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2 ideas
| 9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
| Full Idea: For Frege, the extension of the concept F is an object, as revealed by the fact that we use a name to refer to it. ..We must distinguish the concept, the object that falls under it, and the extension of the concept, which is the set containing the object. | |
| From: report of Gottlob Frege (On Concept and Object [1892]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This I take to be the key distinction needed if one is to grasp Frege's account of what a number is. When we say that Frege is a platonist about numbers, it is because he is committed to the notion that the extension is an object. |
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| Full Idea: I propose that numbers are properties, not sets. Magnitudes are a kind of property, and numbers are magnitudes. …Natural numbers are properties of pluralities, positive reals of continua, and ordinals of series. | |
| From: Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro) | |
| A reaction: Interesting! Since time can have a magnitude (three weeks) just as liquids can (three litres), it is not clear that there is a single natural property we can label 'magnitude'. Anything we can manage to measure has a magnitude. |