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Full Idea
Maybe the axioms of extensionality and the pair set axiom 'force themselves on us' (Gödel's phrase), but I am not convinced about the axioms of infinity, union, power or replacement.
Gist of Idea
A few axioms of set theory 'force themselves on us', but most of them don't
Source
George Boolos (Must We Believe in Set Theory? [1997], p.130)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.130
A Reaction
Boolos is perfectly happy with basic set theory, but rather dubious when very large cardinals come into the picture.
| 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 | Naďve 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] |