34 ideas
| 7460 | The great moments are the death of Aristotle, Machiavelli, and Romanticism [Berlin, by Watson] |
| Full Idea: Berlin says there were three great turning points: after the death of Aristotle (when Greek schools focused on the inner life of individuals, instead of as social beings), Machiavelli's division of political and individual virtues, and Romanticism. | |
| From: report of Isaiah Berlin (The Sense of Reality [1996], p.168-9) by Peter Watson - Ideas Intro | |
| A reaction: I have the impression that Machiavelli introduced a new hard-boiled ethics, which dominated the sixteenth century, but in the seventeenth and eighteenth century they fought back, and Machiavellianism turned out to be just a phase. |
| 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) |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| Full Idea: The main objection to the axiom of choice was that it had to be given by some law or definition, but since sets are arbitrary this seems irrelevant. Formalists consider it meaningless, but set-theorists consider it as true, and practically obvious. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| Full Idea: One can distinguish at least two quite different senses of logic: as an instrument of demonstration, and perhaps as an instrument for the characterization of structures. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: This is trying to capture the proof-theory and semantic aspects, but merely 'characterizing' something sounds like a rather feeble aspiration for the semantic side of things. Isn't it to do with truth, rather than just rule-following? |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| Full Idea: Elementary logic cannot characterize the usual mathematical structures, but seems to be distinguished by its completeness. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| Full Idea: The expressive power of second-order logic is too great to admit a proof procedure, but is adequate to express set-theoretical statements, and open questions such as the continuum hypothesis or the existence of big cardinals are easily stated. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| Full Idea: In sentential logic there is a simple proof that all truth functions, of any number of arguments, are definable from (say) 'not' and 'and'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §0) | |
| A reaction: The point of 'say' is that it can be got down to two connectives, and these are just the usual preferred pair. |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| Full Idea: The symbols ∀ and ∃ may, to start with, be regarded as extrapolations of the truth functional connectives ∧ ('and') and ∨ ('or') to infinite domains. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §5) |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| Full Idea: One might add to one's logic an 'uncountable quantifier', or a 'Chang quantifier', or a 'two-argument quantifier', or 'Shelah's quantifier', or 'branching quantifiers'. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §3) | |
| A reaction: [compressed - just listed for reference, if you collect quantifiers, like collecting butterflies] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| Full Idea: Skolem deduced from the Löwenheim-Skolem theorem that 'the absolutist conceptions of Cantor's theory' are 'illusory'. I think it is clear that this conclusion would not follow even if elementary logic were in some sense the true logic, as Skolem assumed. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §7) | |
| A reaction: [Tharp cites Skolem 1962 p.47] Kit Fine refers to accepters of this scepticism about the arithmetic of infinities as 'Skolemites'. |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| Full Idea: The Löwenheim-Skolem property seems to be undesirable, in that it states a limitation concerning the distinctions the logic is capable of making, such as saying there are uncountably many reals ('Skolem's Paradox'). | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| Full Idea: Soundness would seem to be an essential requirement of a proof procedure, since there is little point in proving formulas which may turn out to be false under some interpretation. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| Full Idea: Putting completeness and compactness together, one has axiomatizability. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §1) |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| Full Idea: In general, if completeness fails there is no algorithm to list the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: I.e. the theory is not effectively enumerable. |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| Full Idea: It is strange that compactness is often ignored in discussions of philosophy of logic, since the most important theories have infinitely many axioms. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: An example of infinite axioms is the induction schema in first-order Peano Arithmetic. |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| Full Idea: The compactness condition seems to state some weakness of the logic (as if it were futile to add infinitely many hypotheses). To look at it another way, formalizations of (say) arithmetic will admit of non-standard models. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| Full Idea: A complete logic has an effective enumeration of the valid formulas. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| Full Idea: Despite completeness, the mere existence of an effective enumeration of the valid formulas will not, by itself, provide knowledge. For example, one might be able to prove that there is an effective enumeration, without being able to specify one. | |
| From: Leslie H. Tharp (Which Logic is the Right Logic? [1975], §2) | |
| A reaction: The point is that completeness is supposed to ensure knowledge (of what is valid but unprovable), and completeness entails effective enumerability, but more than the latter is needed to do the key job. |
| 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) |