21 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] |
18755 | Validity is explained as truth in all models, because that relies on the logical terms [McGee] |
18751 | Natural language includes connectives like 'because' which are not truth-functional [McGee] |
18761 | Second-order variables need to range over more than collections of first-order objects [McGee] |
18753 | An ontologically secure semantics for predicate calculus relies on sets [McGee] |
18754 | Logically valid sentences are analytic truths which are just true because of their logical words [McGee] |
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] |
18757 | Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee] |
17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
18760 | The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee] |
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] |
17639 | Believing a whole science is more than believing each of its propositions [Russell] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
17631 | Induction is inferring premises from consequences [Russell] |
18762 | A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |