Justus [Dover 1940], p.59


A Reaction

One eye for each arm of the people is certainly a fact. Frege uses this equivalence to build numbers. I think Peirce is wrong. If it is not a fact that these people have four eyes, I don't know what 'four' means. It's being two pairs is also a fact.