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All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'Reductive Theories of Modality' and 'Notebooks'

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26 ideas

1. Philosophy / A. Wisdom / 3. Wisdom Deflated
8093 Seek wisdom rather than truth; it is easier [Joubert]
1. Philosophy / D. Nature of Philosophy / 1. Philosophy
8095 We must think with our entire body and soul [Joubert]
1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
9218 Maybe what distinguishes philosophy from science is its pursuit of necessary truths [Sider]
1. Philosophy / E. Nature of Metaphysics / 2. Possibility of Metaphysics
8107 The love of certainty holds us back in metaphysics [Joubert]
2. Reason / A. Nature of Reason / 9. Limits of Reason
8099 The truths of reason instruct, but they do not illuminate [Joubert]
3. Truth / A. Truth Problems / 1. Truth
8098 Truth consists of having the same idea about something that God has [Joubert]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
10482 The logic of ZF is classical first-order predicate logic with identity [Boolos]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10492 A few axioms of set theory 'force themselves on us', but most of them don't [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / d. Naïve logical sets
10485 Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
10484 The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
10491 Infinite natural numbers is as obvious as infinite sentences in English [Boolos]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / f. Uncountable infinities
10483 Mathematics and science do not require very high orders of infinity [Boolos]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / a. For mathematical platonism
10490 Mathematics isn't surprising, given that we experience many objects as abstract [Boolos]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta
10487 I am a fan of abstract objects, and confident of their existence [Boolos]
9. Objects / A. Existence of Objects / 2. Abstract Objects / c. Modern abstracta
10489 We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8101 To know is to see inside oneself [Joubert]
15. Nature of Minds / C. Capacities of Minds / 2. Imagination
8094 The imagination has made more discoveries than the eye [Joubert]
18. Thought / A. Modes of Thought / 1. Thought
8103 A thought is as real as a cannon ball [Joubert]
18. Thought / D. Concepts / 2. Origin of Concepts / c. Nativist concepts
8100 Where does the bird's idea of a nest come from? [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / b. Types of pleasure
8096 He gives his body up to pleasure, but not his soul [Joubert]
22. Metaethics / C. The Good / 3. Pleasure / c. Value of pleasure
8104 What will you think of pleasures when you no longer enjoy them? [Joubert]
23. Ethics / C. Virtue Theory / 1. Virtue Theory / b. Basis of virtue
8097 Virtue is hard if we are scorned; we need support [Joubert]
25. Social Practice / E. Policies / 5. Education / a. Aims of education
8106 In raising a child we must think of his old age [Joubert]
28. God / A. Divine Nature / 6. Divine Morality / c. God is the good
8105 We can't exactly conceive virtue without the idea of God [Joubert]
29. Religion / B. Monotheistic Religion / 4. Christianity / a. Christianity
8102 We cannot speak against Christianity without anger, or speak for it without love [Joubert]