display all the ideas for this combination of philosophers
4 ideas
| 8298 | Sets are instances of numbers (rather than 'collections'); numbers explain sets, not vice versa [Lowe] |
| Full Idea: I favour an account of sets which sees them as being instances of numbers, thereby avoiding the unhelpful metaphor which speaks of a set as being a 'collection' of things. This reverses the normal view, which explains numbers in terms of sets. | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 10) | |
| A reaction: Cf. Idea 8297. Either a set is basic, or a number is. We might graft onto Lowe's view an account of numbers in terms of patterns, which would give an empirical basis to the picture, and give us numbers which could be used to explain sets. |
| 8311 | If 2 is a particular, then adding particulars to themselves does nothing, and 2+2=2 [Lowe] |
| Full Idea: If 2 is a particular, 'adding' it to itself can, it would seem, only leave us with 2, not another number. (If 'Socrates + Socrates' denotes anything, it most plausibly just denotes Socrates). | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 10.7) | |
| A reaction: This suggest Kant's claim that arithmetical sums are synthetic (Idea 5558). It is a nice question why, when you put two 2s together, they come up with something new. Addition is movement. Among patterns, or along abstract sequences. |
| 4241 | If there are infinite numbers and finite concrete objects, this implies that numbers are abstract objects [Lowe] |
| Full Idea: The Peano postulates imply an infinity of numbers, but there are probably not infinitely many concrete objects in existence, so natural numbers must be abstract objects. | |
| From: E.J. Lowe (A Survey of Metaphysics [2002], p.375) | |
| A reaction: Presumably they are abstract objects even if they aren't universals. 'Abstract' is an essential term in our ontological vocabulary to cover such cases. Perhaps possible concrete objects are infinite. |
| 8310 | Does the existence of numbers matter, in the way space, time and persons do? [Lowe] |
| Full Idea: Does it really matter whether the numbers actually exist - in anything like the way in which it matters that space and time or persons actually exist? | |
| From: E.J. Lowe (The Possibility of Metaphysics [1998], 10.6) | |
| A reaction: Nice question! It might matter a lot. I take the question of numbers to be a key test case, popular with philosophers because they are the simplest and commonest candidates for abstract existence. The ontological status of values is the real issue. |