Combining Texts

All the ideas for 'Space and Time', 'works' and 'The Art of the Infinite'

expand these ideas     |    start again     |     specify just one area for these texts

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9 ideas

4. Formal Logic / D. Modal Logic ML / 3. Modal Logic Systems / h. System S5

7791	The simplest of the logics based on possible worlds is Lewis's S5 [Lewis,CI, by Girle]

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 / 2. Nature of Necessity

11002

Equating necessity with informal provability is the S4 conception of necessity [Lewis,CI, by Read]

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

15713

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

27. Natural Reality / C. Space / 6. Space-Time

14014

Space alone, and time alone, will fade away, and only their union has an independent reality [Minkowski]