20 ideas
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| 17629 | Which premises are ultimate varies with context [Russell] |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| 13445 | Descartes showed a one-one order-preserving match between points on a line and the real numbers [Descartes, by Hart,WD] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| 16774 | Descartes thinks distinguishing substances from aggregates is pointless [Descartes, by Pasnau] |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| 7400 | Descartes said images can refer to objects without resembling them (as words do) [Descartes, by Tuck] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 4310 | We have inner awareness of our freedom [Descartes] |
| 6553 | Descartes discussed the interaction problem, and compared it with gravity [Descartes, by Lycan] |
| 6017 | Nomos is king [Pindar] |
| 19676 | Nature is devoid of thought [Descartes, by Meillassoux] |
| 6518 | Matter can't just be Descartes's geometry, because a filler of the spaces is needed [Robinson,H on Descartes] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |