Combining Texts

All the ideas for '27: Book of Daniel', 'Must We Believe in Set Theory?' and 'Philosophy of Science: Very Short Intro (2nd ed)'

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21 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 / C. Structure of Existence / 2. Reduction
22180 Multiple realisability is said to make reduction impossible [Okasha]
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]
14. Science / A. Basis of Science / 3. Experiment
22177 Randomised Control Trials have a treatment and a control group, chosen at random [Okasha]
22172 Not all sciences are experimental; astronomy relies on careful observation [Okasha]
14. Science / A. Basis of Science / 6. Falsification
22174 The discoverers of Neptune didn't change their theory because of an anomaly [Okasha]
22175 Science mostly aims at confirming theories, rather than falsifying them [Okasha]
14. Science / B. Scientific Theories / 1. Scientific Theory
22182 Theories with unobservables are underdetermined by the evidence [Okasha]
14. Science / B. Scientific Theories / 5. Commensurability
22185 Two things can't be incompatible if they are incommensurable [Okasha]
14. Science / C. Induction / 1. Induction
22176 Induction is inferences from examined to unexamined instances of a given kind [Okasha]
14. Science / C. Induction / 6. Bayes's Theorem
22178 If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha]
27. Natural Reality / A. Classical Physics / 1. Mechanics / b. Laws of motion
22173 Galileo refuted the Aristotelian theory that heavier objects fall faster [Okasha]
29. Religion / D. Religious Issues / 2. Immortality / a. Immortality
7482 Resurrection developed in Judaism as a response to martyrdoms, in about 160 BCE [Anon (Dan), by Watson]