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Full Idea
The arithmetic of the many computes sums of unequal units, such as two armies, or two herds, ..but philosopher's arithmetic computes when it is guaranteed that none of those infinitely many units differed in the least from any of the others.
Gist of Idea
Daily arithmetic counts unequal things, but pure arithmetic equalises them
Source
Plato (Philebus [c.353 BCE], 56d)
Book Ref
Plato: 'Complete Works', ed/tr. Cooper,John M. [Hackett 1997], p.446
A Reaction
But of course 'the many' are ironing out the differences too, when they say there are 'three armies'. Shocking snob, Plato. Even philosophers are interested in the difference between three armies and three platoons.
| 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] |