Combining Texts

All the ideas for 'fragments/reports', 'The Book of Chuang Tzu' and 'Thinking About Mathematics'

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31 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
7278 Words of wisdom are precise and clear [Zhuangzi (Chuang Tzu)]
1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
7281 Don't even start, let's just stay put [Zhuangzi (Chuang Tzu)]
2. Reason / C. Styles of Reason / 1. Dialectic
7282 Disagreement means you do not understand at all [Zhuangzi (Chuang Tzu)]
2. Reason / C. Styles of Reason / 3. Eristic
7284 If you beat me in argument, does that mean you are right? [Zhuangzi (Chuang Tzu)]
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 / A. Knowledge / 1. Knowledge
7289 Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8725 Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro]
13. Knowledge Criteria / D. Scepticism / 5. Dream Scepticism
23403 You know you were dreaming when you wake, but there might then be a greater awakening from that [Zhuangzi (Chuang Tzu)]
7285 Did Chuang Tzu dream he was a butterfly, or a butterfly dream he was Chuang Tzu? [Zhuangzi (Chuang Tzu)]
16. Persons / E. Rejecting the Self / 4. Denial of the Self
7277 The perfect man has no self [Zhuangzi (Chuang Tzu)]
7286 To see with true clarity, your self must be irrelevant [Zhuangzi (Chuang Tzu)]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
7279 If words can't be defined, they may just be the chirruping of chicks [Zhuangzi (Chuang Tzu)]
19. Language / D. Propositions / 4. Mental Propositions
23404 Words are for meaning, and once you have that you can forget the words [Zhuangzi (Chuang Tzu)]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
7283 Great courage is not violent [Zhuangzi (Chuang Tzu)]
27. Natural Reality / G. Biology / 2. Life
7280 As all life is one, what need is there for words? [Zhuangzi (Chuang Tzu)]
29. Religion / C. Spiritual Disciplines / 2. Taoism
7288 Go with the flow, and be one with the void of Heaven [Zhuangzi (Chuang Tzu)]
7287 Fish forget about each other in the pond and forget each other in the Tao [Zhuangzi (Chuang Tzu)]