Combining Texts

All the ideas for 'Abstract Objects: a Case Study', 'Second Commentary on 'Isagoge'' and 'On the Foundations of Logic and Arithmetic'

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7 ideas

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17697 The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
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 / 6. Logicism / d. Logicism critique
17698 Logic already contains some arithmetic, so the two must be developed together [Hilbert]
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]
8. Modes of Existence / D. Universals / 5. Universals as Concepts
15035 If universals are not separate, we can isolate them by abstraction [Boethius, by Panaccio]