20 ideas
12124 | Metaphysics is the best knowledge, because it is the simplest [Bacon] |
12123 | Natural history supports physical knowledge, which supports metaphysical knowledge [Bacon] |
12119 | Physics studies transitory matter; metaphysics what is abstracted and necessary [Bacon] |
12120 | Physics is of material and efficient causes, metaphysics of formal and final causes [Bacon] |
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] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
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] |
12121 | We don't assume there is no land, because we can only see sea [Bacon] |
12117 | Science moves up and down between inventions of causes, and experiments [Bacon] |
12127 | Many different theories will fit the observed facts [Bacon] |
12126 | People love (unfortunately) extreme generality, rather than particular knowledge [Bacon] |
12125 | Teleological accounts are fine in metaphysics, but they stop us from searching for the causes [Bacon] |
12118 | Essences are part of first philosophy, but as part of nature, not part of logic [Bacon] |