Combining Texts

All the ideas for 'Symposium', 'The Art of the Infinite' and 'Deriving Kripkean Claims with Abstract Objects'

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

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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]

9. Objects / A. Existence of Objects / 2. Abstract Objects / a. Nature of abstracta

10558

Abstract objects are actually constituted by the properties by which we conceive them [Zalta]

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

15713

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

18. Thought / E. Abstraction / 2. Abstracta by Selection

10557

Abstract objects are captured by second-order modal logic, plus 'encoding' formulas [Zalta]

22. Metaethics / B. Value / 2. Values / h. Fine deeds

5845	Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon]