Combining Philosophers
Ideas for Rescher,N/Oppenheim,P, Michael Tooley and George Cantor
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11 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
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15901
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Trying to represent curves, we study arbitrary functions, leading to the ordinals, which produces set theory [Cantor, by Lavine]
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15946
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Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine]
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9616
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A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
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4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / c. Basic theorems of ST
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13444
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Cantor's Theorem: for any set x, its power set P(x) has more members than x [Cantor, by Hart,WD]
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18098
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Cantor proved that all sets have more subsets than they have members [Cantor, by Bostock]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
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15505
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If a set is 'a many thought of as one', beginners should protest against singleton sets [Cantor, by Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / d. Infinite Sets
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10701
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Cantor showed that supposed contradictions in infinity were just a lack of clarity [Cantor, by Potter]
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10865
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The continuum is the powerset of the integers, which moves up a level [Cantor, by Clegg]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
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17831
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Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / d. Axiom of Unions III
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13016
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The Axiom of Union dates from 1899, and seems fairly obvious [Cantor, by Maddy]
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4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / b. Combinatorial sets
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14199
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Cantor's sets were just collections, but Dedekind's were containers [Cantor, by Oliver/Smiley]
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