Combining Texts

All the ideas for 'Philosophy of Mathematics', 'Form, Matter and Substance' and 'How to Define Theoretical Terms'

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14 ideas

1. Philosophy / E. Nature of Metaphysics / 1. Nature of Metaphysics
Much metaphysical debate concerns what is fundamental, rather than what exists [Koslicki]
2. Reason / D. Definition / 2. Aims of Definition
Defining terms either enables elimination, or shows that they don't require elimination [Lewis]
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]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
Structured wholes are united by the teamwork needed for their capacities [Koslicki]
9. Objects / C. Structure of Objects / 2. Hylomorphism / a. Hylomorphism
The form explains kind, structure, unity and activity [Koslicki]
9. Objects / D. Essence of Objects / 3. Individual Essences
Hylomorphic compounds need an individual form for transworld identity [Koslicki]
10. Modality / E. Possible worlds / 3. Transworld Objects / b. Rigid designation
A logically determinate name names the same thing in every possible world [Lewis]
14. Science / B. Scientific Theories / 8. Ramsey Sentences
The Ramsey sentence of a theory says that it has at least one realisation [Lewis]
A Ramsey sentence just asserts that a theory can be realised, without saying by what [Lewis]
There is a method for defining new scientific terms just using the terms we already understand [Lewis]
It is better to have one realisation of a theory than many - but it may not always be possible [Lewis]