105 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. |
| 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. |
| 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. |
| 14334 | Modest realism says there is a reality; the presumptuous view says we can accurately describe it [Mumford] |
| Full Idea: The claim of modest realism is that there is a subject-independent reality; the presumptuous claim is that we are capable of describing that reality accurately. | |
| From: Stephen Mumford (Dispositions [1998], 09.1) | |
| A reaction: And the super-presumptuous claim is that there only exists one ultimate accurate description of reality. I am happy to call myself a Modest Realist on this one. |
| 14306 | Anti-realists deny truth-values to all statements, and say evidence and ontology are inseparable [Mumford] |
| Full Idea: The anti-realist declines to permit that all statements have truth-values. ...The essence of the anti-realist position is that evidence and ontology cannot be separated. | |
| From: Stephen Mumford (Dispositions [1998], 03.6) | |
| A reaction: [second half on p.51] The idea that evidence and ontology are 'inseparable' strikes me as an absurd idea. The proposal that you should not speculate about ontology without some sort of evidence is, of course, not unreasonable. |
| 4913 | Brain lesions can erase whole categories of perception, suggesting they are hard-wired [Carter,R] |
| Full Idea: The discovery that a single brain lesion can erase all knowledge of man-made artefacts, or all knowledge of animals, suggests that these categories somehow hard-wired into the brain - that we all have a set of 'memory pigeonholes'. | |
| From: Rita Carter (Mapping the Mind [1998], p.190) | |
| A reaction: Presumably something can become 'hard-wired' through experience, rather than from birth. The whole idea of 'hard-wired' seems misleading about the brain. What matters is that the brain physically constructs categories. |
| 14333 | Dispositions and categorical properties are two modes of presentation of the same thing [Mumford] |
| Full Idea: The dispositional and the categorical are correctly understood just as two modes of presentation of the same instantiated properties. | |
| From: Stephen Mumford (Dispositions [1998], 08.6) | |
| A reaction: This is Mumford's own conclusion, after discussing the views of Armstrong. How about 'a disposition is the modal profile' of a categorical property? |
| 14336 | Categorical predicates are those unconnected to functions [Mumford] |
| Full Idea: A predicate which is conceptually connected to no function ... is a categorical predicate. | |
| From: Stephen Mumford (Dispositions [1998], 09.7) | |
| A reaction: This is an expansion of Mumford's own theory of dispositions, as functional. Does a cork in a wine bottle have a function, but without doing anything? It seems to achieve its function purely through its structure. |
| 14315 | Categorical properties and dispositions appear to explain one another [Mumford] |
| Full Idea: Though categorical properties provide explanations for dispositions, categorical properties are also explained by dispositions; hence neither category uniquely explains the other. | |
| From: Stephen Mumford (Dispositions [1998], 05.3) | |
| A reaction: The conclusion doesn't seem to follow. It depends which one is found at the bottom level. It can go up from a basic disposition, to a categorical property, to another disposition - or the other way around. |
| 14332 | There are four reasons for seeing categorical properties as the most fundamental [Mumford] |
| Full Idea: Four reasons for reducing everything to the categorical are: categorical predicates have wider scope; dispositions are variably realised by the categorical; categorical is 1st order, dispositions 2nd; categorical properties are explanatorily basic. | |
| From: Stephen Mumford (Dispositions [1998], 08.5) | |
| A reaction: I particularly reject the fourth reason, as I take categorical properties as still in need of explanation. The categorical view is contingent (and Humean), but I take the categorical properties to be necessitated by the underlying powers. |
| 14302 | A lead molecule is not leaden, and macroscopic properties need not be microscopically present [Mumford] |
| Full Idea: Though lead is said to be composed of molecules of lead, these molecules are not leaden in the everyday sense of the word. This suggests that a property need not be present at the microscopic level in order to be present at the macroscopic level. | |
| From: Stephen Mumford (Dispositions [1998], 02.3) | |
| A reaction: [He quotes Joske] This strikes me as a key principle to grasp about properties. One H2O molecule is not water, any more than a brick is a house! Nearly all properties (or all?) are 'emergent' (in the sensible, non-mystical use of that word). |
| 14294 | Dispositions are attacked as mere regularities of events, or place-holders for unknown properties [Mumford] |
| Full Idea: Dispositions are attacked as either just saying how something will behave (logical fictions about regularities of events), or as primitive pre-scientific terms like 'phlogiston', place-holders used when we are ignorant of real properties. | |
| From: Stephen Mumford (Dispositions [1998], 01.1) | |
| A reaction: [compressed] The first view he calls the Ryle-Wittgenstein view, which seems to track back to Hume. |
| 14310 | Dispositions are classifications of properties by functional role [Mumford] |
| Full Idea: A dispositional property is the classification of a property according to its functional role....[p.85] What is essential to a disposition - its identity condition - is its functional role. | |
| From: Stephen Mumford (Dispositions [1998], 04.5) | |
| A reaction: This is Mumford's view of dispositions. I am wary of any proposal to define something according to its role, because it must have an intrinsic nature which equips it to have that role. |
| 14317 | I say the categorical base causes the disposition manifestation [Mumford] |
| Full Idea: The view I promote is one where the categorical base is a cause of the disposition manifestation. | |
| From: Stephen Mumford (Dispositions [1998], 05.5) | |
| A reaction: It seems to me (I think) that the most basic thing has to be a power, whose nature is intrinsically beyond our grasp, and that categorical properties are the result of these powers. Powers are dispositional in character. |
| 14316 | If dispositions have several categorical realisations, that makes the two separate [Mumford] |
| Full Idea: We might claim that dispositions are variably realized by a number of categorical bases; therefore they must be distinct from those bases. | |
| From: Stephen Mumford (Dispositions [1998], 05.4) | |
| A reaction: Cars can be realised by a variety of models, therefore models are not cars? This might work if dispositions are only characterised functionally, as Mumford proposes, but I'm not convinced. |
| 14313 | All properties must be causal powers (since they wouldn't exist otherwise) [Mumford] |
| Full Idea: It seems that every property must be a causal power, since every property must be causally potent (as a necessary condition of its very existence). | |
| From: Stephen Mumford (Dispositions [1998], 04.7) | |
| A reaction: Mumford cautiously endorses this idea, which seems to rest on the thesis that 'to exist is to have causal powers'. I think I am even keener on it than Mumford is. Powers and properties need to be disentangled, however. |
| 14318 | Intrinsic properties are just causal powers, and identifying a property as causal is then analytic [Mumford] |
| Full Idea: Understanding intrinsic properties as being causal powers is likely to be most profitable, and, if true, renders the causal criterion of property existence true analytically. | |
| From: Stephen Mumford (Dispositions [1998], 06.2) | |
| A reaction: [He cites E.Fales on this] I'm inclined to think that in the ultimate ontology the notion of a 'property' drops out. There are true causal powers, and then conventional human ways of grouping such powers together and naming them. |
| 14293 | Dispositions are ascribed to at least objects, substances and persons [Mumford] |
| Full Idea: Dispositions are ascribed to at least three distinguishable classes of things: objects, substances, and persons. | |
| From: Stephen Mumford (Dispositions [1998], 01.1) | |
| A reaction: Are dispositions not also ascribed to properties? Magnetism has a disposition to attract iron filings? |
| 14326 | Unlike categorical bases, dispositions necessarily occupy a particular causal role [Mumford] |
| Full Idea: The idea of a disposition occupying a different causal role involves a conceptual confusion, ...but there is no conceptual or logical absurdity in a categorical base occupying a different causal role. | |
| From: Stephen Mumford (Dispositions [1998], 07.3) | |
| A reaction: This is the core of Mumford's theory of dispositions. I'm beginning to think that dispositions are merely ways we have of describing and labelling functional mechanisms, and so 'dispositions' drop out of the final story. |
| 14298 | Dispositions can be contrasted either with occurrences, or with categorical properties [Mumford] |
| Full Idea: For some the notion of a disposition is contrasted with the notion of an occurrence; for others, it is contrasted with that of a categorical property. | |
| From: Stephen Mumford (Dispositions [1998], 01.6) | |
| A reaction: I vote for dispositions over the other two, but I take the categorical properties to be the main rival. |
| 14314 | If dispositions are powers, background conditions makes it hard to say what they do [Mumford] |
