Combining Texts

All the ideas for 'A Résumé of Metaphysics', 'The Art of the Infinite' and 'Ordinatio'

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17 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
15717 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
15712 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
15711 The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
15714 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
15715 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
8. Modes of Existence / B. Properties / 1. Nature of Properties
16648 Accidents must have formal being, if they are principles of real action, and of mental action and thought [Duns Scotus]
8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism
15386 If only the singular exists, science is impossible, as that relies on true generalities [Duns Scotus, by Panaccio]
15387 If things were singular they would only differ numerically, but horse and tulip differ more than that [Duns Scotus, by Panaccio]
9. Objects / A. Existence of Objects / 5. Individuation / a. Individuation
16632 We distinguish one thing from another by contradiction, because this is, and that is not [Duns Scotus]
9. Objects / A. Existence of Objects / 5. Individuation / d. Individuation by haecceity
13094 The haecceity is the featureless thing which gives ultimate individuality to a substance [Duns Scotus, by Cover/O'Leary-Hawthorne]
9. Objects / B. Unity of Objects / 1. Unifying an Object / b. Unifying aggregates
16770 It is absurd that there is no difference between a genuinely unified thing, and a mere aggregate [Duns Scotus]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
10919 What prevents a stone from being divided into parts which are still the stone? [Duns Scotus]
9. Objects / F. Identity among Objects / 8. Leibniz's Law
16768 Two things are different if something is true of one and not of the other [Duns Scotus]
14. Science / C. Induction / 3. Limits of Induction
15713 The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
22. Metaethics / C. The Good / 3. Pleasure / a. Nature of pleasure
5049 Intelligent pleasure is the perception of beauty, order and perfection [Leibniz]
28. God / A. Divine Nature / 3. Divine Perfections
5048 Perfection is simply quantity of reality [Leibniz]
29. Religion / D. Religious Issues / 3. Problem of Evil / b. Human Evil
5050 Evil serves a greater good, and pain is necessary for higher pleasure [Leibniz]