26 ideas
| 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) |
| 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) |
| 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) |
| 23445 | Naïve set theory says any formula defines a set, and coextensive sets are identical [Linnebo] |
| Full Idea: Naïve set theory is based on the principles that any formula defines a set, and that coextensive sets are identical. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.2) | |
| A reaction: The second principle is a standard axiom of ZFC. The first principle causes the trouble. |
| 23447 | In classical semantics singular terms refer, and quantifiers range over domains [Linnebo] |
| Full Idea: In classical semantics the function of singular terms is to refer, and that of quantifiers, to range over appropriate domains of entities. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 7.1) |
| 23443 | The axioms of group theory are not assertions, but a definition of a structure [Linnebo] |
| Full Idea: Considered in isolation, the axioms of group theory are not assertions but comprise an implicit definition of some abstract structure, | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.5) | |
| A reaction: The traditional Euclidean approach is that axioms are plausible assertions with which to start. The present idea sums up the modern approach. In the modern version you can work backwards from a structure to a set of axioms. |
| 23444 | To investigate axiomatic theories, mathematics needs its own foundational axioms [Linnebo] |
| Full Idea: Mathematics investigates the deductive consequences of axiomatic theories, but it also needs its own foundational axioms in order to provide models for its various axiomatic theories. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.1) | |
| A reaction: This is a problem which faces the deductivist (if-then) approach. The deductive process needs its own grounds. |
| 23446 | You can't prove consistency using a weaker theory, but you can use a consistent theory [Linnebo] |
| Full Idea: If the 2nd Incompleteness Theorem undermines Hilbert's attempt to use a weak theory to prove the consistency of a strong one, it is still possible to prove the consistency of one theory, assuming the consistency of another theory. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 4.6) | |
| A reaction: Note that this concerns consistency, not completeness. |
| 23448 | Mathematics is the study of all possible patterns, and is thus bound to describe the world [Linnebo] |
| Full Idea: Philosophical structuralism holds that mathematics is the study of abstract structures, or 'patterns'. If mathematics is the study of all possible patterns, then it is inevitable that the world is described by mathematics. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 11.1) | |
| A reaction: [He cites the physicist John Barrow (2010) for this] For me this is a major idea, because the concept of a pattern gives a link between the natural physical world and the abstract world of mathematics. No platonism is needed. |
| 23441 | Logical truth is true in all models, so mathematical objects can't be purely logical [Linnebo] |
| Full Idea: Modern logic requires that logical truths be true in all models, including ones devoid of any mathematical objects. It follows immediately that the existence of mathematical objects can never be a matter of logic alone. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 2) | |
| A reaction: Hm. Could there not be a complete set of models for a theory which all included mathematical objects? (I can't answer that). |
| 23442 | Game Formalism has no semantics, and Term Formalism reduces the semantics [Linnebo] |
| Full Idea: Game Formalism seeks to banish all semantics from mathematics, and Term Formalism seeks to reduce any such notions to purely syntactic ones. | |
| From: Øystein Linnebo (Philosophy of Mathematics [2017], 3.3) | |
| A reaction: This approach was stimulated by the need to justify the existence of the imaginary number i. Just say it is a letter! |
| 14296 | Dispositions are physical states of mechanism; when known, these replace the old disposition term [Quine] |
| Full Idea: Each disposition, in my view, is a physical state or mechanism. ...In some cases nowadays we understand the physical details and set them forth explicitly in terms of the arrangement and interaction of small bodies. This replaces the old disposition. | |
| From: Willard Quine (The Roots of Reference [1990], p.11), quoted by Stephen Mumford - Dispositions 01.3 | |
| A reaction: A challenge to the dispositions and powers view of nature, one which rests on the 'categorical' structural properties, rather than the 'hypothetical' dispositions. But can we define a mechanism without mentioning its powers? |
| 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) |