40 ideas
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| Full Idea: Frege later became fastidious about definitions, and demanded that they must provide for every possible case, and that no function is properly determined unless its value is fixed for every conceivable object as argument. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Crispin Wright - Frege's Concept of Numbers as Objects 3.xiv | |
| A reaction: Presumably definitions come in degrees of completeness, but it seems harsh to describe a desire for the perfect definition as 'fastidious', especially if we are talking about mathematics, rather than defining 'happiness'. |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| Full Idea: Given the reference (bedeutung) of an expression and a part of it, obviously the reference of the remaining part is not always determined. So we may not define a symbol or word by defining an expression in which it occurs, whose remaining parts are known | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §66) | |
| A reaction: Dummett cites this as Frege's rejection of contextual definitions, which he had employed in the Grundlagen. I take it not so much that they are wrong, as that Frege decided to set the bar a bit higher. |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| Full Idea: Only what is logically complex can be defined; what is simple can only be pointed to. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §180), quoted by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.137 | |
| A reaction: Frege presumably has in mind his treasured abstract objects, such as cardinal numbers. It is hard to see how you could 'point to' anything in the phenomenal world that had atomic simplicity. Hodes calls this a 'desperate Kantian move'. |
| 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. |
| 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. |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| Full Idea: The cardinals and the reals are completely disjoint domains. The cardinal numbers answer the question 'How many objects of a given kind are there?', but the real numbers are for measurement, saying how large a quantity is compared to a unit quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §157), quoted by Michael Dummett - Frege philosophy of mathematics Ch.19 | |
| A reaction: We might say that cardinals are digital and reals are analogue. Frege is unusual in totally separating them. They map onto one another, after all. Cardinals look like special cases of reals. Reals are dreams about the gaps between cardinals. |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| Full Idea: Frege fixed on construing real numbers as ratios of quantities (in agreement with Newton). | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: If 3/4 is the same real number as 6/8, which is the correct ratio? Why doesn't the square root of 9/16 also express it? Why should irrationals be so utterly different from rationals? In what sense are they both 'numbers'? |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| Full Idea: For Frege, in 'Grundgesetze', a number is a class of classes of the same cardinality. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| Full Idea: The inconsistency of Grundgesetze was only a minor flaw. Its fundamental flaw was its inability to account for the way in which the senses of number terms are determined. It leaves the reference-magnetic nature of the standard numberer a mystery. | |
| From: comment on Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.139 | |
| A reaction: A point also made by Hofweber. As a logician, Frege was only concerned with the inferential role of number terms, and he felt he had captured their logical form, but it is when you come to look at numbers in natural language that he seem in trouble. |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| Full Idea: Frege's three main objections to radical formalism are that it cannot account for the application of mathematics, that it confuses a formal theory with its metatheory, and it cannot explain an infinite sequence. | |
| From: report of Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §86-137) by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: The application is because we don't design maths randomly, but to be useful. The third objection might be dealt with by potential infinities (from formal rules). The second objection sounds promising. |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| Full Idea: It is applicability alone which elevates arithmetic from a game to the rank of a science. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §91), quoted by Stewart Shapiro - Thinking About Mathematics 6.1.2 | |
| A reaction: This is the basic objection to Formalism. It invites the question of why it is applicable, which platonists like Frege don't seem to answer (though Plato himself has reality modelled on the Forms). This is why I like structuralism. |
| 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). |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| Full Idea: The first demand of logic is of a sharp boundary. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §160), quoted by Michael Dummett - Frege philosophy of mathematics Ch.22 | |
| A reaction: Nothing I have read about vagueness has made me doubt Frege's view of this, although precisification might allow you to do logic with vague concepts without having to finally settle where the actual boundaries are. |
| 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. |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| Full Idea: From geometry we retain the interpretation of a real number as a ratio of quantities or measurement-number; but in more recent times we detach it from geometrical quantities, and from all particular types of quantity. | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §159), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Dummett glosses the 'recent' version as by Cantor and Dedekind in 1872. This use of 'detach' seems to me startlingly like the sort of psychological abstractionism which Frege was so desperate to avoid. |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| Full Idea: If abstracting from the difference between my house and my neighbour's, I were to regard both houses as mine, the defect of the abstraction would soon be made clear. It may, though, be possible to obtain a concept by means of abstraction... | |
| From: Gottlob Frege (Grundgesetze der Arithmetik 2 (Basic Laws) [1903], §99) | |
| A reaction: Note the important concession at the end, which shows Frege could never deny the abstraction process, despite all the modern protests by Geach and Dummett that he totally rejected it. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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. |
| 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. |
| 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. |
| 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. |
| 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. |