Combining Texts

All the ideas for 'Dialektik', 'On Carnap's Views on Ontology' and 'The Art of the Infinite'

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11 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
Quine rejects Carnap's view that science and philosophy are distinct [Quine, by Boulter]
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]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
Names have no ontological commitment, because we can deny that they name anything [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / b. Commitment of quantifiers
We can use quantification for commitment to unnameable things like the real numbers [Quine]
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 / E. Analyticity / 3. Analytic and Synthetic
Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
Concepts are only analytic once the predicate is absorbed into the subject [Schleiermacher]