Combining Texts

All the ideas for 'Defending the Axioms', 'Aristotle on Substance' and 'The Scientific Image'

expand these ideas     |    start again     |     specify just one area for these texts

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]
10. Modality / B. Possibility / 7. Chance
23900 Chance is compatible with necessity, and the two occur together [Weil]
21. Aesthetics / A. Aesthetic Experience / 4. Beauty
23899 The secret of art is that beauty is a just blend of unity and its opposite [Weil]
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]