33 ideas
| 21021 | Keep premises as weak as possible, to avoid controversial difficulties [Nussbaum] |
| Full Idea: One should always choose the weakest premises from which one's conclusion follows, rather than saddling the theory with thicker or more controversial premises. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: I like this because it connects the rather vague Ockham's Razor to the logical concept of Thinning. The key point is that a thinner set of premises that prove something will be more persuasive, because critics may reject premises instead of conclusion. |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 21007 | Storytelling is never neutral; some features of the world must be emphasised [Nussbaum] |
| Full Idea: Storytelling is never neutral; the narrator always directs attention to some features of the world rather than others. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 1) | |
| A reaction: The audience would be a bit stupid if it insisted on neutrality. |
| 21025 | Particularism gives no guidance for the future [Nussbaum] |
| Full Idea: Situation ethics offers no guidance for the future. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: Not sure if Situation Ethics is the same as Particularism. Jonathan Danby famously champions the latter. |
| 21026 | Compassion is unreliable, because it favours people close to us [Nussbaum] |
| Full Idea: Daniel Batson's important research has shown us that compassion is not reliable on its own, because it can easily give priority to people close to the self. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: In Britain animal charities receive vastly more money than children's charities, presumably for this very reason. Kittens - you've got to hate them. |
| 21019 | Social contracts assume equal powers among the participants [Nussbaum] |
| Full Idea: All contract theories, including Rawls's, assume a rough equality of physical and mental power among the participants. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 4) |
| 21011 | We shouldn't focus on actual preferences, which may be distorted by injustices [Nussbaum] |
| Full Idea: When society puts things out of reach for people, they typically learn not to want those things. ..By defining the social goal in terms of satisfaction of actual preferences, utilitarian approaches often reinforce the status quo, which may be very unjust. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: Maximising happiness is potentially very paternalistic, whereas preference satisfaction is not, which aligns utilitarianism better with liberalism. It is notorious that slaves can be contented with their slavery, and battered wives can remain loyal. |
| 21008 | Liberalism does not need a comprehensive account of value [Nussbaum] |
| Full Idea: The role of political liberalism in my theory requires me to prescind from offering any comprehensive account of value. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 2) | |
| A reaction: Obviously liberalism has values, but they are the minimum ones of freedom and respect. Liberals have to tolerate some fairly ugly and miserable societies. Can liberals intervene in family life? |
| 21012 | Women are often treated like children, and not respected for their choices [Nussbaum] |
| Full Idea: Women are often treated as passive dependents, creatures to be cared for (or not), rather than as independent human beings deserving respect for their choices. In other words they are often infantilized. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: Her prime example is from India, but you see the same thing in more subtle forms in the UK, especially among older people, and especially in art galleries. |
| 21015 | Negative liberty is incoherent; all liberties, to do and to be, require the prevention of interference [Nussbaum] |
| Full Idea: The very idea of 'negative liberty' ...is an incoherent idea: all liberties are positive, meaning liberties to do or to be something, which all require the inhibition of interference by others. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: This rejects Isaiah Berlin's well-known claim that negative liberties are good, but positive liberties are far too dangerous. |
| 21017 | Political freedom is an incoherent project, because some freedoms limit other freedoms [Nussbaum] |
| Full Idea: It is unclear whether the idea of promoting freedom is even a coherent political project. Some freedoms limit others. The freedom of rich people to make large donations to political campaigns can limit the equal worth of the right to vote. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 4) | |
| A reaction: It is not just American right-wingers who over-emphasise 'freedom'. French philosophy seems to be riddled with the same thing. |
| 21016 | Political and civil rights are not separate from economic and social rights [Nussbaum] |
| Full Idea: My approach rejects the distinction, common in the human rights movement, between 'first-generation rights' (political and civil) and 'second-generation rights' (economic and social). The second group are preconditions of the first group. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: [last sentence compressed] This sounds like the sort of point Marx argued for. Nowadays it is feminists who make this point most strongly. |
| 21009 | Capabilities: Life, Health, Safety, Mental life, Love, Planning, Joining in, Nature, Play, Control [Nussbaum, by PG] |
| Full Idea: Ten Capabilities: Life (decent), Health (reproduction, shelter), Safety, Mental life (with education), Love (relationships), Planning (with free beliefs), Joining in (and non-discrimination), Nature (relations to), Play, Control (politics and property). | |
| From: report of Martha Nussbaum (Creating Capabilities [2011], 2) by PG - Db (ideas) | |
| A reaction: She gives her crucial list in rather wordy form. To have impact it needs to be reduced to brief simple slogans. |
| 21010 | Justice requires that the ten main capabilities of people are reasonably enabled [Nussbaum] |
| Full Idea: The basic claim of my account of social justice is this: respect for human dignity requires that citizens be placed above an ample (specified) threshold of capability in all ten of the areas. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 2) | |
| A reaction: [The capabilities are given, briefly, in Idea 21009] The one word that bothers me here is 'dignity'. It is very vague, and can, I think, be reduced to much clearer and more obvious concepts. A person lacks dignity when they vomit, in ordinary usage. |
| 21013 | Capabilities are grounded in bare humanity and agency; qualifying as rational is not needed [Nussbaum] |
| Full Idea: The capabilities approach grounds rights claims in bare human birth and minimal agency, not in rationality or any other specific property, something that permits it to recognise the equal human rights of people with cognitive disabilities. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: She says elsewhere that she also sees animals as included in the capabilities approach. This is a rejection of the Kantian grounds for rights (by a well-known Aristotelian). |
| 21014 | Rights are not just barriers against state interference; governments must affirm capabilities of citizens [Nussbaum] |
| Full Idea: A prominent idea, common in the U.S., sees rights as barriers against interfering state action. ...The Capabilities Approach, by contrast, insists that all entitlements involve an affirmative task for government, to actively support capabilities. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 3) | |
| A reaction: This makes her approach very left wing, by U.S. standards, because it needs higher taxation and a degree of government paternalism. Her approach strikes me as an excellent agenda for a fairly interventionist European liberal party. |
| 21020 | Any establishment belief system is incompatible with full respect for all citizens [Nussbaum] |
| Full Idea: The idea of equal respect is difficult or impossible to render compatible with a religious establishment, even one that is benign and noncoercive. Any established church (or government secularism) denigrates nonbelievers, by stating they are an out-group. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 4) | |
| A reaction: This sort of applies to membership of anything. She is sort of right, but there is no reason in principle why full respect should not be accorded to any out-group. |
| 21023 | We should respect animals in the way that we respect the animal nature in humans [Nussbaum] |
| Full Idea: If we show respect to our own animal natures, it is simply inconsistent, and a kind of vicious self-promoting of a sort to which Kantians are especially opposed, to refuse the same respect to our fellow creatures. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: Nussbaum says Kant is hopeless on animals, but Christine Korsgaard offers this Kantian approach that demands genuine respect for animals, even though they are not considered rational. Nussbaum says animals are agents. Did Kant respect our animality? |
| 21024 | It may be no harm to kill an animal which cannot plan for its future [Nussbaum] |
| Full Idea: The painless killing of an animal of a species that does not make plans extending into the future may not be a harm: this depends on how we think about the harm of death. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: Very old human beings may have no plans for the future. I, on the other hand, have got lots and lots of plans. Definitely. No one can specify the harm of death. How can it be distinguished from the harm of not being born? |
| 21022 | The Capabilities Approach sees animals as agents, not just as having feelings [Nussbaum] |
| Full Idea: The Capabilities Approach sees animals as agents, not as receptacles of pleasure or pain. | |
| From: Martha Nussbaum (Creating Capabilities [2011], 8) | |
| A reaction: This is in opposition to the utilitarian view. The key consequence is that animals can be victims of injustice, as well as of cruelty. Nice. |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| Full Idea: Philosophers are the forefathers of heretics. | |
| From: Tertullian (works [c.200]), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 20.2 |
| 6610 | I believe because it is absurd [Tertullian] |
| Full Idea: I believe because it is absurd ('Credo quia absurdum est'). | |
| From: Tertullian (works [c.200]), quoted by Robert Fogelin - Walking the Tightrope of Reason n4.2 | |
| A reaction: This seems to be a rather desperate remark, in response to what must have been rather good hostile arguments. No one would abandon the support of reason if it was easy to acquire. You can't deny its engaging romantic defiance, though. |