49 ideas
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| Full Idea: Impredicative Definitions are definitions of an object by reference to the totality to which the object itself (and perhaps also things definable only in terms of that object) belong. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], n 13) |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| Full Idea: In the superior realist and simple theory of types, the place of the axiom of reducibility is not taken by the axiom of classes, Zermelo's Aussonderungsaxiom. | |
| From: report of Kurt Gödel (Russell's Mathematical Logic [1944], p.140-1) by Bernard Linsky - Russell's Metaphysical Logic 6.1 n3 | |
| A reaction: This is Zermelo's Axiom of Separation, but that too is not an axiom of standard ZFC. |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| Full Idea: 'Mathematical Logic' is a precise and complete formulation of formal logic, and is both a section of mathematics covering classes, relations, symbols etc, and also a science prior to all others, with ideas and principles underlying all sciences. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.447) | |
| A reaction: He cites Leibniz as the ancestor. In this database it is referred to as 'theory of logic', as 'mathematical' seems to be simply misleading. The principles of the subject are standardly applied to mathematical themes. |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| Full Idea: One may, on good grounds, deny that reference to a totality necessarily implies reference to all single elements of it or, in other words, that 'all' means the same as an infinite logical conjunction. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.455) |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| Full Idea: In order to be sure that new expression can be translated into expressions not containing them, it is necessary to have a survey of all possible expressions, and this can be furnished only by syntactical considerations. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.448) | |
| A reaction: [compressed] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| Full Idea: The generalized Continuum Hypothesis says that there exists no cardinal number between the power of any arbitrary set and the power of the set of its subsets. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| Full Idea: It has turned out that the solution of certain arithmetical problems requires the use of assumptions essentially transcending arithmetic. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.449) | |
| A reaction: A nice statement of the famous result, from the great man himself, in the plainest possible English. |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| Full Idea: Classes and concepts may be conceived of as real objects, ..and are as necessary to obtain a satisfactory system of mathematics as physical bodies are necessary for a satisfactory theory of our sense perceptions, with neither case being about 'data'. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.456) | |
| A reaction: Note that while he thinks real objects are essential for mathematics, be may not be claiming the same thing for our knowledge of logic. If logic contains no objects, then how could mathematics be reduced to it, as in logicism? |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| Full Idea: Impredicative definitions are admitted into ordinary mathematics. | |
| From: Kurt Gödel (Russell's Mathematical Logic [1944], p.464) | |
| A reaction: The issue is at what point in building an account of the foundations of mathematics (if there be such, see Putnam) these impure definitions should be ruled out. |
| 15682 | Even fairly simple animals make judgements based on categories [Gelman] |
| Full Idea: All organisms form categories: even mealworms have category-based preferences, and higher-order animals such as pigeons or octopi can display quite sophisticated categorical judgements. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims') | |
| A reaction: [She cites some 1980 research to support this] This comes as no surprise, as I take categorisation as almost definitive of what a mind is. My surmise is that some sort of 'labelling' system is at the heart of it (like Googlemail labels!). |
| 15691 | Children accept real stable categories, with nonobvious potential that gives causal explanations [Gelman] |
| Full Idea: By five children assume that a variety of categories have rich inductive potential, are stable over outward transformations, include crucial nonobvious properties, have innate potential, privilege causal features, can be explained causally, and are real. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'Intro') | |
| A reaction: This is Gelman's helpful summary of the findings of research on childhood essentialising, and says the case for this phenomenon is 'compelling'. |
| 15700 | In India, upper-castes essentialize caste more than lower-castes do [Gelman] |
| Full Idea: The notion of caste in India is more essentialized among upper-caste than lower-caste individuals. | |
| From: Susan A. Gelman (The Essential Child [2003], 08 'Intro') | |
| A reaction: In a book defending fairly innate essentialism in the human race, Gelman offers this point as a warning that large cultural ingredients can be involved. Racism is the classic difficulty with essentialism. |
| 15685 | Essentialism is either natural to us, or an accident of our culture, or a necessary result of language [Gelman] |
| Full Idea: The two views contrasting with essentialism naturally emerging in childhood are the claim that essentialism is a historical accident emerging from Western philosophy, and that essentialism is an inherent consequence of naming things. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Background') | |
| A reaction: Helpful. I take Idea 15682 to rule out the idea that it is just a feature of western culture. I can't conceive of early man surviving without essentialism. I don't think it rules out the naming view. Animals may do what emerges in us as full 'naming'. |
| 15684 | Children's concepts include nonobvious features, like internal parts, functions and causes [Gelman] |
| Full Idea: Children incorporate a variety of nonobvious features into their concepts, including internal parts, functions, causes, and ontological distinctions. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims') | |
| A reaction: This remark sums up the general thesis of her book, which she supports with a wealth of first-hand evidence. It supports my view, that the desire and need for explanation is at the root of essentialist concepts. It's hard wired in us. |
| 15681 | Essentialism: real or representational? sortal, causal or ideal? real particulars, or placeholders? [Gelman] |
| Full Idea: We map types of essentialism by asking is it in the world or in our representations, is it sortal or causal or ideal, and is it specific particulars or placeholders for the unknown? | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims') | |
| A reaction: I am struck by the way that this practising experimental psychologist gets to ask questions and make distinctions much more extensively than most armchair philosophers on the subject. She focuses on the representational, causal, placeholder view. |
| 15678 | Essentialism says categories have a true hidden nature which gives an object its identity [Gelman] |
| Full Idea: Essentialism is the view that categories have an underlying reality or true nature that one cannot observe directly but that gives an object its identity. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Intro') | |
| A reaction: I think the introduction of categories here is a misunderstanding. Does an uncategorisable thing therefore have no identity (even though it has properties)? If categories give objects their identity, what gives categories their identity? |
| 15683 | Sortals are needed for determining essence - the thing must be categorised first [Gelman] |
| Full Idea: I suggest that sortals are likewise required for determining essence. One cannot answer the question 'What is the essence of this?' without supplying the sortal - of this 'what'. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims') | |
| A reaction: I remain baffled by this view. I take the category to be an inductive generalisation from other similar individuals. It can't get off the ground if you don't start with the individuals. Sortals are just a shorthand. |
| 15697 | Kind (unlike individual) essentialism assumes preexisting natural categories [Gelman] |
| Full Idea: With kind essentialism the person assumes that the world is divided up into preexisting natural categories. Individual essentialism seems not to require any such commitment to kind realism. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'Essentialism') | |
| A reaction: This pinpoints my difficulty: how do we decide whether some category or attributed essence is part of a preexisting natural kind? Some natural kinds are self-evident, like water (roughly), but others need subtle teasing out. How is the teasing done? |
| 15687 | Kinship is essence that comes in degrees, and age groups are essences that change over time [Gelman] |
| Full Idea: Kinship is essentialized, but admits of degrees, ...and people can be essentialist even about categories they do not view as fixed over time, such as age groupings. | |
| From: Susan A. Gelman (The Essential Child [2003], 03 'Summary') | |
| A reaction: Given my notion of essence are necessarily explanatory, I embrace both of these points. Being very athletic comes in degrees, and changes over times. |
| 15679 | Essentialism comes from the cognitive need to categorise [Gelman] |
| Full Idea: Essentialism has its source in the cognitive requirement of categorization in certain domains - particularly as they affect the young learner. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Essentialist') | |
| A reaction: I think the phenomenon is better understood as part of the cognitive requirement to understand and explain. Categorisation is just one way to aid explanation. Children try to understand (essentially) a new animal without categorisation. |
| 15698 | We found no evidence that mothers teach essentialism to their children [Gelman] |
| Full Idea: We found no evidence that mothers teach essentialism to their children. ...Mothers teach children about kinds, not about essences, and mothers help children identify which categories are richly structured. | |
| From: Susan A. Gelman (The Essential Child [2003], 07 'Conclusions') | |
| A reaction: This is a psychologist who specialises in this topic. If you think essentialism is inculcated by a our culture, you will have to blame the fathers. |
| 15709 | Essentialism is useful for predictions, but it is not the actual structure of reality [Gelman] |
| Full Idea: Essentialism is a reasoning heuristic that allows us to make fairly good predictions much of the time, but it should not be confused with the structure of reality. | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Discussion') | |
| A reaction: She particularly cites biology as the area where it might be inaccurate. I'm beginning to think that the operations of induction are the place to look for an good understanding of essentialism. |
| 15696 | Peope favor historical paths over outward properties when determining what something is [Gelman] |
| Full Idea: People favor historical paths over outward properties when determining what something is. ...An object looking like a knife is less likely to be called 'a knife' if it is described as having been created by accident. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'Essentialism') | |
| A reaction: I like this because it talks, suggestively, of 'historical paths' rather than of 'origin'. Thus we might judge a person's identity by their traumatic experience rather than by their birth. This doesn't challenge necessity of origin, but affects labels. |
| 15707 | There is intentional, mechanical, teleological, essentialist, vitalist and deontological understanding [Gelman] |
| Full Idea: The modes of understanding (or modes of construal) which have been proposed are intentional, mechanical, teleological, essentialist, vitalist (perhaps), and deontological. | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Broadening') | |
| A reaction: She cites psychological research to support this, and calls it 'a relatively small number' of modes. Compare Aristotle's four modes of cause/explanation. |
| 15703 | Memories often conform to a theory, rather than being neutral [Gelman] |
| Full Idea: Memory is notorious for conforming to theory (rather than memory being a neutral source of information). | |
| From: Susan A. Gelman (The Essential Child [2003], 09 'Theory') | |
| A reaction: This observation by a psychologist is music to sceptics about objectivity. Memory is so fundamental to our basic epistemology that it could even be the nature of thought itself. |
| 15708 | Inductive success is rewarded with more induction [Gelman] |
| Full Idea: Inductive success is rewarded with more induction. | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Broadening') | |
| A reaction: I love this one. Neat, accurate, and central to how we understand the world. I take inductive success to be stored as labels, concepts, categories, words and general truths, which are then our resource for further attempts. |
| 15694 | Children overestimate the power of a single example [Gelman] |
| Full Idea: We suggest that children overestimate the power of a single example. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'The role') | |
| A reaction: This conclusion arises from extensive psychological research. 'My grandma smoked, and she lived to be 97' - adults do this too. Wittgenstein says assuming other minds because of your own is induction from one example! |
| 15695 | Children make errors in induction by focusing too much on categories [Gelman] |
| Full Idea: Because of their narrow focus, children's sensitivity to categories as the basis of induction is a reasoning bias that, though useful much of the time, results in systematic errors. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'The role') | |
| A reaction: This is the bad sense of 'essentialism' which worries its opponents. Presumably, though, my favoured scientific essentialism will be 'scientific', and avoid this problem. The relation between categories and induction needs to be clear. |
| 15692 | People tend to be satisfied with shallow explanations [Gelman] |
| Full Idea: People tend to be satisfied with rather shallow explanations. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'Is essentialism') | |
| A reaction: She cites some psychological research to support this. Pretty obvious really. I take the so-called 'scientific method' to be nothing more than ceasing to be satisfied with such shallowness. |
| 15680 | Folk essentialism rests on belief in natural kinds, in hidden properties, and on words indicating structures [Gelman] |
| Full Idea: The three components of essentialism as a folk belief are the idea that certain categories are natural kinds, the idea that some unobservable property causes the way things are, and the idea that words reflect real structures. | |
| From: Susan A. Gelman (The Essential Child [2003], 01 'Prelims') |
| 15686 | Labels may indicate categories which embody an essence [Gelman] |
| Full Idea: Labels may signal categories that are believed to embody an essence. | |
| From: Susan A. Gelman (The Essential Child [2003], 02 'Privileged') | |
| A reaction: This is quoted by her, as a summary of a substantial body of research which she endorses. I cite it because it pinpoints my own view. I take 'labels' to be basic to minds, as organisers of thought, and this ties essences to labels. Satisfying picture. |
| 15690 | Causal properties are seen as more central to category concepts [Gelman] |
| Full Idea: Properties that enter into causally meaningful links are better remembered and are treated as more central to the category than properties that are not causally meaningful. | |
| From: Susan A. Gelman (The Essential Child [2003], 05 'Causation2') | |
| A reaction: This is a summary of considerable psychological research. This account not only sounds plausible, but would fit better withy why we form concepts and categories in the first place. We are trying to relate to the causations of nature. |
| 15688 | Categories are characterized by distance from a prototype [Gelman] |
| Full Idea: On prototype views, categories are characterized by distance from a prototype. | |
| From: Susan A. Gelman (The Essential Child [2003], 05 'Causation') | |
| A reaction: Gelman observes that this view makes no reference to any causal features of things. This cuts them off from using underlying essences in the process of categorisation and concept-formation. How do you spot a prototype, with no category? |
| 15689 | Theory-based concepts use rich models to show which similarities really matter [Gelman] |
| Full Idea: Theory-based approaches to categories are a response to the limitations of mere similarities holding the category together, and require knowledge-rich explanatory models to say which features are more central to a concept. | |
| From: Susan A. Gelman (The Essential Child [2003], 05 'Causation1') | |
| A reaction: I see a promising account in linking theory theory to essentialism. For a physical object (or even for a process) infer a structure, and then identify what is most important in that structure. That gives you your stable, agreed concept. |
| 15699 | Prelinguistic infants acquire and use many categories [Gelman] |
| Full Idea: Language does not appear to be necessary for forming categories, since prelinguistic infants acquire many categories, and even use categories to form inferences about unknown properties. | |
| From: Susan A. Gelman (The Essential Child [2003], 08 'Intro') | |
| A reaction: She cites lots of research in support of this claim. The idea may come as a surprise to some people, but not to me. I take it that categorisation is what a brain is for, including animal brains. |
| 7590 | Consequentialism emphasises value rather than obligation in morality [Scruton] |
| Full Idea: According to consequentialism, the fundamental concept of morality is not obligation (deontological ethics) but value (axiological ethics). | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'consequentialism') | |
| A reaction: These two views could come dramatically apart, in wartime, or in big ecological crises, or in a family breakup, or in religious disputes. Having identified the pair so clearly, why can we not aim for a civilised (virtuous) balance between the two? |
| 7589 | Altruism is either emotional (where your interests are mine) or moral (where they are reasons for me) [Scruton] |
| Full Idea: Two distinct motives go by the name of altruism: the emotions of liking, love and friendship, making another's interest automatically mine; and the moral motive of respect or considerateness, where another's interests become reasons for me, but not mine. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'altruism') | |
| A reaction: The second one has a strongly Kantian flavour, with its notion of impersonal duty. Virtue theorists will aspire to achieve the first state rather than the second, because good actions are then actively desired, and give pleasure to the doer. |
| 7595 | The idea of a right seems fairly basic; justice may be the disposition to accord rights to people [Scruton] |
| Full Idea: The idea of a right seems to be as basic as any other; we might even define justice in terms of it, as the disposition to accord to every person his rights. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'rights') | |
| A reaction: I am inclined to think that a set of fairly pure values (such as equality, kindness, sympathy, respect) must be in place before the idea of a right would occur to anyone. Aristotle has a powerful moral sense, but rights for slaves don't cross his mind. |
| 7588 | Allegiance is fundamental to the conservative view of society [Scruton] |
| Full Idea: Conservatives have made the concept of allegiance, conceived as a power, fundamental to their description of the experience of society | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'allegiance') | |
| A reaction: This provokes the famous slogan of "My country - right or wrong!" However, the issue here is not going to be decided by a consequentialist analysis, but by a view a of human nature. I think I would want to carefully prise allegiance apart from loyalty. |
| 7594 | Democrats are committed to a belief and to its opposite, if the majority prefer the latter [Scruton] |
| Full Idea: The paradox of democracy (emphasised by Rousseau) is that I am compelled by my belief in democracy to embrace conflicting - perhaps even contradictory - opinions. If I believe A, and the majority vote for B, I am committed to enacting them both. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'paradox of democracy') | |
| A reaction: The paradox would have to be resolved by qualifying what exactly one is committed to by being a democrat. I would say I am committed to the right of my opponents to enact a policy with which I disagree. |
| 7593 | Liberals focus on universal human freedom, natural rights, and tolerance [Scruton, by PG] |
| Full Idea: Liberalism believes (roughly) in the supremacy of the individual, who has freedom and natural rights; it focuses on human, not divine affairs; it claims rights and duties are universal; and it advocates tolerance in religion and morality. | |
| From: report of Roger Scruton (A Dictionary of Political Thought [1982], 'liberalism') by PG - Db (ideas) | |
| A reaction: I find it hard to disagree with these principles, but the upshot in practice is often an excessive commitment to freedom and tolerance, because people fail to realise the subtle long-term erosions of society that can result. |
| 7592 | For positivists law is a matter of form, for naturalists it is a matter of content [Scruton] |
| Full Idea: For the positivist, law is law by virtue of its form; for the naturalist, by virtue of its content. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'law') | |
| A reaction: Clearly a perverse and 'unnatural' social rule (backed by government and implied force) is a 'law' in some sense of the word. It is hard to see how you could gain social consensus for a law if it didn't appear in some way to be 'natural justice'. |
| 7587 | The issue of abortion seems insoluble, because there is nothing with which to compare it [Scruton] |
| Full Idea: The issue of abortion is intractable, partly because of the absence of any other case to which it can be assimilated. | |
| From: Roger Scruton (A Dictionary of Political Thought [1982], 'abortion') | |
| A reaction: This is the legalistic approach to the problem, which always looks for precedents and comparisons. All problems must hav solutions, though (mustn't they?). The problem, though, is not the value of the foetus, but the unique form of 'ownership'. |
| 15693 | One sample of gold is enough, but one tree doesn't give the height of trees [Gelman] |
| Full Idea: We can confidently determine the chemical composition of gold from just a single sample, but we cannot determine the height of trees from just a single tree. | |
| From: Susan A. Gelman (The Essential Child [2003], 06 'The role') | |
| A reaction: The tricky word here is 'confidently'. If you meet one Latvian who is nice, do you assume they are all nice? At what point do you decide gold etc. really are natural kinds, where one sample tells all? Evolution of species... |
| 15701 | Nouns seem to invoke stable kinds more than predicates do [Gelman] |
| Full Idea: Children judged personal characteristics as more stable when they were referred to by a noun ('She is a carrot eater') than by a verbal predicate ('She eats carrots whenever she can') | |
| From: Susan A. Gelman (The Essential Child [2003], 08 'Naming') | |
| A reaction: This fits with my feeling that 'labels' are the basis of how the mind works. The noun invokes a genuine category of thing, where a predicate attaches to some preselected category ('she'). Gelman says names encourage inductions. |
| 15705 | Essentialism encourages us to think about the world scientifically [Gelman] |
| Full Idea: Essentialism encourages a 'scientific' mindset in thinking about the natural world, a belief that intensive study of a natural domain will yield ever more underlying properties. | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Intro') | |
| A reaction: Maybe scientists must be committed to essences, the way mathematicians must be committed to numbers? This idea spendidly opposes the doubts expressed by Popper. |
| 15702 | Essentialism doesn't mean we know the essences [Gelman] |
| Full Idea: Essentialism does not entail that people know what the essence is. | |
| From: Susan A. Gelman (The Essential Child [2003], 09 'Theory') | |
| A reaction: This is a fundamental and (I would say) fairly obvious point, but it needs to be made to the more passionate opponents of essentialism. |
| 15704 | Essentialism starts from richly structured categories, leading to a search for underlying properties [Gelman] |
| Full Idea: If my speculations are correct, then essentialism starts out strictly as a belief that many categories are richly structured kinds, then additionally becomes a search for underlying inherent properties. | |
| From: Susan A. Gelman (The Essential Child [2003], 10 'Figuring') | |
| A reaction: This is her summary of extensive essentialist research among children. She favours the priority of kinds and categories. We actually change taxonomies on the basis of revisions in our accounts of essence. Science negotiates. |
| 15706 | A major objection to real essences is the essentialising of social categories like race, caste and occupation [Gelman] |
| Full Idea: One major argument against the view that essences are real is the rampant essentializing of categories that are socially constructed (such as race, caste and occupation). | |
| From: Susan A. Gelman (The Essential Child [2003], 11 'Is essentialism') | |
| A reaction: You can't argue with that. It raises the question of whether the approach of scientific essentialism has any value in the social, rather than physical, sciences. We jokingly essentialise groups of people such as referees or Oxonians. |