Combining Texts

All the ideas for 'Defending the Axioms', 'On the Very Idea of a Third Dogma' and 'Philosophy'

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10 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]
11. Knowledge Aims / A. Knowledge / 7. Knowledge First
23888 Knowledge is beyond question, as an unavoidable component of thinking [Weil]
19. Language / F. Communication / 6. Interpreting Language / a. Translation
19045 Translation is too flimsy a notion to support theories of cultural incommensurability [Quine]
21. Aesthetics / B. Nature of Art / 1. Defining Art
23887 Art (like philosophy) establishes a relation between world and self, and between oneself and others [Weil]