28 ideas
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [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] |
| 12456 | I aim to establish certainty for mathematical methods [Hilbert] |
| 12461 | We believe all mathematical problems are solvable [Hilbert] |
| 9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
| 12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
| 12462 | Only the finite can bring certainty to the infinite [Hilbert] |
| 12455 | The idea of an infinite totality is an illusion [Hilbert] |
| 12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
| 12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
| 18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
| 9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
| 6237 | Fear of God is not conscience, which is a natural feeling of offence at bad behaviour [Shaftesbury] |
| 6234 | If an irrational creature with kind feelings was suddenly given reason, its reason would approve of kind feelings [Shaftesbury] |
| 6233 | A person isn't good if only tying their hands prevents their mischief, so the affections decide a person's morality [Shaftesbury] |
| 6236 | People more obviously enjoy social pleasures than they do eating and drinking [Shaftesbury] |
| 6235 | Self-interest is not intrinsically good, but its absence is evil, as public good needs it [Shaftesbury] |
| 6232 | Every creature has a right and a wrong state which guide its actions, so there must be a natural end [Shaftesbury] |
| 5642 | For Shaftesbury, we must already have a conscience to be motivated to religious obedience [Shaftesbury, by Scruton] |