Combining Texts

All the ideas for 'Things and Their Parts', 'Letters to Oldenburg' and 'The Art of the Infinite'

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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]
4. Formal Logic / G. Formal Mereology / 1. Mereology
13331 Part and whole contribute asymmetrically to one another, so must differ [Fine,K]
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 / B. Unity of Objects / 1. Unifying an Object / c. Unity as conceptual
13332 Hierarchical set membership models objects better than the subset or aggregate relations do [Fine,K]
9. Objects / C. Structure of Objects / 3. Matter of an Object
13333 The matter is a relatively unstructured version of the object, like a set without membership structure [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects
13326 A 'temporary' part is a part at one time, but may not be at another, like a carburetor [Fine,K]
13327 A 'timeless' part just is a part, not a part at some time; some atoms are timeless parts of a water molecule [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / b. Sums of parts
13329 An 'aggregative' sum is spread in time, and exists whenever a component exists [Fine,K]
13330 An 'compound' sum is not spread in time, and only exists when all the components exists [Fine,K]
9. Objects / C. Structure of Objects / 8. Parts of Objects / c. Wholes from parts
13328 Two sorts of whole have 'rigid embodiment' (timeless parts) or 'variable embodiment' (temporary parts) [Fine,K]
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 / A. Ethics Foundations / 1. Nature of Ethics / f. Ethical non-cognitivism
4867 Whether nature is beautiful or orderly is entirely in relation to human imagination [Spinoza]
28. God / A. Divine Nature / 3. Divine Perfections
4866 God is a being with infinite attributes, each of them infinite or perfect [Spinoza]
28. God / B. Proving God / 3. Proofs of Evidence / e. Miracles
4868 Trying to prove God's existence through miracles is proving the obscure by the more obscure [Spinoza]