Combining Texts

All the ideas for 'Aristotle on Matter', 'Particulars in Particular Clothing' and 'What is Cantor's Continuum Problem?'

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13 ideas

2. Reason / D. Definition / 4. Real Definition
12302 Definitions formed an abstract hierarchy for Aristotle, as sets do for us [Fine,K]
2. Reason / D. Definition / 5. Genus and Differentia
14266 Aristotle sees hierarchies in definitions using genus and differentia (as we see them in sets) [Fine,K]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
8679 We perceive the objects of set theory, just as we perceive with our senses [Gödel]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / o. Axiom of Constructibility V = L
9942 Gödel proved the classical relative consistency of the axiom V = L [Gödel, by Putnam]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / a. Set theory paradoxes
18062 Set-theory paradoxes are no worse than sense deception in physics [Gödel]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / g. Continuum Hypothesis
10868 The Continuum Hypothesis is not inconsistent with the axioms of set theory [Gödel, by Clegg]
13517 If set theory is consistent, we cannot refute or prove the Continuum Hypothesis [Gödel, by Hart,WD]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism
10271 Basic mathematics is related to abstract elements of our empirical ideas [Gödel]
7. Existence / C. Structure of Existence / 1. Grounding / c. Grounding and explanation
14268 Maybe bottom-up grounding shows constitution, and top-down grounding shows essence [Fine,K]
8. Modes of Existence / B. Properties / 13. Tropes / a. Nature of tropes
18431 Internal relations combine some tropes into a nucleus, which bears the non-essential tropes [Simons, by Edwards]
9. Objects / C. Structure of Objects / 6. Constitution of an Object
14267 There is no distinctive idea of constitution, because you can't say constitution begins and ends [Fine,K]
14264 Is there a plausible Aristotelian notion of constitution, applicable to both physical and non-physical? [Fine,K]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / a. Greek matter
14265 The components of abstract definitions could play the same role as matter for physical objects [Fine,K]