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] |
| 5163 | Basic propositions refer to a single experience, are incorrigible, and conclusively verifiable [Ayer] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 5167 | The argument from analogy fails, so the best account of other minds is behaviouristic [Ayer] |
| 5164 | A statement is meaningful if observation statements can be deduced from it [Ayer] |
| 5165 | Directly verifiable statements must entail at least one new observation statement [Ayer] |
| 5166 | The principle of verification is not an empirical hypothesis, but a definition [Ayer] |
| 5162 | Sentences only express propositions if they are meaningful; otherwise they are 'statements' [Ayer] |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| 5168 | Moral approval and disapproval concerns classes of actions, rather than particular actions [Ayer] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |