Combining Texts

All the ideas for 'Clitophon', 'Principia Mathematica' and 'Principle Doctrines ('Kuriai Doxai') (frags)'

expand these ideas     |    start again     |     specify just one area for these texts

38 ideas

1. Philosophy / A. Wisdom / 2. Wise People
14519 It is a great good to show reverence for a wise man [Epicurus]
1. Philosophy / D. Nature of Philosophy / 2. Invocation to Philosophy
14518 In the study of philosophy, pleasure and knowledge arrive simultaneously [Epicurus]
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
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]
8683 Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend]
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 / A. Existence of Objects / 5. Individuation / b. Individuation by properties
14524 Bodies are combinations of shape, size, resistance and weight [Epicurus]
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]
16. Persons / F. Free Will / 6. Determinism / a. Determinism
14521 If everything is by necessity, then even denials of necessity are by necessity [Epicurus]
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 / B. Value / 2. Values / f. Altruism
1590 The just man does not harm his enemies, but benefits everyone [Plato]
22. Metaethics / C. The Good / 2. Happiness / c. Value of happiness
14522 What happens to me if I obtain all my desires, and what if I fail? [Epicurus]
22. Metaethics / C. The Good / 3. Pleasure / e. Role of pleasure
3563 Pleasure and virtue entail one another [Epicurus]
23. Ethics / B. Contract Ethics / 1. Contractarianism
3560 Justice is merely a contract about not harming or being harmed [Epicurus]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
14517 We value our own character, whatever it is, and we should respect the characters of others [Epicurus]
23. Ethics / C. Virtue Theory / 3. Virtues / c. Justice
14513 Justice is a pledge of mutual protection [Epicurus]
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
14515 A law is not just if it is not useful in mutual associations [Epicurus]
25. Social Practice / F. Life Issues / 4. Suicide
14520 It is small-minded to find many good reasons for suicide [Epicurus]