92 ideas
| 17774 | Definitions make our intuitions mathematically useful [Mayberry] |
| Full Idea: Definition provides us with the means for converting our intuitions into mathematically usable concepts. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
| Full Idea: When you have proved something you know not only that it is true, but why it must be true. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) | |
| A reaction: Note the word 'must'. Presumably both the grounding and the necessitation of the truth are revealed. |
| 5728 | The concept of truth was originated by the senses [Lucretius] |
| Full Idea: The concept of truth was originated by the senses. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.479) | |
| A reaction: This is a refreshing challenge to the modern view of truth, which seems entirely entangled with language. Truth seems a useful concept when discussing the workings of an animal mind. As you get closer to an object, you see it more 'truly'. |
| 17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
| Full Idea: Set theory cannot be an axiomatic theory, because the very notion of an axiomatic theory makes no sense without it. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: This will come as a surprise to Penelope Maddy, who battles with ways to accept the set theory axioms as the foundation of mathematics. Mayberry says that the basic set theory required is much more simple and intuitive. |
| 17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
| Full Idea: We can give a semi-categorical axiomatisation of set-theory (all that remains undetermined is the size of the set of urelements and the length of the sequence of ordinals). The system is second-order in formalisation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.413-2) | |
| A reaction: I gather this means the models may not be isomorphic to one another (because they differ in size), but can be shown to isomorphic to some third ingredient. I think. Mayberry says this shows there is no such thing as non-Cantorian set theory. |
| 17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
| Full Idea: The (misnamed!) Axiom of Infinity expresses Cantor's fundamental assumption that the species of natural numbers is finite in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
| Full Idea: The idea of 'generating' sets is only a metaphor - the existence of the hierarchy is established without appealing to such dubious notions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) | |
| A reaction: Presumably there can be a 'dependence' or 'determination' relation which does not involve actual generation. |
| 17803 | Limitation of size is part of the very conception of a set [Mayberry] |
| Full Idea: Our very notion of a set is that of an extensional plurality limited in size. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
| Full Idea: In the mainstream tradition of modern logic, beginning with Boole, Peirce and Schröder, descending through Löwenheim and Skolem to reach maturity with Tarski and his school ...saw logic as a branch of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-1) | |
| A reaction: [The lesser tradition, of Frege and Russell, says mathematics is a branch of logic]. Mayberry says the Fregean tradition 'has almost died out'. |
| 17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
| Full Idea: First-order logic is very weak, but therein lies its strength. Its principle tools (Compactness, Completeness, Löwenheim-Skolem Theorems) can be established only because it is too weak to axiomatize either arithmetic or analysis. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.411-2) | |
| A reaction: He adds the proviso that this is 'unless we are dealing with structures on whose size we have placed an explicit, finite bound' (p.412-1). |
| 17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
| Full Idea: Second-order logic is a powerful tool of definition: by means of it alone we can capture mathematical structure up to isomorphism using simple axiom systems. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
| Full Idea: The 'logica magna' [of the Fregean tradition] has quantifiers ranging over a fixed domain, namely everything there is. In the Boolean tradition the domains differ from interpretation to interpretation. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.410-2) | |
| A reaction: Modal logic displays both approaches, with different systems for global and local domains. |
| 17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
| Full Idea: No logic which can axiomatize real analysis can have the Löwenheim-Skolem property. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
| Full Idea: The purpose of a 'classificatory' axiomatic theory is to single out an otherwise disparate species of structures by fixing certain features of morphology. ...The aim is to single out common features. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) |
| 17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
| Full Idea: The central dogma of the axiomatic method is this: isomorphic structures are mathematically indistinguishable in their essential properties. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.406-2) | |
| A reaction: Hence it is not that we have to settle for the success of a system 'up to isomorphism', since that was the original aim. The structures must differ in their non-essential properties, or they would be the same system. |
| 17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
| Full Idea: The purpose of what I am calling 'eliminatory' axiomatic theories is precisely to eliminate from mathematics those peculiar ideal and abstract objects that, on the traditional view, constitute its subject matter. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-1) | |
| A reaction: A very interesting idea. I have a natural antipathy to 'abstract objects', because they really mess up what could otherwise be a very tidy ontology. What he describes might be better called 'ignoring' axioms. The objects may 'exist', but who cares? |
| 17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
| Full Idea: No logic which can axiomatise arithmetic can be compact or complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) | |
| A reaction: I take this to be because there are new truths in the transfinite level (as well as the problem of incompleteness). |
| 17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
| Full Idea: We eliminate the real numbers by giving an axiomatic definition of the species of complete ordered fields. These axioms are categorical (mutually isomorphic), and thus are mathematically indistinguishable. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: Hence my clever mathematical friend says that it is a terrible misunderstanding to think that mathematics is about numbers. Mayberry says the reals are one ordered field, but mathematics now studies all ordered fields together. |
| 17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
| Full Idea: Quantities for Greeks were concrete things - lines, surfaces, solids, times, weights. At the centre of their science of quantity was the beautiful theory of ratio and proportion (...in which the notion of number does not appear!). | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) | |
| A reaction: [He credits Eudoxus, and cites Book V of Euclid] |
| 17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
| Full Idea: The abstract objects of modern mathematics, the real numbers, were invented by the mathematicians of the seventeenth century in order to simplify and to generalize the Greek science of quantity. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.407-2) |
| 17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
| Full Idea: In Cantor's new vision, the infinite, the genuine infinite, does not disappear, but presents itself in the guise of the absolute, as manifested in the species of all sets or the species of all ordinal numbers. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
| Full Idea: We may describe Cantor's achievement by saying, not that he tamed the infinite, but that he extended the finite. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.414-2) |
| 17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
| Full Idea: If we grant, as surely we must, the central importance of proof and definition, then we must also grant that mathematics not only needs, but in fact has, foundations. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) |
| 17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
| Full Idea: The ultimate principles upon which mathematics rests are those to which mathematicians appeal without proof; and the primitive concepts of mathematics ...themselves are grasped directly, if grasped at all, without the mediation of definition. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-1) | |
| A reaction: This begs the question of whether the 'grasping' is purely a priori, or whether it derives from experience. I defend the latter, and Jenkins puts the case well. |
| 17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
| Full Idea: An account of the foundations of mathematics must specify four things: the primitive concepts for use in definitions, the rules governing definitions, the ultimate premises of proofs, and rules allowing advance from premises to conclusions. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.405-2) |
| 17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
| Full Idea: No axiomatic theory, formal or informal, of first or of higher order can logically play a foundational role in mathematics. ...It is obvious that you cannot use the axiomatic method to explain what the axiomatic method is. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-2) |
| 17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
| Full Idea: The sole theoretical interest of first-order Peano arithmetic derives from the fact that it is a first-order reduct of a categorical second-order theory. Its axioms can be proved incomplete only because the second-order theory is categorical. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
| Full Idea: If we did not know that the second-order axioms characterise the natural numbers up to isomorphism, we should have no reason to suppose, a priori, that first-order Peano Arithmetic should be complete. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-1) |
| 17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
| Full Idea: The idea that set theory must simply be identified with first-order Zermelo-Fraenkel is surprisingly widespread. ...The first-order axiomatic theory of sets is clearly inadequate as a foundation of mathematics. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.412-2) | |
| A reaction: [He is agreeing with a quotation from Skolem]. |
| 17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
| Full Idea: One does not have to translate 'ordinary' mathematics into the Zermelo-Fraenkel system: ordinary mathematics comes embodied in that system. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.415-1) | |
| A reaction: Mayberry seems to be a particular fan of set theory as spelling out the underlying facts of mathematics, though it has to be second-order. |
| 17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
| Full Idea: The fons et origo of all confusion is the view that set theory is just another axiomatic theory and the universe of sets just another mathematical structure. ...The universe of sets ...is the world that all mathematical structures inhabit. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.416-1) |
| 17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
| Full Idea: The abstractness of the old fashioned real numbers has been replaced by generality in the modern theory of complete ordered fields. | |
| From: John Mayberry (What Required for Foundation for Maths? [1994], p.408-2) | |
| A reaction: In philosophy, I'm increasingly thinking that we should talk much more of 'generality', and a great deal less about 'universals'. (By which I don't mean that redness is just the set of red things). |
| 5702 | The senses are much the best way to distinguish true from false [Lucretius] |
| Full Idea: What can be a surer guide to the distinction of true from false than our own senses? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.700) | |
| A reaction: This doesn't say they are the only guide, which leaves room for guides such as what is consistent or self-evident or inferred. There is enough here, though, to show that the Epicureans were empiricists in a fairly modern way. |
| 5729 | If the senses are deceptive, reason, which rests on them, is even worse [Lucretius] |
| Full Idea: The structure of your reasoning must be rickety and defective, if the senses on which it rests are themselves deceptive. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.518) | |
| A reaction: This strikes me as one of the most basic tenets of empiricism. It denies the existence of 'pure' reason, and instead asserts that it is built out of complex and abstracted sense experience, which makes it ultimately a second-class citizen. |
| 5697 | The only possible standard for settling doubts is the foundation of the senses [Lucretius] |
| Full Idea: If a belief resting directly on the foundation of the senses is not valid, there will be no standard to which we can refer any doubt on obscure questions for rational confirmation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.422) | |
| A reaction: A classic statement of empiricist foundationalism. The Epicureans don't appear to have any time for a priori truths at all. I wonder if they settled mathematical disputes by counting objects and drawing diagrams? |
| 5727 | Most supposed delusions of the senses are really misinterpretations by the mind [Lucretius] |
| Full Idea: Paradoxical experiences (such a dreams and illusions) cannot shake our faith in the senses. Most of the illusion is due to the mental assumptions we ourselves superimpose, so that things not perceived by the senses pass for perceptions. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.462) | |
| A reaction: Some misinterpretations of the senses, such as thinking a square tower round, are the result of foolish lack of judgement, but actual delusions within the senses, such as a ringing in the ears, or a pain in a amputated leg, seem like real sense failures. |
| 5714 | Even simple facts are hard to believe at first hearing [Lucretius] |
| Full Idea: No fact is so simple that it is not harder to believe than to doubt at the first presentation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1022) | |
| A reaction: Hence induction is just 'drumming it in' until you come to believe it. There are good evolutionary reasons why we should be like this, because we would otherwise believe all sorts of silly half-perceptions in the gloaming. |
| 5718 | The mind is in the middle of the breast, because there we experience fear and joy [Lucretius] |
| Full Idea: The guiding principle of the whole body is the mind or intellect, which is firmly lodged in the mid-region of the breast. Here is felt fear and alarm, and the caressing pulse of joy. Here, then is the seat of the intellect and mind. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.140) | |
| A reaction: Even by this date thinking people were not clear that the mind is in the brain. They paid insufficient attention to head injuries. The emotions are felt to have a location, but intellect and principles are not. |
| 5717 | The mind is a part of a man, just like a hand or an eye [Lucretius] |
| Full Idea: First, I maintain that the mind, which we often call the intellect, the seat of guidance and control of life, is part of a man, no less than hand or foot or eyes are parts of a whole living creature. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.95) | |
| A reaction: Presumably Lucretius asserts this because some people were denying it. Sounds like common sense to me. The only reason I can see for anyone denying what he says is if they are desperate to survive death. |
| 21387 | The separate elements and capacities of a mind cannot be distinguished [Lucretius] |
| Full Idea: No single element [of the soul] can be separated, nor can their capacities be divided spatially; they are like the multiple powers of a single body | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.262), quoted by A.A. Long - Hellenistic Philosophy 2.7 | |
| A reaction: It is interesting that this comes from someone with a strongly physicalist view of the mind (though not, if I recall, focusing on the brain). He is still totally impressed by the unified phenomenology of mental experience. He is an empiricist. |
| 5709 | The actions of the mind are not determinate and passive, because atoms can swerve [Lucretius] |
| Full Idea: The fact that the mind itself has no internal necessity to determine its every act and compel it to suffer in helpless passivity - this is due to the slight swerve of the atoms at no determinate time or place. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.294) | |
| A reaction: No one likes this proposal much, but it is very intriguing. The Epicureans had seen a problem, one which doesn't bother me much. If, nowadays, you are a reductive physicalist who believes in free will, you have a philosophical nightmare ahead of you. |
| 5695 | Only bodies can touch one another [Lucretius] |
| Full Idea: Nothing can touch or be touched except body. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.303) | |
| A reaction: This is the key objection to interactionism, and the main reason why the atomists have a thoroughly material view of the mind. It is an induction from a very large number of instances, but the argument is not, of course, conclusive. |
| 5711 | The earth is and always has been an insentient being [Lucretius] |
| Full Idea: The earth is and always has been an insentient being. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.658) | |
| A reaction: The fact that Epicurus needs to deny this shows that some idea close to panpsychism must still have been around in his time. He is discussing gods at the time, so maybe pantheism was the view being attacked, but that is a subset of panpsychism. |
| 5712 | Particles may have sensation, but eggs turning into chicks suggests otherwise [Lucretius] |
| Full Idea: There is the possibility that particles have senses like those of an animate being as a whole, …but from the fact that we perceive eggs turning into live fledglings, we may infer that sense can be generated from the insentient. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.914) | |
| A reaction: He gives other arguments for his view. The egg example is not a strong argument, but is precisely our puzzle of how consciousness can emerge from the process of evolution, and natural selection makes dualism look unlikely. |
| 5719 | The mind moves limbs, wakes the body up, changes facial expressions, which involve touch [Lucretius] |
| Full Idea: Mind and spirit are both composed of matter, as we see them propelling limbs, rousing the body from sleep, changing the expression of the face, and guiding the whole man - activities which clearly involves touch, which involves matter. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.164) | |
| A reaction: This is the inverse of Descartes' interaction problem, and strikes me as a straightforward common sense truth. However, if you believe in spiritual gods, this gives you a model for the interaction (however mysterious) of matter and spirit. |
| 5724 | Lions, foxes and deer have distinct characters because their minds share in their bodies [Lucretius] |
| Full Idea: Why are lions ferocious, foxes crafty, and deer timid? It can only be because the mind always shares in the specific growth of the body according to its seed and breed. If it were immortal and reincarnated, living things would have jumbled characters. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.743) | |
| A reaction: A nice argument which I have not encountered in modern times. Of course, even Descartes admits that the mind is intermingled with the body, but it seems that the essential character of a mind is dictated by the body. |
| 5713 | You needn't be made of laughing particles to laugh, so why not sensation from senseless seeds? [Lucretius] |
| Full Idea: One can laugh without being composed of laughing particles, ..so why cannot the things that we see gifted with sensation be compounded of seeds that are wholly senseless? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.988) | |
| A reaction: Lovely argument! You might feel driven to panpsychism in your desperation to explain the 'weirdness' of consciousness, but it would be mad to attribute laughter to basic matter, so comedy has to 'emerge' at some point. |
| 6611 | One man's meat is another man's poison [Lucretius] |
| Full Idea: What is food to one may be literally poison to others. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.638) | |
| A reaction: This seems to be the origin of the well-known saying. This is not relativism of perception, but a relativism of how individuals actually respond to the world. It sums up the position with, say, the operas of Wagner. |
| 5730 | Our bodies weren't created to be used; on the contrary, their creation makes a use possible [Lucretius] |
| Full Idea: Nothing in our bodies was born in order that we might be able to use it, but the thing born creates the use. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], IV.834) | |
| A reaction: This remark (strongly opposed to Aristotle's view of human function and nature) raises the obvious question of why the body is so very useful for staying alive. Most of its uses are not random. Lucretius would abandon this view if he read Darwin. |
| 23110 | Human injustice is not a permanent feature of communities [Rawls] |
| Full Idea: Men's propensity to injustice is not a permanent aspect of community life. | |
| From: John Rawls (A Theory of Justice [1972], p.245), quoted by John Kekes - Against Liberalism | |
| A reaction: This attitude is dismissed by Kekes, with some justification, as naïve optimism. What could be Rawls's grounds for making such a claim? It couldn't be the facts of human history. |
| 5726 | The dead are no different from those who were never born [Lucretius] |
| Full Idea: One who no longer is cannot suffer, or differ in any way from one who has never been born. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.867) | |
| A reaction: There is a special kind of pain in being poor if you were once rich, which is not suffered by those who experience only poverty. Lucretius is right, but we are concerned with how we feel now, not with how we won't feel once dead. |
| 15676 | Rawls defends the priority of right over good [Rawls, by Finlayson] |
| Full Idea: Rawls defends the thesis of the priority of the right over the good. | |
| From: report of John Rawls (A Theory of Justice [1972]) by James Gordon Finlayson - Habermas Ch.7:100 | |
| A reaction: It depends whether you are talking about actions, or about states of affairs. I don't see how any state of affairs can be preferred to the good one. It may be that the highest duty of action is to do what is right, rather than to achieve what is good. |
| 5705 | Nature only wants two things: freedom from pain, and pleasure [Lucretius] |
| Full Idea: Nature only clamours for two things, a body free from pain, a mind released from worry and fear for the enjoyment of pleasurable sensation. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.21) | |
| A reaction: I can't help agreeing with those (like Aristotle) who consider this a very demeaning view of human life. See Idea 99. Bentham agrees with Lucretius (Idea 3777). I think they are largely right, but not entirely. Other motives are possible than sensations. |
| 4123 | A fair arrangement is one that parties can agree to without knowing how it will benefit them personally [Rawls, by Williams,B] |
| Full Idea: Rawls's theory is an elaboration of a simple idea: a fair system of arrangements is one that the parties can agree to without knowing how it will benefit them personally. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Bernard Williams - Ethics and the Limits of Philosophy Ch.5 | |
| A reaction: The essence of modern Kantian contractualism. It is an appealing principle for building a rational world, but I hear Nietzsche turning in his grave. |
| 21051 | Check your rationality by thinking of your opinion pronounced by the supreme court [Rawls] |
| Full Idea: To check whether we are following public reason we might ask: how would our argument strike us presented in the form of a supreme court opinion? | |
| From: John Rawls (Political Liberalism [1993], p.254), quoted by Michael J. Sandel - Justice: What's the right thing to do? 10 | |
| A reaction: A very nice practical implementation of Kantian universalisability. How would your opinion sound if it were written into a constitution? |
| 3279 | Utilitarianism inappropriately scales up the individual willingness to make sacrifices [Rawls, by Nagel] |
| Full Idea: Rawls claims that utilitarianism applies to the problem of many interests a method appropriate for one individual. A single person may accept disadvantages in exchange for benefits, but in society other people get the benefits. | |
| From: report of John Rawls (A Theory of Justice [1972], p.74,104) by Thomas Nagel - Equality §7 |
| 22406 | The maximisation of happiness must be done fairly [Rawls, by Smart] |
| Full Idea: Rawls has suggested that we should maximise the general happiness only if we do so in a fair way. | |
| From: report of John Rawls (Justice as fairness: Political not Metaphysical [1958]) by J.J.C. Smart - Outline of a System of Utilitarianism 6 | |
| A reaction: Rawls is usually seen as an opponent of utilitarianism, but if we allow a few supplementary rules we can improve the theory. After all, it has a meta-rule that 'everybody counts as one'. What other supplementary values can there be? Honesty? |
| 21137 | Rawls rejected cosmopolitanism because it doesn't respect the autonomy of 'peoples' [Rawls, by Shorten] |
| Full Idea: Rawls rejected the cosmopolitan extension of his theory because he thought it failed to respect the political autonomy of 'peoples', which was his term of art for societies or political communities. | |
| From: report of John Rawls (The Law of Peoples [1999], p.115-8) by Andrew Shorten - Contemporary Political Theory 09 | |
| A reaction: Interesting that you might well start with the concept of 'a people', prior to some sort of social contract, but end up with rather alarming conflicts or indifference between rival peoples. Why should my people help in the famine next door? |
| 3280 | Why does the rational agreement of the 'Original Position' in Rawls make it right? [Nagel on Rawls] |
| Full Idea: Why does what it is rational to agree to in Rawls' 'Original Position' determine what is right? | |
| From: comment on John Rawls (A Theory of Justice [1972]) by Thomas Nagel - Equality §7 |
| 20552 | The original position models the idea that citizens start as free and equal [Rawls, by Swift] |
| Full Idea: The original position is presented by Rawls as modelling the sense in which citizens are to be understood as free and equal. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Adam Swift - Political Philosophy (3rd ed) 3 'Strikes' | |
| A reaction: In other words, Rawls's philosophy is not a demonstration of why we should be liberals, but a guidebook for how liberals should go about organising society. |
| 18636 | Choose justice principles in ignorance of your own social situation [Rawls] |
| Full Idea: The principles of justice are chosen behind a veil of ignorance. ...Since all are similarly situated and no one is able to design principles to favor his particular condition, the principles of justice are the rest of a fair agreement or bargain. | |
| From: John Rawls (A Theory of Justice [1972], §03) | |
| A reaction: A famous idea. It tries to impose a Kantian impartiality onto the assessment of political principles. It is a beautifully simple idea, and saying that such impartiality never occurs is no objection to it. Think of a planet far far away. |
| 18631 | All desirable social features should be equal, unless inequality favours the disadvantaged [Rawls] |
