Combining Texts

All the ideas for 'Idealism: a critical survey', 'The Art of the Infinite' and 'works'

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18 ideas

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]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / b. Pro-coherentism
We can no more expect a precise definition of coherence than we can of the moral ideal [Ewing]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
If undetailed, 'coherence' is just a vague words that covers all possible arguments [Ewing]
14. Science / B. Scientific Theories / 3. Instrumentalism
Special relativity, unlike general relativity, was operationalist in spirit [Putnam on Einstein]
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 / C. Causation / 1. Causation
Einstein took causation to be the bedrock of physics [Einstein, by Coveney/Highfield]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
General relativity assumes laws of nature are the same in all frames of reference [Einstein, by Close]
27. Natural Reality / A. Classical Physics / 1. Mechanics / d. Gravity
Newton is a special case of Einstein's general theory, with an infinite speed of light [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 1. Relativity / a. Special relativity
The theory is 'special' because it sticks to observers moving straight, at constant speeds [Einstein, by Farmelo]
Assume the speed of light is constant for all observers, and the laws of physics are the same [Einstein, by Farmelo]
27. Natural Reality / B. Modern Physics / 1. Relativity / b. General relativity
General Relativity says there is no absolute force or acceleration [Einstein, by Close]
27. Natural Reality / B. Modern Physics / 4. Standard Model / d. Mass
Mass is a measure of energy content [Einstein]
27. Natural Reality / C. Space / 6. Space-Time
Space-time arises from the connection between measurements of space and of time [Einstein, by Farmelo]
28. God / C. Attitudes to God / 5. Atheism
I do not believe in a personal God [Einstein]