Combining Texts

All the ideas for 'Defending the Axioms', 'The Book of Chuang Tzu' and 'What is Cantor's Continuum Problem?'

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28 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)]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
7289 Do not try to do things, or to master knowledge; just be empty [Zhuangzi (Chuang Tzu)]
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)]
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)]