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] |