Combining Texts

All the ideas for 'fragments/reports', 'Must We Believe in Set Theory?' and 'Theories of Everything'

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29 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]
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]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / b. Heat
20624 Work degrades into heat, but not vice versa [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / c. Conservation of energy
20623 First Law: energy can change form, but is conserved overall [Close]
27. Natural Reality / A. Classical Physics / 2. Thermodynamics / d. Entropy
20625 Third Law: total order and minimum entropy only occurs at absolute zero [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
20622 All motions are relative and ambiguous, but acceleration is the same in all inertial frames [Close]
20628 The electric and magnetic are tightly linked, and viewed according to your own motion [Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
20635 The general relativity equations relate curvature in space-time to density of energy-momentum [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / a. Electrodynamics
20642 Photon exchange drives the electro-magnetic force [Close]
20627 Electric fields have four basic laws (two by Gauss, one by Ampère, one by Faraday) [Close]
20630 Light isn't just emitted in quanta called photons - light is photons [Close]
20637 In general relativity the energy and momentum of photons subjects them to gravity [Close]
20629 Electro-magnetic waves travel at light speed - so light is electromagnetism! [Close]
20632 In QED, electro-magnetism exists in quantum states, emitting and absorbing electrons [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
20639 Quantum fields contain continual rapid creation and disappearance [Close]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
20641 Electrons get their mass by interaction with the Higgs field [Close]
20631 Dirac showed how electrons conform to special relativity [Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
20626 Modern theories of matter are grounded in heat, work and energy [Close]
27. Natural Reality / B. Modern Physics / 5. Unified Models / a. Electro-weak unity
20633 The Higgs field is an electroweak plasma - but we don't know what stuff it consists of [Close]
27. Natural Reality / C. Space / 6. Space-Time
20640 Space-time is indeterminate foam over short distances [Close]