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Full Idea
Mathematics hooks onto the world by providing representations in the form of structurally similar models.
Gist of Idea
Mathematics represents the world through structurally similar models.
Source
James Robert Brown (Philosophy of Mathematics [1999], Ch. 4)
Book Ref
Brown,James Robert: 'Philosophy of Mathematics' [Routledge 2002], p.49
A Reaction
This is Brown's conclusion. It needs notions of mapping, one-to-one correspondence, and similarity. I like the idea of a 'model', as used in both logic and mathematics, and children's hobbies. The mind is a model-making machine.
| 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] |