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Full Idea
Numbers are classes of classes, and classes are logical fictions, so that numbers are, as it were, fictions at two removes, fictions of fictions.
Gist of Idea
Numbers are classes of classes, and hence fictions of fictions
Source
Bertrand Russell (The Philosophy of Logical Atomism [1918], §VIII)
Book Ref
Russell,Bertrand: 'Russell's Logical Atomism', ed/tr. Pears,David [Fontana 1972], p.129
A Reaction
This summarises the findings of Russell and Whitehead's researches into logicism. Gödel may have proved that project impossible, but there is now debate about that. Personally I think of numbers as names of patterns.
| 4533 | Logic and maths refer to fictitious entities which we have created [Nietzsche] |
| 6104 | Numbers are classes of classes, and hence fictions of fictions [Russell] |
| 18159 | Higher cardinalities in sets are just fairy stories [Bostock] |
| 18155 | A fairy tale may give predictions, but only a true theory can give explanations [Bostock] |
| 8714 | Fictionalists say 2+2=4 is true in the way that 'Oliver Twist lived in London' is true [Field,H] |
| 18214 | Mathematics is only empirical as regards which theory is useful [Field,H] |
| 18216 | Abstractions can form useful counterparts to concrete statements [Field,H] |
| 18210 | Why regard standard mathematics as truths, rather than as interesting fictions? [Field,H] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 8862 | Platonic objects are really created as existential metaphors [Yablo] |
| 22298 | Why is fictional arithmetic applicable to the real world? [Potter] |