more from Ludwig Wittgenstein

Single Idea 11073

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism]

Full Idea

"But doesn't it follow with logical necessity that you get two when you add one to one, and three when you add one to two? and isn't this inexorability the same as that of logical inference? - Yes! it is the same.

Gist of Idea

Two and one making three has the necessity of logical inference


Ludwig Wittgenstein (Remarks on the Foundations of Mathematics [1938], p.38), quoted by Robert Hanna - Rationality and Logic 6

Book Reference

Hanna,Robert: 'Rationality and Logic' [MIT 2006], p.155

A Reaction

This need not be a full commitment to logicism - only to the fact that the inferential procedures in mathematics are the same as those of logic. Mathematics could still have further non-logical ingredients. Indeed, I think it probably does.