102 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 18559 | Philosophy is empty if it does not in some way depend on matters of fact [Machery] |
| Full Idea: Save, maybe, for purely formal (e.g. logical) theories, philosophical claims whose correctness does not depend, however indirectly, on matters of fact are empty: they are neither true nor false. | |
| From: Edouard Machery (Doing Without Concepts [2009], Intro) | |
| A reaction: I subscribe to this view. I'd even say that logic is empty if it is not answerable to the facts. The facts are nature, so this is a naturalistic manifesto. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 17505 | Using proper names properly doesn't involve necessary and sufficient conditions [Putnam] |
| Full Idea: The important thing about proper names is that it would be ridiculous to think that having linguistic competence can be equated in their case with knowledge of a necessary and sufficient condition. | |
| From: Hilary Putnam (Explanation and Reference [1973], II B) |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 18564 | Do categories store causal knowledge, or typical properties, or knowledge of individuals? [Machery] |
| Full Idea: Psychologists have attempted to determine whether a concept of a category stores some causal knowledge about the members, some knowledge about their typical properties, or some knowledge about specific members. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.3.2) | |
| A reaction: I take there to be a psychological process of 'generalisation', so that knowledge of individuals is not and need not be retained. I am dubious about entities called 'properties', so I will vote for causal (including perceptual) knowledge. |
| 18604 | Are quick and slow categorisation the same process, or quite different? [Machery] |
| Full Idea: Are categorisation under time pressure and categorisation without time pressure ...two different cognitive competences? | |
| From: Edouard Machery (Doing Without Concepts [2009], 5.1.1) | |
| A reaction: This is a psychologist's question. Introspectively, they do seem to be rather different, as there is no time for theorising and explaining when you are just casting your eyes over the landscape. |
| 18573 | For each category of objects (such as 'dog') an individual seems to have several concepts [Machery] |
| Full Idea: I contend that the best available evidence suggests that for each category of objects an individual typically has several concepts. For instance, instead of having a single concept of dog, an individual has in fact several concepts of dog. | |
| From: Edouard Machery (Doing Without Concepts [2009], 3) | |
| A reaction: Machery's book is a sustained defence of this hypothesis, with lots of examples from psychology. Any attempt by philosophers to give a neat and tidy account of categorisation looks doomed. |
| 18602 | A thing is classified if its features are likely to be generated by that category's causal laws [Machery] |
| Full Idea: A to-be-classified object is considered a category member to the extent that its features were likely to have been generated by the category's causal laws. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.4.4) | |
| A reaction: [from Bob Rehder, psychologist, 2003] This is an account of categorisation which arises from the Theory Theory view of concepts, of which I am a fan. I love this idea, which slots neatly into the account I have been defending. Locke would like this. |
| 18565 | There may be ad hoc categories, such as the things to pack in your suitcase for a trip [Machery] |
| Full Idea: There may be ad hoc categories, as when people think about the things to pack in a small suitcase for a trip abroad. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.4.1) | |
| A reaction: This seems to be obviously correct, though critics might say that 'category' is too grand a term for such a grouping. |
| 18570 | There may be several ways to individuate things like concepts [Machery] |
| Full Idea: Philosophers have rarely explained why they believe that there is a single correct way of individuating concepts. Many entities can be legitimately individuated in several ways. | |
| From: Edouard Machery (Doing Without Concepts [2009], 2.1.3) | |
| A reaction: I cite this under 'individuation' because I think that is a very garbled concept. I agree with this point, even though I don't really know exactly what individuation is supposed to be. |
| 11908 | Putnam bases essences on 'same kind', but same kinds may not share properties [Mackie,P on Putnam] |
| Full Idea: The only place for essentialism to come from in Putnam's semantic account is out of the 'same kind' relation. But if the same kind relation can be cashed out in terms that do not involve sharing properties (apart from 'being water') there is a gap. | |
| From: comment on Hilary Putnam (Explanation and Reference [1973]) by Penelope Mackie - How Things Might Have Been 10.4 | |
| A reaction: [This is the criticism of Salmon and Mellor] See Mackie's discussion for details. I would always have thought that relations result from essences, so could never be used to define them. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 18616 | If a term doesn't pick out a kind, keeping it may block improvements in classification [Machery] |
| Full Idea: If a hypothesised natural kind term fails to pick out a natural kind, keeping this theoretical term is likely to prevent the development of a new classification system that would identify the relevant kinds. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8.2.3) | |
| A reaction: I'm persuaded. This is why metaphysicians should stop talking about 'properties'. |
| 18614 | Vertical arguments say eliminate a term if it picks out different natural kinds in different theories [Machery] |
| Full Idea: Vertical arguments for eliminativism of theoretical terms note that distinct types of generalisation do not line up with each other. ...It is argued that the theoretical term picks out more than one natural kind. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8.2.3) | |
| A reaction: He mentions 'depression', as behavioural and cognitive; the former includes apes, and the latter doesn't. It is a nice principle for tidying up theories. |
| 18615 | Horizontal arguments say eliminate a term if it fails to pick out a natural kind [Machery] |
| Full Idea: Horizontal arguments for eliminativism of theoretical terms say that some terms should be eliminated if they do not pick out a natural kind. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8.2.3) | |
| A reaction: This is the one Machery likes, but I would say that it is less obvious than the 'vertical' version, since picking out a natural kind may not be the only job of a theoretical term. (p.238: Machery agrees!) |
| 17508 | Science aims at truth, not at 'simplicity' [Putnam] |
| Full Idea: Scientists are not trying to maximise some formal property of 'simplicity'; they are trying to maximise truth. | |
| From: Hilary Putnam (Explanation and Reference [1973], III B) | |
| A reaction: This seems to be aimed at the Mill-Ramsey-Lewis account of laws of nature, as the simplest axioms of experience. I'm with Putnam (as he was at this date). |
| 18609 | Psychologists use 'induction' as generalising a property from one category to another [Machery] |
| Full Idea: Typically, psychologists use 'induction' to refer to the capacity to generalise a property from a category (the source) to another category (the target). | |
| From: Edouard Machery (Doing Without Concepts [2009], 7.1.1) | |
| A reaction: This is because psychologists are interested in the ongoing activities of thought. Philosophers step back a bit, to ask how the whole thing could get started. Philosophical induction has to start with individuals and single observations. |
| 18610 | 'Ampliative' induction infers that all members of a category have a feature found in some of them [Machery] |
| Full Idea: Induction is 'ampliative' when it infers that all or most members of a category possess a property from the fact that some of its members have this property. | |
| From: Edouard Machery (Doing Without Concepts [2009], 7.1.1) | |
| A reaction: This sounds like a simple step in reasoning, but actually it is more like explanation, and will involve overall coherence and probability, rather than a direct conclusion. This invites sceptical questions. The last one observed may be the exception. |
| 18562 | Connectionists cannot distinguish concept-memories from their background, or the processes [Machery] |
| Full Idea: Connectionists typically do not distinguish between processes and memory stores, and, more importantly, it is unclear whether connectionists can draw a distinction between the knowledge stored in a concept and the background. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.1) | |
| A reaction: In other words connectionism fails to capture the structured nature of our thinking. There is an innate structure (which, say I, should mainly be seen as 'mental files'). |
| 18561 | We can identify a set of cognitive capacities which are 'higher order' [Machery] |
| Full Idea: Categorization, deduction, induction, analogy-making, linguistic understanding, and planning - all of these are higher cognitive capacities. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.1) | |
| A reaction: His 'lower' competences are perceptual and motor. I say the entry to the higher competences are abstraction, idealisation and generalisation. If you can't do these (chimpanzees!) you will not be admitted. |
| 18574 | Concepts for categorisation and for induction may be quite different [Machery] |
| Full Idea: In general, concepts that are used when we categorise and concepts that are used when we reason inductively could have little in common. | |
| From: Edouard Machery (Doing Without Concepts [2009], 3.2.1) | |
| A reaction: In the end he is going to reject concepts altogether, so he would say this. Friends of concepts would be very surprised if the mind were so uneconomical in its activities, given that induction seems to be up to its neck in categorisation. |
| 18588 | Concept theories aim at their knowledge, processes, format, acquisition, and location [Machery] |
| Full Idea: A theory of concepts should determine the knowledge stored in them, and the cognitive processes that use concepts. Ideally it should also characterise their format, their acquisition, and (increasingly) localise them in the brain. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4) | |
| A reaction: Machery reveals his dubious scientism in the requirement to localise them in the brain. That strikes me as entirely irrelevant to both philosophy and psychology. I want the format, acquisition and knowledge. |
