16 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] |
| 13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
| 9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
| 17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
| 18758 | Validity is provable, but invalidity isn't, because the model is infinite [Church, by McGee] |
| 18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
| 17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
| 18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
| 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] |
| 10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
| 9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
| 18165 | My Basic Law V is a law of pure logic [Frege] |
| 9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
| 13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |