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Full Idea
The existence of infinitely many natural numbers seems to me no more troubling than that of infinitely many computer programs or sentences of English. There is, for example, no longest sentence, since any number of 'very's can be inserted.
Gist of Idea
Infinite natural numbers is as obvious as infinite sentences in English
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
If you really resisted an infinity of natural numbers, presumably you would also resist an actual infinity of 'very's. The fact that it is unclear what could ever stop a process doesn't guarantee that the process is actually endless.
| 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] |