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Full Idea
To the best of my knowledge nothing in mathematics or science requires the existence of very high orders of infinity.
Gist of Idea
Mathematics and science do not require very high orders of infinity
Source
George Boolos (Must We Believe in Set Theory? [1997], p.122)
Book Ref
Boolos,George: 'Logic, Logic and Logic' [Harvard 1999], p.122
A Reaction
He is referring to particular high orders of infinity implied by set theory. Personally I want to wield Ockham's Razor. Is being implied by set theory a sufficient reason to accept such outrageous entities into our ontology?
| 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] |