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Full Idea
We combine 'Solon was wise' and 'Thales was wise' into 'Solon and Thales were wise', but we can't say 'Solon and Thales were one', which implies that 'one' is not a property in the same way 'wise' is.
Gist of Idea
We can say 'a and b are F' if F is 'wise', but not if it is 'one'
Source
Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], §29)
Book Ref
Frege,Gottlob: 'The Foundations of Arithmetic (Austin)', ed/tr. Austin,J.L. [Blackwell 1980], p.40
A Reaction
Maybe 'one' is still a property, but of a different sort. However, Frege builds up a very persuasive case that just because numbers function as adjectives it does not follow that they are properties. See Idea 8637.
Related Idea
Idea 8637 The number 'one' can't be a property, if any object can be viewed as one or not one [Frege]
| 7485 | For Pythagoreans 'one' is not a number, but the foundation of numbers [Pythagoras, by Watson] |
| 12074 | The one in number just is the particular [Aristotle] |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| 12488 | The idea of 'one' is the simplest, most obvious and most widespread idea [Locke] |
| 8636 | We can say 'a and b are F' if F is 'wise', but not if it is 'one' [Frege] |
| 8654 | One is the Number which belongs to the concept "identical with 0" [Frege] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |