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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?
15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
10112 | The naturals won't map onto the reals, so there are different sizes of infinity [Cantor, by George/Velleman] |
18959 | Sets larger than the continuum should be studied in an 'if-then' spirit [Putnam] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |