Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'The Theory of Transfinite Numbers' and 'Many, but almost one'

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10 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]
7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic
15538 Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
15537 If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
15536 We have one cloud, but many possible boundaries and aggregates for it [Lewis]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
15539 Basic to pragmatics is taking a message in a way that makes sense of it [Lewis]