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] |
| 9169 | A statement can be metaphysically necessary and epistemologically contingent [Putnam] |
| 5819 | Conceivability is no proof of possibility [Putnam] |
| 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] |
| 9168 | I can't distinguish elm trees, but I mean by 'elm' the same set of trees as everybody else [Putnam] |
| 5820 | 'Water' has an unnoticed indexical component, referring to stuff around here [Putnam] |
| 19087 | The meaning or purport of a symbol is all the rational conduct it would lead to [Peirce] |
| 9170 | We need to recognise the contribution of society and of the world in determining reference [Putnam] |
| 5817 | Language is more like a cooperative steamship than an individual hammer [Putnam] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| 5818 | If water is H2O in the actual world, there is no possible world where it isn't H2O [Putnam] |