31 ideas
| 8083 | Boole applied normal algebra to logic, aiming at an algebra of thought [Boole, by Devlin] |
| Full Idea: Boole proposed to use the entire apparatus of a school algebra class, with operations such as addition and multiplication, methods to solve equations, and the like, to produce an algebra of thought. | |
| From: report of George Boole (The Laws of Thought [1854]) by Keith Devlin - Goodbye Descartes Ch.3 | |
| A reaction: The Stoics didn’t use any algebraic notation for their study of propositions, so Boole's idea launched full blown propositional logic, and the rest of modern logic followed. Nice one. |
| 7727 | Boole's notation can represent syllogisms and propositional arguments, but not both at once [Boole, by Weiner] |
| Full Idea: Boole introduced a new symbolic notation in which it was possible to represent both syllogisms and propositional arguments, ...but not both at once. | |
| From: report of George Boole (The Laws of Thought [1854], Ch.3) by Joan Weiner - Frege | |
| A reaction: How important is the development of symbolic notations for the advancement of civilisations? Is there a perfect notation, as used in logical heaven? |
| 8686 | Boole made logic more mathematical, with algebra, quantifiers and probability [Boole, by Friend] |
| Full Idea: Boole (followed by Frege) began to turn logic from a branch of philosophy into a branch of mathematics. He brought an algebraic approach to propositions, and introduced the notion of a quantifier and a type of probabilistic reasoning. | |
| From: report of George Boole (The Laws of Thought [1854], 3.2) by Michèle Friend - Introducing the Philosophy of Mathematics | |
| A reaction: The result was that logic not only became more mathematical, but also more specialised. We now have two types of philosopher, those steeped in mathematical logic and the rest. They don't always sing from the same songsheet. |
| 22277 | Boole's method was axiomatic, achieving economy, plus multiple interpretations [Boole, by Potter] |
| Full Idea: Boole's work was an early example of the axiomatic method, whereby intellectual economy is achieved by studying a set of axioms in which the primitive terms have multiple interpretations. | |
| From: report of George Boole (The Laws of Thought [1854]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 02 'Boole' | |
| A reaction: Unclear about this. I suppose the axioms are just syntactic, and a range of semantic interpretations can be applied. Are De Morgan's Laws interpretations, or implications of the syntactic axioms? The latter, I think. |
| 16669 | Everything that exists is either a being, or some mode of a being [Malebranche] |
| Full Idea: It is absolutely necessary that everything in the world be either a being or a mode [manière] of a being. | |
| From: Nicolas Malebranche (The Search After Truth [1675], III.2.8.ii), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 13.4 |
| 17979 | Research shows perceptual discrimination is sharper at category boundaries [Murphy] |
| Full Idea: Goldstone's research has shown how learning concepts can change perceptual units. For example, perceptual discrimination is heightened along category boundaries. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: [Goldstone 1994, 2000] This is just the sort of research which throws a spanner into the simplistic a priori thinking of many philosophers. |
| 18690 | Induction is said to just compare properties of categories, but the type of property also matters [Murphy] |
| Full Idea: Most theories of induction claim that it should depend primarily on the similarity of the categories involved, but then the type of property should not matter, yet research shows that it does. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: I take this to be good empirical support for Gilbert Harman's view that induction is really inference to the best explanation. The thought (which strikes me as obviously correct) is that we bring nested domains of knowledge to bear in induction. |
| 17980 | The main theories of concepts are exemplar, prototype and knowledge [Murphy] |
| Full Idea: The three main theories of concepts under consideration are the exemplar, the prototype and the knowledge approaches. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) |
| 17973 | The theoretical and practical definitions for the classical view are very hard to find [Murphy] |
| Full Idea: It has been extremely difficult to find definitions for most natural categories, and even harder to find definitions that are plausible psychological representations that people of all ages would be likely to use. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) |
| 17969 | The classical definitional approach cannot distinguish typical and atypical category members [Murphy] |
| Full Idea: The early psychological approaches to concepts took a definitional approach. ...but this view does not have any way of distinguishing typical and atypical category members (...as when a trout is a typical fish and an eel an atypical one). | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) | |
| A reaction: [pp. 12 and 22] Eleanor Rosch in the 1970s is said to have largely killed off the classical view. |
| 17970 | Classical concepts follow classical logic, but concepts in real life don't work that way [Murphy] |
| Full Idea: The classical view of concepts has been tied to traditional logic. 'Fido is a dog and a pet' is true if it has the necessary and sufficient conditions for both, ...but there is empirical evidence that people do not follow that rule. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) | |
| A reaction: Examples given are classifying chess as a sport and/or game, and classifying a tree house (which is agreed to be both a building and not a building!). |
| 17971 | Classical concepts are transitive hierarchies, but actual categories may be intransitive [Murphy] |
| Full Idea: The classical view of concepts explains hierarchical order, where categories form nested sets. But research shows that categories are often not transitive. Research shows that a seat is furniture, and a car seat is a seat, but it is not furniture. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) | |
| A reaction: [compressed] Murphy adds that the nesting of definitions is classically used to match the nesting of hierarchies. This is a nice example of the neatness of the analytic philosopher breaking down when it meets the mess of the world. |
| 17972 | The classical core is meant to be the real concept, but actually seems unimportant [Murphy] |
| Full Idea: A problem with the revised classical view is that the concept core does not seem to be an important part of the concept, despite its name and theoretical intention as representing the 'real' concept. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) | |
| A reaction: Apparently most researchers feel they can explain their results without reference to any core. Not so fast, I would say (being an essentialist). Maybe people acknowledge an implicit core without knowing what it is. See Susan Gelman. |
| 17975 | There is no 'ideal' bird or dog, and prototypes give no information about variability [Murphy] |
| Full Idea: Is there really an 'ideal bird' that could represent all birds? ...Furthermore a single prototype would give no information about the variability of a category. ...Compare the incredible variety of dogs to the much smaller diversity of cats. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 3) | |
| A reaction: The point about variability is particularly noteworthy. You only grasp the concept of 'furniture' when you understand its range, as well as its typical examples. What structure is needed in a concept to achieve this? |
| 17976 | Prototypes are unified representations of the entire category (rather than of members) [Murphy] |
| Full Idea: In the prototype view the entire category is represented by a unified representation rather than separate representations for each member, or for different classes of members. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 3) | |
| A reaction: This is the improved prototype view, as opposed to the implausible idea that there is one ideal exemplar. The new theory still have the problem of how to represent diversity within the category, while somehow remaining 'unified'. |
| 18691 | The prototype theory uses observed features, but can't include their construction [Murphy] |
| Full Idea: Nothing in the prototype model says the shape of an animal is more important than its location in identifying its kind. The theory does not provide a way the features can be constructed, rather than just observed. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: This makes some kind of mental modelling central to thought, and not just a bonus once you have empirically acquired the concepts. We bring our full range of experience to bear on even the most instantaneous observations. |
| 17983 | The prototype theory handles hierarchical categories and combinations of concepts well [Murphy] |
| Full Idea: The prototype view has no trouble with either hierarchical structure or explaining categories. ...Meaning and conceptual combination provide strong evidence for prototypes. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: Prototypes are not vague, making clearer classification possible. A 'mountain lion' is clear, because its components are clear. |
| 17985 | Prototypes theory of concepts is best, as a full description with weighted typical features [Murphy] |
| Full Idea: Our theory of concepts must be primarily prototype-based. That is, it must be a description of an entire concept, with its typical features (presumably weighted by their importance). | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: This is to be distinguished from the discredited 'classical' view of concepts, that the concept consists of its definition. I take Aristotle's account of definition to be closer to a prototype description than to a dictionary definition. |
| 17986 | Learning concepts is forming prototypes with a knowledge structure [Murphy] |
| Full Idea: My proposal is that people attempt to form prototypes as part of a larger knowledge structure when they learn concepts. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: This combines theory theory (knowledge) with the prototype view, and sounds rather persuasive. The formation of prototypes fits with the explanatory account of essentialism I am defending. He later calls prototype formation 'abstraction' (494). |
| 17974 | The most popular theories of concepts are based on prototypes or exemplars [Murphy] |
| Full Idea: The most popular theories of concepts are based on prototype or exemplar theories that are strongly unclassical. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 2) |
| 17977 | The exemplar view of concepts says 'dogs' is the set of dogs I remember [Murphy] |
| Full Idea: In the exemplar view of concepts, the idea that people have a representation that somehow encompasses an entire concept is rejected. ...Instead a person's concept of dogs is the set of dogs that the person remembers. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 3) | |
| A reaction: [The theory was introduced by Medin and Schaffer 1978] I think I have finally met a plausible theory of concepts. When I think 'dog' I conjure up a fuzz of dogs that exhibit the range I have encountered (e.g. tiny to very big). Individuals come first! |
| 17982 | Exemplar theory struggles with hierarchical classification and with induction [Murphy] |
| Full Idea: The exemplar view has trouble with hierarchical classification and with induction in adults. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: To me these both strongly support essentialism - that you form the concept 'dog' from seeing some dogs, but you then extrapolate to large categories and general truths about dogs, on the assumption of the natures of the dogs you have seen. |
| 17981 | Children using knowing and essentialist categories doesn't fit the exemplar view [Murphy] |
| Full Idea: The findings showing that children use knowledge and may be essentialist about category membership do not comport well with the exemplar view. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: Tricky, because Gelman persuaded me of the essentialism, but the exemplar view of concepts looks the most promising. Clearly they must be forced to coexist.... |
| 17984 | Conceptual combination must be compositional, and can't be built up from exemplars [Murphy] |
| Full Idea: The exemplar accounts of conceptual combination are demonstrably wrong, because the meaning of a phrase has to be composed from the meaning of its parts (plus broader knowledge), and it cannot be composed as a function of exemplars. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: This sounds quite persuasive, and I begin to see that my favoured essentialism fits the prototype view of concepts best, though this mustn't be interpreted too crudely. We change our prototypes with experience. 'Bird' is a tricky case. |
| 17987 | The concept of birds from exemplars must also be used in inductions about birds [Murphy] |
| Full Idea: We don't have one concept of birds formed by learning from exemplars, and another concept of birds that is used in induction. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch.13) | |
| A reaction: In other words exemplar concepts break down when we generalise using the concept. The exemplars must be unified, to be usable in thought and language. |
| 17978 | We do not learn concepts in isolation, but as an integrated part of broader knowledge [Murphy] |
| Full Idea: The knowledge approach argues that concepts are part of our general knowledge about the world. We do not learn concepts in isolation, ...but as part of our overall understanding of the world. Animal concepts are integrated with biology, behaviour etc. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 3) | |
| A reaction: This is one of the leading theories of concepts among psychologists. It seems to be an aspect of the true theory, but it needs underpinning with some account of isolated individual concepts. This is also known as the 'theory theory'. |
| 18687 | Concepts with familiar contents are easier to learn [Murphy] |
| Full Idea: A concept's content influences how easy it is to learn. If the concept is grossly incompatible with what people know prior to the experiment, it will be difficult to acquire. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: This is a preliminary fact which leads towards the 'knowledge' theory of concepts (aka 'theory theory'). The point being that the knowledge involved is integral to the concept. Fits my preferred mental files approach. |
| 18688 | Some knowledge is involved in instant use of categories, other knowledge in explanations [Murphy] |
| Full Idea: Some kinds of knowledge are probably directly incorporated into the category representation and used in normal, fast decisions about objects. Other kinds of knowledge, however, may come into play only when it has been solicited. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: This is a summary of empirical research, but seems to fit our normal experience. If you see a hawk, you have some instant understanding, but if you ask what the hawk is doing here, you draw more widely. |
| 18689 | People categorise things consistent with their knowledge, even rejecting some good evidence [Murphy] |
| Full Idea: People tend to positively categorise items that are consistent with their knowledge and to exclude items that are inconsistent, sometimes even overruling purely empirical sources of information. | |
| From: Gregory L. Murphy (The Big Book of Concepts [2004], Ch. 6) | |
| A reaction: The main rival to 'theory theory' is the purely empirical account of how concepts are acquired. This idea reports empirical research in favour of the theory theory (or 'knowledge') approach. |
| 12726 | In a true cause we see a necessary connection [Malebranche] |
| Full Idea: A true cause is one in which the mind perceives a necessary connection between the cause and its effect. | |
| From: Nicolas Malebranche (The Search After Truth [1675], 1.649 (450)), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 5 | |
| A reaction: Presumably Hume was ignorant of 'true' causes, since he says he never saw this connection. But then is the perception done by the mind, or by the senses? |
| 2594 | A true cause must involve a necessary connection between cause and effect [Malebranche] |
| Full Idea: A true cause as I understand it is one such that the mind perceives a necessary connection between it and its effects. | |
| From: Nicolas Malebranche (The Union of Body and Soul [1675], p.116) |