more from this thinker | more from this text
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 Ref
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]
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 9865 | Daily arithmetic counts unequal things, but pure arithmetic equalises them [Plato] |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| 17612 | Arithmetic is just the consequence of counting, which is the successor operation [Dedekind] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 10619 | The truths of arithmetic are just true equations and their universally quantified versions [Smith,P] |
| 10026 | Arithmetic must allow for the possibility of only a finite total of objects [Hodes] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 21665 | The fundamental theorem of arithmetic is that all numbers are composed uniquely of primes [Hofweber] |