50 ideas
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283) | |
| A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence. |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: Thagard picked this remark out, in support of his work on coherence. |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) |
| 18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
| Full Idea: Frege rejected the traditional categories as importing psychological and linguistic impurities into logic. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Ian Rumfitt - The Boundary Stones of Thought 1.2 | |
| A reaction: Resisting such impurities is the main motivation for making logic entirely symbolic, but it doesn't follow that the traditional categories have to be dropped. |
| 8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
| Full Idea: Just as functions are fundamentally different from objects, so also functions whose arguments are and must be functions are fundamentally different from functions whose arguments are objects. The latter are first-level, the former second-level, functions. | |
| From: Gottlob Frege (Function and Concept [1891], p.38) | |
| A reaction: In 1884 he called it 'second-order'. This is the standard distinction between first- and second-order logic. The first quantifies over objects, the second over intensional entities such as properties and propositions. |
| 8492 | Relations are functions with two arguments [Frege] |
| Full Idea: Functions of one argument are concepts; functions of two arguments are relations. | |
| From: Gottlob Frege (Function and Concept [1891], p.39) | |
| A reaction: Nowadays we would say 'two or more'. Another interesting move in the aim of analytic philosophy to reduce the puzzling features of the world to mathematical logic. There is, of course, rather more to some relations than being two-argument functions. |
| 17629 | Which premises are ultimate varies with context [Russell] |
| Full Idea: Premises which are ultimate in one investigation may cease to be so in another. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282) | |
| A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered. |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) | |
| A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments? |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) |
| 8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
| Full Idea: I am of the opinion that arithmetic is a further development of logic, which leads to the requirement that the symbolic language of arithmetic must be expanded into a logical symbolism. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: This may the the one key idea at the heart of modern analytic philosophy (even though logicism may be a total mistake!). Logic and arithmetical foundations become the master of ontology, instead of the servant. The jury is out on the whole enterprise. |
| 18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
| Full Idea: Frege regarded the existence of horses as a property of the concept 'horse'. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by Fred Sommers - Intellectual Autobiography 'Realism' |
| 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. |
| 4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
| Full Idea: Frege's theory of properties (which he calls 'concepts') yields too few properties, by identifying coextensive properties, and also too many, by letting every predicate express a property. | |
| From: comment on Gottlob Frege (Function and Concept [1891]) by DH Mellor / A Oliver - Introduction to 'Properties' §2 | |
| A reaction: Seems right; one extension may have two properties (have heart/kidneys), two predicates might express the same property. 'Cutting nature at the joints' covers properties as well as objects. |
| 8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
| Full Idea: I regard a regular definition of 'object' as impossible, since it is too simple to admit of logical analysis. Briefly: an object is anything that is not a function, so that an expression for it does not contain any empty place. | |
| From: Gottlob Frege (Function and Concept [1891], p.32) | |
| A reaction: Here is the core of the programme for deriving our ontology from our logic and language, followed through by Russell and Quine. Once we extend objects beyond the physical, it becomes incredibly hard to individuate them. |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought. |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) |
| 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. |
| 17631 | Induction is inferring premises from consequences [Russell] |
| Full Idea: The inferring of premises from consequences is the essence of induction. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
| A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
| 9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
| Full Idea: Concepts, for Frege, are the ontological counterparts of predicative expressions. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: That sounds awfully like what many philosophers call 'universals'. Frege, as a platonist (at least about numbers), I would take to be in sympathy with that. At least we can say that concepts seem to be properties. |
| 10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
| Full Idea: Frege had a notorious difficulty over the concept 'horse', when he suggests that if we wish to assert something about a concept, we are obliged to proceed indirectly by speaking of an object that represents it. | |
| From: report of Gottlob Frege (Function and Concept [1891], Ch.2.II) by Bob Hale - Abstract Objects | |
| A reaction: This sounds like the thin end of a wedge. The great champion of objects is forced to accept them here as a façon de parler, when elsewhere they have ontological status. |
| 8488 | A concept is a function whose value is always a truth-value [Frege] |
| Full Idea: A concept in logic is closely connected with what we call a function. Indeed, we may say at once: a concept is a function whose value is always a truth-value. ..I give the name 'function' to what is meant by the 'unsaturated' part. | |
| From: Gottlob Frege (Function and Concept [1891], p.30) | |
| A reaction: So a function becomes a concept when the variable takes a value. Problems arise when the value is vague, or the truth-value is indeterminable. |
| 9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
| Full Idea: For Frege, concepts differ from objects in being inherently incomplete in nature. | |
| From: report of Gottlob Frege (Function and Concept [1891]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.2 | |
| A reaction: This is because they are 'unsaturated', needing a quantified variable to complete the sentence. This could be a pointer towards Quine's view of properties, as simply an intrinsic feature of predication about objects, with no separate identity. |
| 4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
| Full Idea: From sameness of meaning there does not follow sameness of thought expressed. A fact about the Morning Star may express something different from a fact about the Evening Star, as someone may regard one as true and the other false. | |
| From: Gottlob Frege (Function and Concept [1891], p.14) | |
| A reaction: This all gets clearer if we distinguish internalist and externalist theories of content. Why take sides on this? Why not just ask 'what is in the speaker's head?', 'what does the sentence mean in the community?', and 'what is the corresponding situation?' |
| 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. |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275) |
| 8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
| Full Idea: The ontological proof of God's existence suffers from the fallacy of treating existence as a first-level concept. | |
| From: Gottlob Frege (Function and Concept [1891], p.38 n) | |
| A reaction: [See Idea 8490 for first- and second-order functions] This is usually summarised as the idea that existence is a quantifier rather than a predicate. |