Combining Texts

All the ideas for 'Principles of Nature and Grace based on Reason', 'Warrant and Proper Function' 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
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]
7. Existence / A. Nature of Existence / 5. Reason for Existence
5062 First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz]
7. Existence / C. Structure of Existence / 6. Fundamentals / c. Monads
19377 A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz]
12. Knowledge Sources / B. Perception / 1. Perception
19353 'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz]
13. Knowledge Criteria / C. External Justification / 3. Reliabilism / a. Reliable knowledge
6356 Maybe a reliable justification must come from a process working with its 'proper function' [Plantinga, by Pollock/Cruz]
15. Nature of Minds / A. Nature of Mind / 7. Animal Minds
5061 Animals are semi-rational because they connect facts, but they don't see causes [Leibniz]
21. Aesthetics / B. Nature of Art / 8. The Arts / a. Music
5063 Music charms, although its beauty is the harmony of numbers [Leibniz]