Combining Texts

All the ideas for 'Reportatio', 'Practical Necessity' and 'The Art of the Infinite'

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9 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]

10. Modality / A. Necessity / 10. Impossibility

23283

Necessity implies possibility, but in experience it matters which comes first [Williams,B]

14. Science / C. Induction / 3. Limits of Induction

15713

The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]

28. God / A. Divine Nature / 3. Divine Perfections

9111	God is not wise, but more-than-wise; God is not good, but more-than-good [William of Ockham]

28. God / C. Attitudes to God / 4. God Reflects Humanity

9112	We could never form a concept of God's wisdom if we couldn't abstract it from creatures [William of Ockham]