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] |
| 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] |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 6479 | Noninterference requires justification as much as interference does [Nagel] |
| 6450 | Morality must be motivating, and not because of pre-moral motives [Nagel] |
| 6447 | Game theory misses out the motivation arising from the impersonal standpoint [Nagel] |
| 6446 | In ethics we abstract from our identity, but not from our humanity [Nagel] |
| 6477 | I can only universalise a maxim if everyone else could also universalise it [Nagel] |
| 6448 | A legitimate system is one accepted as both impartial and reasonably partial [Nagel] |
| 6478 | Democracy is opposed to equality, if the poor are not a majority [Nagel] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |