Combining Texts

All the ideas for 'The Analysis of Matter', 'fragments/reports' and 'Mathematical logic and theory of types'

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21 ideas

4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
11064 Classes can be reduced to propositional functions [Russell, by Hanna]
5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox
1507 We don't have time for infinite quantity, but we do for infinite divisibility, because time is also divisible [Aristotle on Zeno of Elea]
5109 The fast runner must always reach the point from which the slower runner started [Zeno of Elea, by Aristotle]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / d. Russell's paradox
6407 The class of classes which lack self-membership leads to a contradiction [Russell, by Grayling]
5. Theory of Logic / L. Paradox / 6. Paradoxes in Language / b. The Heap paradox ('Sorites')
1512 Zeno is wrong that one grain of millet makes a sound; why should one grain achieve what the whole bushel does? [Aristotle on Zeno of Elea]
5. Theory of Logic / L. Paradox / 7. Paradoxes of Time
1508 Zeno's arrow paradox depends on the assumption that time is composed of nows [Aristotle on Zeno of Elea]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10418 Type theory seems an extreme reaction, since self-exemplification is often innocuous [Swoyer on Russell]
10047 Russell's improvements blocked mathematics as well as paradoxes, and needed further axioms [Russell, by Musgrave]
23478 Type theory means that features shared by different levels cannot be expressed [Morris,M on Russell]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism
21718 Ramified types can be defended as a system of intensional logic, with a 'no class' view of sets [Russell, by Linsky,B]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
18126 A set does not exist unless at least one of its specifications is predicative [Russell, by Bostock]
18128 Russell is a conceptualist here, saying some abstracta only exist because definitions create them [Russell, by Bostock]
18124 Vicious Circle says if it is expressed using the whole collection, it can't be in the collection [Russell, by Bostock]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
6402 In 1927, Russell analysed force and matter in terms of events [Russell, by Grayling]
9. Objects / A. Existence of Objects / 1. Physical Objects
14732 A perceived physical object is events grouped around a centre [Russell]
9. Objects / B. Unity of Objects / 2. Substance / e. Substance critique
14733 An object produces the same percepts with or without a substance, so that is irrelevant to science [Russell]
11. Knowledge Aims / C. Knowing Reality / 2. Phenomenalism
6418 Russell rejected phenomenalism because it couldn't account for causal relations [Russell, by Grayling]
26. Natural Theory / A. Speculations on Nature / 1. Nature
454 If there are many things they must have a finite number, but there must be endless things between them [Zeno of Elea]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
455 That which moves, moves neither in the place in which it is, nor in that in which it is not [Zeno of Elea]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
21706 At first matter is basic and known by sense-data; later Russell says matter is constructed [Russell, by Linsky,B]
27. Natural Reality / C. Space / 5. Relational Space
1511 If everything is in a place, what is the place in? Place doesn't exist [Zeno of Elea, by Simplicius]