| Full Idea: The realist says that disposition ascriptions are ascriptions of real powers. This leaves unanswered the question, 'power to do what?' The problem of background conditions means that the realist cannot say what it is that a power is a power to do. | |
| From: Stephen Mumford (Dispositions [1998], 04.9) | |
| A reaction: It is hard to say what a disposition will do, under any other account of dispositions. I would take a power to be defined by a 'modal profile', rather than an actual account of what it will lead to. |
| 14325 | Maybe dispositions can replace powers in metaphysics, as what induces property change [Mumford] |
| Full Idea: Dispositions can regain the metaphysical role traditionally ascribed to real powers: the that-in-virtue-of-which-something-will-G, if F. | |
| From: Stephen Mumford (Dispositions [1998], 06.9) | |
| A reaction: The attraction is that dispositions can be specified a little more clearly (especially in Mumford's functional version) whereas there may be no more to say about a power once it has been located and named. |
| 14312 | Orthodoxy says dispositions entail conditionals (rather than being equivalent to them) [Mumford] |
| Full Idea: The orthodox realist view has it that what makes an ascription a disposition ascription is not that it is equivalent to a conditional proposition but that it entails one. | |
| From: Stephen Mumford (Dispositions [1998], 04.7) | |
| A reaction: Mumford says that Martin has shown that dispositions need not entail conditionals (when a 'fink' is operating, something which intervenes between disposition and outcome). |
| 14291 | Dispositions are not just possibilities - they are features of actual things [Mumford] |
| Full Idea: Dispositions should correctly be understood as more than mere possibilities. To say something has a disposition is to say something about how it is actually. | |
| From: Stephen Mumford (Dispositions [1998], Pref) | |
| A reaction: To me this is a basic axiom of metaphysics. The word 'power' serves well for the actual embodiment of a disposition. A power gives rise to one or more dispositions. Or one or more powers give rise to a disposition? |
| 14299 | There could be dispositions that are never manifested [Mumford] |
| Full Idea: It seems plausible that a disposition could be possessed though no manifestation events occur. | |
| From: Stephen Mumford (Dispositions [1998], 01.6) | |
| A reaction: It is more than 'plausible' - it is screamingly obvious to everybody, apart from a few philosophers. "Some mute inglorious Milton here may rest" (Gray's Elegy). |
| 14323 | If every event has a cause, it is easy to invent a power to explain each case [Mumford] |
| Full Idea: Given any event, and the assumption that every event has a cause, then some power can always be invented as the cause of that event. | |
| From: Stephen Mumford (Dispositions [1998], 06.6) | |
| A reaction: This is a useful warning, and probably explains why 'powers' fell out of fashion in scientifice theorising. They seem to make a return, though, as an appropriate term for the bottom level of each of our explanations. |
| 14328 | Traditional powers initiate change, but are mysterious between those changes [Mumford] |
| Full Idea: In the old-fashioned sense, 'powers' are real potentialities that initiate changes but seem to have a mysterious existence in between those changes. | |
| From: Stephen Mumford (Dispositions [1998], 07.10) | |
| A reaction: What is a person when they are asleep? What is a dishwasher when it isn't running? What is gunpowder when it doesn't explode? We all understand latent powers. To see them as a 'mystery' is to want to know too much. |
| 14331 | Categorical eliminativists say there are no dispositions, just categorical states or mechanisms [Mumford] |
| Full Idea: The categorical eliminativist claims that there are no dispositional properties. All properties must be conceived of as categorical states or mechanisms, in the spirit of Boyle's explanation of powers. | |
| From: Stephen Mumford (Dispositions [1998], 08.3A) | |
| A reaction: What is the difference between a structure and a mechanism? How do we distinguish an active from an inactive mechanism? Without powers or dispositions, nature is dead junk. |
| 14295 | Many artefacts have dispositional essences, which make them what they are [Mumford] |
| Full Idea: Thermostats, thermometers, axes, spoons, and batteries have dispositional essences, which make them what they are. | |
| From: Stephen Mumford (Dispositions [1998], 01.2 iv) | |
| A reaction: I would have thought that we could extend this proposal well beyond artefacts, but it certainly seems particularly clear in artefacts, where a human intention seems to be inescapably involved. |
| 14309 | Truth-functional conditionals can't distinguish whether they are causal or accidental [Mumford] |
