79 ideas
| 9766 | Study vagueness first by its logic, then by its truth-conditions, and then its metaphysics [Fine,K] |
| Full Idea: My investigation of vagueness began with the question 'What is the correct logic of vagueness?', which led to the further question 'What are the correct truth-conditions for a vague language?', which led to questions of meaning and existence. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], Intro) | |
| A reaction: This is the most perfect embodiment of the strategy of analytical philosophy which I have ever read. It is the strategy invented by Frege in the 'Grundlagen'. Is this still the way to go, or has this pathway slowly sunk into the swamp? |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 8625 | What physical facts could underlie 0 or 1, or very large numbers? [Frege on Mill] |
| Full Idea: What in the world can be the observed fact, or the physical fact, which is asserted in the definition of the number 777864? ...What a pity that Mill did not also illustrate the physical facts underlying the numbers 0 and 1! | |
| From: comment on John Stuart Mill (System of Logic [1843]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §7 | |
| A reaction: I still think patterns could be an empirical foundation for arithmetic, though you still have to grasp the abstract concept of the pattern. An innate capacity to spot resemblance gets you a long way. |
| 9775 | Excluded Middle, and classical logic, may fail for vague predicates [Fine,K] |
| Full Idea: Maybe classical logic fails for vagueness in Excluded Middle. If 'H bald ∨ ¬(H bald)' is true, then one disjunct is true. But if the second is true the first is false, and the sentence is either true or false, contrary to the borderline assumption. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 4) | |
| A reaction: Fine goes on to argue against the implication that we need a special logic for vague predicates. |
| 17895 | Combining two distinct assertions does not necessarily lead to a single 'complex proposition' [Mill] |
| Full Idea: In 'Caesar is dead, and Brutus is alive' ...there are here two distinct assertions; and we might as well call a street a complex house, as these two propositions a complex proposition. | |
| From: John Stuart Mill (System of Logic [1843], 1.04.3) | |
| A reaction: Arthur Prior, in his article on 'tonk', cites this to claim that the mere account of the and-introduction rule does not guarantee the existence of any conjunctive proposition that can result from it. Mill says you are adding a third proposition. |
| 10427 | All names are names of something, real or imaginary [Mill] |
| Full Idea: All names are names of something, real or imaginary. | |
| From: John Stuart Mill (System of Logic [1843], p.32), quoted by Mark Sainsbury - The Essence of Reference 18.2 | |
| A reaction: Mill's example of of being like a chalk mark on a door, but Sainsbury points out that names can be detached from bearers in a way that chalk marks can't. |
| 4944 | Mill says names have denotation but not connotation [Mill, by Kripke] |
| Full Idea: It is a well known doctrine of Mill that names have denotation but not connotation. | |
| From: report of John Stuart Mill (System of Logic [1843]) by Saul A. Kripke - Naming and Necessity lectures Lecture 1 | |
| A reaction: A nice starting point for any discussion of the topic. The obvious response is that a name like 'Attila the Hun' seems to have a very vague denotation for most of us, but a rather powerful connotation. |
| 7762 | Proper names are just labels for persons or objects, and the meaning is the object [Mill, by Lycan] |
| Full Idea: Mill seemed to defend the view that proper names are merely labels for individual persons or objects, and contribute no more than those individuals themselves to the meanings of sentences in which they occur. | |
| From: report of John Stuart Mill (System of Logic [1843]) by William Lycan - Philosophy of Language | |
| A reaction: Identity statements can become trivial on this view ('Twain is Clemens'). Modern views have become more sympathetic to Mill, since externalism places meanings outside the head of the speaker. |
| 9771 | Logic holding between indefinite sentences is the core of all language [Fine,K] |
| Full Idea: If language is like a tree, then penumbral connection (logic holding among indefinite sentences) is the seed from which the tree grows, for it provides an initial repository of truths that are to be retained throughout all growth. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 2) | |
| A reaction: A nice incidental insight arising from his investigation of vagueness. People accept one another's reasons even when they are confused, or hopeless at expressing themselves. Nice. |
