Combining Texts

All the ideas for 'Elucidation of some points in E.Schröder', 'Axiomatic Thought' and 'Letter to the Editor about Bayle'

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9 ideas

4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14238 A class is an aggregate of objects; if you destroy them, you destroy the class; there is no empty class [Frege]
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]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / c. Essence and laws
11945 In addition to laws, God must also create appropriate natures for things [Leibniz]
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]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
19348 All that is real in motion is the force or power which produces change [Leibniz]