more from this thinker | more from this text
Full Idea
Set theory is not innocent. Its trouble is that when we have one thing, then somehow we have another wholly distinct thing, the singleton. And another, and another....ad infinitum. But that's the price for mathematical power. Pay it.
Gist of Idea
Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it
Source
David Lewis (Parts of Classes [1991], 3.6)
Book Ref
Lewis,David: 'Parts of Classes' [Blackwell 1991], p.87
| 15510 | Classes are a host of ethereal, platonic, pseudo entities [Goodman] |
| 7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
| 15508 | If singletons are where their members are, then so are all sets [Lewis] |
| 15514 | A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis] |
| 15523 | Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis] |
| 13631 | Are sets part of logic, or part of mathematics? [Shapiro] |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| 10109 | ZFC can prove that there is no set corresponding to the concept 'set' [George/Velleman] |