Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Properties' and 'Counterfactuals'

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11 ideas

2. Reason / D. Definition / 8. Impredicative Definition
Predicative definitions only refer to entities outside the defined collection [Horsten]
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 / 6. Mathematics as Set Theory / a. Mathematics is set theory
The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
8. Modes of Existence / B. Properties / 2. Need for Properties
We accept properties because of type/tokens, reference, and quantification [Edwards]
8. Modes of Existence / B. Properties / 10. Properties as Predicates
Quineans say that predication is primitive and inexplicable [Edwards]
8. Modes of Existence / E. Nominalism / 2. Resemblance Nominalism
Resemblance nominalism requires a second entity to explain 'the rose is crimson' [Edwards]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
That a whole is prior to its parts ('priority monism') is a view gaining in support [Edwards]
10. Modality / B. Possibility / 8. Conditionals / c. Truth-function conditionals
Lewis says indicative conditionals are truth-functional [Lewis, by Jackson]
10. Modality / B. Possibility / 9. Counterfactuals
In good counterfactuals the consequent holds in world like ours except that the antecedent is true [Lewis, by Horwich]
26. Natural Theory / D. Laws of Nature / 4. Regularities / b. Best system theory
A law of nature is a general axiom of the deductive system that is best for simplicity and strength [Lewis]