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Full Idea
The set theorist cannot tell us anything about the true relationship of membership.
Gist of Idea
The set theorist cannot tell us what 'membership' is
Source
Charles Chihara (A Structural Account of Mathematics [2004], 01.5)
Book Ref
Chihara,Charles: 'A Structural Account of Mathematics' [OUP 2004], p.24
A Reaction
If three unrelated objects suddenly became members of a set, it is hard to see how the world would have changed, except in the minds of those thinking about it.
| 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] |