28 ideas
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
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] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
16864 | If principles are provable, they are theorems; if not, they are axioms [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] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
20945 | Belief is no more rational than is tasting and smelling [Hamann] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
7666 | God is not a mathematician, but a poet [Hamann, by Berlin] |