30 ideas
| 16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
| 11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
| 16878 | We must be clear about every premise and every law used in a proof [Frege] |
| 16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
| 16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
| 16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
| 16865 | 'Theorems' are both proved, and used in proofs [Frege] |
| 16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
| 16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
| 16871 | A truth can be an axiom in one system and not in another [Frege] |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| 16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
| 16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 411 | If we succeed in speaking the truth, we cannot know we have done it [Xenophanes] |
| 412 | If God had not created honey, men would say figs are sweeter [Xenophanes] |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| 16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
| 16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
| 16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
| 16874 | The parts of a thought map onto the parts of a sentence [Frege] |
| 23569 | The only just cause for a war is a wrong received [Vitoria] |
| 23601 | Leaders can only attack foreigners who have done wrong (as with their own subjects) [Vitoria] |
| 23566 | Princes should not justify a war to their subjects, and doing so would undermine the state [Vitoria] |
| 23576 | Sacking a city is lawful if it motivates the attacking troops [Vitoria] |
| 1640 | The basic Eleatic belief was that all things are one [Xenophanes, by Plato] |
| 3055 | Xenophanes said the essence of God was spherical and utterly inhuman [Xenophanes, by Diog. Laertius] |
| 408 | Ethiopian gods have black hair, and Thracian gods have red hair [Xenophanes] |
| 407 | Mortals believe gods are born, and have voices and clothes just like mortals [Xenophanes] |