Combining Texts

All the ideas for 'Transworld Identity or worldbound Individuals?', 'Epistemic Justification' and 'The Art of the Infinite'

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15 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]
10. Modality / E. Possible worlds / 1. Possible Worlds / a. Possible worlds
Asserting a possible property is to say it would have had the property if that world had been actual [Plantinga]
10. Modality / E. Possible worlds / 2. Nature of Possible Worlds / a. Nature of possible worlds
A possible world is a maximal possible state of affairs [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / a. Transworld identity
If possible Socrates differs from actual Socrates, the Indiscernibility of Identicals says they are different [Plantinga]
It doesn't matter that we can't identify the possible Socrates; we can't identify adults from baby photos [Plantinga]
If individuals can only exist in one world, then they can never lack any of their properties [Plantinga]
10. Modality / E. Possible worlds / 3. Transworld Objects / c. Counterparts
The counterparts of Socrates have self-identity, but only the actual Socrates has identity-with-Socrates [Plantinga]
Counterpart Theory absurdly says I would be someone else if things went differently [Plantinga]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
'Access' internalism says responsibility needs access; weaker 'mentalism' needs mental justification [Kvanvig]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / a. Foundationalism
Strong foundationalism needs strict inferences; weak version has induction, explanation, probability [Kvanvig]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]