Combining Texts

All the ideas for 'Grounding, Transitivity and Contrastivity', 'fragments/reports' and 'Believing the Axioms I'

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17 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
13011 New axioms are being sought, to determine the size of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / b. Axiom of Extensionality I
13014 Extensional sets are clearer, simpler, unique and expressive [Maddy]
13013 The Axiom of Extensionality seems to be analytic [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / f. Axiom of Infinity V
13021 The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy]
13022 Infinite sets are essential for giving an account of the real numbers [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / g. Axiom of Powers VI
13023 The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
13024 Efforts to prove the Axiom of Choice have failed [Maddy]
13025 Modern views say the Choice set exists, even if it can't be constructed [Maddy]
13026 A large array of theorems depend on the Axiom of Choice [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / e. Iterative sets
13019 The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy]
4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
13018 Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
17306 If ground is transitive and irreflexive, it has a strict partial ordering, giving structure [Schaffer,J]
17304 As causation links across time, grounding links the world across levels [Schaffer,J]
13. Knowledge Criteria / D. Scepticism / 3. Illusion Scepticism
2667 A false object might give the same presentation as a true one [Arcesilaus, by Cicero]
14. Science / D. Explanation / 2. Types of Explanation / b. Contrastive explanations
17308 Explaining 'Adam ate the apple' depends on emphasis, and thus implies a contrast [Schaffer,J]
26. Natural Theory / A. Speculations on Nature / 1. Nature
17305 I take what is fundamental to be the whole spatiotemporal manifold and its fields [Schaffer,J]
26. Natural Theory / C. Causation / 1. Causation
17307 Nowadays causation is usually understood in terms of equations and variable ranges [Schaffer,J]