16 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 5044 | Reality must be made of basic unities, which will be animated, substantial points [Leibniz] |
| 5045 | No machine or mere organised matter could have a unified self [Leibniz] |
| 5046 | The soul does know bodies, although they do not influence one another [Leibniz] |
| 3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
| 5043 | To regard animals as mere machines may be possible, but seems improbable [Leibniz] |