Combining Texts

All the ideas for 'God and Human Attributes', 'Ontological Relativity' and 'Believing the Axioms I'

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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]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
21642 If quantification is all substitutional, there is no ontology [Quine]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
1633 Absolute ontological questions are meaningless, because the answers are circular definitions [Quine]
7. Existence / D. Theories of Reality / 11. Ontological Commitment / d. Commitment of theories
18964 Ontology is relative to both a background theory and a translation manual [Quine]
9. Objects / F. Identity among Objects / 1. Concept of Identity
18965 We know what things are by distinguishing them, so identity is part of ontology [Quine]
13. Knowledge Criteria / E. Relativism / 5. Language Relativism
1634 Two things are relative - the background theory, and translating the object theory into the background theory [Quine]
19. Language / B. Reference / 1. Reference theories
8470 Reference is inscrutable, because we cannot choose between theories of numbers [Quine, by Orenstein]
19. Language / F. Communication / 6. Interpreting Language / b. Indeterminate translation
18963 Indeterminacy translating 'rabbit' depends on translating individuation terms [Quine]
28. God / B. Proving God / 2. Proofs of Reason / c. Moral Argument
20713 God must be fit for worship, but worship abandons morally autonomy, but there is no God [Rachels, by Davies,B]