Combining Texts

All the ideas for 'Defending the Axioms', 'Aristotle on Substance' and 'fragments/reports'

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12 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 / C. Structure of Objects / 3. Matter of an Object
16083 Aristotelian matter seriously threatens the intrinsic unity and substantiality of its object [Gill,ML]
23. Ethics / C. Virtue Theory / 2. Elements of Virtue Theory / e. Character
541 Virtue comes more from habit than character [Critias]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / b. Prime matter
17006 Prime matter has no place in Aristotle's theories, and passages claiming it are misread [Gill,ML]
16093 Prime matter is actually nothing and potentially everything (or potentially an element) [Gill,ML]
28. God / C. Attitudes to God / 5. Atheism
542 Fear of the gods was invented to discourage secret sin [Critias]