Combining Philosophers

All the ideas for William Crathorn, R Feldman / E Conee and R Kaplan / E Kaplan

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11 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
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
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
The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / f. Arithmetic
'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan]
'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan]
11. Knowledge Aims / A. Knowledge / 4. Belief / a. Beliefs
Involuntary beliefs can still be evaluated [Feldman/Conee]
13. Knowledge Criteria / B. Internal Justification / 3. Evidentialism / b. Evidentialism
Evidentialism is the view that justification is determined by the quality of the evidence [Feldman/Conee]
Beliefs should fit evidence, and if you ought to believe it, then you are justified [Feldman/Conee]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
If someone rejects good criticism through arrogance, that is irrelevant to whether they have knowledge [Feldman/Conee]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
27. Natural Reality / D. Time / 1. Nature of Time / e. Eventless time
Time is independent of motion, because God could stop everything for a short or long time [Crathorn, by Pasnau]