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All the ideas for 'Thinking About Mathematics', 'Henry V' and 'An Outline of Philosophy'

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25 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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
22. Metaethics / A. Ethics Foundations / 1. Nature of Ethics / d. Ethical theory
21740 I doubt whether ethics is part of philosophy [Russell]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / h. Expressivism
21741 'You ought to do p' primarily has emotional content, expressing approval [Russell]
22. Metaethics / B. Value / 2. Values / g. Love
21746 Unlike hate, all desires can be satisfied by love [Russell]
22. Metaethics / C. The Good / 1. Goodness / b. Types of good
21747 Goodness is a combination of love and knowledge [Russell]
22. Metaethics / C. The Good / 2. Happiness / d. Routes to happiness
21743 In wartime, happiness is hating the enemy, because it gives the war a purpose [Russell]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
21742 Originally virtue was obedience, to gods, government, or custom [Russell]
23. Ethics / D. Deontological Ethics / 4. Categorical Imperative
21745 Act so as to produce harmonious rather than discordant desires [Russell]
25. Social Practice / D. Justice / 3. Punishment / d. Reform of offenders
21744 Legally curbing people's desires is inferior to improving their desires [Russell]
25. Social Practice / E. Policies / 1. War / b. Justice in war
23565 Our obedience to the king erases any crimes we commit for him [Shakespeare]
27. Natural Reality / D. Time / 3. Parts of Time / e. Present moment
22891 We could be aware of time if senses briefly vibrated, extending their experience of movement [Russell, by Bardon]