display all the ideas for this combination of philosophers
3 ideas
| 8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
| Full Idea: My view is that numbers are universals, beings kinds of sets (that is, kinds whose particular instances are individual sets of appropriate cardinality). | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 10) | |
| A reaction: [That is, 12 is the set of all sets which have 12 members] This would mean, I take it, that if the number of objects in existence was reduced to 11, 12 would cease to exist, which sounds wrong. Or are we allowed imagined instances? |
| 8266 | Simple counting is more basic than spotting that one-to-one correlation makes sets equinumerous [Lowe] |
| Full Idea: That one-to-one correlated sets of objects are equinumerous is a more sophisticated achievement than the simple ability to count sets of objects. | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 2.9) | |
| A reaction: This is an objection to Frege's way of defining numbers, in terms of equinumerous sets. I take pattern-recognition to be the foundation of number, and so spotting a pattern would have to precede spotting that two patterns were identical. |
| 8302 | Fs and Gs are identical in number if they one-to-one correlate with one another [Lowe] |
| Full Idea: What is now known as Hume's Principle says the number of Fs is identical with the number of Gs if and only if the Fs and the Gs are one-to-one correlated with one another. | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 10.3) | |
| A reaction: This seems popular as a tool in attempts to get the concept of number off the ground. Although correlations don't seem to require numbers ('find yourself a partner'), at some point you have to count the correlations. Sets come first, to identify the Fs. |