Combining Texts

All the ideas for 'Mathematics and Philosophy: grand and little', 'The Art of the Infinite' and 'The Absurd'

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15 ideas

1. Philosophy / D. Nature of Philosophy / 1. Philosophy

3269	If your life is to be meaningful as part of some large thing, the large thing must be meaningful [Nagel]

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / e. Philosophy as reason

9808	Philosophy aims to reveal the grandeur of mathematics [Badiou]

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 / 1. Mathematics

9812	In mathematics, if a problem can be formulated, it will eventually be solved [Badiou]

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]

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

9813	Mathematics shows that thinking is not confined to the finite [Badiou]

7. Existence / A. Nature of Existence / 3. Being / a. Nature of Being

9809	Mathematics inscribes being as such [Badiou]

7. Existence / A. Nature of Existence / 6. Criterion for Existence

9811	It is of the essence of being to appear [Badiou]

13. Knowledge Criteria / C. External Justification / 8. Social Justification

3270	Justifications come to an end when we want them to [Nagel]

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

15713

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

21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature

9814	All great poetry is engaged in rivalry with mathematics [Badiou]

23. Ethics / F. Existentialism / 2. Nihilism

3268	If a small brief life is absurd, then so is a long and large one [Nagel]