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Single Idea 16929

[from 'Prolegomena to Any Future Metaphysic' by Immanuel Kant, in 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic ]

Full Idea

The concept of twelve is in no way already thought by merely thinking the unification of seven and five, and though I analyse my concept of such a possible sum as long as I please, I shall never find twelve in it.

Gist of Idea

7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12

Source

Immanuel Kant (Prolegomena to Any Future Metaphysic [1781], 269)

Book Reference

Kant,Immanuel: 'Prolegomena to Any Future Metaphysic', ed/tr. Lucas,Peter G. [Manchester UP 1971], p.19


A Reaction

It might be more plausible to claim that an analysis of 12 would reveal the concept of 7+5. Doesn't the concept of two collections of objects contain the concept of their combined cardinality?

Related Ideas

Idea 16926 Analytic judgements say clearly what was in the concept of the subject [Kant]

Idea 16927 Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant]