Combining Texts

All the ideas for 'fragments/reports', 'Letters to Johann Bernoulli' and 'The Art of the Infinite'

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15 ideas

1. Philosophy / B. History of Ideas / 2. Ancient Thought
Thales was the first western thinker to believe the arché was intelligible [Roochnik on Thales]
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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
A piece of flint contains something resembling perceptions and appetites [Leibniz]
Entelechies are analogous to souls, as other minds are analogous to our own minds [Leibniz]
10. Modality / C. Sources of Modality / 5. Modality from Actuality
Nothing is stronger than necessity, which rules everything [Thales, by Diog. Laertius]
10. Modality / D. Knowledge of Modality / 4. Conceivable as Possible / c. Possible but inconceivable
What we cannot imagine may still exist [Leibniz]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
22. Metaethics / B. Value / 2. Values / e. Death
Death is just the contraction of an animal [Leibniz]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
Thales said water is the first principle, perhaps from observing that food is moist [Thales, by Aristotle]
27. Natural Reality / A. Classical Physics / 1. Mechanics / a. Explaining movement
Thales must have thought soul causes movement, since he thought magnets have soul [Thales, by Aristotle]
29. Religion / A. Polytheistic Religion / 2. Greek Polytheism
Thales said the gods know our wrong thoughts as well as our evil actions [Thales, by Diog. Laertius]