Combining Texts

All the ideas for 'Philosophy of Mathematics', 'The Nature of Musical Expression' and 'Reflections on Knowledge, Truth and Ideas'

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10 ideas

2. Reason / D. Definition / 1. Definitions
19426 'Nominal' definitions just list distinguishing characteristics [Leibniz]
2. Reason / D. Definition / 8. Impredicative Definition
10882 Predicative definitions only refer to entities outside the defined collection [Horsten]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
10884 A theory is 'categorical' if it has just one model up to isomorphism [Horsten]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
10885 Computer proofs don't provide explanations [Horsten]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10881 The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
19424 Knowledge needs clarity, distinctness, and adequacy, and it should be intuitive [Leibniz]
18. Thought / C. Content / 2. Ideas
19427 True ideas represent what is possible; false ideas represent contradictions [Leibniz]
21. Aesthetics / B. Nature of Art / 4. Art as Expression
12165 Romantics say music expresses ideas, or the Will, or intuitions, or feelings [Scruton]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
12164 Expressing melancholy is a good thing, but arousing it is a bad thing [Scruton]
26. Natural Theory / C. Causation / 2. Types of cause
19425 In the schools the Four Causes are just lumped together in a very obscure way [Leibniz]