26 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] |
| 17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
| 17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
| 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] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| 17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
| 17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| 16422 | The necessity of a proposition concerns reality, not our words or concepts [Stalnaker] |
| 16423 | Conceptual possibilities are metaphysical possibilities we can conceive of [Stalnaker] |
| 16421 | Critics say there are just an a priori necessary part, and an a posteriori contingent part [Stalnaker] |
| 16429 | A 'centred' world is an ordered triple of world, individual and time [Stalnaker] |
| 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] |
| 16428 | Meanings aren't in the head, but that is because they are abstract [Stalnaker] |
| 16432 | One view says the causal story is built into the description that is the name's content [Stalnaker] |
| 16430 | Two-D says that a posteriori is primary and contingent, and the necessity is the secondary intension [Stalnaker] |
| 16431 | In one view, the secondary intension is metasemantic, about how the thinker relates to the content [Stalnaker] |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |