Combining Texts

All the ideas for 'fragments/reports', 'Philosophy of Mathematics' and 'Concepts without Boundaries'

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10 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
Even pointing a finger should only be done for a reason [Epictetus]
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]
7. Existence / D. Theories of Reality / 10. Vagueness / b. Vagueness of reality
If 'red' is vague, then membership of the set of red things is vague, so there is no set of red things [Sainsbury]
7. Existence / E. Categories / 2. Categorisation
We should abandon classifying by pigeon-holes, and classify around paradigms [Sainsbury]
9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects
Vague concepts are concepts without boundaries [Sainsbury]
If concepts are vague, people avoid boundaries, can't spot them, and don't want them [Sainsbury]
Boundaryless concepts tend to come in pairs, such as child/adult, hot/cold [Sainsbury]