Combining Texts

All the ideas for 'On What Grounds What', 'Review of Chihara 'Struct. Accnt of Maths'' and 'The Theory of Logical Types'

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23 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
13734 Modern Quinean metaphysics is about what exists, but Aristotelian metaphysics asks about grounding [Schaffer,J]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
13751 If you tore the metaphysics out of philosophy, the whole enterprise would collapse [Schaffer,J]
2. Reason / B. Laws of Thought / 6. Ockham's Razor
13743 We should not multiply basic entities, but we can have as many derivative entities as we like [Schaffer,J]
5. Theory of Logic / E. Structures of Logic / 5. Functions in Logic
21566 'Propositional functions' are ambiguous until the variable is given a value [Russell]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21567 'All judgements made by Epimenedes are true' needs the judgements to be of the same type [Russell]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10185 Set theory is the standard background for modern mathematics [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
10184 Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess]
10189 There is no one relation for the real number 2, as relations differ in different models [Burgess]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
10186 If set theory is used to define 'structure', we can't define set theory structurally [Burgess]
10187 Abstract algebra concerns relations between models, not common features of all the models [Burgess]
10188 How can mathematical relations be either internal, or external, or intrinsic? [Burgess]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
13741 If 'there are red roses' implies 'there are roses', then 'there are prime numbers' implies 'there are numbers' [Schaffer,J]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
23457 Type theory cannot identify features across levels (because such predicates break the rules) [Morris,M on Russell]
21556 Classes are defined by propositional functions, and functions are typed, with an axiom of reducibility [Russell, by Lackey]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
21568 A one-variable function is only 'predicative' if it is one order above its arguments [Russell]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
13748 Grounding is unanalysable and primitive, and is the basic structuring concept in metaphysics [Schaffer,J]
7. Existence / C. Structure of Existence / 5. Supervenience / a. Nature of supervenience
13747 Supervenience is just modal correlation [Schaffer,J]
7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete
13744 The cosmos is the only fundamental entity, from which all else exists by abstraction [Schaffer,J]
7. Existence / E. Categories / 4. Category Realism
13739 Maybe categories are just the different ways that things depend on basic substances [Schaffer,J]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13742 There exist heaps with no integral unity, so we should accept arbitrary composites in the same way [Schaffer,J]
13752 The notion of 'grounding' can explain integrated wholes in a way that mere aggregates can't [Schaffer,J]
10. Modality / E. Possible worlds / 1. Possible Worlds / b. Impossible worlds
13749 Belief in impossible worlds may require dialetheism [Schaffer,J]
11. Knowledge Aims / B. Certain Knowledge / 2. Common Sense Certainty
13740 'Moorean certainties' are more credible than any sceptical argument [Schaffer,J]