Combining Texts

All the ideas for 'Laches', 'On the Ultimate Origination of Things' and 'The Art of the Infinite'

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15 ideas

1. Philosophy / A. Wisdom / 1. Nature of Wisdom
Wisdom involves the desire to achieve perfection [Leibniz]
1. Philosophy / A. Wisdom / 3. Wisdom Deflated
Don't assume that wisdom is the automatic consequence of old age [Plato]
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 / A. Nature of Existence / 5. Reason for Existence
Leibniz first asked 'why is there something rather than nothing?' [Leibniz, by Jacquette]
There must be a straining towards existence in the essence of all possible things [Leibniz]
Because something does exist, there must be a drive in possible things towards existence [Leibniz]
10. Modality / A. Necessity / 7. Natural Necessity
The world is physically necessary, as its contrary would imply imperfection or moral absurdity [Leibniz]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
20. Action / C. Motives for Action / 3. Acting on Reason / a. Practical reason
We follow the practical rule which always seeks maximum effect for minimum cost [Leibniz]
23. Ethics / C. Virtue Theory / 3. Virtues / d. Courage
Being unafraid (perhaps through ignorance) and being brave are two different things [Plato]
26. Natural Theory / A. Speculations on Nature / 1. Nature
The principle of determination in things obtains the greatest effect with the least effort [Leibniz]