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All the ideas for 'Good and Evil', 'Philosophy of Chemistry' and 'Principia Mathematica'

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38 ideas

4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
9542 The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility
21720 Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead]
4. Formal Logic / F. Set Theory ST / 8. Critique of Set Theory
10044 Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro]
18208 We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead]
5. Theory of Logic / B. Logical Consequence / 7. Strict Implication
8204 Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead]
9359 Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead]
5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic
21707 Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B]
5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic
10036 In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts
18248 A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / a. Defining numbers
18152 Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
10025 Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes]
10037 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / b. Type theory
10093 The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman]
8691 The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
10305 In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / a. Constructivism
8684 Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8746 To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro]
9. Objects / F. Identity among Objects / 7. Indiscernible Objects
12033 An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
10040 Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel]
14. Science / D. Explanation / 2. Types of Explanation / i. Explanations by mechanism
17472 Thick mechanisms map whole reactions, and thin mechanism chart the steps [Weisberg/Needham/Hendry]
17471 Using mechanisms as explanatory schemes began in chemistry [Weisberg/Needham/Hendry]
18. Thought / A. Modes of Thought / 6. Judgement / a. Nature of Judgement
21725 The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B]
23474 A judgement is a complex entity, of mind and various objects [Russell/Whitehead]
23455 The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead]
23480 The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead]
18275 Only the act of judging completes the meaning of a statement [Russell/Whitehead]
19. Language / D. Propositions / 3. Concrete Propositions
23453 Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead]
22. Metaethics / C. The Good / 1. Goodness / a. Form of the Good
22489 'Good' is an attributive adjective like 'large', not predicative like 'red' [Geach, by Foot]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / f. Ancient elements
17465 Lavoisier's elements included four types of earth [Weisberg/Needham/Hendry]
27. Natural Reality / F. Chemistry / 1. Chemistry
17468 Over 100,000,000 compounds have been discovered or synthesised [Weisberg/Needham/Hendry]
17469 'H2O' just gives the element proportions, not the microstructure [Weisberg/Needham/Hendry]
17470 Water molecules dissociate, and form large polymers, explaining its properties [Weisberg/Needham/Hendry]
17473 It is unlikely that chemistry will ever be reduced to physics [Weisberg/Needham/Hendry]
17474 Quantum theory won't tell us which structure a set of atoms will form [Weisberg/Needham/Hendry]
17475 For temperature to be mean kinetic energy, a state of equilibrium is also required [Weisberg/Needham/Hendry]
27. Natural Reality / F. Chemistry / 2. Modern Elements
17467 Isotopes (such as those of hydrogen) can vary in their rates of chemical reaction [Weisberg/Needham/Hendry]
27. Natural Reality / F. Chemistry / 3. Periodic Table
17466 Mendeleev systematised the elements, and also gave an account of their nature [Weisberg/Needham/Hendry]