18 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] |
| 11211 | If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt] |
| 11210 | Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt] |
| 11212 | The sense of a connective comes from primitively obvious rules of inference [Rumfitt] |
| 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] |
| 20795 | Some things are their own criterion, such as straightness, a set of scales, or light [Sext.Empiricus] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 20794 | How can sceptics show there is no criterion? Weak without, contradiction with [Sext.Empiricus] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 11214 | We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |