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Full Idea
The application of a system of numbers is counting and measurement.
Gist of Idea
The application of a system of numbers is counting and measurement
Source
Paul Benacerraf (What Numbers Could Not Be [1965], I)
Book Ref
'Philosophy of Mathematics: readings (2nd)', ed/tr. Benacerraf/Putnam [CUP 1983], p.274
A Reaction
A simple point, but it needs spelling out. Counting seems prior, in experience if not in logic. Measuring is a luxury you find you can indulge in (by imagining your quantity) split into parts, once you have mastered counting.
| 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] |