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] |
17640 | Finding the axioms may be the only route to some new results [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] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
17644 | Metaphysical realism is committed to there being one ultimate true theory [Putnam] |
17648 | It is an illusion to think there could be one good scientific theory of reality [Putnam] |
17643 | Shape is essential relative to 'statue', but not essential relative to 'clay' [Putnam] |
17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
17642 | The old view that sense data are independent of mind is quite dotty [Putnam] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
17631 | Induction is inferring premises from consequences [Russell] |
17645 | An alien might think oxygen was the main cause of a forest fire [Putnam] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |