Combining Texts

All the ideas for 'fragments/reports', 'New System and Explanation of New System' and 'The Art of the Infinite'

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11 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]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
Reality must be made of basic unities, which will be animated, substantial points [Leibniz]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
15. Nature of Minds / A. Nature of Mind / 5. Unity of Mind
No machine or mere organised matter could have a unified self [Leibniz]
17. Mind and Body / A. Mind-Body Dualism / 5. Parallelism
The soul does know bodies, although they do not influence one another [Leibniz]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / c. Ultimate substances
For Anaximenes nature is air, which takes different forms by rarefaction and condensation [Anaximenes, by Simplicius]
27. Natural Reality / G. Biology / 2. Life
To regard animals as mere machines may be possible, but seems improbable [Leibniz]