27 ideas
| 1749 | If all laws were abolished, philosophers would still live as they do now [Aristippus elder] |
| 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] |
| 16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
| 16871 | A truth can be an axiom in one system and not in another [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] |
| 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] |
| 3558 | Only the Cyrenaics reject the idea of a final moral end [Aristippus elder, by Annas] |
| 5835 | The road of freedom is the surest route to happiness [Aristippus elder, by Xenophon] |
| 1751 | Pleasure is the good, because we always seek it, it satisfies us, and its opposite is the most avoidable thing [Aristippus elder, by Diog. Laertius] |
| 3018 | People who object to extravagant pleasures just love money [Aristippus elder, by Diog. Laertius] |
| 20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |
| 1755 | Errors result from external influence, and should be corrected, not hated [Aristippus elder, by Diog. Laertius] |