Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'Believing the Axioms I' and 'Letters to Bentley'

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18 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]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / a. Numbers
13152 We can talk of 'innumerable number', about the infinite points on a line [Newton]
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
13151 Not all infinites are equal [Newton]
23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues
7903 The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
26. Natural Theory / D. Laws of Nature / 1. Laws of Nature
15863 The principles of my treatise are designed to fit with a belief in God [Newton]
26. Natural Theory / D. Laws of Nature / 4. Regularities / a. Regularity theory
8340 I do not pretend to know the cause of gravity [Newton]
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / e. Anti scientific essentialism
13150 The motions of the planets could only derive from an intelligent agent [Newton]
12178 That gravity should be innate and essential to matter is absurd [Newton]