Combining Texts

All the ideas for 'Two Problems of Epistemology', 'The Art of the Infinite' and 'The Character of Physical Law'

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11 ideas

1. Philosophy / D. Nature of Philosophy / 7. Despair over Philosophy
People generalise because it is easier to understand, and that is mistaken for deep philosophy [Feynman]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / g. Real numbers
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
14. Science / A. Basis of Science / 6. Falsification
Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
Physical Laws are rhythms and patterns in nature, revealed by analysis [Feynman]
27. Natural Reality / B. Modern Physics / 2. Electrodynamics / d. Quantum mechanics
Nobody understands quantum mechanics [Feynman]
27. Natural Reality / C. Space / 3. Points in Space
We should regard space as made up of many tiny pieces [Feynman, by Mares]