Combining Texts
Ideas for
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16 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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18395
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Sets are mereological sums of the singletons of their members [Lewis, by Armstrong]
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15496
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We can build set theory on singletons: classes are then fusions of subclasses, membership is the singleton [Lewis]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
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15500
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Classes divide into subclasses in many ways, but into members in only one way [Lewis]
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15499
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A subclass of a subclass is itself a subclass; a member of a member is not in general a member [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
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15503
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We needn't accept this speck of nothingness, this black hole in the fabric of Reality! [Lewis]
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15498
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We can accept the null set, but there is no null class of anything [Lewis]
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15502
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There are four main reasons for asserting that there is an empty set [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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15497
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We can replace the membership relation with the member-singleton relation (plus mereology) [Lewis]
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15506
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If we don't understand the singleton, then we don't understand classes [Lewis]
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15511
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If singleton membership is external, why is an object a member of one rather than another? [Lewis]
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15513
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Maybe singletons have a structure, of a thing and a lasso? [Lewis]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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15507
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Set theory has some unofficial axioms, generalisations about how to understand it [Lewis]
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10191
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Set theory reduces to a mereological theory with singletons as the only atoms [Lewis, by MacBride]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / a. Sets as existing
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15523
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Set theory isn't innocent; it generates infinities from a single thing; but mathematics needs it [Lewis]
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15508
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If singletons are where their members are, then so are all sets [Lewis]
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15514
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A huge part of Reality is only accepted as existing if you have accepted set theory [Lewis]
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