Combining Texts

All the ideas for 'Three Varieties of Knowledge', 'The Beautiful in Music' and 'Axiomatic Thought'

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14 ideas

2. Reason / A. Nature of Reason / 5. Objectivity
Objective truth arises from interpersonal communication [Davidson]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers [Hilbert]
11. Knowledge Aims / A. Knowledge / 4. Belief / e. Belief holism
A belief requires understanding the distinctions of true-and-false, and appearance-and-reality [Davidson]
13. Knowledge Criteria / E. Relativism / 2. Knowledge as Convention
Objectivity is intersubjectivity [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
If we know other minds through behaviour, but not our own, we should assume they aren't like me [Davidson]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / c. Knowing other minds
Knowing other minds rests on knowing both one's own mind and the external world [Davidson, by Dummett]
19. Language / F. Communication / 4. Private Language
Content of thought is established through communication, so knowledge needs other minds [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
The principle of charity attributes largely consistent logic and largely true beliefs to speakers [Davidson]
21. Aesthetics / C. Artistic Issues / 4. Emotion in Art
Music is not an expressive art, because it expresses no familiar emotions [Hanslick, by Wollheim]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]