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Full Idea
The logic of ZF Set Theory is classical first-order predicate logic with identity.
Gist of Idea
The logic of ZF is classical first-order predicate logic with identity
Source
George Boolos (Must We Believe in Set Theory? [1997], p.121)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.121
A Reaction
This logic seems to be unable to deal with very large cardinals, precisely those that are implied by set theory, so there is some sort of major problem hovering here. Boolos is fairly neutral.
| 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] |