| Full Idea: All social primary goods - liberty and opportunity, income and wealth, and the bases of self-respect - are to be distributed equally unless an unequal distribution of any or all of these goods is to the advantage of the least favoured. | |
| From: John Rawls (A Theory of Justice [1972], §46) | |
| A reaction: In the wholehearted capitalism of the 21st century this sounds like cloud-cuckoo land. As an 'initial position' (just as in the 'Republic') the clean slate brings out some interesting principles. Actual politics takes vested interests as axiomatic. |
| 21119 | Power is only legitimate if it is reasonable for free equal citizens to endorse the constitution [Rawls] |
| Full Idea: Exercise of political power is fully proper only when it is exercised in accordance with a constitution the essentials of which all citizens as free and equal may reasonably be expected to endorse in light of principles and ideals acceptable to reason. | |
| From: John Rawls (Political Liberalism [1993], p.217), quoted by Andrew Shorten - Contemporary Political Theory 02 | |
| A reaction: This is not the actual endorsement of Rousseau, or the tacit endorsement of Locke (by living there), but adds a Kantian appeal to a rational consensus, on which rational people should converge. Very Enlightenment. 'Hypothetical consent'. |
| 20538 | Utilitarians lump persons together; Rawls somewhat separates them; Nozick wholly separates them [Swift on Rawls] |
| Full Idea: Rawls objects to utilitarianism because it fails to take seriously the separateness of persons (because there is no overall person to enjoy the overall happiness). But Nozick thinks Rawls does not take the separateness of persons seriously enough. | |
| From: comment on John Rawls (A Theory of Justice [1972]) by Adam Swift - Political Philosophy (3rd ed) 1 'Nozick' | |
| A reaction: In this sense, Nozick seems to fit our picture of a liberal more closely than Rawls does. I think they both exaggerate the separateness of persons, based on a false concept of human nature. |
| 9277 | Rawls's account of justice relies on conventional fairness, avoiding all moral controversy [Gray on Rawls] |
| Full Idea: Rawls's account of justice works only with widely accepted intuitions of fairness and relies at no point on controversial positions in ethics. The fruit of this modesty is a pious commentary on conventional moral beliefs. | |
| From: comment on John Rawls (A Theory of Justice [1972]) by John Gray - Straw Dogs 3.6 | |
| A reaction: Presumably this is the thought which provoked Nozick to lob his grenade on the subject. It resembles the charges of Schopenhauer and Nietzsche against Kant, that he was just dressing up conventional morality. Are 'controversial' ethics good? |
| 23420 | In a pluralist society we can't expect a community united around one conception of the good [Rawls] |
| Full Idea: The fact of pluralism means that the hope of political community must be abandoned, if by such a community we mean a political society united in affirming a general and comprehensive conception of the good. | |
| From: John Rawls (The Idea of Overlapping Consensus [1987]), quoted by Will Kymlicka - Community 'legitimacy' | |
| A reaction: A moderate pluralism might be manageable, but strong, diverse and dogmatic beliefs among sub-groups probably make it impossible. |
| 20527 | Liberty Principle: everyone has an equal right to liberties, if compatible with others' liberties [Rawls] |
| Full Idea: First Principle [Liberty]: Each person is to have an equal right to the most extensive total system of equal basic liberties compatible with a similar system of liberty for all. | |
| From: John Rawls (A Theory of Justice [1972], 46) | |
| A reaction: This is the result of consensus after the initial ignorant position of assessment. It is characteristic of liberalism. I'm struggling to think of a disagreement. |
| 21018 | The social contract has problems with future generations, national boundaries, disabilities and animals [Rawls, by Nussbaum] |
| Full Idea: Rawls saw four difficulties for justice in the social contract approach: future generations; justice across national boundaries; fair treatment of people with disabilities; and moral issues involving non-human animals. | |
| From: report of John Rawls (A Theory of Justice [1972]) by Martha Nussbaum - Creating Capabilities 4 | |
| A reaction: These are all classic examples of groups who do not have sufficient power to negotiate contracts. |
| 21041 | Justice concerns not natural distributions, or our born location, but what we do about them [Rawls] |
| Full Idea: The natural distribution is neither just nor unjust; nor is it unjust that persons are born into society at some particular position. These are simply natural facts. What is just and unjust is the way that institutions deal with these facts. | |
| From: John Rawls (A Theory of Justice [1972], 17) | |
| A reaction: Lovely quotation. There is no point in railing against the given, and that includes what is given by history, as well as what is given by nature. It comes down to intervening, in history and in nature. How much intervention will individuals tolerate? |
| 23583 | If an aggression is unjust, the constraints on how it is fought are much stricter [Rawls] |
| Full Idea: When a country's right to war is questionable and uncertain, the constraints on the means it can use are all the more severe. | |
| From: John Rawls (A Theory of Justice [1972], p.379), quoted by Michael Walzer - Just and Unjust Wars 14 | |
| A reaction: This is Rawls opposing the idea that combatants are moral equals. The restraints are, of course, moral. In practice aggressors are usually the worst behaved. |
| 5716 | Nature runs the universe by herself without the aid of gods [Lucretius] |
| Full Idea: Nature is free and uncontrolled by proud masters and runs the universe by herself without the aid of gods. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1094) | |
| A reaction: A nice remark. This apparent personification of nature implies the application of laws to an essentially passive reality. See Idea 5442 and Nature|Laws of Nature|Essentialism for a different view. |
| 5704 | There can be no centre in infinity [Lucretius] |
| Full Idea: There can be no centre in infinity. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.1069) | |
| A reaction: This is highly significant, because if we can establish that the universe is infinite (as Epicurus believes), it follows that the human race cannot be at the centre of it, as the Ptolemaic/medieval view proposed. |
| 5703 | The universe must be limitless, since there could be nothing outside to limit it [Lucretius] |
| Full Idea: The universe is not bounded in any direction. If it were, it would necessarily have a limit somewhere, but a thing cannot have a limit unless there is something outside to limit it. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.959) | |
| A reaction: This is a subtler argument than the mere enquiry about why you would have to stop at the end of the universe. It still seems a nice argument, though Einstein's curvature of space seems to have thwarted it. |
| 5693 | Everything is created and fed by nature from atoms, and they return to atoms in death [Lucretius] |
| Full Idea: The ultimate realities of heaven and the gods are the atoms, from which nature creates all things and increases and feeds them, and into which, when they perish, nature again resolves them. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.46) | |
| A reaction: Sounds right to me. Nothing in modern particle theory and string theory has refuted this claim. But what makes the atoms move, and what makes them combine in an orderly way? Is the orderliness of atoms made of atoms? Essences? |
| 5701 | If an object is infinitely subdivisible, it will be the same as the whole universe [Lucretius] |
| Full Idea: If there are no atoms, the smallest bodies will have infinite parts, since they can be endlessly halved. ..But then there will be no difference between the smallest thing and the whole universe, as they will equally have infinite parts. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.620) | |
| A reaction: Another argument which remains effective even now. There must surely (intuitively) be more divisions possible in a large object than in a small one? Unless of course there were many different sizes of infinity…. See Cantor. |
| 5708 | In downward motion, atoms occasionally swerve slightly for no reason [Lucretius] |
| Full Idea: When atoms are travelling straight down through empty space by their own weight, at quite indeterminate times and places they swerve ever so little from their course. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.217) | |
| A reaction: Never a popular theory because it seems to breach the Principle of Sufficient Reason (Ideas 306 + 3646). This seems to be the beginning of a strong need for the concept of free will, and an underlying explanation. Most thinkers put mind outside nature. |
| 17004 | Nothing can break the binding laws of eternity [Lucretius] |
| Full Idea: Nothing has power to break the binding laws of eternity. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], 5.56) | |
| A reaction: This seems to be virtually the only remark from the ancient world suggesting that there are 'laws' of nature, so I'm guessing it is a transient metaphor, not a theory about nature. 'Even the gods must bow to necessity'. |
| 5706 | Atoms move themselves [Lucretius] |
| Full Idea: Atoms move themselves. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.133) | |
| A reaction: Something has to move itself, I suppose, but then that could be psuché, giving us free will (see Idea 1424). Why does Epicurus need the 'swerve' if atoms are self-movers? See Idea 5708. |
| 5696 | If there were no space there could be no movement, or even creation [Lucretius] |
| Full Idea: We see movement everywhere, but if there were no empty space, things would be denied the power of movement - or rather, they could not possibly have come into existence, embedded as they would have been in motionless matter. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.342) | |
| A reaction: This still seems a good argument, if reality is made of particles. People can move in a crowd until it becomes too dense. |
| 5700 | It is quicker to break things up than to assemble them [Lucretius] |
| Full Idea: Anything can be more speedily disintegrated than put together again. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.558) | |
| A reaction: Clearly the concept of entropy was around long before anyone tried to give a systematic or mathematical account of it. |
| 5698 | We can only sense time by means of movement, or its absence [Lucretius] |
| Full Idea: It must not be claimed that anyone can sense time by itself apart from the movement of things or their restful immobility. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.465) | |
| A reaction: This seems a remarkably Einsteinian remark, though he is only talking of the epistemology of the matter, not the ontology. We are not far from the concept of space-time here. |
| 5715 | This earth is very unlikely to be the only one created [Lucretius] |
| Full Idea: It is in the highest degree unlikely that this earth and sky is the only one to have been created. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.1057) | |
