Combining Texts

All the ideas for 'Explaining the A Priori', 'Freedom and Action' 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]
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 / D. Concepts / 2. Origin of Concepts / a. Origin of concepts
17722 The concept 'red' is tied to what actually individuates red things [Peacocke]
20. Action / A. Definition of Action / 1. Action Theory
20062 If a desire leads to a satisfactory result by an odd route, the causal theory looks wrong [Chisholm]
20. Action / B. Preliminaries of Action / 2. Willed Action / c. Agent causation
20054 There has to be a brain event which is not caused by another event, but by the agent [Chisholm]