| Full Idea: If a conditional remains truth-functional it is incapable of expressing the fact that the connection between antecedent and consequent in the conditional is a causal one rather than merely accidental | |
| From: Stephen Mumford (Dispositions [1998], 03.8) | |
| A reaction: This is the first step towards an account of conditionals which will work in real life rather than merely in classical logic. |
| 14311 | Dispositions are not equivalent to stronger-than-material conditionals [Mumford] |
| Full Idea: The conclusion that disposition ascriptions are not equivalent to stronger-than-material conditionals is largely to be accepted. | |
| From: Stephen Mumford (Dispositions [1998], 04.7) | |
| A reaction: [he attributes the view to C.B.Martin 1994] It is hard to see how to describe a disposition in anything other than conditional terms. Mumford's 'functional role' probably has to be described conditionally. It is how the conditional cashes out. |
| 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. |
| 4910 | Sense organs don't discriminate; they reduce various inputs to the same electrical pulses [Carter,R] |
| Full Idea: Despite their variety, each sense organ translates its stimulus into electrical pulses; rather than discriminating one type of input from another, the sense organs actually make them more alike. | |
| From: Rita Carter (Mapping the Mind [1998], p.174) | |
| A reaction: An illuminating observation, which modern 'naïve realists' should bear in mind. Secondary qualities are entirely unrelated to the nature of the input, and are merely 'what the brain decides to make of it'. Discrimination is in our neurons. |
| 4911 | The recognition sequence is: classify, name, locate, associate, feel [Carter,R, by PG] |
| Full Idea: The sequence of events in the brain for perceptual recognition is first identifying a rough class for the object, then a name, then a location, then some associations, and finally an emotion. | |
| From: report of Rita Carter (Mapping the Mind [1998], p.181) by PG - Db (ideas) | |
| A reaction: This seems to be one of those places where neuro-science trumps philosophy. You can't argue with empirical research, so philosophical theories had better adapt themselves to this sequence. The big modern discovery is the place of emotion in recognition. |
| 4919 | There seems to be no dividing line between a memory and a thought [Carter,R] |
| Full Idea: It has become clear from research that there is no clear dividing line between a memory and a thought. | |
| From: Rita Carter (Mapping the Mind [1998], p.308) | |
| A reaction: This always struck me as an obvious criticism of Descartes, when he claimed that memory was not an essential part of the 'thinking thing'. How can you think or understand without memory of the different phases of your thoughts? No memory, no mind! |
| 14319 | Nomothetic explanations cite laws, and structural explanations cite mechanisms [Mumford] |
| Full Idea: A nomothetic explanation appeals to laws where the explanandum is shown to be an instance of a general law. ...The alternative is a structural explanation, which postulates a mechanism, opening up a hidden world. | |
| From: Stephen Mumford (Dispositions [1998], 06.4) | |
| A reaction: [He cites E.McMullin 1978] I am very much in favour of structural explanations, and opposed to nomothetic ones. That is, nomothetic accounts are only the first step towards an explanation - perhaps a mere identification of the explanandum. |
| 14342 | General laws depend upon the capacities of particulars, not the other way around [Mumford] |
| Full Idea: Laws, qua true generalities, if they exist at all, are ontologically parasitic upon the capacities of particulars, rather than the other way round. | |
| From: Stephen Mumford (Dispositions [1998], 10.6) | |
| A reaction: Quite so. And hence trying to explain a particular behaviour by saying that it falls under a law is absurdly circular and vacuous. |
| 14322 | If fragile just means 'breaks when dropped', it won't explain a breakage [Mumford] |
| Full Idea: If fragile means nothing more than 'breaks when dropped', then it is no explanation of why something breaks when dropped. | |
| From: Stephen Mumford (Dispositions [1998], 06.5) | |
| A reaction: His point is that you have to unpack the notion of fragile, which presumably cites underlying mechanisms. This is the 'virtus dormitiva' problem - but that explanation of opium's dormitive powers is not entirely stupid. |
| 14337 | Maybe dispositions can replace the 'laws of nature' as the basis of explanation [Mumford] |
| Full Idea: I will consider the case for an ontology of real dispositions replacing the so-called laws of nature as the basic building blocks of explanation. | |
| From: Stephen Mumford (Dispositions [1998], 10.1) | |
