Combining Texts

All the ideas for 'fragments/reports', 'Defending the Axioms' and 'Two Notions of Being: Entity and Essence'

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15 ideas

1. Philosophy / E. Nature of Metaphysics / 3. Metaphysical Systems
13917 Metaphysics aims to identify categories of being, and show their interdependency [Lowe]
1. Philosophy / E. Nature of Metaphysics / 6. Metaphysics as Conceptual
13919 Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe]
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 / B. Unity of Objects / 3. Unity Problems / d. Coincident objects
13918 Holes, shadows and spots of light can coincide without being identical [Lowe]
9. Objects / D. Essence of Objects / 8. Essence as Explanatory
13921 All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe]
9. Objects / D. Essence of Objects / 14. Knowledge of Essences
13922 Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe]
9. Objects / E. Objects over Time / 8. Continuity of Rivers
579 Cratylus said you couldn't even step into the same river once [Cratylus, by Aristotle]
9. Objects / F. Identity among Objects / 4. Type Identity
13920 Each thing has to be of a general kind, because it belongs to some category [Lowe]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
578 Cratylus decided speech was hopeless, and his only expression was the movement of a finger [Cratylus, by Aristotle]