48 ideas
| 3600 | Slow and accurate thought makes the greatest progress [Descartes] |
| 3601 | Most things in human life seem vain and useless [Descartes] |
| 3602 | Almost every daft idea has been expressed by some philosopher [Descartes] |
| 13917 | Metaphysics aims to identify categories of being, and show their interdependency [Lowe] |
| 13919 | Philosophy aims not at the 'analysis of concepts', but at understanding the essences of things [Lowe] |
| 3603 | Methodical thinking is cautious, analytical, systematic, and panoramic [Descartes, by PG] |
| 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] |
| 3612 | Clear and distinct conceptions are true because a perfect God exists [Descartes] |
| 3610 | Truth is clear and distinct conception - of which it is hard to be sure [Descartes] |
| 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] |
| 13918 | Holes, shadows and spots of light can coincide without being identical [Lowe] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 13921 | All things must have an essence (a 'what it is'), or we would be unable to think about them [Lowe] |
| 13922 | Knowing an essence is just knowing what the thing is, not knowing some further thing [Lowe] |
| 13920 | Each thing has to be of a general kind, because it belongs to some category [Lowe] |
| 3605 | We can believe a thing without knowing we believe it [Descartes] |
| 1583 | In morals Descartes accepts the conventional, but rejects it in epistemology [Roochnik on Descartes] |
| 3607 | In thinking everything else false, my own existence remains totally certain [Descartes] |
| 3617 | I aim to find the principles and causes of everything, using the seeds within my mind [Descartes] |
| 3611 | Understanding, rather than imagination or senses, gives knowledge [Descartes] |
| 3606 | I was searching for reliable rock under the shifting sand [Descartes] |
| 3604 | When rebuilding a house, one needs alternative lodgings [Descartes] |
| 3618 | Only experiments can settle disagreements between rival explanations [Descartes] |
| 3615 | Little reason is needed to speak, so animals have no reason at all [Descartes] |
| 3609 | I am a thinking substance, which doesn't need a place or material support [Descartes] |
| 3608 | I can deny my body and the world, but not my own existence [Descartes] |
| 3613 | Reason is universal in its responses, but a physical machine is constrained by its organs [Descartes] |
| 3616 | The soul must unite with the body to have appetites and sensations [Descartes] |
| 16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
| 16875 | We use signs to mark receptacles for complex senses [Frege] |
| 3614 | A machine could speak in response to physical stimulus, but not hold a conversation [Descartes] |
| 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] |
| 1581 | Greeks elevate virtues enormously, but never explain them [Descartes] |
| 16686 | God has established laws throughout nature, and implanted ideas of them within us [Descartes] |