53 ideas
| 10807 | Mathematics reduces to set theory, which reduces, with some mereology, to the singleton function [Lewis] |
| Full Idea: It is generally accepted that mathematics reduces to set theory, and I argue that set theory in turn reduces, with some aid of mereology, to the theory of the singleton function. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10809 | We can accept the null set, but not a null class, a class lacking members [Lewis] |
| Full Idea: In my usage of 'class', there is no such things as the null class. I don't mind calling some memberless thing - some individual - the null set. But that doesn't make it a memberless class. Rather, that makes it a 'set' that is not a class. | |
| From: David Lewis (Mathematics is Megethology [1993], p.05) | |
| A reaction: Lewis calls this usage 'idiosyncratic', but it strikes me as excellent. Set theorists can have their vital null class, and sensible people can be left to say, with Lewis, that classes of things must have members. |
| 10811 | The null set plays the role of last resort, for class abstracts and for existence [Lewis] |
| Full Idea: The null set serves two useful purposes. It is a denotation of last resort for class abstracts that denote no nonempty class. And it is an individual of last resort: we can count on its existence, and fearlessly build the hierarchy of sets from it. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: This passage assuages my major reservation about the existence of the null set, but at the expense of confirming that it must be taken as an entirely fictional entity. |
| 10812 | The null set is not a little speck of sheer nothingness, a black hole in Reality [Lewis] |
| Full Idea: Should we accept the null set as a most extraordinary individual, a little speck of sheer nothingness, a sort of black hole in the fabric of Reality itself? Not that either, I think. | |
| From: David Lewis (Mathematics is Megethology [1993], p.09) | |
| A reaction: Correct! |
| 10813 | What on earth is the relationship between a singleton and an element? [Lewis] |
| Full Idea: A new student of set theory has just one thing, the element, and he has another single thing, the singleton, and not the slightest guidance about what one thing has to do with the other. | |
| From: David Lewis (Mathematics is Megethology [1993], p.12) |
| 10814 | Are all singletons exact intrinsic duplicates? [Lewis] |
| Full Idea: Are all singletons exact intrinsic duplicates? | |
| From: David Lewis (Mathematics is Megethology [1993], p.13) |
| 10806 | Megethology is the result of adding plural quantification to mereology [Lewis] |
| Full Idea: Megethology is the result of adding plural quantification, as advocated by George Boolos, to the language of mereology. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) |
| 10816 | We can use mereology to simulate quantification over relations [Lewis] |
| Full Idea: We can simulate quantification over relations using megethology. Roughly, a quantifier over relations is a plural quantifier over things that encode ordered pairs by mereological means. | |
| From: David Lewis (Mathematics is Megethology [1993], p.18) | |
| A reaction: [He credits this idea to Burgess and Haven] The point is to avoid second-order logic, which quantifies over relations as ordered n-tuple sets. |
| 10808 | Mathematics is generalisations about singleton functions [Lewis] |
| Full Idea: We can take the theory of singleton functions, and hence set theory, and hence mathematics, to consist of generalisations about all singleton functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.03) | |
| A reaction: At first glance this sounds like a fancy version of the somewhat discredited Greek idea that mathematics is built on the concept of a 'unit'. |
| 10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
| Full Idea: We needn't believe in 'abstract structures' to have general structural truths about all successor functions. | |
| From: David Lewis (Mathematics is Megethology [1993], p.16) |
| 22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
| Full Idea: The substance of the absolute conception [of external reality] lies in the idea that it could nonvacuously explain how it itself, and the various perspectival views of the world, are possible. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], p.139), quoted by Reiss,J/Spreger,J - Scientific Objectivity 2.1 | |
| A reaction: I like this. Explanation and understanding strike me as more important than justified truths, and I am struck by the complete inability of subjectivists, relativists and anti-realists to give any kinds of good explanation. |
| 16185 | Causality indicates which properties are real [Cartwright,N] |
| Full Idea: Causality is a clue to what properties are real. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 9.3) | |
| A reaction: An interesting variant on the Shoemaker proposal that properties actually are causal. I'm not sure that there is anything more to causality that the expression in action of properties, which I take to be powers. Structures are not properties. |
| 10810 | I say that absolutely any things can have a mereological fusion [Lewis] |
| Full Idea: I accept the principle of Unrestricted Composition: whenever there are some things, no matter how many or how unrelated or how disparate in character they may be, they have a mereological fusion. ...The trout-turkey is part fish and part fowl. | |
| From: David Lewis (Mathematics is Megethology [1993], p.07) | |
| A reaction: This nicely ducks the question of when things form natural wholes and when they don't, but I would have thought that that might be one of the central issues of metaphysicals, so I think I'll give Lewis's principle a miss. |
| 4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
| Full Idea: The fact that people can and must react when confronted with another culture, and do so by applying existing notions, seems to show that ethical thought of a given culture can always stretch beyond its boundaries. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 9) | |
| A reaction: Hardly conclusive, but it does seem to show that there is an element of universalising in values, no matter how local you may consider them to be. |
| 4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
| Full Idea: Some people believe a properly relativist view requires you to be equally well disposed to everybody's ethical beliefs, but this is seriously confused, as relativism has led to a nonrelativist morality of universal toleration. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 9) | |
| A reaction: Good point. This need not stop a relativist from passionately defending tolerance - it is only that the lack of rational support for the passion must be recognised. |
| 16182 | Two main types of explanation are by causes, or by citing a theoretical framework [Cartwright,N] |
| Full Idea: In explaining a phenomenon one can cite the causes of that phenomenon; or one can set the phenomenon in a general theoretical framework. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 4.1) | |
| A reaction: The thing is, you need to root an explanation in something taken as basic, and theoretical frameworks need further explanation, whereas causes seem to be basic. |
| 16184 | An explanation is a model that fits a theory and predicts the phenomenological laws [Cartwright,N] |
| Full Idea: To explain a phenomenon is to find a model that fits it into the basic framework of the theory and that thus allows us to derive analogues for the messy and complicated phenomenological laws that are true of it. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 8.3) | |
| A reaction: This summarises the core of her view in this book. She is after models rather than laws, and the models are based on causes. |
| 16171 | The covering law view assumes that each phenomenon has a 'right' explanation [Cartwright,N] |
| Full Idea: The covering-law account supposes that there is, in principle, one 'right' explanation for each phenomenon. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: Presumably the law is held to be 'right', but there must be a bit of flexibility in describing the initial conditions, and the explanandum itself. |
| 16167 | Laws get the facts wrong, and explanation rests on improvements and qualifications of laws [Cartwright,N] |
| Full Idea: We explain by ceteris paribus laws, by composition of causes, and by approximations that improve on what the fundamental laws dictate. In all of these cases the fundamental laws patently do not get the facts right. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: It is rather headline-grabbing to say in this case that laws do not get the facts right. If they were actually 'wrong' and 'lied', there wouldn't be much point in building explanations on them. |
| 16169 | Laws apply to separate domains, but real explanations apply to intersecting domains [Cartwright,N] |
| Full Idea: When different kinds of causes compose, we want to explain what happens in the intersection of different domains. But the laws we use are designed only to tell truly what happens in each domain separately. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: Since presumably the laws are discovered through experiments which try to separate out a single domain, in those circumstances they actually are true, so they don't 'lie'. |
| 16176 | Covering-law explanation lets us explain storms by falling barometers [Cartwright,N] |
| Full Idea: Much criticism of the original covering-law model objects that it lets in too much. It seems we can explain Henry's failure to get pregnant by his taking birth control pills, and we can explain the storm by the falling barometer. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.0) | |
| A reaction: I take these examples to show that true explanations must be largely causal in character. The physicality of causation is what matters, not 'laws'. I'd say the same of attempts to account for causation through counterfactuals. |
| 16177 | I disagree with the covering-law view that there is a law to cover every single case [Cartwright,N] |
| Full Idea: Covering-law theorists tend to think that nature is well-regulated; in the extreme, that there is a law to cover every case. I do not. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.2) | |
| A reaction: The problem of coincidence is somewhere at the back of this thought. Innumerable events have their own explanations, but it is hard to explain their coincidence (see Aristotle's case of bumping into a friend in the market). |
| 16180 | You can't explain one quail's behaviour by just saying that all quails do it [Cartwright,N] |
| Full Idea: 'Why does that quail in the garden bob its head up and down in that funny way whenever it walks?' …'Because they all do'. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.5) | |
| A reaction: She cites this as an old complaint against the covering-law model of explanation. It captures beautifully the basic error of the approach. We want to know 'why', rather than just have a description of the pattern. 'They all do' is useful information. |
| 16183 | In science, best explanations have regularly turned out to be false [Cartwright,N] |
| Full Idea: There are a huge number of cases in the history of science where we now know our best explanations were false. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 5.3) | |
| A reaction: [She cites Laudan 1981 for this] The Ptolemaic system and aether are the standard example cited for this. I believe strongly in the importance of best explanation. Only a fool would just accept the best explanation available. Coherence is needed. |
| 4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
| Full Idea: If there is a truth about the subject matter of ethics, why should it be simple? ..I shall argue that philosophy should not try to produce ethical theories. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 1) | |
| A reaction: Bizarrely defeatist - in parallel with Mysterians about the mind like McGinn. Is there any point in thinking at all? I suggest the aim of life as the best starting point. |
| 4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
| Full Idea: Intuitionism in ethics has been demolished by a succession of critics, and the ruins of it that remain above ground are not impressive enough to invite much history of what happened to it. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 6) | |
| A reaction: Why does intuitionism have such appeal to beginners in moral philosophy? There is a truth buried in it somewhere. See 'Sources of the Self' by Charles Taylor. |
| 4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
| Full Idea: The category of person is a poor foundation for ethical thought, because it looks like a sortal or classificatory notion while in fact it signals characteristics that almost all come in degrees (responsibility, self-reflection etc). | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 6) | |
| A reaction: On the contrary, it must be the basis of moral theory, and its shifting character is strong support for Aristotle's approach to moral growth and responsibility. |
| 4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
| Full Idea: That "I simply don't like staying at good hotels" is intelligible brings out the basic weakness of prescriptive accounts of the evaluative. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 7) | |
| A reaction: This might be an elision of two different prescriptions, mine and most people's. In what sense do I think the hotel good, as opposed to other people? |
| 4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
| Full Idea: Some 'thicker' ethical notions, such as 'treachery', 'promise', 'brutality' and 'courage', seem to express a union of facts and values. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 8) | |
| A reaction: The onus does seem to be on the followers of Hume to disentangle what the rest of us have united. They may, of course, manage it. |
| 4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
| Full Idea: We do not merely want the world to contain certain states of affairs (it is a deep error of consequentialism to believe that this is all we want). Among the things we basically want is to act in certain ways. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 4) | |
| A reaction: A key objection. Does it matter whether Hiroshima is destroyed by earthquake or bombing? |
| 4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
| Full Idea: The institution of promise keeping operates to provide portable reliability, by offering a formula that will confer high deliberative priority on what might not otherwise receive it. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch.10) | |
| A reaction: This is a bit pessimistic. We do not perceive promise keeping as a mere suggestion that we should bear something in mind when making a decision. 'May I rot in hell if I fail you'. |
| 4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
| Full Idea: A particular weakness of the contractual theory is that it is unstable with respect to a superior agent, one more intelligent and resourceful and persuasive than the rest. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 3) | |
| A reaction: The very weak are equally a problem. Democratic societies produce fewer inequalities. Hierarchical societies are miserable (I expect..). |
| 4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
| Full Idea: Recently there has been much emphasis on the importance of our capacity to have second-order desires - the desire to have certain desires - and its significance for ethical reflection and the practical consciousness. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 1) | |
| A reaction: This is a crucial point if we are to defend a reasonably rational view of morality against (say) emotivism. I agree that it is crucial to morality. |
| 4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
| Full Idea: There is no ancient Greek word for duty; the word 'deon' (the basis of 'deontology') means what one must do. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 1) | |
| A reaction: Presumably it covered compulsions which were not duties, such as the need to eat or drink. Greeks thought morally, but lacked a good moral vocabulary? |
| 4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
| Full Idea: Obligation and duty look backwards; the acts they require lie in the future, but the reasons for those acts lie in the fact that I have already promised, the job I have undertaken, the position I am already in. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 1) | |
| A reaction: Maybe the central issue in morality is forwards versus backwards. It reflects two types of human temperament. Tomorrow is another day. Spilt milk. |
| 4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
| Full Idea: "Ought implies can" is a famous formula in connection with moral obligation. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch.10) | |
| A reaction: Williams says it is true in particular instances, but is not generally true of 'ought'. Maybe you 'ought' before you know whether you 'can'. |
| 4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
| Full Idea: Not every conclusion of moral deliberation expresses an obligation; for example, some moral conclusions merely announce that you 'may' do something. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch.10) | |
| A reaction: An important point for any deontological ethics. It may be possible to translate what 'may' be done into some form of duty, but it will probably involve contortions. |
| 4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
| Full Idea: The concept of a 'duty to myself' is fraudulent. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch.10) | |
| A reaction: The only person who can offer a rebuttal of this is Aristotle. With the magnet of the Platonic Form of the Good, I can perceive the natural excellences of which I am capable, and feel a duty to pursue them. |
| 4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
| Full Idea: Why should I think of myself as a legislator and at the same time a citizen of a republic governed by some notional laws? | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 4) | |
| A reaction: Kant's answer is supposed to be 'because you are rational, and hence must want consistency'. If we were all rational, Kant would be right. |
| 4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
| Full Idea: How can an 'I' that has taken on the perspective of impartiality be left with enough identity to live a life that respects its own interests? | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 4) | |
| A reaction: Not a big problem. Thought constantly flips between objective and subjective, as Nagel has shown us. Compare Nagel in Idea 6446. |
| 4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
| Full Idea: Utilitarian benevolence involves no particular attachments, and it is immune to the inverse square law. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 5) | |
