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All the ideas for 'Precis of 'Limits of Abstraction'', 'Philosophy of Mathematics' and 'Anti-essentialism'

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14 ideas

2. Reason / D. Definition / 2. Aims of Definition
Definitions concern how we should speak, not how things are [Fine,K]
2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
Logical space is abstracted from the actual world [Stalnaker]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / d. Hume's Principle
If Hume's Principle can define numbers, we needn't worry about its truth [Fine,K]
Hume's Principle is either adequate for number but fails to define properly, or vice versa [Fine,K]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
9. Objects / C. Structure of Objects / 7. Substratum
For the bare particular view, properties must be features, not just groups of objects [Stalnaker]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / a. Essence as necessary properties
An essential property is one had in all the possible worlds where a thing exists [Stalnaker]
9. Objects / D. Essence of Objects / 7. Essence and Necessity / b. Essence not necessities
Necessarily self-identical, or being what it is, or its world-indexed properties, aren't essential [Stalnaker]
9. Objects / D. Essence of Objects / 15. Against Essentialism
Bare particular anti-essentialism makes no sense within modal logic semantics [Stalnaker]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
Why imagine that Babe Ruth might be a billiard ball; nothing useful could be said about the ball [Stalnaker]
18. Thought / E. Abstraction / 7. Abstracta by Equivalence
An abstraction principle should not 'inflate', producing more abstractions than objects [Fine,K]