| 9801 | Numbers must be assumed to have identical units, as horses are equalised in 'horse-power' [Mill] |
| Full Idea: There is one hypothetical element in the basis of arithmetic, without which none of it would be true: all the numbers are numbers of the same or of equal units. When we talk of forty horse-power, we assume all horses are of equal strength. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.3) | |
| A reaction: Of course, horses are not all of equal strength, so there is a problem here for your hard-line empiricist. Mill needs processes of idealisation and abstraction before his empirical arithmetic can get off the ground. |
| 8742 | The only axioms needed are for equality, addition, and successive numbers [Mill, by Shapiro] |
| Full Idea: Mill says arithmetic has two axioms, that 'things which are equal to the same thing are equal to each other', and 'equals added to equals make equal sums', plus a definition for each numeral as 'formed by the addition of a unit to the previous number'. | |
| From: report of John Stuart Mill (System of Logic [1843], p.610?) by Stewart Shapiro - Thinking About Mathematics 4.3 | |
| A reaction: The difficulty here seems to be the definition of 1, and (even worse for an empiricist), of 0. Then he may have a little trouble when he reaches infinity. |
| 9800 | Arithmetic is based on definitions, and Sums of equals are equal, and Differences of equals are equal [Mill] |
| Full Idea: The inductions of arithmetic are based on so-called definitions (such as '2 and 1 are three'), and on two axioms: The sums of equals are equal, The differences of equals are equal. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.3) | |
| A reaction: These are axioms for arithmetical operations, rather than for numbers themselves (which, for Mill, do not require axioms as they are empirically derived). |
| 5201 | Mill says logic and maths is induction based on a very large number of instances [Mill, by Ayer] |
| Full Idea: Mill maintained that the truths of logic and mathematics are not necessary or certain, by saying these propositions are inductive generalisations based on an extremely large number of instances. | |
| From: report of John Stuart Mill (System of Logic [1843]) by A.J. Ayer - Language,Truth and Logic Ch.4 | |
| A reaction: Ayer asserts that they are necessary (but only because they are tautological). I like the idea that maths is the 'science of patterns', but that might lead from an empirical start to a rationalist belief in a priori synthetic truths. |
| 9360 | If two black and two white objects in practice produced five, what colour is the fifth one? [Lewis,CI on Mill] |
| Full Idea: If Mill has a demon who, every time two things are brought together with two other things, always introduces a fifth, then if two black marbles and two white ones are put in an urn, the demon could choose his color, but there would be more of one colour. | |
| From: comment on John Stuart Mill (System of Logic [1843]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.367 | |
| A reaction: Nice to see philosophers fighting back against demons. This is a lovely argument against the absurdity of thinking that experience could ever controvert a priori knowledge (though Lewis is no great fan of the latter). |
| 9888 | Mill mistakes particular applications as integral to arithmetic, instead of general patterns [Dummett on Mill] |
| Full Idea: Mill's mistake is taking particular applications as integral to the sense of arithmetical propositions. But what is integral to arithmetic is the general principle that explains its applicability, and determines the pattern of particular applications. | |
| From: comment on John Stuart Mill (System of Logic [1843], 2.6) by Michael Dummett - Frege philosophy of mathematics Ch.20 | |
| A reaction: [Dummett is summarising Frege's view] Sounds like a tidy objection, but you still have to connect the general principles and patterns to the physical world. 'Structure' could be the magic word to achieve this. |
| 9794 | There are no such things as numbers in the abstract [Mill] |
| Full Idea: There are no such things as numbers in the abstract. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: Depends. Would we want to say that 'horses don't exist' (although each individual horse does exist)? It sounds odd to say of an idea that it doesn't exist, when you are currently thinking about it. I am, however, sympathetic to Mill. |
| 9795 | Numbers have generalised application to entities (such as bodies or sounds) [Mill] |
| Full Idea: 'Ten' must mean ten bodies, or ten sounds, or ten beatings of the pulse. But though numbers must be numbers of something, they may be numbers of anything. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: Mill always prefers things in close proximity, in space or time. 'I've had ten headaches in the last year'. 'There are ten reasons for doubting p'. His second point puts him very close to Aristotle in his view. |
| 9796 | Things possess the properties of numbers, as quantity, and as countable parts [Mill] |
| Full Idea: All things possess quantity; consist of parts which can be numbered; and in that character possess all the properties which are called properties of numbers. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: Here Mill is skating on the very thinnest of ice, and I find myself reluctantly siding with Frege. It is a very optimistic empiricist who hopes to find the numbers actually occurring as properties of experienced objects. A pack of cards, for example. |
| 9798 | Different parcels made from three pebbles produce different actual sensations [Mill] |
| Full Idea: Three pebbles make different sense impressions in one parcel or in two. That the same pebbles by an alteration of place and arrangement may be made to produce either sensation is not the identical proposition. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: [compressed] Not quite clear, but Mill seems to be adamant that we really must experience the separation, and not just think what 'may' happen, so Frege is right that Mill is lucky that everything is not 'nailed down'. |
| 9797 | '2 pebbles and 1 pebble' and '3 pebbles' name the same aggregation, but different facts [Mill] |
| Full Idea: The expressions '2 pebbles and 1 pebble' and '3 pebbles' stand for the same aggregation of objects, but do not stand for the same physical fact. They name the same objects in different states, 'denoting' the same things, with different 'connotations'. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: Nothing in this would convert me from the analytic view to the empirical view of simple arithmetic, if I were that way inclined. Personally I think of three pebbles as 4 minus 1, because I am haunted by the thought of a missing stone. |
| 9799 | 3=2+1 presupposes collections of objects ('Threes'), which may be divided thus [Mill] |
| Full Idea: 'Three is two and one' presupposes that collections of objects exist, which while they impress the senses thus, ¶¶¶, may be separated into two parts, thus, ¶¶ ¶. This being granted, we term all such parcels Threes. | |
| From: John Stuart Mill (System of Logic [1843], 2.6.2) | |
| A reaction: Mill is clearly in trouble here because he sticks to simple arithmetic. He must deal with parcels too big for humans to count, and parcels so big that they could not naturally exist, and that is before you even reach infinite parcels. |
| 9802 | Numbers denote physical properties of physical phenomena [Mill] |
| Full Idea: The fact asserted in the definition of a number is a physical fact. Each of the numbers two, three, four denotes physical phenomena, and connotes a physical property of those phenomena. Two denotes all pairs of things, and twelve all dozens. | |
| From: John Stuart Mill (System of Logic [1843], 3.24.5) | |
| A reaction: The least plausible part of Mill's thesis. Is the fact that a pair of things is fewer than five things also a property? You see two boots, or you see a pair of boots, depending partly on you. Is pure two a visible property? Courage and an onion? |
| 9803 | We can't easily distinguish 102 horses from 103, but we could arrange them to make it obvious [Mill] |
| Full Idea: 102 horses are not as easily distinguished from 103 as two are from three, yet the horses may be so placed that a difference will be perceptible. | |
| From: John Stuart Mill (System of Logic [1843], 3.24.5) | |
| A reaction: More trouble for Mill. We are now moving from the claim that we actually perceive numbers to the claim that we could if we arranged things right. But we would still only see which group of horses was bigger by one, not how many horses there were. |
| 9804 | Arithmetical results give a mode of formation of a given number [Mill] |
| Full Idea: Every statement of the result of an arithmetical operation is a statement of one of the modes of formation of a given number. | |
| From: John Stuart Mill (System of Logic [1843], 3.24.5) | |
| A reaction: Although Mill sticks cautiously to very simple arithmetic, inviting empirical accounts of much higher mathematics, I think the phrase 'modes of formation' of numbers is very helpful. It could take us either into structuralism, or into constructivism. |
| 9805 | 12 is the cube of 1728 means pebbles can be aggregated a certain way [Mill] |
| Full Idea: When we say 12 is the cube of 1728, we affirm that if we had sufficient pebbles, we put them into parcels or aggregates called twelves, and put those twelves into similar collections, and make twelve of these largests parcels, we have the aggregate 1728. | |
| From: John Stuart Mill (System of Logic [1843], 3.24.5) | |
| A reaction: There is always hidden modal thinking in Mill's proposals, despite his longing to stick to actual experience. Imagination actually plays a much bigger role in his theory than sense experience does. |
| 8741 | Numbers must be of something; they don't exist as abstractions [Mill] |
| Full Idea: All numbers must be numbers of something: there are no such things as numbers in the abstract. | |
| From: John Stuart Mill (System of Logic [1843], p.245?), quoted by Stewart Shapiro - Thinking About Mathematics 4.3 | |
| A reaction: This shows why the concept of 'abstraction' is such a deep problem. Numbers can't be properties of objects, because two boots can become one boot without changing the surviving boot. But why should abstractions have to 'exist'? |
| 12411 | Mill is too imprecise, and is restricted to simple arithmetic [Kitcher on Mill] |
| Full Idea: The problem with Mill is that many of his formulations are imprecise, and he only considers the most rudimentary parts of arithmetic. | |
| From: comment on John Stuart Mill (System of Logic [1843]) by Philip Kitcher - The Nature of Mathematical Knowledge Intro | |
| A reaction: This is from a fan of Mill, trying to restore his approach in the face of the authoritative and crushing criticisms offered by Frege. I too am a fan of Mill's approach. Patterns can be discerned in arrangements of pebbles. Infinities are a problem. |
| 5656 | Empirical theories of arithmetic ignore zero, limit our maths, and need probability to get started [Frege on Mill] |
| Full Idea: Mill does not give us a clue as to how to understand the number zero, he limits our mathematical knowledge to the limits of our experience, ..and induction can only give you probability, but that presupposes arithmetical laws. | |
| From: comment on John Stuart Mill (System of Logic [1843]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) | |
| A reaction: This summarises Frege's criticisms of Mill's empirical account of maths. I like 'maths is the science of patterns', in which case zero is just a late-introduced trick (it is hardly a Platonic Form!), and induction is the wrong account to give. |
| 9624 | Numbers are a very general property of objects [Mill, by Brown,JR] |
| Full Idea: Mill held that numbers are a kind of very general property that objects possess. | |
| From: report of John Stuart Mill (System of Logic [1843], Ch.4) by James Robert Brown - Philosophy of Mathematics | |
| A reaction: Intuitively this sounds hopeless, because if you place one apple next to another you introduce 'two', but which apple has changed its property? Both? It seems to be a Cambridge change. It isn't a change that would bother the apples. Kitcher pursues this. |
| 9768 | Vagueness is semantic, a deficiency of meaning [Fine,K] |
| Full Idea: I take vagueness to be a semantic feature, a deficiency of meaning. It is to be distinguished from generality, undecidability, and ambiguity. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], Intro) | |
| A reaction: Sounds good. If we cut nature at the joints with our language, then nature is going to be too subtle and vast for our finite and gerrymandered language, and so it will break down in tricky situations. But maybe epistemology precedes semantics? |
| 9776 | A thing might be vaguely vague, giving us higher-order vagueness [Fine,K] |
| Full Idea: There is a possibility of 'higher-order vagueness'. The vague may be vague, or vaguely vague, and so on. If J has few hairs on his head than H, then he may be a borderline case of a borderline case. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 5) | |
| A reaction: Such slim grey areas can also be characterised as those where you think he is definitely bald, but I am not so sure. |
| 9767 | A vague sentence is only true for all ways of making it completely precise [Fine,K] |
| Full Idea: A vague sentence is (roughly stated) true if and only if it is true for all ways of making it completely precise (the 'super-truth theory'). | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], Intro) | |
| A reaction: Intuitively this sounds quite promising. Personally I think we should focus on the 'proposition' rather than the 'sentence' (where fifteen sentences might be needed before we can agree on the one proposition). |
| 9770 | Logical connectives cease to be truth-functional if vagueness is treated with three values [Fine,K] |
| Full Idea: With a three-value approach, if P is 'blob is pink' and R is 'blob is red', then P&P is indefinite, but P&R is false, and P∨P is indefinite, but P∨R is true. This means the connectives & and ∨ are not truth-functional. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 1) | |
| A reaction: The point is that there could then be no logic in any way classical for vague sentences and three truth values. A powerful point. |
| 9772 | Meaning is both actual (determining instances) and potential (possibility of greater precision) [Fine,K] |
| Full Idea: The meaning of an expression is the product of both its actual meaning (what helps determine its instances and counter-instances), and its potential meaning (the possibilities for making it more precise). | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 2) | |
| A reaction: A modal approach to meaning is gloriously original. Being quite a fan of real modalities (the possibilities latent in actuality), I find this intuitively appealing. |
| 9773 | With the super-truth approach, the classical connectives continue to work [Fine,K] |
| Full Idea: With the super-truth approach, if P is 'blob is pink' and R is 'blob is red', then P&R is false, and P∨R is true, since one of P and R is true and one is false in any complete and admissible specification. It encompasses all 'penumbral truths'. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 3) | |
| A reaction: [See Idea 9767 for the super-truth approach, and Idea 9770 for a contrasting view] The approach, which seems quite appealing, is that we will in no circumstances give up basic classical logic, but we will make maximum concessions to vagueness. |
| 9774 | Borderline cases must be under our control, as capable of greater precision [Fine,K] |
| Full Idea: Any borderline case must be under our control, in the sense that it can be settled by making the predicates more precise. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 3) | |
| A reaction: Sounds good. Consider an abstract concept like the equator. It is precise on a map of the world, but vague when you are in the middle of the tropics. But we can always form a committee to draw a (widish) line on the ground delineating it. |
| 9769 | Vagueness can be in predicates, names or quantifiers [Fine,K] |
| Full Idea: There are three possible sources of vagueness: the predicates, the names, and the quantifiers. | |
| From: Kit Fine (Vagueness, Truth and Logic [1975], 1) | |
| A reaction: Presumably a vagueness about the domain of discussion would be a vagueness in the quantifier. This is a helpful preliminary division, in the semantic approach to vagueness. |
| 9806 | Whatever is made up of parts is made up of parts of those parts [Mill] |
| Full Idea: Whatever is made up of parts is made up of parts of those parts. | |
| From: John Stuart Mill (System of Logic [1843], 3.24.5) | |
| A reaction: Mill considers this principle to be fundamental to the possibilities of arithmetic. Presumably he thought of it as an inductive inference from our dealings with physical objects. |
| 11156 | The essence is that without which a thing can neither be, nor be conceived to be [Mill] |
| Full Idea: The essence of a thing was said to be that without which the thing could neither be, nor be conceived to be. | |
| From: John Stuart Mill (System of Logic [1843], 1.6.2) | |
| A reaction: Fine cites this as the 'modal' account of essence, as opposed to the 'definitional' account. |
| 12190 | Necessity is what will be, despite any alternative suppositions whatever [Mill] |
| Full Idea: That which is necessary, that which must be, means that which will be, whatever suppositions we may make in regard to all other things. | |
| From: John Stuart Mill (System of Logic [1843], 3.06.6) | |
| A reaction: [Mill discusses causal necessity] This is quoted by McFetridge. This slightly firms up the definition as 'what has to be true', though it makes it dependent on our 'suppositions'. Presumably nothing beyond our powers of supposition could matter either. |
| 22623 | Necessity can only mean what must be, without conditions of any kind [Mill] |
| Full Idea: If there be any meaning which confessedly belongs to the term necessity, it is unconditionalness. That which is necessary, that which must be, means that which will be whatever supposition we make with regard to other things. | |
| From: John Stuart Mill (System of Logic [1843], p.339 [1974 ed]), quoted by R.D. Ingthorsson - A Powerful Particulars View of Causation 5.3 | |
| A reaction: 'It is necessary to leave now, if you want to catch the train' is a genuine type of necessity. Mill's type is probably Absolute necessity, to which nothing could make any difference. Or Metaphysical necessity, determined by all things. |
| 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) |
| 16859 | Most perception is one-tenth observation and nine-tenths inference [Mill] |
| Full Idea: In almost every act of our perceiving faculties, observation and inference are intimately blended. What we are said to observe is usually a compound result, of which one-tenth may be observation, and the remaining nine-tenths inference. | |
| From: John Stuart Mill (System of Logic [1843], 4.1.2), quoted by Peter Lipton - Inference to the Best Explanation (2nd) 11 'The scientific' | |
| A reaction: We seem to think that his kind of observation is a great realisation of twentieth century thought, but thoughtful empiricists spotted it much earlier. |
| 9082 | Clear concepts result from good observation, extensive experience, and accurate memory [Mill] |
| Full Idea: The principle requisites of clear conceptions, are habits of attentive observation, an extensive experience, and a memory which receives and retains an exact image of what is observed. | |
| From: John Stuart Mill (System of Logic [1843], 4.2.5) | |
| A reaction: Empiricists are always crying out for people to 'attend to the evidence', and this is the deeper reason why. Not only will one know the world better in a direct way, but one will actually think more clearly. Darwin is the perfect model for this. |
| 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) |
| 16860 | Inductive generalisation is more reliable than one of its instances; they can't all be wrong [Mill] |
| Full Idea: A general proposition collected from particulars is often more certainly true than any one of the particular propositions from which, by an act of induction, it was inferred. It might be erroneous in any instance, but cannot be erroneous in all of them. | |
| From: John Stuart Mill (System of Logic [1843], 4.1.2), quoted by Peter Lipton - Inference to the Best Explanation (2nd) 11 'The scientific' | |
| A reaction: One anomaly can be ignored, but several can't, especially if the anomalies agree. |
| 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) |
| 16845 | The whole theory of induction rests on causes [Mill] |
| Full Idea: The notion of cause is the root of the whole theory of induction. | |
| From: John Stuart Mill (System of Logic [1843], 3.05.2), quoted by Peter Lipton - Inference to the Best Explanation (2nd) 08 'From cause' | |
| A reaction: This sounds much better to me than the Humean view that it rests on the psychology of regularity and habit. However, maybe Hume describes induction, and Mill is adding abduction (inference to the best explanation). |
| 16843 | Mill's methods (Difference,Agreement,Residues,Concomitance,Hypothesis) don't nail induction [Mill, by Lipton] |
| Full Idea: The Method of Difference, and even the full four 'experimental methods' (Difference, Agreement, Residues and Concomitant Variations) are agreed on all sides to be incomplete accounts of inductive inference. Mill himself added the Method of Hypothesis. | |
| From: report of John Stuart Mill (System of Logic [1843], 3.14.4-5) by Peter Lipton - Inference to the Best Explanation (2nd) 08 'Improved' | |
| A reaction: If induction is just 'learning from experience' (my preferred definition) then there is unlikely to be a precise account of its methods. Mill seems to have done a lovely job. |
| 17086 | Surprisingly, empiricists before Mill ignore explanation, which seems to transcend experience [Mill, by Ruben] |
| Full Idea: It is surprising that no empiricist philosopher before Mill turned in an explicit way to the scrutiny of the concept of explanation, which had …every appearance of being experience-transcendent. | |
| From: report of John Stuart Mill (System of Logic [1843]) by David-Hillel Ruben - Explaining Explanation Ch 4 | |
| A reaction: Yes indeed! This is why explanation is absolutely basic, to philosophy and to human understanding. The whole of philosophy is a quest for explanations, so to be strictly empirical about it strikes me as crazy. |
| 17091 | Explanation is fitting of facts into ever more general patterns of regularity [Mill, by Ruben] |
| Full Idea: For Mill, explanation was always the fitting of facts into ever more general patterns of regularity. | |
| From: report of John Stuart Mill (System of Logic [1843]) by David-Hillel Ruben - Explaining Explanation Ch 6 | |
| A reaction: This seems to nicely capture the standard empirical approach to explanation. If you say that this fitting in doesn't explain much, the answer (I think) is that this is the best we can do. |
