66 ideas
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| Full Idea: The best known axiomatization of PL is Whitehead/Russell. There are four axioms: (p∨p)→p, q→(p∨q), (p→q)→(q∨p), and (q→r)→((p∨q)→(p∨r)), plus Substitution and Modus Ponens rules. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by GE Hughes/M Cresswell - An Introduction to Modal Logic Ch.1 |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| Full Idea: The axiom of Reducibility ...is crucial in the reduction of classes to logic, ...and seems to be a quite legitimate logical notion for Russell. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 6.4 | |
| A reaction: This is an unusual defence of the axiom, which is usually presumed to have been kicked into the long grass by Quine. If one could reduce classes to logic, that would destroy the opposition to logicism in a single neat coup. |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell adduces two reasons against the extensional view of classes, namely the existence of the null class (which cannot very well be a collection), and the unit classes (which would have to be identical with their single elements). | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Structure and Ontology p.459 | |
| A reaction: Gödel believes in the reality of classes. I have great sympathy with Russell, when people start to claim that sets are not just conveniences to help us think about things, but actual abstract entities. Is the singleton of my pencil is on this table? |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| Full Idea: Classes, so far as we introduce them, are merely symbolic or linguistic conveniences, not genuine objects. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.72), quoted by Penelope Maddy - Naturalism in Mathematics III.2 |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| Full Idea: Russell call 'if...then' implication, when the material conditional is a much better account; C.I.Lewis (in founding modern modal logic) preserved Russell's confusion by creating 'strict implication', and called that implication. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Willard Quine - Reply to Professor Marcus p.177 | |
| A reaction: [A compession of Quine's paragraph]. All of this assumes that logicians can give an accurate account of what if...then means, when ordinary usage is broad and vague. Strict implication seems to drain all the normal meaning out of 'if...then'. |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| Full Idea: In Mr Russell's idea of implication, if twenty random sentences from a newspaper were put in a hat, and two of them drawn at random, one will certainly imply the other, and it is an even bet the implication will be mutual. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by C.I. Lewis - A Pragmatic Conception of the A Priori p.366 | |
| A reaction: This sort of lament leads modern logicians to suggest 'relevance' as an important criterion. It certainly seems odd that so-called 'classical logic' should contain a principle so at variance with everyday reasoning. |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| Full Idea: Russell did not view logic as an uninterpreted calculus awaiting interpretations [the modern view]. Rather, logic is a single 'interpreted' body of a priori truths, of propositions rather than sentence forms - but maximally general and topic neutral. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 1 | |
| A reaction: This is the view which Wittgenstein challenged, saying logic is just conventional. Linsky claims that Russell's logicism is much more plausible, once you understand his view of logic. |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| Full Idea: In 'Principia' a young science was enriched with a new abstract theory of relations, ..and not only Cantor's set theory but also ordinary arithmetic and the theory of measurement are treated from this abstract relational standpoint. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 | |
| A reaction: I presume this is accounting for relations in terms of ordered sets. |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| Full Idea: For Russell the real number 2 is the class of rationals less than 2 (i.e. 2/1). ...Notice that on this definition, real numbers are classes of rational numbers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| Full Idea: Although Russell takes numbers to be certain classes, his 'no-class' theory then eliminates all mention of classes in favour of the 'propositional functions' that define them; and in the case of the numbers these just are the numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by David Bostock - Philosophy of Mathematics 9.B.4 |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| Full Idea: Russell and Whitehead took arithmetic to be higher-order logic, ..and came close to identifying numbers with numerical quantifiers. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Harold Hodes - Logicism and Ontological Commits. of Arithmetic p.148 | |
| A reaction: The point here is 'higher-order'. |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| Full Idea: Unlike Frege, Russell and Whitehead were not realists about mathematical objects, and whereas Frege thought that only arithmetic and analysis are branches of logic, they think the vast majority of mathematics (including geometry) is essentially logical. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: If, in essence, Descartes reduced geometry to algebra (by inventing co-ordinates), then geometry ought to be included. It is characteristic of Russell's hubris to want to embrace everything. |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| Full Idea: What is missing, above all, in 'Principia', is a precise statement of the syntax of the formalism. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.448 |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| Full Idea: Russell and Whitehead's ramified theory of types worked not with sets, but with propositional functions (similar to Frege's concepts), with a more restrictive assignment of variables, insisting that bound, as well as free, variables be of lower type. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.3 | |
| A reaction: I don't fully understand this (and no one seems much interested any more), but I think variables are a key notion, and there is something interesting going on here. I am intrigued by ordinary language which behaves like variables. |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| Full Idea: The Russell/Whitehead type theory reduces mathematics to a consistent founding discipline, but is criticised for not really being logic. They could not prove the existence of infinite sets, and introduced a non-logical 'axiom of reducibility'. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.6 | |
| A reaction: To have reduced most of mathematics to a founding discipline sounds like quite an achievement, and its failure to be based in pure logic doesn't sound too bad. However, it seems to reduce some maths to just other maths. |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| Full Idea: In the system of 'Principia Mathematica', it is not only the axioms of infinity and reducibility which go beyond pure logic, but also the initial conception of a universal domain of individuals and of a domain of predicates. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.267) by Paul Bernays - On Platonism in Mathematics p.267 | |
| A reaction: This sort of criticism seems to be the real collapse of the logicist programme, rather than Russell's paradox, or Gödel's Incompleteness Theorems. It just became impossible to stick strictly to logic in the reduction of arithmetic. |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| Full Idea: Russell and Whitehead are particularly careful to avoid paradox, and consider the paradoxes to indicate that we create mathematical reality. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Michčle Friend - Introducing the Philosophy of Mathematics 3.1 | |
| A reaction: This strikes me as quite a good argument. It is certainly counterintuitive that reality, and abstractions from reality, would contain contradictions. The realist view would be that we have paradoxes because we have misdescribed the facts. |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| Full Idea: Russell insisted on the vicious circle principle, and thus rejected impredicative definitions, which resulted in an unwieldy ramified type theory, with the ad hoc axiom of reducibility. Ramsey's simpler theory was impredicative and avoided the axiom. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Stewart Shapiro - Thinking About Mathematics 5.2 | |
| A reaction: Nowadays the theory of types seems to have been given up, possibly because it has no real attraction if it lacks the strict character which Russell aspired to. |
| 5953 | For the Cyrenaics experience was not enough to give certainty about reality [Aristippus young, by Plutarch] |
| Full Idea: The Cyrenaics, placing all experience within themselves, thought such evidence was insufficient warrant for certainty about reality, and withdrew as in a siege from the world, admitting that objects 'appear', but refusing to pronounce the word 'are'. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Plutarch - 74: Reply to Colotes §1120 | |
| A reaction: This seems to be the most extreme position found in ancient thought. It accompanies their extreme hedonism, based on the reality of experience and lack of interest in anything external. A bit daft, really. |
| 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. |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| Full Idea: Trivially, the Identity of Indiscernibles says that two individuals, Castor and Pollux, cannot have all properties in common. For Castor must have the properties of being identical with Castor and not being identical with Pollux, which Pollux can't share. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913], I p.57) by Robert Merrihew Adams - Primitive Thisness and Primitive Identity 2 | |
| A reaction: I suspect that either the property of being identical with itself is quite vacuous, or it is parasytic on primitive identity, or it is the criterion which is actually used to define identity. Either way, I don't find this claim very illuminating. |
| 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. |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| Full Idea: By analyzing the paradoxes to which Cantor's set theory had led, ..Russell brought to light the amazing fact that our logical intuitions (concerning such notions as truth, concept, being, class) are self-contradictory. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Kurt Gödel - Russell's Mathematical Logic p.452 | |
| A reaction: The main intuition that failed was, I take it, that every concept has an extension, that is, there are always objects which will or could fall under the concept. |
| 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') |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| Full Idea: The multiple relations theory of judgement proposes that assertions about propositions are dependent upon genuine facts involving belief and other attitude relations, subjects of those attitudes, and the constituents of the belief. | |
| From: report of B Russell/AN Whitehead (Principia Mathematica [1913]) by Bernard Linsky - Russell's Metaphysical Logic 7.2 | |
| A reaction: This seems to require a commitment to universals (especially relations) with which we can be directly acquainted. I prefer propositions, but as mental entities, not platonic entities. |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| Full Idea: When a judgement occurs, there is a certain complex entity, composed of the mind and the various objects of the judgement. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44) | |
| A reaction: This is Russell's multiple-relation theory of judgement, which replaced his earlier belief in unified propositions (now 'false abstractions'). He seems to have accepted Locke's view, that the act of judgement produces the unity. |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus | |
| A reaction: Morris says this is Russell's multiple-relations theory of judgement. The theory accompanies the rejection of the concept of the unified proposition. When I hear 'Socrates had a mole on his shoulder' I get the meaning without judging. |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| Full Idea: When Russell moved to his multiple relation theory of judgement …he then faced difficulties making sense of the unity of sentences. | |
| From: comment on B Russell/AN Whitehead (Principia Mathematica [1913], p.44) by Michael Morris - Guidebook to Wittgenstein's Tractatus 3A | |
| A reaction: Roughly, he seems committed to saying that there is only unity if you think there is unity; there is no unity in a sentence prior to the act of judgement. |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| Full Idea: When I judge 'Socrates is human', the meaning is completed by the act of judging, and we no longer have an incomplete symbol. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap | |
| A reaction: Personally I would have thought that you needed to know the meaning properly before you could make the judgement, but then he is Bertrand Russell and I'm not. |
| 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. |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| Full Idea: A 'proposition', in the sense in which a proposition is supposed to be the object of a judgement, is a false abstraction, because a judgement has several objects, not one. | |
| From: B Russell/AN Whitehead (Principia Mathematica [1913], p.44), quoted by Michael Morris - Guidebook to Wittgenstein's Tractatus 2E | |
| A reaction: This is the rejection of the 'Russellian' theory of propositions, in favour of his multiple-relations theory of judgement. But why don't the related objects add up to a proposition about a state of affairs? |
| 3023 | Even the foolish may have some virtues [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics say that some of the virtues may exist even in the foolish. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3026 | Actions are influenced by circumstances, so Cyrenaics say felons should be reformed, not hated [Aristippus young, by Diog. Laertius] |
| Full Idea: Cyrenaics say errors should be pardoned, because men do not err intentionally but are influenced by circumstances; one should not hate a person, but only teach him better. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.9 | |
| A reaction: A very appealing suggestion, and rather wonderful for its time. There is still implied agreement about what is 'error', and what counts as 'better'. |
| 3024 | Cyrenaics teach that honour, justice and shame are all based on custom and fashion [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics taught that there was nothing naturally and intrinsically just, or honourable, or disgraceful; but that things were considered so because of law and fashion. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 | |
| A reaction: As we would say now, values and virtues are 'cultural constructs'. This obviously contains a lot of truth, but I don't think our opposition of genocide is just 'fashion'. |
| 3025 | For a Cyrenaic no one is of equal importance to himself [Aristippus young, by Diog. Laertius] |
| Full Idea: A Cyrenaic will not consider anyone else of equal importance with himself. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.9 |
| 3019 | No one pleasure is different from or more pleasant than another [Aristippus young, by Diog. Laertius] |
| Full Idea: No one pleasure is different from or more pleasant than another. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3021 | The Cyrenaics asserted that corporeal pleasures were superior to mental ones [Aristippus young, by Diog. Laertius] |
| Full Idea: The Cyrenaics asserted that corporeal pleasures were superior to mental ones. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.8 |
| 3027 | Cyrenaics say wise men are self-sufficient, needing no friends [Aristippus young, by Diog. Laertius] |
| Full Idea: Cyrenaics say wise men are sufficient to themselves, and so have no need of friends. | |
| From: report of Aristippus the younger (fragments/reports [c.335 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.7.13 |
| 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. |