more from Immanuel Kant

Single Idea 2795

[catalogued under 6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique]

Full Idea

Kant claimed that 7+5=12 is synthetic a priori. If the concept of 12 analytically involves knowing 7+5, it also involves an infinity of other arithmetical ways to reach 12, which is inadmissible.

Gist of Idea

If 7+5=12 is analytic, then an infinity of other ways to reach 12 have to be analytic

Source

report of Immanuel Kant (Critique of Pure Reason [1781], B205/A164) by Jonathan Dancy - Intro to Contemporary Epistemology 14.3

Book Reference

Dancy,Jonathan: 'Introduction to Contemporary Epistemology' [Blackwell 1985], p.216