| 16805 | Causal inference is by spotting either Agreements or Differences [Mill, by Lipton] |
| Full Idea: The best known account of causal inference is Mill's Method of Agreement (only one antecedent is shared by the effects), and the Method of Difference (there is only one difference prior to the effect occurring or not occurring). | |
| From: report of John Stuart Mill (System of Logic [1843], 3.07) by Peter Lipton - Inference to the Best Explanation (2nd) 01 'Descr' | |
| A reaction: [my summary of Lipton's summary of Mill] |
| 16835 | The Methods of Difference and of Agreement are forms of inference to the best explanation [Mill, by Lipton] |
| Full Idea: Like Mill's Method of Difference, applications of the Method of Agreement are naturally construed as inferences to the best explanation. | |
| From: report of John Stuart Mill (System of Logic [1843], 3.07/8) by Peter Lipton - Inference to the Best Explanation (2nd) 06 'The Method' | |
| A reaction: This sort of thoroughly sensible approach to understanding modes of investigation has been absurdly sidelined by the desire to 'deduce' observations from 'laws'. Scientific investigation is no different from enquiry in daily life. Where are my glasses? |
| 9079 | We can focus our minds on what is common to a whole class, neglecting other aspects [Mill] |
| Full Idea: The voluntary power which the mind has, of attending to one part of what is present at any moment, and neglecting another part, enables us to be unaffected by anything in the idea which is not really common to the whole class. | |
| From: John Stuart Mill (System of Logic [1843], 4.2.1) | |
| A reaction: There is a question for empiricists of whether abstraction is a 'voluntary' power or a mechanical one. Associationism presents it as more mechanical. I would say, with Mill, that it is a least partly voluntary, and even rational. |
| 9081 | We don't recognise comparisons by something in our minds; the concepts result from the comparisons [Mill] |
| Full Idea: It is not a law of our intellect that in comparing things and noting their agreements we recognise as realized in the outward world something we already had in our minds. The conception found its way to us as the result of such a comparison. | |
| From: John Stuart Mill (System of Logic [1843], 4.2.2) | |
| A reaction: He recognises, of course, that this gradually becomes a two-way process. In the physicalist view of things, it is not really of great importance which concepts are hard-wired, and which constructed culturally or through perception. |
| 9080 | General conceptions are a necessary preliminary to Induction [Mill] |
| Full Idea: Forming general conceptions is a necessary preliminary to Induction. | |
| From: John Stuart Mill (System of Logic [1843], 4.2.1) | |
| A reaction: A key link in the framework of empirical philosophies, which gets us from experience to science. Induction is the very process of generalisation. We can't bring a concept like 'evolution' to preliminary observations, so it must be formulated inductively. |
| 9078 | The study of the nature of Abstract Ideas does not belong to logic, but to a different science [Mill] |
| Full Idea: The metaphysical inquiry into the nature and composition of what have been called Abstract Ideas, or in other words, of the notions which answer in the mind to classes and to general names, belongs not to Logic, but to a different science. | |
| From: John Stuart Mill (System of Logic [1843], 4.2.1) | |
| A reaction: He doesn't name the science, but the point here seems to be precisely what Frege so vigorously disagreed with. I would say that the state of being 'abstract' has logical aspects, and can be partly described by logic, but that Mill is basically right. |
| 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) |
| 8345 | A cause is the total of all the conditions which inevitably produce the result [Mill] |
| Full Idea: A cause is the sum total of the conditions positive and negative taken together ...which being realized, the consequent invariably follows. | |
| From: John Stuart Mill (System of Logic [1843]), quoted by Donald Davidson - Causal Relations §1 | |
| A reaction: This has obvious problems. The absence of Napoleon was a cause of the English Civil War. The Big Bang was a cause of, well, every event. As Davidson notes, some narrowing down is needed. |
| 10391 | Causes and conditions are not distinct, because we select capriciously from among them [Mill] |
| Full Idea: Nothing can better show the absence of any scientific ground for the distinction between the cause of a phenomena and its conditions, than the capricious manner in which we select from among the conditions that which we choose to denominate the cause. | |