| A reaction: This precisely summarises the view I am exploring, with a particular focus on real essences. I certainly think the 'laws of nature' must go. See Mumford's second book on this. |
| 14343 | To avoid a regress in explanations, ungrounded dispositions will always have to be posited [Mumford] |
| Full Idea: The nature of explanation is such that ungrounded dispositions will always have to be posited in order to avoid a regress of explanation. | |
| From: Stephen Mumford (Dispositions [1998], 10.6) | |
| A reaction: This seems to be right, but leaves it open to mock the proposals as 'virtus dormitiva' - empty place-holders that ground explanations but do no explanatory work. What else can be done, though? |
| 14320 | Subatomic particles may terminate explanation, if they lack structure [Mumford] |
| Full Idea: The behaviour of subatomic particles cannot be further analysed into structures and this may tempt us to regard these as instances of 'brute' ungrounded dispositions which end any possible regress of explanation. | |
| From: Stephen Mumford (Dispositions [1998], 06.4) | |
| A reaction: This seems right, if it is 'structural' explanations we are after (as I think we are) which look for mechanisms. An electron seems to be just three dispositions and no structure, so there is nothing more to say. Ladyman scorns this account. |
| 14324 | Ontology is unrelated to explanation, which concerns modes of presentation and states of knowledge [Mumford] |
| Full Idea: Nothing about ontology is at stake in questions of explanation, for explanatory success is contingent upon the modes of presentation of explanans and explananda, and relative states of knowledge and ignorance. | |
| From: Stephen Mumford (Dispositions [1998], 06.8) | |
| A reaction: There are real facts about the immediate and unusual causes which immediately precede an event, and these might be candidates for a real explanation. There are also real mechanisms and powers which dictate a things behaviour. |
| 4908 | No one knows if animals are conscious [Carter,R] |
| Full Idea: No one knows if animals are conscious. | |
| From: Rita Carter (Mapping the Mind [1998], p.155) | |
| A reaction: This is a report from the front line of brain research, and should be born in mind when over-confident people make pronouncements about this topic. It strikes me as important to grasp that animals MIGHT not be conscious. |
| 4902 | Pain doesn't have one brain location, but is linked to attention and emotion [Carter,R] |
| Full Idea: Scans show there is no such thing as a pain centre; pain springs mainly from the activation of areas associated with attention and emotion. | |
| From: Rita Carter (Mapping the Mind [1998], p. 12) | |
| A reaction: Most brain research points to the complex multi-layered nature of experiences that were traditionally considered simple. We can be distracted from a pain, and an enormous number of factors can affect our degree of dislike of a given pain. |
| 4904 | Proper brains appear at seven weeks, and neonates have as many neurons as adults do [Carter,R] |
| Full Idea: The main sections of the brain, including the cerebral cortex, are visible within seven weeks of conception, and by the time the child is born the brain contains as many neurons - about 100 billion - as it will have as an adult. | |
| From: Rita Carter (Mapping the Mind [1998], p. 17) | |
| A reaction: Of interest in the abortion debate, and also in thinking about personal identity. However, it seems clear that the number of connections, rather than neurons, is what really matters. A small infant may well lack personal identity. |
| 4915 | In primates, brain size correlates closely with size of social group [Carter,R] |
| Full Idea: Brain size in primates is closely associated with the size of the social group in which the animal lives. | |
| From: Rita Carter (Mapping the Mind [1998], p.257) | |
| A reaction: Intriguing. Humans can have huge social groups because of language, which suggests a chicken-or-egg question. Language, intelligence and size of social group must have expanded together in humans. |
| 4917 | Consciousness involves awareness, perception, self-awareness, attention and reflection [Carter,R] |
| Full Idea: Awareness, perception, self-awareness, attention and reflection are all separate components of consciousness, and the quality of our experience varies according to which and how many of them are present. | |
| From: Rita Carter (Mapping the Mind [1998], p.300) | |
| A reaction: Philosophers like to emphasise 'qualia' and 'intentionality'. This remark slices the cake differently. 'Attention' is interesting, dividing consciousness into two areas, with some experience fading away into the darkness. Hume denied self-awareness. |
| 4916 | There is enormous evidence that consciousness arises in the frontal lobes of the brain [Carter,R] |
| Full Idea: A huge volume of evidence suggests that consciousness emerges from the activity of the cerebral cortex, and in particular from the frontal lobes. | |
| From: Rita Carter (Mapping the Mind [1998], p.298) | |
| A reaction: Dualists must face up to this, and even many physicalists have a rather vague notion about the location of awareness, but we are clearly homing in very precise physical substances which have consciousness as a feature. |
| 4905 | Normal babies seem to have overlapping sense experiences [Carter,R] |
| Full Idea: Connections in a baby's brain probably give the infant the experience of 'seeing' sounds and 'hearing' colours - which occasionally continues into adulthood, where it is known as 'synaesthesia'. | |
| From: Rita Carter (Mapping the Mind [1998], p. 19) | |
| A reaction: A fact to remember when discussing secondary qualities, and the relativism involved in the way we perceive the world. If you have done your philosophy right, you shouldn't be surprised by this discovery. |
| 4918 | In blindsight V1 (normal vision) is inactive, but V5 (movement) lights up [Carter,R] |
| Full Idea: Scans show that a sub-section of the visual cortex called V5 - the area that registers movement - lights up during blindsight, even though V1 - the primary sensory area that is essential for normal sight - is not active. | |
| From: Rita Carter (Mapping the Mind [1998], p.307) | |
| A reaction: The whole point of blindsight is to make us realise that vision involves not one module, but a whole team of them. The inference is that V1 involves consciousness, but other areas of the visual cortex don't. |
| 4912 | Out-of-body experiences may be due to temporary loss of proprioception [Carter,R] |
| Full Idea: Out-of-body experiences may be due to temporary loss of proprioception. | |
| From: Rita Carter (Mapping the Mind [1998], p.187) | |
| A reaction: This is only a speculation, but it is an effect which can be caused by brain injury, and dualists should face the possibility that this evidence (prized by many dualists) can have a physical explanation. |
| 4903 | Scans of brains doing similar tasks produce very similar patterns of activation [Carter,R] |
| Full Idea: The pattern of brain activation during, say, a word retrieval task is usually similar enough among the dozen or so participants who typically take part in such studies for their scans to be overlaid and still show a clear pattern. | |
| From: Rita Carter (Mapping the Mind [1998], p. 17) | |
| A reaction: This doesn't surprise me, though it could be interpreted as supporting type-type identity, or as supporting functionalism. Armstrong and Lewis endorse a sort of reductive functionalism which would fit this observation. |
| 4920 | Thinking takes place on the upper side of the prefrontal cortex [Carter,R] |
| Full Idea: The nuts and bolts of thinking - holding ideas in mind and manipulating them - takes place on the upper side of the prefrontal cortex. | |
| From: Rita Carter (Mapping the Mind [1998], p.312) | |
| A reaction: Keep this firmly in view! Imagine that the skull is transparent, and brain activity moves in waves of colour. Dualism would, in those circumstances, never have even occurred to anyone. |
| 4906 | Babies show highly emotional brain events, but may well be unaware of them [Carter,R] |
| Full Idea: Babies show emotion dramatically, but the areas of the brain that in adults are linked to the conscious experience of emotions are not active in newborn babies. Such emotions may therefore be unconscious. | |
| From: Rita Carter (Mapping the Mind [1998], p. 19) | |
| A reaction: Traditionally, 'unconscious emotion' is a contradiction, but I think we should accept this new evidence and rethink the nature of mind. Not only might emotion be non-conscious, but we should even consider that rational thinking could be too. |
| 4909 | The only way we can control our emotions is by manipulating the outside world that influences them [Carter,R] |
| Full Idea: We try to manipulate our emotions all the time, but all we are doing is arranging the outside world so it triggers certain emotions - we cannot control our reactions directly. | |
| From: Rita Carter (Mapping the Mind [1998], p.155) | |
| A reaction: This seems to me to throw a very illuminating light on a huge amount of human behaviour, such as going to the cinema or listening to music. The romantic movement encouraged direct internal manipulation. Compare sex fantasies with viewing pornography. |
| 4914 | A frog will starve to death surrounded by dead flies [Carter,R] |
| Full Idea: A frog will starve to death surrounded by dead flies. | |
| From: Rita Carter (Mapping the Mind [1998], p.195) | |
