44 ideas
| 3853 | For science to be rational, we must explain scientific change rationally [Newton-Smith] |
| 3859 | We do not wish merely to predict, we also want to explain [Newton-Smith] |
| 3870 | The real problem of science is how to choose between possible explanations [Newton-Smith] |
| 3855 | Critics attack positivist division between theory and observation [Newton-Smith] |
| 3854 | Positivists hold that theoretical terms change, but observation terms don't [Newton-Smith] |
| 1403 | A rational donkey would starve to death between two totally identical piles of hay [Buridan, by PG] |
| 3869 | More truthful theories have greater predictive power [Newton-Smith] |
| 3861 | Theories generate infinite truths and falsehoods, so they cannot be used to assess probability [Newton-Smith] |
| 17926 | Rejecting double negation elimination undermines reductio proofs [Colyvan] |
| 17925 | Showing a disproof is impossible is not a proof, so don't eliminate double negation [Colyvan] |
| 17924 | Excluded middle says P or not-P; bivalence says P is either true or false [Colyvan] |
| 17929 | Löwenheim proved his result for a first-order sentence, and Skolem generalised it [Colyvan] |
| 17930 | Axioms are 'categorical' if all of their models are isomorphic [Colyvan] |
| 17928 | Ordinal numbers represent order relations [Colyvan] |
| 17923 | Intuitionists only accept a few safe infinities [Colyvan] |
| 17941 | Infinitesimals were sometimes zero, and sometimes close to zero [Colyvan] |
| 17922 | Reducing real numbers to rationals suggested arithmetic as the foundation of maths [Colyvan] |
| 17936 | Transfinite induction moves from all cases, up to the limit ordinal [Colyvan] |
| 17940 | Most mathematical proofs are using set theory, but without saying so [Colyvan] |
| 17931 | Structuralism say only 'up to isomorphism' matters because that is all there is to it [Colyvan] |
| 17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |
| 16678 | Without magnitude a thing would retain its parts, but they would have no location [Buridan] |
| 16793 | A thing is (less properly) the same over time if each part is succeeded by another [Buridan] |
| 3867 | De re necessity arises from the way the world is [Newton-Smith] |
| 3872 | We must assess the truth of beliefs in identifying them [Newton-Smith] |
| 16726 | Why can't we deduce secondary qualities from primary ones, if they cause them? [Buridan] |
| 3857 | Defeat relativism by emphasising truth and reference, not meaning [Newton-Smith] |
| 3858 | A full understanding of 'yellow' involves some theory [Newton-Smith] |
| 16577 | Induction is not demonstration, because not all of the instances can be observed [Buridan] |
| 3862 | All theories contain anomalies, and so are falsified! [Newton-Smith] |
| 3863 | The anomaly of Uranus didn't destroy Newton's mechanics - it led to Neptune's discovery [Newton-Smith] |
| 3864 | Anomalies are judged against rival theories, and support for the current theory [Newton-Smith] |
| 3865 | Why should it matter whether or not a theory is scientific? [Newton-Smith] |
| 3866 | If theories are really incommensurable, we could believe them all [Newton-Smith] |
| 16576 | Science is based on induction, for general truths about fire, rhubarb and magnets [Buridan] |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| 17939 | Mathematics can reveal structural similarities in diverse systems [Colyvan] |
| 17938 | Mathematics can show why some surprising events have to occur [Colyvan] |
| 17934 | Proof by cases (by 'exhaustion') is said to be unexplanatory [Colyvan] |
| 17933 | Reductio proofs do not seem to be very explanatory [Colyvan] |
| 17935 | If inductive proofs hold because of the structure of natural numbers, they may explain theorems [Colyvan] |
| 17942 | Can a proof that no one understands (of the four-colour theorem) really be a proof? [Colyvan] |
| 17937 | Mathematical generalisation is by extending a system, or by abstracting away from it [Colyvan] |
| 3871 | Explaining an action is showing that it is rational [Newton-Smith] |