Combining Philosophers

All the ideas for Rayo,A/Uzquiasno,G, Zoltn Gendler Szab and Carl Friedrich Gauss

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11 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
What is a singleton set, if a set is meant to be a collection of objects? [Szabó]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / m. Axiom of Separation
Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 2. Domain of Quantification
We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano]
Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
Abstract entities don't depend on their concrete entities ...but maybe on the totality of concrete things [Szabó]
15. Nature of Minds / C. Capacities of Minds / 3. Abstraction by mind
Geometrical circles cannot identify a circular paint patch, presumably because they lack something [Szabó]
18. Thought / E. Abstraction / 5. Abstracta by Negation
Abstractions are imperceptible, non-causal, and non-spatiotemporal (the third explaining the others) [Szabó]
19. Language / F. Communication / 5. Pragmatics / a. Contextual meaning
The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano]