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] |
17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
9558 | All scientific tests will verify mathematics, so it is a background, not something being tested [Sober] |
13857 | Truth-functional possibilities include the irrelevant, which is a mistake [Edgington] |
13853 | It is a mistake to think that conditionals are statements about how the world is [Edgington] |
13855 | A conditional does not have truth conditions [Edgington] |
13859 | X believes 'if A, B' to the extent that A & B is more likely than A & ¬B [Edgington] |
13854 | Conditionals express what would be the outcome, given some supposition [Edgington] |
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] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |