Combining Texts

All the ideas for 'The Mind and the Soul', 'Precepts for Advancing Science and Arts' and 'Axiomatic Thought'

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11 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]
8. Modes of Existence / B. Properties / 1. Nature of Properties
Not only substances have attributes; events, actions, states and qualities can have them [Teichmann]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
I don't recommend universal doubt; we constantly seek reasons for things which are indubitable [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 2. Interactionism
Body-spirit interaction ought to result in losses and increases of energy in the material world [Teichmann]
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]
29. Religion / D. Religious Issues / 2. Immortality / b. Soul
The Soul has no particular capacity (in the way thinking belongs to the mind) [Teichmann]
No individuating marks distinguish between Souls [Teichmann]