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Full Idea
I cannot convince myself that when you add one to one either the first or the second one becomes two, or they both become two by the addition of the one to the other, ...or that when you divide one, the cause of becoming two is now the division.
Gist of Idea
If you add one to one, which one becomes two, or do they both become two?
Source
Plato (Phaedo [c.382 BCE], 097d)
Book Ref
Plato: 'The Last Days of Socrates', ed/tr. Tredennick,Hugh [Penguin 1969], p.154
A Reaction
Lovely questions, all leading to the conclusion that two consists of partaking in duality, to which you can come by several different routes.
| 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] |