Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'Thinking About Mathematics' and 'The Communist Manifesto'

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24 ideas

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
8729 Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8763 The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / h. Reals from Cauchy
18249 Cauchy gave a formal definition of a converging sequence. [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 1. Foundations for Mathematics
8764 Categories are the best foundation for mathematics [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / f. Zermelo numbers
8762 Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
8760 Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro]
8761 A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
8744 Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro]
6. Mathematics / C. Sources of Mathematics / 7. Formalism
8749 Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro]
8750 Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro]
8752 Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / b. Intuitionism
8753 Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / c. Conceptualism
8731 Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro]
6. Mathematics / C. Sources of Mathematics / 10. Constructivism / d. Predicativism
8730 'Impredicative' definitions refer to the thing being described [Shapiro]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
13128 'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
5303 For the proletariate, law, morality and religion are just expressions of bourgeois interests [Marx/Engels]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / j. Ethics by convention
21998 Bourgeois interests create our morality, law and religion [Marx/Engels]
24. Political Theory / D. Ideologies / 9. Communism
5302 Modern governments are just bourgeois management committees [Marx/Engels]
5304 Communism aims to abolish not all property, but bourgeois property [Marx/Engels]
5307 Many of the bourgeois rights grievances are a form of self-defence [Marx/Engels]
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
5306 The free development of each should be the condition for the free development of all [Marx/Engels]
25. Social Practice / E. Policies / 5. Education / b. Education principles
5305 Communists want to rescue education from the ruling class [Marx/Engels]
25. Social Practice / E. Policies / 5. Education / d. Study of history
5301 The history of all existing society is the history of class struggles [Marx/Engels]