Combining Texts

All the ideas for 'Abstract of 'The Fourfold Root'', 'Foundations of Geometry' and 'What is Analytic Philosophy?'

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14 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis
Analysis must include definitions, search for simples, concept analysis, and Kant's analysis [Glock]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
'There is nothing without a reason why it should be rather than not be' (a generalisation of 'Why?') [Schopenhauer]
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]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
All necessity arises from causation, which is conditioned; there is no absolute or unconditioned necessity [Schopenhauer]
11. Knowledge Aims / A. Knowledge / 2. Understanding
All understanding is an immediate apprehension of the causal relation [Schopenhauer]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
German and British idealism is not about individual ideas, but the intelligibility of reality [Glock]
16. Persons / C. Self-Awareness / 2. Knowing the Self
What we know in ourselves is not a knower but a will [Schopenhauer]
16. Persons / D. Continuity of the Self / 3. Reference of 'I'
The knot of the world is the use of 'I' to refer to both willing and knowing [Schopenhauer]
18. Thought / D. Concepts / 4. Structure of Concepts / h. Family resemblance
We might say that the family resemblance is just a consequence of meaning-as-use [Glock]
The variety of uses of 'game' may be that it has several meanings, and isn't a single concept [Glock]
27. Natural Reality / D. Time / 1. Nature of Time / b. Relative time
Time may be defined as the possibility of mutually exclusive conditions of the same thing [Schopenhauer]