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] |
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] |
21506 | A coherence theory of justification can combine with a correspondence theory of truth [Bonjour] |
21509 | There will always be a vast number of equally coherent but rival systems [Bonjour] |
21503 | Empirical coherence must attribute reliability to spontaneous experience [Bonjour] |
21511 | A well written novel cannot possibly match a real belief system for coherence [Bonjour] |
21510 | The objection that a negated system is equally coherent assume that coherence is consistency [Bonjour] |
21505 | A coherent system can be justified with initial beliefs lacking all credibility [Bonjour] |
21504 | The best explanation of coherent observations is they are caused by and correspond to reality [Bonjour] |
21508 | Anomalies challenge the claim that the basic explanations are actually basic [Bonjour] |
17631 | Induction is inferring premises from consequences [Russell] |
17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |