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Full Idea
Is there a notion of set in the jurisdiction of logic, or does it belong to mathematics proper?
Gist of Idea
Are sets part of logic, or part of mathematics?
Source
Stewart Shapiro (Foundations without Foundationalism [1991], Pref)
Book Ref
Shapiro,Stewart: 'Foundations without Foundationalism' [OUP 1991], p.-9
A Reaction
It immediately strikes me that they might be neither. I don't see that relations between well-defined groups of things must involve number, and I don't see that mapping the relations must intrinsically involve logical consequence or inference.
| 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] |