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All the ideas for 'Must We Believe in Set Theory?st1=George Boolos', 'works' and 'works'

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22 ideas

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]
7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being
22121 The concept of being has only one meaning, whether talking of universals or of God [Duns Scotus, by Dumont]
22122 Being (not sensation or God) is the primary object of the intellect [Duns Scotus, by Dumont]
8. Modes of Existence / D. Universals / 1. Universals
10488 It is lunacy to think we only see ink-marks, and not word-types [Boolos]
8. Modes of Existence / D. Universals / 4. Uninstantiated Universals
22125 Duns Scotus was a realist about universals [Duns Scotus, by Dumont]
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]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
22127 Scotus said a substantial principle of individuation [haecceitas] was needed for an essence [Duns Scotus, by Dumont]
9. Objects / D. Essence of Objects / 2. Types of Essence
22126 Avicenna and Duns Scotus say essences have independent and prior existence [Duns Scotus, by Dumont]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
22129 Certainty comes from the self-evident, from induction, and from self-awareness [Duns Scotus, by Dumont]
11. Knowledge Aims / C. Knowing Reality / 1. Perceptual Realism / b. Direct realism
22130 Scotus defended direct 'intuitive cognition', against the abstractive view [Duns Scotus, by Dumont]
12. Knowledge Sources / A. A Priori Knowledge / 2. Self-Evidence
22128 Augustine's 'illumination' theory of knowledge leads to nothing but scepticism [Duns Scotus, by Dumont]
16. Persons / F. Free Will / 2. Sources of Free Will
22131 The will retains its power for opposites, even when it is acting [Duns Scotus, by Dumont]
22. Metaethics / A. Ethics Foundations / 2. Source of Ethics / e. Human nature
4366 We can't accept Aristotle's naturalism about persons, because it is normative and unscientific [Williams,B, by Hursthouse]
28. God / A. Divine Nature / 2. Divine Nature
22123 The concept of God is the unique first efficient cause, final cause, and most eminent being [Duns Scotus, by Dumont]
28. God / B. Proving God / 3. Proofs of Evidence / a. Cosmological Proof
22124 We can't infer the infinity of God from creation ex nihilo [Duns Scotus, by Dumont]