| A reaction: I can only admire the science fiction imagination of this, which roughly agrees with the assessment of modern cosmologists. We think imagination was cramped in the ancient world, and now wanders free - but that is not so. |
| 5694 | Nothing can be created by divine power out of nothing [Lucretius] |
| Full Idea: In studying the workings of nature, our starting-point will be this principle: nothing can ever be created by divine power out of nothing. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.152) | |
| A reaction: This claim seems to cry out for a bit of empiricist caution. What observation has convinced Lucretius that creation out of nothing is impossible? The early Christians switched to the view that divine creation is 'ex nihilo' - out of nothing. |
| 5699 | If matter wasn't everlasting, everything would have disappeared by now [Lucretius] |
| Full Idea: If the matter in things had not been everlasting, everything by now would have gone back to nothing, and the things we see would be the product of rebirth out of nothing. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], I.544) | |
| A reaction: See Idea 1431, which is Aquinas's Third Way of proving God. Aquinas thinks there must be a necessary being outside of the system, but Lucretius thinks there must be some necessary existence within the system (as Hume had suggested). |
| 5707 | The universe can't have been created by gods, because it is too imperfect [Lucretius] |
| Full Idea: The universe was certainly not created for us by divine power: it is so full of imperfections. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.180) | |
| A reaction: This is certainly a problem if God is 'supremely perfect', as Descartes proposed, because then the universe would also have to be supremely perfect. See Idea 2114 for a possible answer from Leibniz. Hume agrees with Epicurus about design. |
| 5710 | Gods are tranquil and aloof, and have no need of or interest in us [Lucretius] |
| Full Idea: The nature of deity is to enjoy immortal existence in utter tranquillity, aloof and detached from our affairs. It is free from all pain and peril, strong in its own resources, exempt from any need of us, indifferent to our merits and immune from anger. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], II.652) | |
| A reaction: This seems to be the seed of late seventeenth century deism - the idea of a Creator who is now absent, and ignores our prayers. At that time 'Epicurean' became a synonym for atheist, but Epicureans never quite reached that point. |
| 5731 | Why does Jupiter never hurl lightning from a blue sky? [Lucretius] |
| Full Idea: Why does Jupiter never hurl his thunderbolt upon the earth and let loose his thunder out of a sky that is wholly blue? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], VI.400) | |
| A reaction: Nice question! It really doesn't take very much to see through superstition, and the fact that most people believed such things shows how staggeringly uncritical they were in their thinking, until philosophers appeared and taught them how to reason. |
| 5722 | For a separated spirit to remain sentient it would need sense organs attached to it [Lucretius] |
| Full Idea: If spirit is immortal and can remain sentient when divorced from our body, we must credit it with possession of five senses; but eyes or nostrils or hand or tongue or ears cannot be attached to a disembodied spirit. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.624) | |
| A reaction: This is a powerful argument against immortality. If you are going to see, you must interact with photons; to hear you must respond to compression waves; to smell you must react to certain molecules. Immortality without those would be a bit dull. |
| 5725 | An immortal mind couldn't work harmoniously with a mortal body [Lucretius] |
| Full Idea: It is crazy to couple a mortal object with an eternal and suppose that they can work in harmony and mutually interact. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.799) | |
| A reaction: An interesting thought, though not a terrible persuasive argument. A god would indeed be a bit restless if it were chained to a human being, but it would presumably knuckle down to the task if firmly instructed to do it by Zeus. |
| 5720 | Spirit is mortal [Lucretius] |
| Full Idea: Spirit is mortal. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.542) | |
| A reaction: This is asserted at an historical moment when immortality is beginning to grip everyone's imagination. |
| 5721 | The mind is very small smooth particles, which evaporate at death [Lucretius] |
| Full Idea: Since the substance of the mind is extraordinarily mobile, it must consist of particles exceptionally small and smooth and round, ..so that, when the spirit has escaped from the body, the outside of the limbs appears intact and there is no loss of weight. | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.201) | |
| A reaction: Lucretius is wonderfully attentive to interesting evidence. He goes on to compare it to the evaporation of perfume. The fine-grained connections of the brain are not far off what he is proposing. |
| 5723 | If spirit is immortal and enters us at birth, why don't we remember a previous existence? [Lucretius] |
| Full Idea: If the spirit is by nature immortal and is slipped into the body at birth, why do we retain no memory of an earlier existence, no impress of antecedent events? | |
| From: Lucretius (On the Nature of the Universe [c.60 BCE], III.670) | |
| A reaction: Plato took the view that we do recall previous existence, as seen in our innate ideas. This problem forced the Christian church into the uncomfortable claim that God creates the soul at conception, but that it then goes on to immortality. |