| A reaction: A nice warning against assuming that rationality is operating when a frog feels hungry and 'decides' to have lunch. We should take comfort from the fact that humans are NOT this stupid, and philosophers should try to accurately describe our gift. |
| 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. |
| 4907 | The 'locus coeruleus' is one of several candidates for the brain's 'pleasure centre' [Carter,R] |
| Full Idea: Noradrenaline is an excitatory chemical that induces physical and mental arousal and heightens mood. Production is centred in an area of the brain called the locus coeruleus, which is one of several candidates for the brain's 'pleasure' centre. | |
| From: Rita Carter (Mapping the Mind [1998], p. 30) | |
| A reaction: It seems to me very morally desirable that people understand facts of this kind, so that they can be more objective about pleasure. Pleasure is one cog in the machine that makes a person, not the essence of human life. |
| 14344 | Natural kinds, such as electrons, all behave the same way because we divide them by dispositions [Mumford] |
| Full Idea: Regularities exist because we classify kinds on the basis of their dispositions, not on pre-established divisions of kinds. The dispositions are the basis for the division into kinds, which is why all electrons behave in the same way. | |
| From: Stephen Mumford (Dispositions [1998], 10.7) | |
| A reaction: This strikes me as being so obvious that it is hardly worth saying, and yet an enormous number of philosophers seem to have been led up the garden path by the notion of a 'kind', probably under the influence of Kripke, Putnam and Wiggins. |
| 14338 | In the 'laws' view events are basic, and properties are categorical, only existing when manifested [Mumford] |
| Full Idea: In the 'laws' world view, events are the basic ontological unit and properties are parasitic upon them. Properties exist only in virtue of their instantiation in events. Properties are categorical, because they are only manifested in the present. | |
| From: Stephen Mumford (Dispositions [1998], 10.2) | |
| A reaction: Mumford rejects this view, and I am with him all the way. The first requirement is that properties be active, and not inert. See Leibniz on this. |
| 14339 | Without laws, how can a dispositionalist explain general behaviour within kinds? [Mumford] |
| Full Idea: The problem is how, without general laws, can the dispositionalist explain why generalities in behaviour are true of kinds. | |
| From: Stephen Mumford (Dispositions [1998], 10.3) | |
| A reaction: And the answer is to make kinds depend on individuals, and not vice versa, and then point to the necessary patterns that arise from conjunctions of individual dispositions, given their identity in many individuals. |
| 14341 | Dretske and Armstrong base laws on regularities between individual properties, not between events [Mumford] |
| Full Idea: The improved Dretske/Armstrong regularity view of laws dispenses with the empiricist articulation of them in terms of events, and construes them as singular statements of fact that describe relations between properties. | |
| From: Stephen Mumford (Dispositions [1998], 10.4) | |
| A reaction: They then seem to go a bit mystical, by insisting that the properties are 'universals' (even if they have to be instantiated). Universals explain nothing. |
| 14340 | It is a regularity that whenever a person sneezes, someone (somewhere) promptly coughs [Mumford] |
| Full Idea: It is no doubt a true regularity that every time I sneeze, someone, somewhere in the world, immediately coughs. | |
| From: Stephen Mumford (Dispositions [1998], 10.4) | |
| A reaction: Not a huge problem for the regularity theory of laws, but the first challenge that it must meet. |
| 14345 | The necessity of an electron being an electron is conceptual, and won't ground necessary laws [Mumford] |
| Full Idea: The logical necessity of physical laws is not required by dispositional essentialism. An electron would not be an electron if its behaviour were different from the behaviour it has in the actual world, but this necessity is purely conceptual. | |
| From: Stephen Mumford (Dispositions [1998], 10.8) | |
| A reaction: [He is particularly aiming this at Ellis and Lierse 1994] This may be missing the point. Given those electron dispositions, the electrons necessitate law-like happenings. Whether a variable entity is called an 'electron' is trivial. |
| 14307 | Some dispositions are so far unknown, until we learn how to manifest them [Mumford] |
| Full Idea: It seems reasonable to assume that there are some dispositions of some things of which we are not aware because we have not yet discovered the way to get these dispositions to manifest. | |
| From: Stephen Mumford (Dispositions [1998], 03.7) | |
| A reaction: This strikes me as a pretty good description of what scientists are currently doing when, for example, they build a new particle accelerator. |