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Full Idea
The logicist idea is that if mathematics is logic, and logic is the most general of disciplines, one that applies to all rational thought regardless of its content, then it is not surprising that mathematics is widely applicable.
Gist of Idea
Logicists say mathematics is applicable because it is totally general
Source
A.George / D.J.Velleman (Philosophies of Mathematics [2002], Ch.2)
Book Ref
George,A/Velleman D.J.: 'Philosophies of Mathematics' [Blackwell 2002], p.19
A Reaction
Frege was keen to emphasise this. You are left wondering why pure logic is applicable to the physical world. The only account I can give is big-time Platonism, or Pythagoreanism. Logic reveals the engine-room of nature, where the design is done.
| 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] |