more from this thinker | more from this text
Full Idea
Number words as singular terms seem to refer to objects; numbers words in determiner or adjectival position are tied to counting. How these objects are related to counting is what the application problem is about.
Gist of Idea
How can words be used for counting if they are objects?
Source
Thomas Hofweber (Ontology and the Ambitions of Metaphysics [2016], 06.1.3)
Book Ref
Hofweber,Thomas: 'Ontology and the Ambitions of Metaphysics' [OUP 2018], p.160
A Reaction
You can't use stones for counting, so there must be more to numbers than the announcement that they are 'objects'. They seem to have internal relations, which makes them unusual objects.
| 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] |