Combining Texts

All the ideas for 'Defending the Axioms', 'Perceptual experience has conceptual content' and 'On Carnap's Views on Ontology'

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12 ideas

1. Philosophy / E. Nature of Metaphysics / 4. Metaphysics as Science
22153 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
17610 The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy]
5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
17620 Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
17605 Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy]
17625 If two mathematical themes coincide, that suggest a single deep truth [Maddy]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
17615 Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
17618 Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
17614 The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / a. Ontological commitment
19485 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
19486 We can use quantification for commitment to unnameable things like the real numbers [Quine]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8875 Sense experiences must have conceptual content, since they are possible reasons for judgements [Brewer,B]
19. Language / E. Analyticity / 3. Analytic and Synthetic
19487 Without the analytic/synthetic distinction, Carnap's ontology/empirical distinction collapses [Quine]