Combining Texts

All the ideas for 'Defending the Axioms', 'Conditional Assertion and Restricted Quantification' and 'Abstract Entities'

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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]
7. Existence / A. Nature of Existence / 4. Abstract Existence
14592 Some abstract things have a beginning and end, so may exist in time (though not space) [Swoyer]
7. Existence / D. Theories of Reality / 1. Ontologies
14594 Ontologists seek existence and identity conditions, and modal and epistemic status for a thing [Swoyer]
8. Modes of Existence / B. Properties / 1. Nature of Properties
14595 Can properties exemplify other properties? [Swoyer]
9. Objects / A. Existence of Objects / 5. Simples
14593 Quantum field theory suggests that there are, fundamentally, no individual things [Swoyer]
14. Science / C. Induction / 5. Paradoxes of Induction / b. Raven paradox
19000 Read 'all ravens are black' as about ravens, not as about an implication [Belnap]