Combining Texts

All the ideas for 'Defending the Axioms', 'Vindication of Religion (extract)' and 'Possible Worlds and Necessary A Posteriori'

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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 / D. Essence of Objects / 9. Essence and Properties
14633 How do we tell a table's being contingently plastic from its being essentially plastic? [Jackson]
14635 An x is essentially F if it is F in every possible world in which it appears [Jackson]
9. Objects / D. Essence of Objects / 15. Against Essentialism
14632 Quine may have conflated de re and de dicto essentialism, but there is a real epistemological problem [Jackson]
10. Modality / D. Knowledge of Modality / 3. A Posteriori Necessary
14631 How can you show the necessity of an a posteriori necessity, if it might turn out to be false? [Jackson]
23. Ethics / C. Virtue Theory / 3. Virtues / h. Respect
1460 Religious experience deserves the same respect as our other key experiences, and is best called 'holy' [Taylor,AE, by PG]