40 ideas
| 15879 | The Square of Opposition has two contradictory pairs, one contrary pair, and one sub-contrary pair [Harré] |
| Full Idea: Square of Opposition: 'all A are B' and 'no A are B' are contraries; 'some A are B' and 'some A are not B' are sub-contraries; the pairs 'all A are B'/'some A are B' and 'no A are B'/'some A are B' are contradictories. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: [the reader may construct his own diagram from this description!] The contraries are at the extremes of contradiction, but the sub-contraries are actual compatible. You could add possible worlds to this picture. |
| 12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
| Full Idea: Not to the mathematician, but to the psychologist, belongs the task of explaining why ...we are averse to so-called contradictory systems in which the negative as well as the positive of certain propositions are valid. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.79) | |
| A reaction: Was the turning point of Graham Priest's life the day he read this sentence? I don't agree. I take the principle of non-contradiction to be a highly generalised observation of how the world works (and Russell agrees with me). |
| 15941 | For intuitionists excluded middle is an outdated historical convention [Brouwer] |
| Full Idea: From the intuitionist standpoint the dogma of the universal validity of the principle of excluded third in mathematics can only be considered as a phenomenon of history of civilization, like the rationality of pi or rotation of the sky about the earth. | |
| From: Luitzen E.J. Brouwer (works [1930]), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: [Brouwer 1952:510-11] |
| 15891 | Traditional quantifiers combine ordinary language generality and ontology assumptions [Harré] |
| Full Idea: The generalising function and the ontological function of discourse are elided in the traditional quantifier. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: This simple point strikes me as helping enormously to disentangle the mess created by over-emphasis on formal logic in ontology, and especially in the Quinean concept of 'ontological commitment'. |
| 15878 | Some quantifiers, such as 'any', rule out any notion of order within their range [Harré] |
| Full Idea: The quantifier 'any' unambiguously rules out any presupposition of order in the members of the range of individuals quantified. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: He contrasts this with 'all', 'each' and 'every', which are ambiguous in this respect. |
| 18119 | Mathematics is a mental activity which does not use language [Brouwer, by Bostock] |
| Full Idea: Brouwer made the rather extraordinary claim that mathematics is a mental activity which uses no language. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: Since I take language to have far less of a role in thought than is commonly believed, I don't think this idea is absurd. I would say that we don't use language much when we are talking! |
| 18247 | Brouwer saw reals as potential, not actual, and produced by a rule, or a choice [Brouwer, by Shapiro] |
| Full Idea: In his early writing, Brouwer took a real number to be a Cauchy sequence determined by a rule. Later he augmented rule-governed sequences with free-choice sequences, but even then the attitude is that Cauchy sequences are potential, not actual infinities. | |
| From: report of Luitzen E.J. Brouwer (works [1930]) by Stewart Shapiro - Philosophy of Mathematics 6.6 | |
| A reaction: This is the 'constructivist' view of numbers, as espoused by intuitionists like Brouwer. |
| 12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
| Full Idea: A large part of the natural laws introduced by science treat only of the mutual relations between the results of counting and measuring. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.77) | |
| A reaction: His point, I take it, is that the higher reaches of numbers have lost touch with the original point of the system. I now see the whole issue as just depending on conventions about the agreed extension of the word 'number'. |
| 18118 | Brouwer regards the application of mathematics to the world as somehow 'wicked' [Brouwer, by Bostock] |
| Full Idea: Brouwer regards as somehow 'wicked' the idea that mathematics can be applied to a non-mental subject matter, the physical world, and that it might develop in response to the needs which that application reveals. | |
| From: report of Luitzen E.J. Brouwer (Mathematics, Science and Language [1928]) by David Bostock - Philosophy of Mathematics 7.1 | |
| A reaction: The idea is that mathematics only concerns creations of the human mind. It presumably has no more application than, say, noughts-and-crosses. |
| 12454 | Intuitionists only accept denumerable sets [Brouwer] |
| Full Idea: The intuitionist recognises only the existence of denumerable sets. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: That takes you up to omega, but not beyond, presumably because it then loses sight of the original intuition of 'bare two-oneness' (Idea 12453). I sympathise, but the word 'number' has shifted its meaning a lot these days. |
| 12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
| Full Idea: Neo-intuitionism sees the falling apart of moments, reunited while remaining separated in time, as the fundamental phenomenon of human intellect, passing by abstracting to mathematical thinking, the intuition of bare two-oneness. | |
| From: Luitzen E.J. Brouwer (Intuitionism and Formalism [1912], p.80) | |
| A reaction: [compressed] A famous and somewhat obscure idea. He goes on to say that this creates one and two, and all the finite ordinals. |
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 15874 | Scientific properties are not observed qualities, but the dispositions which create them [Harré] |
| Full Idea: The properties of material things with which the sciences deal are not the qualities we observe them to have, but the dispositions of those things to engender the states and qualities we observe. | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: I take this to be the correct use of the word 'qualities', so that properties are not qualities (in the way Heil would like). |
| 15884 | Laws of nature remain the same through any conditions, if the underlying mechanisms are unchanged [Harré] |
| Full Idea: A statement is a law of nature if it is true in all those worlds which differ only as to their initial conditions, that is in which the underlying mechanisms of nature are the same. | |
| From: Rom Harré (Laws of Nature [1993], 4) | |
| A reaction: Harré takes it that laws of nature have to be necessary, by definition. I like this way of expressing natural necessity, in terms of 'mechanisms' rather than of 'laws'. Where do the mechanisms get their necessity? |
| 15880 | In physical sciences particular observations are ordered, but in biology only the classes are ordered [Harré] |
| Full Idea: In the physical sciences the particular observations and experimental results are usually orderable, while in the biological sciences it is the classes of organism which are ordered, not the particular organisms. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: Harré is interesting on the role of ordering in science. Functions can be defined by an order. Maths feeds on orderings. Physics, he notes, focuses on things which vary together. |
| 15869 | Reports of experiments eliminate the experimenter, and present results as the behaviour of nature [Harré] |
| Full Idea: In accounts of experiments, by Faraday and others, the role of the guiding hand of the actual experimenter is written out in successive accounts. The effect is to display the phenomenon as a natural occurrence, existing independently of the experiments. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: He records three stages in Faraday's reports. The move from active to passive voice is obviously part of it. The claim of universality is thus implicit rather than explicit. |
| 15881 | We can save laws from counter-instances by treating the latter as analytic definitions [Harré] |
| Full Idea: When we come upon a counter-instance to a generalisation we can save the putative law, by treating it as potentially analytic and claiming it as a definition. ...Thus magnetism doesn't hold for phosphorus, so we say phosphorus is not a magnetic substance. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: He notes this as being particularly true when the laws concern the dispositions of substances, rather than patterns of events. |
| 15882 | Since there are three different dimensions for generalising laws, no one system of logic can cover them [Harré] |
| Full Idea: Since there are three different dimensions of generality into which every law of nature is generalised, there can be no one system of logic which will govern inference to or from every law of every kind. | |
| From: Rom Harré (Laws of Nature [1993], 3) | |
| A reaction: This is aimed at the covering-law approach, which actually aims to output observations as logical inferences from laws. Wrong. |
| 15888 | The grue problem shows that natural kinds are central to science [Harré] |
| Full Idea: The grue problem illustrates the enormous importance that the concept of a natural-kind plays in real science. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: The point is that we took emeralds to be a natural kind, but 'grue' proposes that they aren't, since stability is the hallmark of a natural kind. |
| 15887 | 'Grue' introduces a new causal hypothesis - that emeralds can change colour [Harré] |
| Full Idea: In introducing the predicate 'grue' we also introduce an additional causal hypothesis into our chemistry and physics; namely, that when observed grue emeralds change from blue to green. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: [The 'when observered' is a Harré addition] I hate 'grue'. Only people who think our predicates have very little to do with reality are impressed by it. Grue is a behaviour, not a colour. |
| 15889 | It is because ravens are birds that their species and their colour might be connected [Harré] |
| Full Idea: It is because ravens are birds that it makes sense to contemplate the possibility of a lawful relation between their species and their colour. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: Compare the 'laws' concerning leaf colour in autumn, and the 'laws' concerning packaging colour in supermarkets. Harré's underlying point is that raven colour concerns mechanism. |
| 15890 | Non-black non-ravens just aren't part of the presuppositions of 'all ravens are black' [Harré] |
| Full Idea: Non-black non-ravens have no role to play in assessing the plausibility of 'All ravens are black' because their existence is not among the existential presuppositions of that statement. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: [He cites Strawson for the 'presupposition' approach] |
| 15885 | The necessity of Newton's First Law derives from the nature of material things, not from a mechanism [Harré] |
| Full Idea: The 'must' of Newton's First Law is different. There is no deeper level relative to the processes described to give a mechanism which generates uniform motion. There is no such mechanism. ..It specifies what it is for something to be a material thing. | |
| From: Rom Harré (Laws of Nature [1993], 4) | |
| A reaction: Harré says the law can only exist as part of a network of other ideas. |
| 15868 | Idealisation idealises all of a thing's properties, but abstraction leaves some of them out [Harré] |
| Full Idea: An 'idealisation' preserves all the properties of the source but it possesses these properties in some ideal or perfect form. ...An 'abstraction', on the other hand, lacks certain features of its source. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: Yet another example in contemporary philosophy of a clear understanding of the sort of abstraction which Geach and others have poured scorn on. |
| 3193 | Turing showed that logical rules can be specified computationally and mechanically [Turing, by Rey] |
| Full Idea: Turing showed that any formal process can be specified computationally, and captured by a Turing Machine. Hence logical rules (and arithmetic) could be obeyed not by someone representing and following them, but by causal organisation of the brain. | |
| From: report of Alan Turing (works [1935]) by Georges Rey - Contemporary Philosophy of Mind 8.2 | |
| A reaction: It is questionable whether logic is an entirely formal process, if it involves truth. You would need an entirely formal notion of truth for that. But a brain can do whatever a flow diagram can do. |
| 3979 | The Turing Machine is the best idea yet about how the mind works [Fodor on Turing] |
| Full Idea: Alan Turing had (in his theory of the 'Turing Machine') what I suppose is the best thought about how the mind works that anyone has had so far. | |
| From: comment on Alan Turing (Computing Machinery and Intelligence [1950]) by Jerry A. Fodor - Jerry A. Fodor on himself p.296 | |
| A reaction: I am not convinced, because I don't think rationality is possible without consciousness. The brain may bypass the representations used by a computer. |
| 5321 | In 50 years computers will successfully imitate humans with a 70% success rate [Turing] |
| Full Idea: In about fifty years' time it will be possible to program computers to play the imitation game so well that an average interrogator will not have more than 70% chance of making the right identification after five minutes of questioning. | |
| From: Alan Turing (Computing Machinery and Intelligence [1950], p.57), quoted by Robert Kirk - Mind and Body §5.9 | |
| A reaction: This is the famous prophecy called 'The Turing Test'. The current state (2004) seems to be that the figure of 70% is very near, but no one sees much prospect of advancing much further in the next 100 years. Dennett sees jokes as a big problem. |
| 10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
| Full Idea: The concern of mathematical intuitionists was that the use of certain forms of inference generates, not contradiction, but unjustified assertions. | |
| From: report of Luitzen E.J. Brouwer (Intuitionism and Formalism [1912]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
| A reaction: This seems to be the real origin of the verificationist idea in the theory of meaning. It is a hugely revolutionary idea - that ideas are not only ruled out of court by contradiction, but that there are other criteria which should also be met. |
| 15886 | Science rests on the principle that nature is a hierarchy of natural kinds [Harré] |
| Full Idea: The animating principle behind the material and discursive practices of science is the thesis that nature exemplifies multiple hierarchies of natural kinds. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: I agree. I take it to be a brute fact that there seem to be lots of stable natural kinds, which are worth investigating as long as they stay stable. If they are unstable, there needs to be something stable to measure that by - or we give up. |
| 15864 | Classification is just as important as laws in natural science [Harré] |
| Full Idea: Classification systems, or taxonomies, are as important a part of the natural sciences as are the laws of nature. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: This illustrates how our view of science is radically shifted if we give biology equal prominence with physics. |
| 15865 | Newton's First Law cannot be demonstrated experimentally, as that needs absence of external forces [Harré] |
| Full Idea: We can never devise an experimental situation in which there are no external forces to act on a body. It follows that Newton's First Law could never be demonstrated by means of experiment or observation. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: It can't be wholly demonstrated, but certain observations conform to it, such as the movement of low friction bodies, or the movements of planetary bodies. |
| 15862 | Laws can come from data, from theory, from imagination and concepts, or from procedures [Harré] |
| Full Idea: Boyle's Law generalises a mass of messy data culled from an apparatus; Snell's Law is an experimentally derived law deducible from theory; Newton's First Law derives from concepts and thought experiments; Mendel's Law used an experimental procedure. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: Nice examples, especially since Boyle's and Newton's laws are divided by a huge gulf, and arrived at about the same time. On p.35 Harré says these come down to two: abstraction from experiment, and derivation from deep assumptions. |
| 15870 | Are laws of nature about events, or types and universals, or dispositions, or all three? [Harré] |
| Full Idea: What is Newton's First Law about? Is it about events? Is it about types or universals? Is it about dispositions? Or is it, in some peculiar way, about all three? | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: If laws merely chart regularities, then I suppose they are about events (which exhibit the regular patterns). If laws explain, which would be nice, then they are only about universals if you are a platonist. Hence laws are about dispositions. |
| 15871 | Are laws about what has or might happen, or do they also cover all the possibilities? [Harré] |
| Full Idea: Is Newton's First Law about what has actually happened or is it about what might, or could possibly happen? Is it about the actual events and states of the world, or possible events and states? | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: I presume the first sentence distinguishes between what 'might (well)' happen, and what 'could (just) possibly happen'. I take it for granted that laws predict the actual future. The question is are they true of situations which will never occur? |
| 15876 | Maybe laws of nature are just relations between properties? [Harré] |
| Full Idea: The idea of the Dretske-Armstrong-Tooley view is very simple: the laws of nature relate properties to properties. | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: Presumably the relations are necessary ones. I don't see why we need to mention these wretched 'universals' in order to expound this theory. It sounds much more plausible if you just say a property is defined by the way it relates to other properties. |
| 15872 | Must laws of nature be universal, or could they be local? [Harré] |
| Full Idea: Is a law of nature about everything in the universe or just about a restricted group of things? | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: I presume the answer is that while a law may only refer to a small group of things, the law would still have to apply if that group moved or spread or enlarged, so it would have to be universals. A laws confined to one time or place? Maybe. |
| 15867 | Laws describe abstract idealisations, not the actual mess of nature [Harré] |
| Full Idea: The laws of nature are not simple descriptions of what can be seen to happen. They are descriptions of abstractions and idealisations from a somewhat messy reality. | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: This view seems to have increasingly gripped modern philosophers, so that the old view of God decreeing a few simple equations to run the world has faded away. |
| 15860 | We take it that only necessary happenings could be laws [Harré] |
| Full Idea: We do not take laws to be recordings of what happens perchance or for the most part, but specifications of what happens necessarily | |
| From: Rom Harré (Laws of Nature [1993], 1) | |
| A reaction: This sounds like a plausible necessary condition for a law, but it may not be a sufficient one. Are trivial necessities laws? On this view if there are no necessities then there are no laws. |
| 15892 | Laws of nature state necessary connections of things, events and properties, based on models of mechanisms [Harré] |
| Full Idea: A law of nature tells us what kinds of things, events and properties (all else being equal) go along with what. The 'must' of natural necessity has its place here because it is bound up with a model or analogy representing generative mechanisms. | |
| From: Rom Harré (Laws of Nature [1993], 5) | |
| A reaction: This is Harré's final page summary of laws. I agree with it. I would say that the laws are therefore descriptive, of the patterns of behaviour that arise when generative mechanisms meet. Maybe laws concern 'transformations'. |
| 15875 | In counterfactuals we keep substances constant, and imagine new situations for them [Harré] |
| Full Idea: In drawing 'countefactual' conclusions we can be thought imaginatively to vary the conditions under which the substance, set-up etc. is manipulated or stimulated, while maintaining constant our conception of the nature of the being in question. | |
| From: Rom Harré (Laws of Nature [1993], 2) | |
| A reaction: Presumably you could vary the substance and keep the situation fixed, but then the counterfactual seems to be 'about' something different. Either that or the 'situation' is a actually a set of substances to be tested. |