Combining Texts

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

expand these ideas     |    start again     |     specify just one area for these texts

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]
14. Science / B. Scientific Theories / 1. Scientific Theory
19594 General statements about nature are not valid [Novalis]
17. Mind and Body / A. Mind-Body Dualism / 8. Dualism of Mind Critique
19596 The whole body is involved in the formation of thoughts [Novalis]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5996 Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]
25. Social Practice / E. Policies / 5. Education / d. Study of history
19593 Persons are shaped by a life history; splendid persons are shaped by world history [Novalis]
26. Natural Theory / A. Speculations on Nature / 1. Nature
19595 Nature is a whole, and its individual parts cannot be wholly understood [Novalis]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
19592 The basic relations of nature are musical [Novalis]