Combining Texts

All the ideas for 'Defending the Axioms', 'On Medical Experience' and 'The Analytic/Synthetic Distinction'

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17 ideas

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]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
20298 The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey]
19. Language / A. Nature of Meaning / 8. Synonymy
20300 Externalist synonymy is there being a correct link to the same external phenomena [Rey]
19. Language / E. Analyticity / 1. Analytic Propositions
20293 Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey]
20294 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey]
20297 Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey]
20301 The meaning properties of a term are those which explain how the term is typically used [Rey]
20302 An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey]
20303 Research throws doubts on the claimed intuitions which support analyticity [Rey]
19. Language / E. Analyticity / 4. Analytic/Synthetic Critique
20299 If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / f. The Mean
7453 Galen's medicine followed the mean; each illness was balanced by opposite treatment [Galen, by Hacking]