| A reaction: Nicely put. The point is that the theory is inhuman, but Mill says it tells us what we should do, not what we actually tend to do. |
| 4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
| Full Idea: The view that the only alternative to the intellect is the will, and the source of ethical conviction is decisions about principles and ways of life, cannot be right; ethical conviction, like any conviction, must to some extent come to you passively. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 9) | |
| A reaction: Seems right. We cannot choose our factual beliefs (look at the sun and believe it is cloudy!). Could I 'decide' that it was right to betray my family just for fun? |
| 4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
| Full Idea: If ethics is a matter of decision, and we must face the responsibility and burden of those decisions, this ignores the obvious point that if we are uncertain, then we are uncertain what to decide. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 9) | |
| A reaction: Good point. The defence would be that the decision itself contains the seeds of certainty. Do something rather than nothing, and the sense of it will emerge. Modify as you go along. |
| 4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
| Full Idea: It is a mark of our having ethical values that we aim to reproduce them in our children. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 9) | |
| A reaction: Maybe beliefs imply education. A commitment to truth is an aspiration that others will agree, especially those over whom we have the greatest influence. |
| 4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
| Full Idea: Few women see a spontaneous abortion or early miscarriage as the same thing as having a child who is stillborn or who dies very soon after birth. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 6) | |
| A reaction: This implies a theory about the nature of what is lost. Everyone sees the difference between potential and actual. |
| 4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
| Full Idea: Speciesism is falsely modelled on racism and sexism, which really are prejudices; ..our arguments have to be founded on the human point of view; they cannot be derived from a point of view that is no one's point of view at all. | |
| From: Bernard Williams (Ethics and the Limits of Philosophy [1985], Ch. 6) | |
| A reaction: This must be wrong. How else are we going to judge cruelty to animals as wrong? The 'point of view of the Universe' (Sidgwick) is not an empty concept. |
| 16175 | A cause won't increase the effect frequency if other causes keep interfering [Cartwright,N] |
| Full Idea: A cause ought to increase the frequency of the effect, but this fact may not show up in the probabilities if other causes are at work. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 1.1) | |
| A reaction: [She cites Patrick Suppes for this one] Presumably in experimental situations you can weed out the interference, but that threatens to eliminate mere 'probability' entirely. |
| 6781 | There are fundamental explanatory laws (false!), and phenomenological laws (regularities) [Cartwright,N, by Bird] |
| Full Idea: Nancy Cartwright distinguishes between 'fundamental explanatory laws', which we should not believe, and 'phenomenological laws', which are regularities established on the basis of observation. | |
| From: report of Nancy Cartwright (How the Laws of Physics Lie [1983]) by Alexander Bird - Philosophy of Science Ch.4 | |
| A reaction: The distinction is helpful, so that we can be clearer about what everyone is claiming. We can probably all agree on the phenomenological laws, which are epistemological. Personally I claim truth for the best fundamental explanatory laws. |
| 16166 | Laws of appearances are 'phenomenological'; laws of reality are 'theoretical' [Cartwright,N] |
| Full Idea: Philosophers distinguish phenomenological from theoretical laws. Phenomenological laws are about appearances; theoretical ones are about the reality behind the appearances. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: I'm suspecting that Humeans only really believe in the phenomenological kind. I'm only interested in the theoretical kind, and I take inference to the best explanation to be the bridge between the two. Cartwright rejects the theoretical laws. |
| 16179 | Good organisation may not be true, and the truth may not organise very much [Cartwright,N] |
| Full Idea: There is no reason to think that the principles that best organise will be true, nor that the principles that are true will organise much. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.5) | |
| A reaction: This is aimed at the Mill-Ramsey-Lewis account of laws, as axiomatisations of the observed patterns in nature. |
| 16178 | There are few laws for when one theory meets another [Cartwright,N] |
| Full Idea: Where theories intersect, laws are usually hard to come by. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 2.3) | |
| A reaction: There are attempts at so-called 'bridge laws', to get from complex theories to simple ones, but her point is well made about theories on the same 'level'. |
| 16170 | To get from facts to equations, we need a prepared descriptions suited to mathematics [Cartwright,N] |
| Full Idea: To get from a detailed factual knowledge of a situation to an equation, we must prepare the description of the situation to meet the mathematical needs of the theory. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], Intro) | |
| A reaction: She is clearly on to something here, as Galileo is blatantly wrong in his claim that the book of nature is written in mathematics. Mathematics is the best we can manage in getting a grip on the chaos. |
| 16181 | Simple laws have quite different outcomes when they act in combinations [Cartwright,N] |
| Full Idea: For explanation simple laws must have the same form when they act together as when they act singly. ..But then what the law states cannot literally be true, for the consequences that occur if it acts alone are not what occurs when they act in combination. | |
| From: Nancy Cartwright (How the Laws of Physics Lie [1983], 3.6) | |
| A reaction: This is Cartwright's basic thesis. Her point is that the laws 'lie', because they claim to predict a particular outcome which never ever actually occurs. She says we could know all the laws, and still not be able to explain anything. |