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2 ideas
18392 | Classes have cardinalities, so their members must all be treated as units [Armstrong] |
Full Idea: Classes, because they have a particular cardinality, are essentially a certain number of ones, things that, within the particular class, are each taken as a unit. | |
From: David M. Armstrong (Truth and Truthmakers [2004], 09.1) | |
A reaction: [Singletons are exceptions] So units are basic to set theory, which is the foundations of technical analytic philosophy (as well as, for many, of mathematics). If you can't treat something as a unit, it won't go into set theory. Vagueness... |
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. |