Combining Texts

All the ideas for 'Defending the Axioms', 'Schopenhauer' and 'Conjectures and Refutations'

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13 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]
9. Objects / D. Essence of Objects / 11. Essence of Artefacts
12177 Human artefacts may have essences, in their purposes [Popper]
11. Knowledge Aims / C. Knowing Reality / 3. Idealism / d. Absolute idealism
21912 Fichte, Schelling and Hegel rejected transcendental idealism [Lewis,PB]
21911 Fichte, Hegel and Schelling developed versions of Absolute Idealism [Lewis,PB]
14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation
12176 Science does not aim at ultimate explanations [Popper]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / a. Scientific essentialism
12175 Galilean science aimed at true essences, as the ultimate explanations [Popper]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
12179 Essentialist views of science prevent further questions from being raised [Popper]