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All the ideas for 'Thinking About Mathematics', 'Address to the Voters of Bristol' and 'The Morality of Happiness'

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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]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
3546 'Phronesis' should translate as 'practical intelligence', not as prudence [Annas]
22. Metaethics / C. The Good / 3. Pleasure / d. Sources of pleasure
3547 Epicureans achieve pleasure through character development [Annas]
23. Ethics / A. Egoism / 3. Cyrenaic School
3543 Cyrenaics pursue pleasure, but don't equate it with happiness [Annas]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / c. Motivation for virtue
3541 Ancient ethics uses attractive notions, not imperatives [Annas]
23. Ethics / D. Deontological Ethics / 1. Deontology
3550 Principles cover life as a whole, where rules just cover actions [Annas]
23. Ethics / D. Deontological Ethics / 2. Duty
3551 Virtue theory tries to explain our duties in terms of our character [Annas]
23. Ethics / D. Deontological Ethics / 6. Motivation for Duty
3552 If excessively good actions are admirable but not required, then duty isn't basic [Annas]
23. Ethics / E. Utilitarianism / 1. Utilitarianism
3542 We should do good when necessary, not maximise it [Annas]
24. Political Theory / D. Ideologies / 5. Democracy / d. Representative democracy
20558 Your representative owes you his judgement, and betrays you if he gives your opinion instead [Burke]