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All the ideas for 'Precis of 'Limits of Abstraction'', 'Philosophy' and 'Abstract Objects: a Case Study'

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10 ideas

2. Reason / D. Definition / 2. Aims of Definition
10528 Definitions concern how we should speak, not how things are [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
10529 If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
10530 Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
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]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
23888 Knowledge is beyond question, as an unavoidable component of thinking [Weil]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
10527 An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]
21. Aesthetics / B. Nature of Art / 1. Defining Art
23887 Art (like philosophy) establishes a relation between world and self, and between oneself and others [Weil]