19 ideas
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] |
13010 | In order to select the logic justified by experience, we would need to use a lot of logic [Boghossian on Quine] |
9002 | Elementary logic requires truth-functions, quantifiers (and variables), identity, and also sets of variables [Quine] |
13681 | Logical consequence is marked by being preserved under all nonlogical substitutions [Quine, by Sider] |
13829 | If logical truths essentially depend on logical constants, we had better define the latter [Hacking on Quine] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
9003 | Set theory was struggling with higher infinities, when new paradoxes made it baffling [Quine] |
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] |
9004 | If set theory is not actually a branch of logic, then Frege's derivation of arithmetic would not be from logic [Quine] |
9006 | Commitment to universals is as arbitrary or pragmatic as the adoption of a new system of bookkeeping [Quine] |
9001 | Frege moved Kant's question about a priori synthetic to 'how is logical certainty possible?' [Quine] |
9005 | Examination of convention in the a priori begins to blur the distinction with empirical knowledge [Quine] |
17402 | Mendeleev saw three principles in nature: matter, force and spirit (where the latter seems to be essence) [Mendeleev, by Scerri] |
17399 | Elements don't survive in compounds, but the 'substance' of the element does [Mendeleev] |
17401 | Mendeleev had a view of elements which allowed him to overlook some conflicting observations [Mendeleev] |
17400 | Mendeleev focused on abstract elements, not simple substances, so he got to their essence [Mendeleev, by Scerri] |