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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.
Gist of Idea
Numbers are properties, not sets (because numbers are magnitudes)
Source
Keith Hossack (Knowledge and the Philosophy of Number [2020], Intro)
Book Ref
Hossack, Keith: 'Knowledge and the Philosophy of Number' [Routledge 2021], p.1
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.
| 23621 | Numbers are properties, not sets (because numbers are magnitudes) [Hossack] |
| 23622 | We can only mentally construct potential infinities, but maths needs actual infinities [Hossack] |
| 23623 | Predicativism says only predicated sets exist [Hossack] |
| 23624 | The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack] |
| 23625 | Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack] |
| 23626 | Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack] |
| 23627 | 'Before' and 'after' are not two relations, but one relation with two orders [Hossack] |
| 23628 | The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack] |