21 ideas
21544 | It seems that when a proposition is false, something must fail to subsist [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] |
21539 | Excluded middle can be stated psychologically, as denial of p implies assertion of not-p [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] |
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] |
6408 | Russell needed three extra axioms to reduce maths to logic: infinity, choice and reducibility [Grayling] |
21538 | If two people perceive the same object, the object of perception can't be in the mind [Russell] |
21534 | The only thing we can say about relations is that they relate [Russell] |
21540 | Relational propositions seem to be 'about' their terms, rather than about the relation [Russell] |
21536 | When I perceive a melody, I do not perceive the notes as existing [Russell] |
21535 | Objects only exist if they 'occupy' space and time [Russell] |
21533 | Contingency arises from tensed verbs changing the propositions to which they refer [Russell] |
21537 | I assume we perceive the actual objects, and not their 'presentations' [Russell] |
6414 | Two propositions might seem self-evident, but contradict one another [Grayling] |
21532 | Full empiricism is not tenable, but empirical investigation is always essential [Russell] |
21542 | Do incorrect judgements have non-existent, or mental, or external objects? [Russell] |
21541 | The complexity of the content correlates with the complexity of the object [Russell] |
21543 | If p is false, then believing not-p is knowing a truth, so negative propositions must exist [Russell] |