Combining Texts

All the ideas for 'fragments/reports', 'works' and 'Fourfold Root of Princ of Sufficient Reason'

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15 ideas

2. Reason / A. Nature of Reason / 1. On Reason
For clear questions posed by reason, reason can also find clear answers [Gödel]
2. Reason / B. Laws of Thought / 2. Sufficient Reason
Sufficient Reason can't be proved, because all proof presupposes it [Schopenhauer, by Lewis,PB]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
7. Existence / E. Categories / 1. Categories
No need for a priori categories, since sufficient reason shows the interrelations [Schopenhauer, by Lewis,PB]
10. Modality / A. Necessity / 3. Types of Necessity
Necessity is physical, logical, mathematical or moral [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
For Schopenhauer, material things would not exist without the mind [Schopenhauer, by Janaway]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / b. Transcendental idealism
Object for a subject and representation are the same thing [Schopenhauer]
14. Science / D. Explanation / 2. Types of Explanation / a. Types of explanation
The four explanations: objects by causes, concepts by ground, maths by spacetime, ethics by motive [Schopenhauer, by Lewis,PB]
18. Thought / D. Concepts / 2. Origin of Concepts / b. Empirical concepts
Concepts are abstracted from perceptions [Schopenhauer, by Lewis,PB]
20. Action / C. Motives for Action / 3. Acting on Reason / c. Reasons as causes
Motivation is causality seen from within [Schopenhauer]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
Musical performance can reveal a range of virtues [Damon of Ath.]