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Full Idea
There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants.
Gist of Idea
The old view is that mathematics is useful in the world because it describes the world
Source
Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1)
Book Ref
Kitcher,Philip: 'The Nature of Mathematical Knowledge' [OUP 1984], p.105
A Reaction
He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us.
| 19390 | Everything is subsumed under number, which is a metaphysical statics of the universe, revealing powers [Leibniz] |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| 9897 | The application of a system of numbers is counting and measurement [Benacerraf] |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9946 | Logicists say mathematics is applicable because it is totally general [George/Velleman] |
| 21649 | How can words be used for counting if they are objects? [Hofweber] |
| 20660 | At one level maths and nature are very similar, suggesting some deeper origin [Wolfram] |
| 19677 | What is mathematically conceivable is absolutely possible [Meillassoux] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |