Combining Texts

All the ideas for 'Two Problems of Epistemology', 'The Art of the Infinite' and 'Reality without Reference'

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12 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]
14. Science / A. Basis of Science / 6. Falsification
Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper]
14. Science / C. Induction / 3. Limits of Induction
The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan]
19. Language / A. Nature of Meaning / 1. Meaning
A minimum requirement for a theory of meaning is that it include an account of truth [Davidson]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
A theory of truth tells us how communication by language is possible [Davidson]
19. Language / B. Reference / 1. Reference theories
Is reference the key place where language and the world meet? [Davidson]
With a holistic approach, we can give up reference in empirical theories of language [Davidson]
19. Language / B. Reference / 4. Descriptive Reference / b. Reference by description
To explain the reference of a name, you must explain its sentence-role, so reference can't be defined nonlinguistically [Davidson]