| From: John Stuart Mill (System of Logic [1843]), quoted by Jonathan Schaffer - The Metaphysics of Causation 2.2 | |
| A reaction: [ref Mill p.196, 1846 edn] Schaffer gives this as the main argument for the 'no-basis' view of the selection of what causes an event. The usual thought is that it is entirely our immediate interests which make us select THE cause. Not convinced. |
| 14547 | The strict cause is the total positive and negative conditions which ensure the consequent [Mill] |
| Full Idea: The cause, philosophically speaking, is the sum total of the conditions, positive and negative taken together; the whole of the contigencies of every description, which being realized, the consequent invariably follows. | |
| From: John Stuart Mill (System of Logic [1843], 3.05.3) | |
| A reaction: This somewhat notorious remark is not going to be much help in a law court or a laboratory. It is that view which says that the Big Bang must be included in every causal list ever compiled. Well, yes... |
| 8377 | Causation is just invariability of succession between every natural fact and a preceding fact [Mill] |
| Full Idea: The Law of Causation, the recognition of which is the main pillar of inductive science, is but the familiar truth, that invariability of succession is found by observation between every fact in nature and some other fact which has preceded it. | |
| From: John Stuart Mill (System of Logic [1843], 3.5.2), quoted by Bertrand Russell - On the Notion of Cause p.178 | |
| A reaction: Note that Mill rests causation on 'facts'. In the empiricist Mill endorsing the views of Hume. Russell attacks the bogus claim that science rests on causation. Personally I think Mill's view is incorrect. |
| 14545 | A cause is an antecedent which invariably and unconditionally leads to a phenomenon [Mill] |
| Full Idea: We may define the cause of a phenomenon to be the antecedent, or the concurrence of the antecedents, on which it is invariably and unconditionally consequent. | |
| From: John Stuart Mill (System of Logic [1843], 3.05.6) | |
| A reaction: This ignores the possibility of the world ending just before the effect occurs, the 'ceteris paribus' clause. If it only counts as a cause if the effect has actually occurred, we begin to suspect tautology. |
| 4773 | Mill's regularity theory of causation is based on an effect preceded by a conjunction of causes [Mill, by Psillos] |
| Full Idea: Millian causation is a version of the Regularity Theory, but with the addition that when claiming that an effect invariably follows from the cause, the cause is not a single factor, but a whole conjunction of necessary and sufficient conditions. | |
| From: report of John Stuart Mill (System of Logic [1843], p.217) by Stathis Psillos - Causation and Explanation §2.2 | |
| A reaction: Psillos endorses this as an improvement on Hume. But while we may replicate one event preceding another to get regularity, groups of events are hardly ever identical, so no precise pattern will ever be seen. |
| 4775 | In Mill's 'Method of Agreement' cause is the common factor in a range of different cases [Mill, by Psillos] |
| Full Idea: In Mill's 'Method of Agreement' the cause is the common factor in a number of otherwise different cases in which the effect occurs. | |
| From: report of John Stuart Mill (System of Logic [1843], p.255) by Stathis Psillos - Causation and Explanation §2.3 | |
| A reaction: This looks more likely to be good evidence for the cause of an event, rather than a definition of what a cause actually is. Suppose a footballer only scores if and only if I go to watch him? |
| 4776 | In Mill's 'Method of Difference' the cause is what stops the effect when it is removed [Mill, by Psillos] |
| Full Idea: In Mill's 'Method of Difference' the cause is the factor which is different in two cases which are similar, except that in one the effect occurs, and in the other it doesn't. | |
| From: report of John Stuart Mill (System of Logic [1843], p.256) by Stathis Psillos - Causation and Explanation §2.3 | |
| A reaction: Like the Method of Agreement, this is a good test, but is unlikely to be a conclusive hallmark of causation. A footballer may never score unless I go to watch him. I become his lucky mascot… |
| 9417 | What are the fewest propositions from which all natural uniformities could be inferred? [Mill] |
| Full Idea: What are the fewest general propositions from which all the uniformities which exist in the universe might be deductively inferred? | |
| From: John Stuart Mill (System of Logic [1843], 3.4.1) | |
| A reaction: This is the germ of the Mill-Ramsey-Lewis view. |