Combining Texts

All the ideas for 'fragments/reports', 'Knowledge and the Philosophy of Number' and 'Explanation - Opening Address'

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22 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 / 5. Conceptions of Set / d. Naïve logical sets
23623 Predicativism says only predicated sets exist [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
23624 The iterative conception has to appropriate Replacement, to justify the ordinals [Hossack]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
23625 Limitation of Size justifies Replacement, but then has to appropriate Power Set [Hossack]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / d. and
23628 The connective 'and' can have an order-sensitive meaning, as 'and then' [Hossack]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
23627 'Before' and 'after' are not two relations, but one relation with two orders [Hossack]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / h. Ordinal infinity
23626 Transfinite ordinals are needed in proof theory, and for recursive functions and computability [Hossack]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / b. Mathematics is not set theory
23621 Numbers are properties, not sets (because numbers are magnitudes) [Hossack]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
23622 We can only mentally construct potential infinities, but maths needs actual infinities [Hossack]
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]
25. Social Practice / E. Policies / 5. Education / b. Education principles
13304 Learned men gain more in one day than others do in a lifetime [Posidonius]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
17063 Unlike Newton, Einstein's general theory explains the perihelion of Mercury [Smart]
27. Natural Reality / D. Time / 1. Nature of Time / d. Time as measure
20820 Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus]