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All the ideas for 'Thinking About Mathematics', 'Sociobiology' and 'The DhammaPada'

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24 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
7893 Our life is the creation of our mind [Anon (Dham)]
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]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / a. Idealism
7898 The world is just the illusion of an appearance [Anon (Dham)]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / d. Biological ethics
22187 Genetic behaviours that have enhanced human success include aggression, rape and xenophobia [Wilson,EO, by Okasha]
22. Metaethics / B. Value / 2. Values / g. Love
7894 Hate is conquered by love [Anon (Dham)]
22. Metaethics / C. The Good / 3. Pleasure / f. Dangers of pleasure
7899 Even divine pleasure will not satisfy the wise, as it is insatiable, and leads to pain [Anon (Dham)]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
7896 The foolish gradually fill with evil, like a slowly-filled water-jar [Anon (Dham)]
7897 The wise gradually fill with good, like a slowly-filled water-jar [Anon (Dham)]
23. Ethics / C. Virtue Theory / 4. External Goods / d. Friendship
7895 Don't befriend fools; either find superior friends, or travel alone [Anon (Dham)]
29. Religion / C. Spiritual Disciplines / 3. Buddhism
7900 Speak the truth, yield not to anger, give what you can to him who asks [Anon (Dham)]