18 ideas
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
5062 | First: there must be reasons; Second: why anything at all?; Third: why this? [Leibniz] |
19377 | A monad and its body are living, so life is everywhere, and comes in infinite degrees [Leibniz] |
19353 | 'Perception' is basic internal representation, and 'apperception' is reflective knowledge of perception [Leibniz] |
5061 | Animals are semi-rational because they connect facts, but they don't see causes [Leibniz] |
5063 | Music charms, although its beauty is the harmony of numbers [Leibniz] |
541 | Virtue comes more from habit than character [Critias] |
542 | Fear of the gods was invented to discourage secret sin [Critias] |