Combining Texts

All the ideas for 'On the Question of Absolute Undecidability', 'Letters to Russell' and 'Explanation - Opening Address'

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21 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
7085 The main problem of philosophy is what can and cannot be thought and expressed [Wittgenstein, by Grayling]
2. Reason / A. Nature of Reason / 6. Coherence
17070 Coherence is consilience, simplicity, analogy, and fitting into a web of belief [Smart]
17072 We need comprehensiveness, as well as self-coherence [Smart]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
17884 Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner]
17893 'Reflection principles' say the whole truth about sets can't be captured [Koellner]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17894 We have no argument to show a statement is absolutely undecidable [Koellner]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity
17890 There are at least eleven types of large cardinal, of increasing logical strength [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / d. Peano arithmetic
17887 PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17891 Arithmetical undecidability is always settled at the next stage up [Koellner]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
23463 Atomic facts correspond to true elementary propositions [Wittgenstein]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / a. Evidence
17073 I simply reject evidence, if it is totally contrary to my web of belief [Smart]
14. Science / D. Explanation / 1. Explanation / c. Direction of explanation
17077 The height of a flagpole could be fixed by its angle of shadow, but that would be very unusual [Smart]
17078 Universe expansion explains the red shift, but not vice versa [Smart]
14. Science / D. Explanation / 2. Types of Explanation / c. Explanations by coherence
17061 Explanation of a fact is fitting it into a system of beliefs [Smart]
17074 Explanations are bad by fitting badly with a web of beliefs, or fitting well into a bad web [Smart]
17076 Deducing from laws is one possible way to achieve a coherent explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / d. Consilience
17071 An explanation is better if it also explains phenomena from a different field [Smart]
14. Science / D. Explanation / 2. Types of Explanation / g. Causal explanations
17062 If scientific explanation is causal, that rules out mathematical explanation [Smart]
14. Science / D. Explanation / 2. Types of Explanation / j. Explanations by reduction
17075 Scientific explanation tends to reduce things to the unfamiliar (not the familiar) [Smart]
19. Language / D. Propositions / 4. Mental Propositions
23490 A thought is mental constituents that relate to reality as words do [Wittgenstein]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
17063 Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart]