31 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. |
| 13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
| Full Idea: In current set theory, the search is on for new axioms to determine the size of the continuum. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §0) | |
| A reaction: This sounds the wrong way round. Presumably we seek axioms that fix everything else about set theory, and then check to see what continuum results. Otherwise we could just pick our continuum, by picking our axioms. |
| 13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
| Full Idea: Most writers agree that if any sense can be made of the distinction between analytic and synthetic, then the Axiom of Extensionality should be counted as analytic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [Boolos is the source of the idea] In other words Extensionality is not worth discussing, because it simply tells you what the world 'set' means, and there is no room for discussion about that. The set/class called 'humans' varies in size. |
| 13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
| Full Idea: The extensional view of sets is preferable because it is simpler, clearer, and more convenient, because it individuates uniquely, and because it can simulate intensional notions when the need arises. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.1) | |
| A reaction: [She cites Fraenkel, Bar-Hillet and Levy for this] The difficulty seems to be whether the extensional notion captures our ordinary intuitive notion of what constitutes a group of things, since that needs flexible size and some sort of unity. |
| 13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
| Full Idea: The Axiom of Infinity is a simple statement of Cantor's great breakthrough. His bold hypothesis that a collection of elements that had lurked in the background of mathematics could be infinite launched modern mathematics. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: It also embodies one of those many points where mathematics seems to depart from common sense - but then most subjects depart from common sense when they get more sophisticated. Look what happened to art. |
| 13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
| Full Idea: If one is interested in analysis then infinite sets are indispensable since even the notion of a real number cannot be developed by means of finite sets alone. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.5) | |
| A reaction: [Maddy is citing Fraenkel, Bar-Hillel and Levy] So Cantor's great breakthrough (Idea 13021) actually follows from the earlier acceptance of the real numbers, so that's where the departure from common sense started. |
| 13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
| Full Idea: The Power Set Axiom is indispensable for a set-theoretic account of the continuum, ...and in so far as those attempts are successful, then the power-set principle gains some confirmatory support. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.6) | |
| A reaction: The continuum is, of course, notoriously problematic. Have we created an extra problem in our attempts at solving the first one? |
| 13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
| Full Idea: Jordain made consistent and ill-starred efforts to prove the Axiom of Choice. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This would appear to be the fate of most axioms. You would presumably have to use a different system from the one you are engaged with to achieve your proof. |
| 13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
| Full Idea: Resistance to the Axiom of Choice centred on opposition between existence and construction. Modern set theory thrives on a realistic approach which says the choice set exists, regardless of whether it can be defined, constructed, or given by a rule. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: This seems to be a key case for the ontology that lies at the heart of theory. Choice seems to be an invaluable tool for proofs, so it won't go away, so admit it to the ontology. Hm. So the tools of thought have existence? |
| 13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
| Full Idea: Many theorems depend on the Axiom of Choice, including that a countable union of sets is countable, and results in analysis, topology, abstract algebra and mathematical logic. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.7) | |
| A reaction: The modern attitude seems to be to admit anything if it leads to interesting results. It makes you wonder about the modern approach of using mathematics and logic as the cutting edges of ontological thinking. |
| 13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
| Full Idea: The Iterative Conception (Zermelo 1930) says everything appears at some stage. Given two objects a and b, let A and B be the stages at which they first appear. Suppose B is after A. Then the pair set of a and b appears at the immediate stage after B. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: Presumably this all happens in 'logical time' (a nice phrase I have just invented!). I suppose we might say that the existence of the paired set is 'forced' by the preceding sets. No transcendental inferences in this story? |
| 13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
| Full Idea: The 'limitation of size' is a vague intuition, based on the idea that being too large may generate the paradoxes. | |
| From: Penelope Maddy (Believing the Axioms I [1988], §1.3) | |
| A reaction: This is an intriguing idea to be found right at the centre of what is supposed to be an incredibly rigorous system. |
| 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. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
| 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. |