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Full Idea
Cantor's theories exhibited the contradictions others had claimed to derive from the supposition of infinite sets as confusions resulting from the failure to mark the necessary distinctions with sufficient clarity.
Gist of Idea
Cantor showed that supposed contradictions in infinity were just a lack of clarity
Source
report of George Cantor (works [1880]) by Michael Potter - Set Theory and Its Philosophy Intro 1
Book Ref
Potter,Michael: 'Set Theory and Its Philosophy' [OUP 2004], p.3
| 10183 | An infinite set maps into its own proper subset [Dedekind, by Reck/Price] |
| 10865 | The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg] |
| 10701 | Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter] |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| 9944 | We understand some statements about all sets [Putnam] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 8666 | Infinite sets correspond one-to-one with a subset [Friend] |