Combining Texts
Ideas for
'The Boundary Stones of Thought', 'Mathematics is Megethology' and 'Foundations of Philosophical Knowledge'
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11 ideas
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10807
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Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis]
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18830
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Most set theorists doubt bivalence for the Continuum Hypothesis, but still use classical logic [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
10809
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We can accept the null set, but not a null class, a class lacking members [Lewis]
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10811
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The null set plays the role of last resort, for class abstracts and for existence [Lewis]
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10812
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The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis]
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4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
10813
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What on earth is the relationship between a singleton and an element? [Lewis]
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10814
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Are all singletons exact intrinsic duplicates? [Lewis]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
18843
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The iterated conception of set requires continual increase in axiom strength [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
18836
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A set may well not consist of its members; the empty set, for example, is a problem [Rumfitt]
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18837
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A set can be determinate, because of its concept, and still have vague membership [Rumfitt]
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4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
18845
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If the totality of sets is not well-defined, there must be doubt about the Power Set Axiom [Rumfitt]
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