22 ideas
3859 | We do not wish merely to predict, we also want to explain [Newton-Smith] |
Full Idea: We do not wish merely to predict, we also want to explain. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], II.3) |
3870 | The real problem of science is how to choose between possible explanations [Newton-Smith] |
Full Idea: Once we move beyond investigating correlations between observables the question of what does or should guide our choice between alternative explanatory accounts becomes problematic. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], IX.2) |
3853 | For science to be rational, we must explain scientific change rationally [Newton-Smith] |
Full Idea: We are only justified in regarding scientific practice as the very paradigm of rationality if we can justify the claim that scientific change is rationally explicable. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], I.2) |
3855 | Critics attack positivist division between theory and observation [Newton-Smith] |
Full Idea: The critics of positivism attacked the conception of a dichotomy between theory and observation. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], I.4) |
3854 | Positivists hold that theoretical terms change, but observation terms don't [Newton-Smith] |
Full Idea: For positivists it was taken that while theory change meant change in the meaning of theoretical terms, the meaning of observational terms was invariant under theory change. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], I.4) |
3869 | More truthful theories have greater predictive power [Newton-Smith] |
Full Idea: If a theory is a better approximation to the truth, then it is likely that it will have greater predictive power. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], VIII.8) |
3861 | Theories generate infinite truths and falsehoods, so they cannot be used to assess probability [Newton-Smith] |
Full Idea: We cannot explicate a useful notion of verisimilitude in terms of the number of truths and the number of falsehoods generated by a theory, because they are infinite. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], III.4) |
17833 | The first-order ZF axiomatisation is highly non-categorical [Hallett,M] |
Full Idea: The first-order Sermelo-Fraenkel axiomatisation is highly non-categorical. | |
From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1213) |
17834 | Non-categoricity reveals a sort of incompleteness, with sets existing that the axioms don't reveal [Hallett,M] |
Full Idea: The non-categoricity of the axioms which Zermelo demonstrates reveals an incompleteness of a sort, ....for this seems to show that there will always be a set (indeed, an unending sequence) that the basic axioms are incapable of revealing to be sets. | |
From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1215) | |
A reaction: Hallett says the incompleteness concerning Zermelo was the (transfinitely) indefinite iterability of the power set operation (which is what drives the 'iterative conception' of sets). |
17837 | Zermelo allows ur-elements, to enable the widespread application of set-theory [Hallett,M] |
Full Idea: Unlike earlier writers (such as Fraenkel), Zermelo clearly allows that there might be ur-elements (that is, objects other than the empty set, which have no members). Indeed he sees in this the possibility of widespread application of set-theory. | |
From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
17836 | The General Continuum Hypothesis and its negation are both consistent with ZF [Hallett,M] |
Full Idea: In 1938, Gödel showed that ZF plus the General Continuum Hypothesis is consistent if ZF is. Cohen showed that ZF and not-GCH is also consistent if ZF is, which finally shows that neither GCH nor ¬GCH can be proved from ZF itself. | |
From: Michael Hallett (Introduction to Zermelo's 1930 paper [1996], p.1217) |
13191 | The properties of a thing flow from its essence [Leibniz] |
Full Idea: It is the same to look for perfection in an essence and in the properties that flow from an essence. | |
From: Gottfried Leibniz (Letters to Wolff [1715], 1715.05.18) | |
A reaction: It is helpful to have Leibniz spelling out his commitment to the traditional view of essence, as that from which the more evident properties flow. |
3867 | De re necessity arises from the way the world is [Newton-Smith] |
Full Idea: A necessary truth is 'de re' if its necessity arises from the way the world is. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], VII.6) |
3872 | We must assess the truth of beliefs in identifying them [Newton-Smith] |
Full Idea: We cannot determine what someone's beliefs are independently of assessing to some extent the truth or falsity of the beliefs. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], X.4) |
3857 | Defeat relativism by emphasising truth and reference, not meaning [Newton-Smith] |
Full Idea: The challenge of incommensurability can be met once it is realised that in comparing theories the notions of truth and reference are more important than that of meaning. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], I.6) |
3858 | A full understanding of 'yellow' involves some theory [Newton-Smith] |
Full Idea: A full grasp of the concept '…is yellow' involves coming to accept as true bits of theory; that is, generalisations involving the term 'yellow'. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], II.2) |
3862 | All theories contain anomalies, and so are falsified! [Newton-Smith] |
Full Idea: According to Feyerabend all theories are born falsified, because no theory has ever been totally free of anomalies. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], III.9) |
3863 | The anomaly of Uranus didn't destroy Newton's mechanics - it led to Neptune's discovery [Newton-Smith] |
Full Idea: When scientists observed the motion of Uranus, they did not give up on Newtonian mechanics. Instead they posited the existence of Neptune. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], III.9) |
3864 | Anomalies are judged against rival theories, and support for the current theory [Newton-Smith] |
Full Idea: Whether to reject an anomaly has to be decided on the basis of the availability of a rival theory, and on the basis of the positive evidence for the theory in question. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], III.9) |
3865 | Why should it matter whether or not a theory is scientific? [Newton-Smith] |
Full Idea: Why should it be so important to distinguish between theories that are scientific and those that are not? | |
From: W.H. Newton-Smith (The Rationality of Science [1981], IV.3) |
3866 | If theories are really incommensurable, we could believe them all [Newton-Smith] |
Full Idea: If theories are genuinely incommensurable why should I be faced with the problem of choosing between them? Why not believe them all? | |
From: W.H. Newton-Smith (The Rationality of Science [1981], VII.1) |
3871 | Explaining an action is showing that it is rational [Newton-Smith] |
Full Idea: To explain an action as an action is to show that it is rational. | |
From: W.H. Newton-Smith (The Rationality of Science [1981], X.2) |