77 ideas
| 23248 | Early empiricists said reason was just a useless concept introduced by philosophers [Galen, by Frede,M] |
| Full Idea: The so-called Empiricists in Hellenistic times [as cited by Galen] denied the existence of reason, treating it as a useless theoretical postulate introduced by some philosophers | |
| From: report of Galen (An Outline of Empiricism [c.170], 87.4-9.28ff) by Michael Frede - Intro to 'Rationality in Greek Thought' p.3 | |
| A reaction: I think 'be sensible' is understood by everyone, but 'use your reason' is far from obvious. The main role of reason seems to be as an identifier for human exceptionalism. Animals obviously make good judgements. Frede thinks the empiricists were right. |
| 9023 | If you say that a contradiction is true, you change the meaning of 'not', and so change the subject [Quine] |
| Full Idea: Those who regard the conjunction p.not-p as true think they are talking about negation, 'not', but this ceases to be recognisable as negation. The deviant logician's predicament is when he tries to deny the doctrine he only changes the subject. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |
| A reaction: The charge of 'changing the subject' has become a classic move in modern discussions of non-standard logics. It is an important idea in discussions of arguments, and is found in Kant's account of the Ontological Argument. |
| 9012 | Talk of 'truth' when sentences are mentioned; it reminds us that reality is the point of sentences [Quine] |
| Full Idea: The truth predicate has its utility in places where we are compelled to mention sentences. It then serves to point through the sentence to the reality; it serves as a reminder that though sentences are mentioned, reality is still the whole point. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: A sensible interpretation of the Tarskian account of truth as disquotation. Quine neatly combines a common sense correspondence with a sophisticated logicians view of the role of truth. So what does "I want the truth here" mean? |
| 9011 | Truth is redundant for single sentences; we do better to simply speak the sentence [Quine] |
| Full Idea: Rather than speak of truth, we do better simply to say the sentence and so speak not about language but about the world. Of singly given sentences, the perfect theory of truth is the 'disappearance theory of truth' (Sellars). | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: Quine defends truth as the crucial link between language and reality, but only for large groups of sentences. If someone accuses you of lying or being incorrect, you can respond by repeating your sentence in a firmer tone of voice. |
| 9013 | We can eliminate 'or' from our basic theory, by paraphrasing 'p or q' as 'not(not-p and not-q)' [Quine] |
| Full Idea: The construction of 'alternation' (using 'or') is useful in practice, but superfluous in theory. It can be paraphrased using only negation and conjunction. We say that 'p or q' is paraphrased as 'not(not-p and not-q)'. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: Quine treats 'not' and 'and' as the axiomatic logical connectives, and builds the others from those, presumably because that is the smallest number he could get it down to. I quite like it, because it seems to mesh with basic thought procedures. |
| 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. |
| 9020 | My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine] |
| Full Idea: We chose a standard grammar in which the simple sentences are got by predication, and all further sentences are generated from these by negation, conjunction, and existential quantification. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.3) | |
| A reaction: It is interesting that we 'choose' our logic, apparently guided by an imperative to achieve minimal ontology. Of these basic ingredients, negation and predication are the more mysterious, especially the latter. Quine is a bit of an 'ostrich' about that. |
| 9028 | Maybe logical truth reflects reality, but in different ways in different languages [Quine] |
| Full Idea: Perhaps the logical truths owe their truth to certain traits of reality which are reflected in one way by the grammar of our language, in another way by the grammar of another language, and in a third way by the grammar and lexicon of a third language. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.7) | |
| A reaction: This explains Quine's subsequent interest in translation, and the interest of his pupil Davidson in charity, and whether there could actually be rival conceptual schemes. I like the link between logical truths and reality, which follows Russell. |
| 10014 | Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes] |
| Full Idea: Quine is unwilling to suppose second-order logic intelligible. He holds to Mill's account of the referential role of a predicate: it multiply denotes any and all objects to which it applies, and there is no need for a further 'predicative' entity. | |
| From: report of Willard Quine (Philosophy of Logic [1970]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.130 | |
| A reaction: If we assume that 'quantifying over' something is a commitment to its existence, then I think I am with Quine, because you end up with a massive commitment to universals, which I prefer to avoid. |
| 10828 | Quantifying over predicates is treating them as names of entities [Quine] |