| 18611 | We should abandon 'concept', and just use 'prototype', 'exemplar' and 'theory' [Machery] |
| Full Idea: The notion of 'concept' ought to be eliminated from the theoretical vocabulary of psychology, and replaced by the notions of prototype, exemplar, and theory. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8) | |
| A reaction: Machery's main thesis. I think similarly about 'property' in metaphysics. It embraces different ideas, and if we eliminated 'property' (and used predicate, class, fundamental power, complex power) we would do better. Psychologists have dropped 'memory'. |
| 18567 | In the philosophy of psychology, concepts are usually introduced as constituents of thoughts [Machery] |
| Full Idea: In the philosophy of psychology, concepts are usually introduced as constituents, components, or parts of thoughts. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.4.3) | |
| A reaction: My instincts are against this. I take the fundamentals of concepts to be mental responses to distinct individual items in the world. Thought builds up from that. He says psychologists themselves don't see it this way. Influence of Frege. |
| 18569 | In philosophy theories of concepts explain how our propositional attitudes have content [Machery] |
| Full Idea: A philosophical theory of concepts is a semantic theory for our propositional attitudes: it explains how our thoughts can have the content they have. | |
| From: Edouard Machery (Doing Without Concepts [2009], 2.1.2) | |
| A reaction: I suppose this is what I am interested in. I want to know in what way concepts form a bridge between content and world. I am more interested in the propositions, and less interested in our attitudes towards them. |
| 18563 | By 'concept' psychologists mean various sorts of representation or structure [Machery] |
| Full Idea: Psychologists use 'concept' interchangeably with 'mental representation', 'category representation', 'knowledge representation', 'knowledge structure', 'semantic representation', and 'conceptual structures'. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.1) | |
| A reaction: [Machery gives references for each of these] Machery is moving in to attack these, but we look to psychologists to give some sort of account of what a concept might consist of, such that it could be implemented by neurons. |
| 18558 | Concept theorists examine their knowledge, format, processes, acquisition and location [Machery] |
| Full Idea: Psychological theories of concepts try to describe the knowledge stored in concepts, the format of concepts, the cognitive processes that use the concepts, the acquisition of concepts, and the localization of concepts in the brain. | |
| From: Edouard Machery (Doing Without Concepts [2009], Intro) | |
| A reaction: I suppose it would the first two that are of central interest. What individuates a concept (its 'format') and what are the contents of a concept. The word 'stored' seems to imply a mental files view. |
| 18557 | Psychologists treat concepts as long-term knowledge bodies which lead to judgements [Machery] |
| Full Idea: In psychology, concepts are characterized as those bodies of knowledge that are stored in long-term memory and used most higher cognitive competences when these processes result in judgements. | |
| From: Edouard Machery (Doing Without Concepts [2009], Intro) | |
| A reaction: Machery mounts an attack on this idea. I like the 'mental files' idea, where a concept starts as a label, and then acquires core knowledge, and then further information. The 'concept' is probably no more than a label, and minimal starter information. |
| 18560 | Psychologist treat concepts as categories [Machery] |
| Full Idea: Psychologists often use 'concept' and 'category' interchangeably. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.1) | |
| A reaction: Well they shouldn't. Some concepts are no more than words, and don't categorise anything. Some things may be categorised by a complex set of concepts. |
| 18592 | The concepts OBJECT or AGENT may be innate [Machery] |
| Full Idea: Several concepts, such as OBJECT or AGENT, may be innate. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.1.4) | |
| A reaction: It is one thing to say that we respond to objects and agents, and another to say that we have those 'concepts'. Presumably birds, and even bees, have to relate to similar features. Add PROCESS? |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 18566 | Concepts should contain working memory, not long-term, because they control behaviour [Machery] |
| Full Idea: We ought to reserve the term 'concept' for the bodies of knowledge in working memory, and not for our knowledge of long-term memory, because the former, and not the latter, 'control behaviour'. | |
| From: Edouard Machery (Doing Without Concepts [2009], 1.4.1) | |
| A reaction: [He cites the psychologist Barsalou 1993] Some more theoretical concepts can only be recalled with difficulty, and control our theorising rather than our behaviour. But we act on some theories, so there is no clear borderline. |
| 18584 | One hybrid theory combines a core definition with a prototype for identification [Machery] |
| Full Idea: One hybrid theory of concepts says they have both a core and an identification procedure. The core is a definition (necessary and sufficient conditions), while the identification procedure consists of a prototype (the properties typical of a category). | |
| From: Edouard Machery (Doing Without Concepts [2009], 3.3.1) | |
| A reaction: This combines the classical and prototype theories of concepts. I like it because it fits the idea of 'mental files' nicely (see Recanati). If concepts are files (as in a database) they will have aspects like labels, basic info, and further details. |
| 18585 | Heterogeneous concepts might have conflicting judgements, where hybrid theories will not [Machery] |
| Full Idea: The Heterogeneity Hypothesis, but not the hybrid theory of concepts, predicts that the coreferential bodies of knowledge it posits will occasionally lead to conflicting outcomes, such as inconsistent judgements. | |
| From: Edouard Machery (Doing Without Concepts [2009], 3.3.2) | |
| A reaction: Machery's book champions the Heterogeneous Hypothesis. Hybrid views say the aspects of a concept are integrated, but Heterogeneity says there are separate processes. My preferred 'file' approach would favour integration. |
| 18578 | Concepts as definitions was rejected, and concepts as prototypes, exemplars or theories proposed [Machery] |
| Full Idea: Since the rejection of the classical theory of concepts (that they are definitions), three paradigms have successively emerged in the psychology of concepts: the prototype paradigm, the exemplar paradigm, and the theory paradigm. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4) | |
| A reaction: I am becoming a fan of the 'theory theory' proposal, because the concepts centre around what explains the phenomenon, which fits my explanatory account of essentialism. Not that it's right because it agrees with me, of course..... |
| 18575 | The concepts for a class typically include prototypes, and exemplars, and theories [Machery] |
| Full Idea: Across domains (such as biology and psychology) classes of physical objects, substances and events are typically represented by a prototype, by a set of exemplars, and by a theory. | |
| From: Edouard Machery (Doing Without Concepts [2009], 3.2.3) | |
| A reaction: In other words he thinks that all of the major psychological theories of concepts are partially correct, and he argues for extensive pluralism in the true picture. Bad news for neat philosophy, but real life is a right old mess. |
| 18591 | Classical theory can't explain facts like typical examples being categorised quicker [Machery] |
| Full Idea: The nail in the coffin of the classical theory is its lack of explanatory power. For example it doesn't explain the fact that typical x's are categorised more quickly and more reliably than atypical x's. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.1.3) | |
| A reaction: [He cites Rosch and Mervis: 1975:ch 5] This research launched the 'prototype' theory, which has since been challenged by the 'exemplar' and 'theory theory' rivals (and neo-empiricism, and idealisation). |
| 18583 | Many categories don't seem to have a definition [Machery] |
| Full Idea: For many categories there is simply no definition to learn (such as Wittgenstein's example of a 'game'). | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.1.4) |
| 18590 | Classical theory implies variety in processing times, but this does not generally occur [Machery] |
| Full Idea: If a concept is defined by means of another, such as MURDER by means of KILL, then processing the former concept should take longer in the classical theory, but several experiments show that this is not the case. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.1.3) | |
| A reaction: For the philosopher there is no escaping the findings of neuroscience when it comes to the study of concepts. This invites the question of the role, if any, of philosophy. I take philosophy to concern the big picture, or it is nothing. |
| 18594 | Knowing typical properties of things is especially useful in induction [Machery] |
| Full Idea: Knowing which properties are typical of a class is particularly useful when you have to draw inductions about the members of a class. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.2.1) |
| 18593 | The term 'prototype' is used for both typical category members, and the representation [Machery] |
| Full Idea: The term 'prototype' is used ambiguously to designate the most typical members of a category, and the representation of a category. (I use the term in the second sense). | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.2.1 n25) |
| 18595 | Prototype theories are based on computation of similarities with the prototype [Machery] |
| Full Idea: The most important property of prototype theories is that cognitive processes are assumed to involve the computation of the similarity between prototypes and other representations. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.2.3) | |
| A reaction: [He cites J.A.Hampton 1998, 2006] This presumably suits theories of the mind as largely computational (e.g. Fodor's account, based on the Turing machine). |
| 18596 | Prototype theorists don't tell us how we select the appropriate prototype [Machery] |
| Full Idea: We are typically not told how prototypes are selected, that is, what determines whether a specific prototype is retrieved from memory in order to be involved in the categorisation process. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.2.4) | |
| A reaction: One of the aims of this database is to make people aware of ideas that people have already thought of. This one was spotted 2,400 years ago. It's the Third Man problem. How do you even start to think about a particular thing? |
| 18603 | Maybe concepts are not the typical properties, but the ideal properties [Machery] |
| Full Idea: Barsalou (1983,1985) introduced the idea of ideals instead of prototypes. An ideal is a body of knowledge about the properties a thing should possess (rather than its typical actual properties). ... A 'bully' might be perfect, rather than typical. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.5.3) | |
| A reaction: [compressed] Machery offers this as an interesting minor variant, with little experimental support. I take idealisation to be one of the three key mental operations that enable us to think about the world (along with abstraction and generalisation). |
| 18605 | It is more efficient to remember the prototype, than repeatedly create it from exemplars [Machery] |
| Full Idea: Instead of regularly producing a prototype out of the exemplars stored in long-term memory, it seems more efficient to extract a prototype from category members during concept learning and to use this prototype when needed. | |
| From: Edouard Machery (Doing Without Concepts [2009], 6.3.2) | |
| A reaction: [This is a critique of Barsalou's on-the-fly proposal for prototypes] If the exemplar theory is right, then some sort of summary must occur when faced with a new instance. So this thought favours prototypes against exemplars. |
| 18606 | The prototype view predicts that typical members are easier to categorise [Machery] |
| Full Idea: The prototype paradigm of concepts makes the strong prediction that typical members should be easier to categorise than atypical members. | |
| From: Edouard Machery (Doing Without Concepts [2009], 6.4.1) | |
| A reaction: This is why philosophers should approach the topic of concepts with caution. Clearly empirical testing is going to settle this matter, not abstract theorising. |
| 18597 | Concepts as exemplars are based on the knowledge of properties of each particular [Machery] |
| Full Idea: The exemplar paradigm of concepts is built around the idea that concepts are sets of exemplars. In turn, an exemplar is a body of knowledge about the properties believed to be possessed by a particular member of a class. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.3.1) | |
| A reaction: I like the fact that this theory is rooted in particulars, where the prototype theory doesn't seem to say much about how prototypes are derived. But you have to do more than just contemplate a bunch of exemplars. |
| 18598 | Exemplar theories need to explain how the relevant properties are selected from a multitude of them [Machery] |
| Full Idea: Exemplar theories have a selection problem. Given that individuals have an infinite number of properties, they need to explain why exemplars represent such and such properties, instead of others. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.3.1) | |
| A reaction: I have the impression that this idea rests on the 'abundant' view of properties - that every true predicate embodies a property. A sparse view of properties might give a particular quite a restricted set of properties. |
| 18599 | In practice, known examples take priority over the rest of the set of exemplars [Machery] |
| Full Idea: An object that is extremely similar to a specific known category member, but only moderately similar to others, is more likely to be categorised as a category member than an object that is moderately similar to most known category members. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.3.3) | |
| A reaction: This research finding is a problem for the Exemplar Theory, in which all the exemplars have equal status. It is even a problem for the Prototype Theory, since the known member may not be like the prototype. |
| 18600 | Theory Theory says category concepts are knowledge stores explaining membership [Machery] |
| Full Idea: According to theory theorists, a concept of a category stores some knowledge that can explain the properties of the category members. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.4.1) | |
| A reaction: This is the account of essentialism which I defended in my PhD thesis. So naturally I embrace a theory of the nature of concepts which precisely dovetails with my view. I take explanation to be the central concept in metaphysics. |
| 18601 | Theory Theory says concepts are explanatory knowledge, and concepts form domains [Machery] |
| Full Idea: The two core ideas of the Theory Theory are that concepts are bodies of knowledge that underlie explanation, where explanation rests on folk examples, and concepts are organised in domains which use similar knowledge. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.4.1) | |
| A reaction: Folk explanation is opposed to scientific explanation, as expounded by Hempel etc. This sounds better and better, since the domains reflect the structure of reality. Machery defends Theory Theory as part of the right answer, but it's my favourite bit. |
| 18607 | Theory theorists rely on best explanation, rather than on similarities [Machery] |
| Full Idea: Theory theorists deny that categorisation depends on similarity; they often propose that categorisation involves some kind of inference to the best explanation. | |
| From: Edouard Machery (Doing Without Concepts [2009], 6.5.1) | |
| A reaction: Love it. Any theory of concepts should, in my view, be continuous with a plausible account of animal minds, and best explanations are not their strong suit. Maybe its explanations for slow categorising, and something else when it's quick. |
| 18608 | If categorisation is not by similarity, it seems to rely on what properties things might have [Machery] |
| Full Idea: It seems that when subjects are not categorising by similarity, they are relying on what properties objects can and cannot have - that is, on some modal knowledge. | |
| From: Edouard Machery (Doing Without Concepts [2009], 6.5.1) | |
| A reaction: I would call this essentialist categorisation, based on the inner causal powers which generate the modal profile of the thing. We categorise bullets and nails very differently, because of their modal profiles. |
| 18587 | The theory account is sometimes labelled as 'knowledge' or 'explanation' in approach [Machery] |
| Full Idea: The theory paradigm is sometimes called 'the knowledge approach' (Murphy 2002) or 'explanation-based views' (Komatsu 1992). | |
| From: Edouard Machery (Doing Without Concepts [2009], 4) | |
| A reaction: The word 'explanation' is music to my ears, so I am immediately sympathetic to the theory theory of concepts, even if it falls at the final hurdle. |
| 18577 | The word 'grandmother' may be two concepts, with a prototype and a definition [Machery] |
| Full Idea: If a prototype of grandmothers represents them as grey-haired old women, and a definition of grandmothers represents them as being necessarily the mother of a parent ....we may fail to recognise that 'grandmother' represents two distinct concepts. | |
| From: Edouard Machery (Doing Without Concepts [2009], 3.3.4) | |
| A reaction: He is referring to two distinct theories about what a concept is. He argues that both theories apply, so words do indeed represent several different concepts. Nice example. |
| 18589 | For behaviourists concepts are dispositions to link category members to names [Machery] |
| Full Idea: Behaviourists identified concepts with a mere disposition to associate category members with a given name. | |
| From: Edouard Machery (Doing Without Concepts [2009], 4.1.1) | |
| A reaction: This is one reason why the word 'disposition' triggers alarm bells in the immediately post-behaviourist generation of philosophers. The proposal is far too linguistic in character. |
| 17506 | I now think reference by the tests of experts is a special case of being causally connected [Putnam] |
| Full Idea: In previous papers I suggested that the reference is fixed by a test known to experts; it now seems to me that this is just a special case of my use being causally connected to an introducing event. | |
| From: Hilary Putnam (Explanation and Reference [1973], II C) | |
| A reaction: I think he was probably right the first time, and has now wandered off course. |
| 18612 | Americans are more inclined to refer causally than the Chinese are [Machery] |
| Full Idea: Tests suggest that American subjects were significantly more likely than Chinese subjects to have intuitions in line with causal-historical theories of reference. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8.1.3) | |
| A reaction: This is an example of 'experimental philosophy' in action (of which Machery is a champion). The underlying idea is that Americans are generally more disposed to think causally than the Chinese are. So more scientific? What do the Hopi do? |
| 18613 | Artifacts can be natural kinds, when they are the object of historical enquiry [Machery] |
| Full Idea: Some artifacts are the objects of inquiry in the social sciences ...such as prehistoric tools ...and hence, artifacts are bona fide natural kinds. | |
| From: Edouard Machery (Doing Without Concepts [2009], 8.2.1) | |
| A reaction: Presumably if a bird's nest can be a natural kind, then so can a flint axe, but then so can a mobile phone, for an urban anthropologist. 'Natural' is, to put it mildly, a tricky word. |
| 17507 | Natural kind stereotypes are 'strong' (obvious, like tiger) or 'weak' (obscure, like molybdenum) [Putnam] |
| Full Idea: Natural kinds can be associated with 'strong' stereotypes (giving a strong picture of a typical member, like a tiger), or with 'weak' stereotypes (with no idea of a sufficient condition, such as molybdenum or elm). | |
| From: Hilary Putnam (Explanation and Reference [1973], II C) |
| 11904 | Express natural kinds as a posteriori predicate connections, not as singular terms [Putnam, by Mackie,P] |
| Full Idea: Putnam implies dispensing with the designation of natural kinds by singular terms in favour of the postulation of necessary but a posteriori connections between predicates. ...We might call this 'predicate essentialism', but not 'de re essentialism'. | |
| From: report of Hilary Putnam (Explanation and Reference [1973]) by Penelope Mackie - How Things Might Have Been 10.1 | |
| A reaction: It is characteristic of modern discussion that the logical form of natural kind statements is held to be crucial, rather than an account of nature in any old ways that do the job. So do I prefer singular terms, or predicate-connections. Hm. |