Combining Texts

All the ideas for 'Foundations of Geometry', 'Logological Fragments II' and 'Principles of Nature and Grace based on Reason'

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14 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / c. Philosophy as generalisation
The highest aim of philosophy is to combine all philosophies into a unity [Novalis]
Philosophy relies on our whole system of learning, and can thus never be complete [Novalis]
1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / d. Philosophy as puzzles
Philosophers feed on problems, hoping they are digestible, and spiced with paradox [Novalis]
1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
Philosophy aims to produce a priori an absolute and artistic world system [Novalis]
5. Theory of Logic / A. Overview of Logic / 8. Logic of Mathematics
Logic (the theory of relations) should be applied to mathematics [Novalis]
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
7. Existence / A. Nature of Existence / 5. Reason for Existence
First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
12. Knowledge Sources / B. Perception / 1. Perception
'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
Music charms, although its beauty is the harmony of numbers [Leibniz]