34 ideas
| 13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
| Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2 | |
| A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths). |
| 9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
| Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1 | |
| A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries. |
| 18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
| Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2 | |
| A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy. |
| 18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
| Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms. | |
| From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3 | |
| A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field. |
| 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. |
| 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. |
| 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. |
| 7658 | Obviously there can't be a functional anaylsis of qualia if they are defined by intrinsic properties [Dennett] |
| Full Idea: If you define qualia as intrinsic properties of experiences considered in isolation from all their causes and effects, logically independent of all dispositional properties, then they are logically guaranteed to elude all broad functional analysis. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.8) | |
| A reaction: This is a good point - it seems daft to reify qualia and imagine them dangling in mid-air with all their vibrant qualities - but that is a long way from saying there is nothing more to qualia than functional roles. Functions must be exlained too. |
| 7655 | The work done by the 'homunculus in the theatre' must be spread amongst non-conscious agencies [Dennett] |
| Full Idea: All the work done by the imagined homunculus in the Cartesian Theater must be distributed among various lesser agencies in the brain, none of which is conscious. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: Dennett's account crucially depends on consciousness being much more fragmentary than most philosophers claim it to be. It is actually full of joints, which can come apart. He may be right. |
| 7657 | Intelligent agents are composed of nested homunculi, of decreasing intelligence, ending in machines [Dennett] |
| Full Idea: As long as your homunculi are more stupid and ignorant than the intelligent agent they compose, the nesting of homunculi within homunculi can be finite, bottoming out, eventually, with agents so unimpressive they can be replaced by machines. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.6) | |
| A reaction: [Dennett first proposed this in 'Brainstorms' 1978]. This view was developed well by Lycan. I rate it as one of the most illuminating ideas in the modern philosophy of mind. All complex systems (like aeroplanes) have this structure. |
| 7656 | I don't deny consciousness; it just isn't what people think it is [Dennett] |
| Full Idea: I don't maintain, of course, that human consciousness does not exist; I maintain that it is not what people often think it is. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.3) | |
| A reaction: I consider Dennett to be as near as you can get to an eliminativist, but he is not stupid. As far as I can see, the modern philosopher's bogey-man, the true total eliminativist, simply doesn't exist. Eliminativists usually deny propositional attitudes. |
| 7654 | What matters about neuro-science is the discovery of the functional role of the chemistry [Dennett] |
| Full Idea: Neuro-science matters because - and only because - we have discovered that the many different neuromodulators and other chemical messengers that diffuse throughout the brain have functional roles that make important differences. | |
| From: Daniel C. Dennett (Sweet Dreams [2005], Ch.1) | |
| A reaction: I agree with Dennett that this is the true ground for pessimism about spectacular breakthroughs in artificial intelligence, rather than abstract concerns about irreducible features of the mind like 'qualia' and 'rationality'. |
| 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? |
| 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. |
| 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. |
| 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. |
| 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'. |
| 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. |