Combining Texts

All the ideas for 'Hilbert's Programme', 'Abstract Objects: a Case Study' and 'Reference and Reflexivity'

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8 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
17809 Gödel showed that the syntactic approach to the infinite is of limited value [Kreisel]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
17810 The study of mathematical foundations needs new non-mathematical concepts [Kreisel]
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]
18. Thought / A. Modes of Thought / 9. Indexical Thought
16391 Indexical thoughts are about themselves, and ascribe properties to themselves [Perry, by Recanati]
27. Natural Reality / C. Space / 3. Points in Space
17811 The natural conception of points ducks the problem of naming or constructing each point [Kreisel]