Combining Texts

All the ideas for 'fragments/reports', 'Axiomatic Thought' and 'Counterfactuals'

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10 ideas

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]
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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]
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]
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]