Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'The Theory of Transfinite Numbers' and 'The Logical Structure of the World (Aufbau)'

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8 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
9616 A set is a collection into a whole of distinct objects of our intuition or thought [Cantor]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
15896 Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
10580 Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics
10579 Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
10577 Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
10578 We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
14. Science / B. Scientific Theories / 1. Scientific Theory
18699 Carnap tried to define all scientific predicates in terms of primitive relations, using type theory [Carnap, by Button]
18. Thought / D. Concepts / 4. Structure of Concepts / g. Conceptual atomism
12131 All concepts can be derived from a few basics, making possible one science of everything [Carnap, by Brody]