Combining Texts

All the ideas for 'fragments/reports', 'Believing the Axioms I' and 'Relations'

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19 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
13013 The Axiom of Extensionality seems to be analytic [Maddy]
13014 Extensional sets are clearer, simpler, unique and expressive [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]
8. Modes of Existence / A. Relations / 1. Nature of Relations
21339 We want the ontology of relations, not just a formal way of specifying them [Heil]
21349 Two people are indirectly related by height; the direct relation is internal, between properties [Heil]
21340 Maybe all the other features of the world can be reduced to relations [Heil]
8. Modes of Existence / A. Relations / 2. Internal Relations
21348 In the case of 5 and 6, their relational truthmaker is just the numbers [Heil]
21351 Truthmaking is a clear example of an internal relation [Heil]
21344 If R internally relates a and b, and you have a and b, you thereby have R [Heil]
8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence
21350 If properties are powers, then causal relations are internal relations [Heil]
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
468 Musical performance can reveal a range of virtues [Damon of Ath.]