Combining Philosophers

All the ideas for David Hilbert, Alan McMichael and Martha Nussbaum

unexpand these ideas     |    start again     |     specify just one area for these philosophers


56 ideas

2. Reason / B. Laws of Thought / 6. Ockham's Razor
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.
3. Truth / G. Axiomatic Truth / 1. Axiomatic Truth
If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert]
     Full Idea: If the arbitrarily given axioms do not contradict each other with all their consequences, then they are true and the things defined by the axioms exist. For me this is the criterion of truth and existence.
     From: David Hilbert (Letter to Frege 29.12.1899 [1899]), quoted by R Kaplan / E Kaplan - The Art of the Infinite 2 'Mind'
     A reaction: If an axiom says something equivalent to 'fairies exist, but they are totally undetectable', this would seem to avoid contradiction with anything, and hence be true. Hilbert's idea sounds crazy to me. He developed full Formalism later.
5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle
You would cripple mathematics if you denied Excluded Middle [Hilbert]
     Full Idea: Taking the principle of Excluded Middle away from the mathematician would be the same, say, as prohibiting the astronomer from using the telescope or the boxer from using his fists.
     From: David Hilbert (The Foundations of Mathematics [1927], p.476), quoted by Ian Rumfitt - The Boundary Stones of Thought 9.4
     A reaction: [p.476 in Van Heijenoort]
5. Theory of Logic / K. Features of Logics / 1. Axiomatisation
The facts of geometry, arithmetic or statics order themselves into theories [Hilbert]
     Full Idea: The facts of geometry order themselves into a geometry, the facts of arithmetic into a theory of numbers, the facts of statics, electrodynamics into a theory of statics, electrodynamics, or the facts of the physics of gases into a theory of gases.
     From: David Hilbert (Axiomatic Thought [1918], [03])
     A reaction: This is the confident (I would say 'essentialist') view of axioms, which received a bit of a setback with Gödel's Theorems. I certainly agree that the world proposes an order to us - we don't just randomly invent one that suits us.
Axioms must reveal their dependence (or not), and must be consistent [Hilbert]
     Full Idea: If a theory is to serve its purpose of orienting and ordering, it must first give us an overview of the independence and dependence of its propositions, and second give a guarantee of the consistency of all of the propositions.
     From: David Hilbert (Axiomatic Thought [1918], [09])
     A reaction: Gödel's Second theorem showed that the theory can never prove its own consistency, which made the second Hilbert requirement more difficult. It is generally assumed that each of the axioms must be independent of the others.
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend]
     Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought.
     From: report of David Hilbert (works [1900], 6.7) by Michèle Friend - Introducing the Philosophy of Mathematics
     A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault.
I aim to establish certainty for mathematical methods [Hilbert]
     Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods.
     From: David Hilbert (On the Infinite [1925], p.184)
     A reaction: This is the clearest statement of the famous Hilbert Programme, which is said to have been brought to an abrupt end by Gödel's Incompleteness Theorems.
We believe all mathematical problems are solvable [Hilbert]
     Full Idea: The thesis that every mathematical problem is solvable - we are all convinced that it really is so.
     From: David Hilbert (On the Infinite [1925], p.200)
     A reaction: This will include, for example, Goldbach's Conjecture (every even is the sum of two primes), which is utterly simple but with no proof anywhere in sight.
6. Mathematics / A. Nature of Mathematics / 2. Geometry
Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD]
     Full Idea: One of Hilbert's aims in 'The Foundations of Geometry' was to eliminate number [as measure of lengths and angles] from geometry.
     From: report of David Hilbert (Foundations of Geometry [1899]) by William D. Hart - The Evolution of Logic 2
     A reaction: Presumably this would particularly have to include the elimination of ratios (rather than actual specific lengths).
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite
No one shall drive us out of the paradise the Cantor has created for us [Hilbert]
     Full Idea: No one shall drive us out of the paradise the Cantor has created for us.
     From: David Hilbert (On the Infinite [1925], p.191), quoted by James Robert Brown - Philosophy of Mathematics
     A reaction: This is Hilbert's famous refusal to accept any account of mathematics, such as Kant's, which excludes actual infinities. Cantor had laid out a whole glorious hierarchy of different infinities.
We extend finite statements with ideal ones, in order to preserve our logic [Hilbert]
     Full Idea: To preserve the simple formal rules of ordinary Aristotelian logic, we must supplement the finitary statements with ideal statements.
     From: David Hilbert (On the Infinite [1925], p.195)
     A reaction: I find very appealing the picture of mathematics as rooted in the physical world, and then gradually extended by a series of 'idealisations', which should perhaps be thought of as fictions.
Only the finite can bring certainty to the infinite [Hilbert]
     Full Idea: Operating with the infinite can be made certain only by the finitary.
     From: David Hilbert (On the Infinite [1925], p.201)
     A reaction: See 'Compactness' for one aspect of this claim. I think Hilbert was fighting a rearguard action, and his idea now has few followers.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite
The idea of an infinite totality is an illusion [Hilbert]
     Full Idea: Just as in the limit processes of the infinitesimal calculus, the infinitely large and small proved to be a mere figure of speech, so too we must realise that the infinite in the sense of an infinite totality, used in deductive methods, is an illusion.
     From: David Hilbert (On the Infinite [1925], p.184)
     A reaction: This is a very authoritative rearguard action. I no longer think the dispute matters much, it being just a dispute over a proposed new meaning for the word 'number'.
6. Mathematics / A. Nature of Mathematics / 5. The Infinite / j. Infinite divisibility
There is no continuum in reality to realise the infinitely small [Hilbert]
     Full Idea: A homogeneous continuum which admits of the sort of divisibility needed to realise the infinitely small is nowhere to be found in reality.
     From: David Hilbert (On the Infinite [1925], p.186)
     A reaction: He makes this remark as a response to Planck's new quantum theory (the year before the big works of Heisenberg and Schrödinger). Personally I don't see why infinities should depend on the physical world, since they are imaginary.
6. Mathematics / B. Foundations for Mathematics / 2. Proof in Mathematics
To decide some questions, we must study the essence of mathematical proof itself [Hilbert]
     Full Idea: It is necessary to study the essence of mathematical proof itself if one wishes to answer such questions as the one about decidability in a finite number of operations.
     From: David Hilbert (Axiomatic Thought [1918], [53])
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara]
     Full Idea: Hilbert's geometrical axioms were existential in character, asserting the existence of certain geometrical objects (points and lines). Euclid's postulates do not assert the existence of anything; they assert the possibility of certain constructions.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Charles Chihara - A Structural Account of Mathematics 01.1
     A reaction: Chihara says geometry was originally understood modally, but came to be understood existentially. It seems extraordinary to me that philosophers of mathematics can have become more platonist over the centuries.
Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew]
     Full Idea: In his formal investigation of Euclidean geometry, Hilbert uncovered congruence axioms that implicitly played a role in Euclid's proofs but were not explicitly recognised.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Horsten,L/Pettigrew,R - Mathematical Methods in Philosophy 2
     A reaction: The writers are offering this as a good example of the benefits of a precise and formal approach to foundational questions. It's hard to disagree, but dispiriting if you need a PhD in maths before you can start doing philosophy.
Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H]
     Full Idea: Hilbert's formulation of the Euclidean theory is of special interest because (besides being rigorously axiomatised) it does not employ the real numbers in the axioms.
     From: report of David Hilbert (Foundations of Geometry [1899]) by Hartry Field - Science without Numbers 3
     A reaction: Notice that this job was done by Hilbert, and not by the fictionalist Hartry Field.
The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert]
     Full Idea: The linearity of the equation of the plane and of the orthogonal transformation of point-coordinates is completely adequate to produce the whole broad science of spatial Euclidean geometry purely by means of analysis.
     From: David Hilbert (Axiomatic Thought [1918], [05])
     A reaction: This remark comes from the man who succeeded in producing modern axioms for geometry (in 1897), so he knows what he is talking about. We should not be wholly pessimistic about Hilbert's ambitious projects. He had to dig deeper than this idea...
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / a. Axioms for numbers
Number theory just needs calculation laws and rules for integers [Hilbert]
     Full Idea: The laws of calculation and the rules of integers suffice for the construction of number theory.
     From: David Hilbert (Axiomatic Thought [1918], [05])
     A reaction: This is the confident Hilbert view that the whole system can be fully spelled out. Gödel made this optimism more difficult.
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert]
     Full Idea: The standpoint of pure experience seems to me to be refuted by the objection that the existence, possible or actual, of an arbitrarily large number can never be derived through experience, that is, through experiment.
     From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.130)
     A reaction: Alternatively, empiricism refutes infinite numbers! No modern mathematician will accept that, but you wonder in what sense the proposed entities qualify as 'numbers'.
6. Mathematics / C. Sources of Mathematics / 6. Logicism / d. Logicism critique
Logic already contains some arithmetic, so the two must be developed together [Hilbert]
     Full Idea: In the traditional exposition of the laws of logic certain fundamental arithmetic notions are already used, for example in the notion of set, and to some extent also of number. Thus we turn in a circle, and a partly simultaneous development is required.
     From: David Hilbert (On the Foundations of Logic and Arithmetic [1904], p.131)
     A reaction: If the Axiom of Infinity is meant, it may be possible to purge the arithmetic from the logic. Then the challenge to derive arithmetic from it becomes rather tougher.
6. Mathematics / C. Sources of Mathematics / 7. Formalism
The grounding of mathematics is 'in the beginning was the sign' [Hilbert]
     Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign.
     From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience.
Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman]
     Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1).
     From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application.
Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter]
     Full Idea: Hilbert proposed to circuvent the paradoxes by means of the doctrine (already proposed by Poincaré) that in mathematics consistency entails existence.
     From: report of David Hilbert (On the Concept of Number [1900], p.183) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 19 'Exist'
     A reaction: Interesting. Hilbert's idea has struck me as weird, but it makes sense if its main motive is to block the paradoxes. Roughly, the idea is 'it exists if it isn't paradoxical'. A low bar for existence (but then it is only in mathematics!).
The subject matter of mathematics is immediate and clear concrete symbols [Hilbert]
     Full Idea: The subject matter of mathematics is the concrete symbols themselves whose structure is immediately clear and recognisable.
     From: David Hilbert (On the Infinite [1925], p.192)
     A reaction: I don't think many people will agree with Hilbert here. Does he mean token-symbols or type-symbols? You can do maths in your head, or with different symbols. If type-symbols, you have to explain what a type is.
6. Mathematics / C. Sources of Mathematics / 8. Finitism
Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman]
     Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning.
     From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6
     A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem.
Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert]
     Full Idea: We can conceive mathematics to be a stock of two kinds of formulas: first, those to which the meaningful communications of finitary statements correspond; and secondly, other formulas which signify nothing and which are ideal structures of our theory.
     From: David Hilbert (On the Infinite [1925], p.196), quoted by David Bostock - Philosophy of Mathematics 6.1
9. Objects / D. Essence of Objects / 3. Individual Essences
Only individuals have essences, so numbers (as a higher type based on classes) lack them [McMichael]
     Full Idea: Essentialism is not verified by the observation that numbers have interesting essential properties, since they are properties of classes and so are entities of a higher logical type than individuals.
     From: Alan McMichael (The Epistemology of Essentialist Claims [1986], Intro)
     A reaction: This relies on a particular view of number (which might be challenged), but is interesting when it comes to abstract entities having essences. Only ur-elements in set theory could have essences, it seems. Why? Rising in type destroys essence?
9. Objects / D. Essence of Objects / 9. Essence and Properties
Essences are the interesting necessary properties resulting from a thing's own peculiar nature [McMichael]
     Full Idea: Essentialism says some individuals have certain 'interesting' necessary properties. If it exists, it has that property. The properties are 'interesting' as had in virtue of their own peculiar natures, rather than as general necessary truths.
     From: Alan McMichael (The Epistemology of Essentialist Claims [1986], Intro)
     A reaction: [compressed] This is a modern commentator caught between two views. The idea that essence is the non-trivial-necessary properties is standard, but adding their 'peculiar natures' connects him to Aristotle, and Kit Fine's later papers. Good!
Maybe essential properties have to be intrinsic, as well as necessary? [McMichael]
     Full Idea: There is a tendency to think of essential properties as having some characteristic in addition to their necessity, such as intrinsicality.
     From: Alan McMichael (The Epistemology of Essentialist Claims [1986], VIII)
     A reaction: Personally I am inclined to take this view of all properties, and not just the 'essential' ones. General necessities, relations, categorisations, disjunctions etc. should not be called 'properties', even if they are 'predicates'. Huge confusion results.
9. Objects / D. Essence of Objects / 15. Against Essentialism
Essentialism is false, because it implies the existence of necessary singular propositions [McMichael]
     Full Idea: Essentialism entails the existence of necessary singular propositions that are not instances of necessary generalizations. Therefore, since there are no such propositions, essentialism is false.
     From: Alan McMichael (The Epistemology of Essentialist Claims [1986], I)
     A reaction: This summarises the attack which McMichael wishes to deal with. I am wickedly tempted to say that essences actually have a contingent existence (or a merely hypothetical dependent necessity), and this objection might be grist for my mill.
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
My theory aims at the certitude of mathematical methods [Hilbert]
     Full Idea: The goal of my theory is to establish once and for all the certitude of mathematical methods.
     From: David Hilbert (On the Infinite [1925], p.184), quoted by James Robert Brown - Philosophy of Mathematics Ch.5
     A reaction: This dream is famous for being shattered by Gödel's Incompleteness Theorem a mere six years later. Neverless there seem to be more limited certainties which are accepted in mathematics. The certainty of the whole of arithmetic is beyond us.
21. Aesthetics / B. Nature of Art / 8. The Arts / b. Literature
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.
21. Aesthetics / C. Artistic Issues / 7. Art and Morality
The Aristotelian idea that choices can be perceived needs literary texts to expound it [Nussbaum]
     Full Idea: To show forth the Aristotelian claim that 'the decision rests with perception', we need - either side by side with a philosophical outline or inside it - literary texts which display the complexity, indeterminacy, and sheer difficulty of moral choice.
     From: Martha Nussbaum (The Golden Bowl, and Lit as Moral Philosophy [1983], II)
     A reaction: Berys Gaut observes that this depends on a particularist view of moral choice (usually seen as Aristotelian), with little interest in principles.
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
Philosophers after Aristotle endorsed the medical analogy for eudaimonia [Nussbaum, by Flanagan]
     Full Idea: Nussbaum says the post-Aristotelian philosophers did much more than simply advancing and refining Aristotle's ethics. They advanced eudaimonics by explicitly endorsing the medical analogy.
     From: report of Martha Nussbaum (The Therapy of Desire [1994]) by Owen Flanagan - The Really Hard Problem 4 'Eudaimoncs'
     A reaction: Since Aristotle is all about the successful functioning of the psuche, this idea is obviously implicit in his original texts. It needs a positive concept of mental health, and not a mere absence of mental illness. See the Mindapples campaign.
23. Ethics / C. Virtue Theory / 1. Virtue Theory / c. Particularism
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.
23. Ethics / C. Virtue Theory / 3. Virtues / f. Compassion
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.
24. Political Theory / B. Nature of a State / 2. State Legitimacy / c. Social contract
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)
24. Political Theory / D. Ideologies / 4. Social Utilitarianism
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.
24. Political Theory / D. Ideologies / 6. Liberalism / a. Liberalism basics
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?
24. Political Theory / D. Ideologies / 12. Feminism
Liberals must respect family freedom - but families are the great oppressors of women [Nussbaum]
     Full Idea: A liberal society should give people considerable latitude to form families as they choose. …On the other hand the family …is one of the most notorious homes of sex hierarchy, denial of sexual opportunity, and sex-based violence and humiliation.
     From: Martha Nussbaum (Rawls and Feminism [2003], 03), quoted by Andrew Shorten - Contemporary Political Theory
     A reaction: The question of how the state might intervene in the family rarely seems to turn up in standard political theory. This idea shows why that is a mistake.
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.
25. Social Practice / A. Freedoms / 5. Freedom of lifestyle
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.
25. Social Practice / A. Freedoms / 6. Political freedom
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.
25. Social Practice / C. Rights / 1. Basis of Rights
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.
25. Social Practice / D. Justice / 1. Basis of justice
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.
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.
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).
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.
25. Social Practice / E. Policies / 2. Religion in Society
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.
25. Social Practice / F. Life Issues / 6. Animal Rights
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?
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?
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.
26. Natural Theory / D. Laws of Nature / 5. Laws from Universals
Individuals enter into laws only through their general qualities and relations [McMichael]
     Full Idea: Individuals appear to enter into laws only through their general qualities and relations.
     From: Alan McMichael (The Epistemology of Essentialist Claims [1986], VIII)
     A reaction: This is a very significant chicken-or-egg issue. The remark seems to offer the vision of pre-existing general laws, which individuals then join (like joining a club). But surely the laws are derived from the individuals? Where else could they come from?
26. Natural Theory / D. Laws of Nature / 8. Scientific Essentialism / d. Knowing essences
By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert]
     Full Idea: By pushing ahead to ever deeper layers of axioms ...we also win ever-deeper insights into the essence of scientific thought itself, and become ever more conscious of the unity of our knowledge.
     From: David Hilbert (Axiomatic Thought [1918], [56])
     A reaction: This is the less fashionable idea that scientific essentialism can also be applicable in the mathematic sciences, centring on the project of axiomatisation for logic, arithmetic, sets etc.