Combining Texts

All the ideas for 'Explanation - Opening Address', 'Mathematics without Foundations' and 'The Ways of Paradox'

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25 ideas

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 / 3. Types of Set / d. Infinite Sets
9944 We understand some statements about all sets [Putnam]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
21695 The set scheme discredited by paradoxes is actually the most natural one [Quine]
4. Formal Logic / F. Set Theory ST / 7. Natural Sets
21693 Russell's antinomy challenged the idea that any condition can produce a set [Quine]
5. Theory of Logic / L. Paradox / 3. Antinomies
21691 Antinomies contradict accepted ways of reasoning, and demand revisions [Quine]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
21690 Whenever the pursuer reaches the spot where the pursuer has been, the pursued has moved on [Quine]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
21689 A barber shaves only those who do not shave themselves. So does he shave himself? [Quine]
21694 Membership conditions which involve membership and non-membership are paradoxical [Quine]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / a. The Liar paradox
21692 If we write it as '"this sentence is false" is false', there is no paradox [Quine]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
9937 I do not believe mathematics either has or needs 'foundations' [Putnam]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
9939 It is conceivable that the axioms of arithmetic or propositional logic might be changed [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
9940 Maybe mathematics is empirical in that we could try to change it [Putnam]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
9941 Science requires more than consistency of mathematics [Putnam]
7. Existence / D. Theories of Reality / 4. Anti-realism
9943 You can't deny a hypothesis a truth-value simply because we may never know it! [Putnam]
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]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
17063 Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart]