Combining Texts

All the ideas for 'Aristotle and Descartes on Matter', 'Causality: Production and Propagation' and 'Axiomatic Thought'

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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]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
Prime matter is nothing when it is at rest [Leibniz]
26. Natural Theory / C. Causation / 4. Naturalised causation
A causal interaction is when two processes intersect, and correlated modifications persist afterwards [Salmon]
26. Natural Theory / C. Causation / 5. Direction of causation
Cause must come first in propagations of causal interactions, but interactions are simultaneous [Salmon]
26. Natural Theory / C. Causation / 8. Particular Causation / b. Causal relata
Instead of localised events, I take enduring and extended processes as basic to causation [Salmon]
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]