30 ideas
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| 8378 | Philosophers usually learn science from each other, not from science [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] |
| 8195 | Undecidable statements result from quantifying over infinites, subjunctive conditionals, and the past tense [Dummett] |
| 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] |
| 8194 | Surely there is no exact single grain that brings a heap into existence [Dummett] |
| 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] |
| 8190 | Intuitionists rely on the proof of mathematical statements, not their truth [Dummett] |
| 8198 | A 'Cambridge Change' is like saying 'the landscape changes as you travel east' [Dummett] |
| 8192 | I no longer think what a statement about the past says is just what can justify it [Dummett] |
| 8375 | 'Necessary' is a predicate of a propositional function, saying it is true for all values of its argument [Russell] |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| 8199 | The existence of a universe without sentience or intelligence is an unintelligible fantasy [Dummett] |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| 17631 | Induction is inferring premises from consequences [Russell] |
| 8193 | Verification is not an individual but a collective activity [Dummett] |
| 8189 | Truth-condition theorists must argue use can only be described by appeal to conditions of truth [Dummett] |
| 8191 | The truth-conditions theory must get agreement on a conception of truth [Dummett] |
| 4396 | The law of causality is a source of confusion, and should be dropped from philosophy [Russell] |
| 8376 | If causes are contiguous with events, only the last bit is relevant, or the event's timing is baffling [Russell] |
| 8380 | Striking a match causes its igniting, even if it sometimes doesn't work [Russell] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| 8379 | In causal laws, 'events' must recur, so they have to be universals, not particulars [Russell] |
| 8381 | The constancy of scientific laws rests on differential equations, not on cause and effect [Russell] |
| 8197 | Maybe past (which affects us) and future (which we can affect) are both real [Dummett] |
| 8196 | The present cannot exist alone as a mere boundary; past and future truths are rendered meaningless [Dummett] |