Combining Texts

All the ideas for 'Defending the Axioms', 'God in Plato' and 'Reality is Not What it Seems'

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23 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / c. Classical philosophy
23889 Among the Greeks Aristotle is the only philosopher in the modern style [Weil]
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]
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 / 4. Paradoxes in Logic / a. Achilles paradox
20457 Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli]
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]
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 / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / B. Change in Existence / 2. Processes
20468 Quantum mechanics deals with processes, rather than with things [Rovelli]
7. Existence / B. Change in Existence / 4. Events / b. Events as primitive
20467 Quantum mechanics describes the world entirely as events [Rovelli]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
20469 There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
20461 The basic ideas of fields and particles are merged in quantum mechanics [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / b. Fields
20462 Because it is quantised, a field behaves like a set of packets of energy [Rovelli]
20463 There are about fifteen particles fields, plus a few force fields [Rovelli]
20464 The world consists of quantum fields, with elementary events happening in spacetime [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / c. Electrons
20459 Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli]
20460 Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
20466 Quantum Theory describes events and possible interactions - not how things are [Rovelli]
27. Natural Reality / B. Modern Physics / 4. Standard Model / a. Concept of matter
20465 Nature has three aspects: granularity, indeterminacy, and relations [Rovelli]
27. Natural Reality / C. Space / 4. Substantival Space
20458 The world is just particles plus fields; space is the gravitational field [Rovelli]
27. Natural Reality / D. Time / 2. Passage of Time / g. Time's arrow
20470 Only heat distinguishes past from future [Rovelli]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
23892 The only legitimate proof of God by order derives from beauty [Weil]