display all the ideas for this combination of texts
3 ideas
| 16014 | It is controversial whether only 'numerical identity' allows two things to be counted as one [Noonan] |
| Full Idea: 'Numerical identity' implies the controversial view that it is the only identity relation in accordance with which we can properly count (or number) things: x and y are to be properly counted as one just in case they are numerically identical. | |
| From: Harold Noonan (Identity [2009], §1) | |
| A reaction: Noonan cites Geach, presumably to remind us of relative identity, where two things may be one or two, depending on what they are relative to. The one 'guard on the gate' may actually be two men. |
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| 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. | |
| From: Plato (Phaedo [c.382 BCE], 097d) | |
| 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. |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| Full Idea: If one is, there must also necessarily be number - Necessarily - But if there is number, there would be many, and an unlimited multitude of beings. ..So if all partakes of being, each part of number would also partake of it. | |
| From: Plato (Parmenides [c.364 BCE], 144a) | |
| A reaction: This seems to commit to numbers having being, then to too many numbers, and hence to too much being - but without backing down and wondering whether numbers had being after all. Aristotle disagreed. |