Combining Texts

All the ideas for 'The Internalist Conception of Justification', 'Axiomatic Thought' and 'Set Theory and the Continuum Hypothesis'

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8 ideas

2. Reason / A. Nature of Reason / 6. Coherence
4262 If the only aim was consistent beliefs then new evidence and experiments would be irrelevant [Goldman]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17963 The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
17966 Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
17967 To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
17965 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
17964 Number theory just needs calculation laws and rules for integers [Hilbert]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
14248 We could accept the integers as primitive, then use sets to construct the rest [Cohen]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
17968 By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]