| Full Idea: To put the predicate letter 'F' in a quantifier is to treat predicate position suddenly as name position, and hence to treat predicates as names of entities of some sort. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |
| A reaction: It is tricky to distinguish quantifying over predicates in a first-order way (by reifying them), and in a second-order way (where it is not clear whether you are quantifying over a property or a unified set of things. |
| 9024 | Excluded middle has three different definitions [Quine] |
| Full Idea: The law of excluded middle, or 'tertium non datur', may be pictured variously as 1) Every closed sentence is true or false; or 2) Every closed sentence or its negation is true; or 3) Every closed sentence is true or not true. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |
| A reaction: Unlike many top philosophers, Quine thinks clearly about such things. 1) is the classical bivalent reading of excluded middle; 2) is the purely syntactic version; 3) leaves open how we interpret the 'not-true' option. |
| 10012 | Quantification theory can still be proved complete if we add identity [Quine] |
| Full Idea: Complete proof procedures are available not only for quantification theory, but for quantification theory and identity together. Gödel showed that the theory is still complete if we add self-identity and the indiscernability of identicals. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |
| A reaction: Hence one talks of first-order logic 'with identity', even though, as Quine observes, it is unclear whether identity is actually a logical or a mathematical notion. |
| 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. |
| 9016 | Names are not essential, because naming can be turned into predication [Quine] |
| Full Idea: Names are convenient but redundant, because Fa is equivalent to (an x)(a=x,Fx), so a need only occur in the context a=, but this can be rendered as a simple predicate A, so that Fa gives way to (an x)(Ax.Fx). | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: In eliminating names from analysis, Quine takes Russell's strategy a step further. It is probably this which provoked Kripke into going right back to Mill's view of names as basic labels. The name/description boundary is blurred. Mr Gradgrind. |
| 9015 | Universal quantification is widespread, but it is definable in terms of existential quantification [Quine] |
| Full Idea: Universal quantification is prominent in logical practice but superfluous in theory, since (for all x)Fx obviously amounts to not(exists an x)not-Fx. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: The equivalence between these two works both ways, some you could take the universal quantifier as primitive instead, which would make general truths prior to particular ones. Is there something deep at stake here? |
| 9025 | You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine] |
| Full Idea: A customary argument against quantification based on substitution of names for variables refers to the theorem of set theory that irrational numbers cannot all be assigned integers. Although the integers can all be named, the irrationals therefore can't. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |
| A reaction: [He names Ruth Marcus as a source of substitutional quantification] This sounds like more than a mere 'argument' against substitutional quantification, but an actual disproof. Or maybe you just can't quantify once you run out of names. |
| 9026 | Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine] |
| Full Idea: An existential quantification could turn out false when substitutionally construed and true when objectually construed, because of there being objects of the purported kind but only nameless ones. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.6) | |
| A reaction: (Cf. Idea 9025) Some irrational numbers were his candidates for nameless objects, but as decimals they are infinite in length which seems unfair. I don't take even pi or root-2 to be objects in nature, so not naming irrationals doesn't bother me. |
| 10705 | Putting a predicate letter in a quantifier is to make it the name of an entity [Quine] |
| Full Idea: To put the predicate letter 'F' in a quantifier is to treat predicate positions suddenly as name positions, and hence to treat predicates as names of entities of some sort. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.5) | |
| A reaction: Quine's famous objection to second-order logic. But Quine then struggles to give an account of predicates and properties, and hence is accused by Armstrong of being an 'ostrich'. Boolos 1975 also attacks Quine here. |
| 9027 | A sentence is logically true if all sentences with that grammatical structure are true [Quine] |
| Full Idea: A sentence is logically true if all sentences with that grammatical structure are true. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.7) | |
| A reaction: Quine spends some time on the tricky question of deciding which parts of a sentence are grammatical structure ('syncategorematic'), and which parts are what he calls 'lexicon'. I bet there is a Quinean argument which blurs the boundary. |
| 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. |
| 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. |
| 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. |
| 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. |
| 9017 | Predicates are not names; predicates are the other parties to predication [Quine] |
| Full Idea: Predicates are not names; predicates are the other parties to predication. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: Does a wife only exist as party to a marriage? There's something missing here. We are taking predication to be primitive, but we then seem to single out one part of the process - the object - while ignoring the remainder. What are Quinean objects? |
| 9018 | A physical object is the four-dimensional material content of a portion of space-time [Quine] |
| Full Idea: We might think of a physical object as simply the whole four-dimensional material content, however sporadic and heterogeneous, of some portion of space-time. If it is firm and coherent internally, we call it a body. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: An early articulation of one of the two standard views of objects in recent philosophy. I think I prefer the Quinean view, but I am still looking into that one... |
| 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. |
| 9019 | Four-d objects helps predication of what no longer exists, and quantification over items from different times [Quine] |
| Full Idea: The four-dimensional view of objects aids relativity, and the grammar of tenses, but in logic it makes sense of applying a predicate to something that no longer exists, or of quantifying over objects that never coexisted at any one time. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: Since you can predicate of or quantify over hypothetical or fictional objects ('Hamlet is gloomy', 'phlogiston explained fire quite well', 'peace and quiet would be nice') I don't see the necessity for this bold ontological commitment, on these grounds. |
| 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. |
| 9014 | Some conditionals can be explained just by negation and conjunction: not(p and not-q) [Quine] |
| Full Idea: Often the purpose of a conditional, 'if p, q', can be served simply by negation and conjunction: not(p and not-q), the so-called 'material conditional'. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.2) | |
| A reaction: Logicians love the neatness of that, but get into trouble elsewhere with conditionals, particularly over the implications of not-p. |
| 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. |
| 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. |
| 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. |
| 9009 | Single words are strongly synonymous if their interchange preserves truth [Quine] |
| Full Idea: We can define, it would seem, a strong synonymy relation for single words by them being interchangeable salva veritate. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: This is a first step in Quine's rejection of synonymous sentences. He goes on to raise the problem of renate/cordate. Presumably any two word types can have different connotations, and hence not always be interchangeable - in poetry, for example. |
| 9007 | It makes no sense to say that two sentences express the same proposition [Quine] |
| Full Idea: My objection to propositions is not parsimony, or disapproval of abstract entities, ..but that propositions induce a relation of synonymy or equivalence between sentences (expressing the same proposition), and this makes no objective sense. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: Personally I think propositions are unavoidable when you try to connect language to activities of the brain, and also when you consider animal thought. And also when you introspect about your own language processes. Mr Quine, he wrong. |
| 9008 | There is no rule for separating the information from other features of sentences [Quine] |
| Full Idea: There is no evident rule for separating the information from the stylistic or other immaterial features of the sentences. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: There is no rule for deciding precisely when night falls, so I don't believe in night. I take a proposition, prima facie, as an answer to the question 'What exactly do you mean by that remark?' How do you extract logical form from sentences? |
| 9010 | We can abandon propositions, and just talk of sentences and equivalence [Quine] |
| Full Idea: Why not just talk of sentences and equivalence and let the propositions go? Propositions have been projected as shadows of sentences, but at best they will give us nothing the sentences will not give. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.1) | |
| A reaction: I don't understand how you decide that two sentences are equivalent. 'There's someone in that wood'; 'yes, there's a person amongst those trees'. Identical truth-conditions. We can formulate a non-linguistic fact about those truth-conditions. |
| 9021 | A good way of explaining an expression is saying what conditions make its contexts true [Quine] |
| Full Idea: A reasonable way of explaining an expression is by saying what conditions make its various contexts true. | |
| From: Willard Quine (Philosophy of Logic [1970], Ch.3) | |
| A reaction: I like the circumspect phrasing of this, which carefully avoids any entities such as 'meanings' or 'truth conditions'. Maybe the whole core of philosophy of language should shift from theories of meaning to just trying to 'explain' sentences. |
| 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. |