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Full Idea
It is no surprise that we should be able to reason mathematically about many of the things we experience, for they are already 'abstract'.
Gist of Idea
Mathematics isn't surprising, given that we experience many objects as abstract
Source
George Boolos (Must We Believe in Set Theory? [1997], p.129)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.129
A Reaction
He has just given a list of exemplary abstract objects (Idea 10489), but I think there is a more interesting idea here - that our experience of actual physical objects is to some extent abstract, as soon as it is conceptualised.
Related Idea
Idea 10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
| 10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
| 10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
| 10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
| 10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
| 10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
| 10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
| 10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
| 10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
| 10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
| 10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |