106 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? |
| 3807 | Reason is and ought to be the slave of the passions [Hume] |
| Full Idea: Reason is and ought to be the slave of the passions, and can never pretend to any other office than to serve and obey them. | |
| From: David Hume (Treatise of Human Nature [1739], II.III.3) |
| 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. |
| 21717 | Reducibility undermines type ramification, and is committed to the existence of functions [Quine, by Linsky,B] |
| Full Idea: Quine charges that the axiom of Reducibility both undoes the effect of the ramification, and commits the theory to a platonist view of propositional functions (which is a theory of sets, once use/mention confusions are cleared up). | |
| From: report of Willard Quine (Set Theory and its Logic [1963], p.249-58) by Bernard Linsky - Russell's Metaphysical Logic 6.1 |
| 13441 | Naďve 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. Naďve 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. |
| 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) |
| 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. |
| 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? |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 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) |
| 8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
| Full Idea: When two numbers are so combin'd, as that the one has always a unit answering to every unit of the other, we pronounce them equal. | |
| From: David Hume (Treatise of Human Nature [1739], I.III.1) | |
| A reaction: This became known as Hume's Principle after Frege made use of it for logicism (Foundations §63). It reduces equality to something fairly simple and visual (one-to-one correspondence). But we also say that two logicians or musicians are 'equal' in ability. |
| 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) |
| 21291 | There is no medium state between existence and non-existence [Hume] |
| Full Idea: Betwixt unity and number there can be no medium; no more than betwixt existence and non-existence. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) | |
| A reaction: Just to confirm that, as you would expect, the great empiricist has no time for 'subsistence', or shadows and holes having lower grade existece. |
| 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. |
| 11942 | Power is the possibility of action, as discovered by experience [Hume] |
| Full Idea: Power consists in the possibility or probability of any action, as discovered by experience and the practice of the world. | |
| From: David Hume (Treatise of Human Nature [1739], p.313), quoted by George Molnar - Powers 5 | |
| A reaction: [page in OUP edn] This strikes me as blatantly false, and typical of those who confuse epistemology with ontology. It implies that a power that takes everyone by surprise is impossible, by definition. |
| 11949 | There may well be powers in things, with which we are quite unacquainted [Hume] |
| Full Idea: I am, indeed, ready to allow, that there may be several qualities both in material and immaterial objects, with which we are utterly unacquainted; and if we please to call these powers and efficiency, 'twill be be of little consequence to the world. | |
| From: David Hume (Treatise of Human Nature [1739], p.168), quoted by George Molnar - Powers 7.2.1 | |
| A reaction: A delightful air of casual indifference. What the classic empiricists needed was a notion of 'best explanation', which would allow them to leap beyond immediate experience. They made plenty of other leaps beyond experience, though Hume hated them. |
| 11950 | We have no idea of powers, because we have no impressions of them [Hume] |
| Full Idea: We never have any impression that contains any power or efficacy. We never therefore have any idea of power. | |
| From: David Hume (Treatise of Human Nature [1739], p.161), quoted by George Molnar - Powers 7.2.1 | |
| A reaction: [page in Selby-Bigges edn] It seems to me plausible that Hume is utterly wrong, because our own mental lives are a direct and constant experience of the physical powers and efficacies of material objects. |
| 11941 | The distinction between a power and its exercise is entirely frivolous [Hume] |
| Full Idea: The distinction which we sometimes make betwixt a power and the exercise of it is entirely frivolous, and ... neither man nor any other being ought ever to be thought possesst of any ability, unless it be exerted and put into action. | |
| From: David Hume (Treatise of Human Nature [1739], p.311), quoted by George Molnar - Powers 5 | |
| A reaction: [page in OUP] Molnar says this strong intuition is shared by most of us, but I take the world to be full of people who can play the piano or speak Spanish, but never actually do it. [but see Idea 11942] Most wasps never sting anything. |
| 11098 | Momentary impressions are wrongly identified with one another on the basis of resemblance [Hume, by Quine] |
| Full Idea: Momentary impressions, according to Hume, are wrongly identified with one another on the basis of resemblance. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Willard Quine - Identity, Ostension, and Hypostasis 3 | |
| A reaction: I don't have a Hume quotation for this yet, but Quine is plausibly claiming Hume as a resemblance nominalist, equipped with an error theory about universals. |
| 7954 | If we see a resemblance among objects, we apply the same name to them, despite their differences [Hume] |
| Full Idea: When we have found a resemblance among several objects, that often occur to us, we apply the same name to all of them, whatever differences we may observe in the degrees of their quantity and quality, and whatever other differences may appear among them. | |
| From: David Hume (Treatise of Human Nature [1739], I.I.7) | |
| A reaction: This must to some extent by right, whatever objections can be found. Russell's objection (Idea 4441) wouldn't alter the truth of Hume's observation, thought Hume is attacking universals and Russell defending them. |
| 21293 | Individuation is only seeing that a thing is stable and continuous over time [Hume] |
| Full Idea: The principle of individuation is nothing but the invariableness and uninterruptedness of any object through a supposed variation of time, by which the mind can trace it in the different periods of its existence. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) | |
| A reaction: Not convinced by this. I can individuate something by an almost instantaneous glimpse. I don't increasingly individuate it as time passes. Instant viewing of type and structure may be enough. |
| 12048 | The only meaning we have for substance is a collection of qualities [Hume] |
| Full Idea: We have no idea of substance, distinct from that of a collection of particular qualities, nor have we any other meaning when we either talk or reason concerning it. | |
| From: David Hume (Treatise of Human Nature [1739], I.I.6) | |
| A reaction: This is the standard empiricist view of such things, firmly stated. It is tempting to say that Hume has simply misunderstood the word, since it is precisely intended to mean not the qualities, but what underlies them, and persists. |
| 13424 | Aristotelians propose accidents supported by substance, but they don't understand either of them [Hume] |
| Full Idea: The peripatetic philosophers carry their fictions still further, and both suppose a substance supporting, which they do not understand, and an accident supported, of which they have as imperfect an idea. The whole system is entirely incomprehensible. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.3) | |
| A reaction: It seems to me that if you put it to Aristotle that he didn't understand 'substantial form', he would concede the point, but nevertheless say that it was ideal at which knowledge aimed. Locke is much more astute than Hume on this. |
| 21299 | Changing a part can change the whole, not absolutely, but by its proportion of the whole [Hume] |
| Full Idea: Though the change of any considerable part of a mass of matter destroys the identity of the whole, yet we must measure the greatness of the part, not absolutely, but by its proportion to the whole. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: This seems to nicely demonstrate that the wholeness is in the mind of the perceiver, and does not simply depend on objective facts. Compare the proportion needed to change my pile of mud and my pile of gold. |
| 21300 | A change more obviously destroys an identity if it is quick and observed [Hume] |
| Full Idea: A change in any considerable part of a body destroys its identity; but 'tis remarkable that where the change is produced gradually and insensibly we are less apt to ascribe to it the same effect. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Broad spotted that landscapes change too, but so slowly that we barely admit any change at all. The type of change also matters. If my car slowly changes to chocolate the speed of change is a minor factor. |
| 1321 | If identity survives change or interruption, then resemblance, contiguity or causation must unite the parts of it [Hume] |
| Full Idea: The objects which are variable or interrupted, and yet are supposed to continue the same, are such only as consist of a succession of parts, connected together by resemblance, contiguity, or causation. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) |
| 1330 | If a republic can retain identity through many changes, so can an individual [Hume] |
| Full Idea: As the same individual republic may not only change its members, but also its laws and constitutions; in like manner the same person may vary his character and disposition, as well as his impressions and ideas, without losing his identity. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) |
| 21302 | If a ruined church is rebuilt, its relation to its parish makes it the same church [Hume] |
| Full Idea: If a church which was formerly of brick fell to ruin, the parish can build the same church of free-stone, with modern architecture. Neither the form nor materials are the same, but their relation to the parishioners is sufficient to say they are the same. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: The clearly invites the question of whether this is type-identity or token-identity. If the parish decided they wanted two churches they obviously wouldn't be the same (even if they then demolished the first one). |
| 21303 | We accept the identity of a river through change, because it is the river's nature [Hume] |
| Full Idea: Where the objects are in their nature changeable and inconstant, we admit of a more sudden transition. The nature of a river consists in the motion and change of parts. What is expected appears of less moment than what is unusual and extraordinary. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Aha! Little does Hume realise how Aristotelian he is! Aristotle may have a more objective view of the 'nature' of a thing, but making inferences about identity over time from a thing's essential nature is pure Aristotle. |
| 21301 | The purpose of the ship makes it the same one through all variations [Hume] |
| Full Idea: The common end [of a ship], in which the parts conspire, is the same under all variations, and affords an easy transition of the imagination from one situation of the body to another. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: It is not true that a ship remains the same under ALL variations. Consider gradually changing a yacht into a racing powerboat. You might say the purpose is then changed, but the slight variations in a yacht can slightly change its purpose. |
| 21290 | Multiple objects cannot convey identity, because we see them as different [Hume] |
| Full Idea: A mutiplicity of objects can never convey the idea of identity. The mind always pronounces the one not to be the other. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) | |
| A reaction: However, if we are talking on the phone about two objects we are viewing, such as two buildings, our descriptions might lead us to conclude that our objects are identical. Thus experience might imply identity. |
| 1207 | Both number and unity are incompatible with the relation of identity [Hume] |
| Full Idea: Both number and unity are incompatible with the relation of identity. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) |
| 21289 | 'An object is the same with itself' is meaningless; it expresses unity, not identity [Hume] |
| Full Idea: In that proposition 'an object is the same with itself', if the idea expressed by the word 'object' were no way distinguished from that meant by 'itself', we should really mean nothing. ...One single object conveys the idea of unity, not that of identity. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) | |
| A reaction: As far as I can see it is mathematicians who like self-identity, to justify x=x, which they need. To say 'this vase is identical with itself' is an empty locution. It expresses either unity or stability over time. See Idea 21292. |
| 21292 | Saying an object is the same with itself is only meaningful over a period of time [Hume] |
| Full Idea: We cannot, in any propriety of speech, say that an object is the same with itself, unless we mean that the object existent at one time is the same with itself at another time. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.2) | |
| A reaction: This seems correct, but the strict language of identity is superfluous when identifying stolen goods. 'This is my watch', not 'this watch is identical with my watch'. |
| 9428 | Nothing we clearly imagine is absolutely impossible [Hume] |
| Full Idea: 'Tis an established maxim in metaphysics, that whatever the mind clearly conceives includes the idea of possible existence, or in other words, that nothing we imagine is absolutely impossible. | |
| From: David Hume (Treatise of Human Nature [1739], I.II.2) | |
| A reaction: It is important to note that this empiricist approach to what is impossible requires that we 'clearly' conceive the possibility - but how do we evaluate whether we are being clear or not? |
| 4766 | Necessity only exists in the mind, and not in objects [Hume] |
| Full Idea: Necessity …is nothing but an internal impression of the mind, or a determination to carry our thoughts from one object to another. | |
| From: David Hume (Treatise of Human Nature [1739], I.III.16) | |
| A reaction: The classic statement of the empiricist position. Personally I don't believe it. Non-mental necessities are likely to be natural, or to be features of 'Platonic' objects. A big issue… |
| 6526 | Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H] |
| Full Idea: Hume's idea is that we move from private impressions to the physical world, not by an unconscious analytical construction but by a spontaneous imaginative leap. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Howard Robinson - Perception IX.6 | |
| A reaction: The idea that objects are 'constructions' seems to have originated with Russell. Hume seems closer to the actual process, which is virtually instantaneous. They both forget that you can follow up the construction or leap with a cool evaluation. |
| 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. |
| 6489 | Associationism results from having to explain intentionality just with sense-data [Robinson,H on Hume] |
| Full Idea: The limited theories of Berkeley and Hume have to be reductive, because they have to explain intentionality in terms of some kind of relation between sense-data; this predicament gives rise to the associationist accounts of psychology and meaning. | |
| From: comment on David Hume (Treatise of Human Nature [1739]) by Howard Robinson - Perception 1.4 | |
| A reaction: An illuminating explanation. Robinson seems to be implying that we should accept something like Searle's 'intrinsic' intentionality as basic, rather than intentionality built up from smaller components as Hume and Dennett suggest. |
| 6182 | Even Hume didn't include mathematics in his empiricism [Hume, by Kant] |
| Full Idea: Even Hume did not make empiricism so universal as to include mathematics in it. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Immanuel Kant - Critique of Practical Reason Pref | |
| A reaction: Hume didn't actually exclude mathematics, and the notion of 'relations of ideas' is a pointer. Subsequent empiricist have offered promising accounts. Personally I like the idea that patterns are the key idea. |
| 12417 | Mathematicians only accept their own proofs when everyone confims them [Hume] |
| Full Idea: There is no Mathematician so expert as to place entire confidence in any truth upon his discovery of it. ..Every time he runs over his proofs his confidence encreases, ..and is rais'd to perfection by the applause of the learned world. | |
| From: David Hume (Treatise of Human Nature [1739], IV.1.4) | |
| A reaction: [compressed] Quoted by Kitcher, and a nice example of the social nature of 'warrants', even in mathematics. It was illustrated well in the 1990s by the story of the proof of Fermat's Last Theorem by Andrew Wiles. |
| 5548 | Hume became a total sceptic, because he believed that reason was a deception [Hume, by Kant] |
| Full Idea: David Hume gave way entirely to scepticism, since he believed himself to have discovered in what is generally held to be reason a deception of our faculty of cognition. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Immanuel Kant - Critique of Pure Reason B128 | |
| A reaction: Unfair to Hume, who was very opposed to global scepticism (see Ideas 2240 and 2241), and voted only for 'mitigated scepticism' (see Idea 2242). On the other hand, there is no greater opposition in philosophy than Kant and Hume on 'pure reason'. |
| 7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
| Full Idea: Hume's sceptical problem of induction could not have arisen much before 1660, for there was no concept of inductive evidence in terms of which to raise it. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Ian Hacking - The Emergence of Probability Cont 19 | |
| A reaction: Hacking is the expert, but Ideas 1683 and 1886 suggest there was some thinking on the problem in the ancient world. The worry about whether the future would be like the past must occasionally have bothered someone. |
| 21806 | Memory, senses and understanding are all founded on the imagination [Hume] |
| Full Idea: The memory, senses, and understanding are all of them founded on the imagination, or the vivacity of our ideas. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.7.3), quoted by Stephan Schmid - Faculties in Early Modern Philosophy 5 | |
| A reaction: He seems to have in mind his theory of associations, which are not rational. |
| 3819 | Hume's 'bundle' won't distinguish one mind with ten experiences from ten minds [Searle on Hume] |
| Full Idea: Hume's thought that each perception is separate and distinct cannot be right, because then we can't distinguish between one consciousness with ten experiences and ten different consciousnesses. | |
| From: comment on David Hume (Treatise of Human Nature [1739]) by John Searle - Rationality in Action Ch.3.VI | |
| A reaction: Why can't the only connection between them be that they all occur to the speaker who reports to them? How would I know if one of 'my' mental events actually belonged to a neighbour and had strayed. If it was coherent, I would accept it. |
| 1317 | A person is just a fast-moving bundle of perceptions [Hume] |
| Full Idea: I affirm of the rest of mankind, that they are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in perpetual flux and movement. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Note that Hume is not just saying what we can know of ourselves, but is asserting a view of what we actually are. The minimal objection to this is to ask how we know that a perception is a member of one big bundle rather than several small ones. |
| 1331 | The parts of a person are always linked together by causation [Hume] |
| Full Idea: Whatever changes a person endures, his several parts are still connected by the relation of causation. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: However, the opposite ends of the universe are linked together by causation, so that will not suffice for a theory of personal identity. One might try to specify a complex and tight network of causation (like a brain!) instead of just 'connection'. |
| 1388 | Hume gives us an interesting sketchy causal theory of personal identity [Perry on Hume] |
| Full Idea: I believe Hume offers an interesting if sketchy theory of personal identity, a causal theory, disguised as the revolutionary discovery that there is no such thing as personal identity | |
| From: comment on David Hume (Treatise of Human Nature [1739], I.IV.6) by John Perry - Introduction to 'Personal Identity' Intro | |
| A reaction: There is certainly a theory there, even though Hume ceased to believe in it, which is nowadays covered by the idea that personal identity is a 'fiction', an arbitrary idea that reifies the focus and direction of a bundle of mental events. |
| 21297 | A person is simply a bundle of continually fluctuating perceptions [Hume] |
| Full Idea: [People] are nothing but a bundle or collection of different perceptions, which succeed each other with an inconceivable rapidity, and are in a continual flux and movement. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Nowadays we must say that this misses the huge non-conscious aspect of what a person is. He seems to see all mental events as equal. Isn't the experience of deciding to focus on this sentence more 'central' than awareness of your feet? |
| 1316 | Introspection always discovers perceptions, and never a Self without perceptions [Hume] |
| Full Idea: I never can catch myself at any time without a perception, and never can observe any thing but the perception. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: The first half can hardly be denied, but I think the second half is just false. What you observe is not just a raw neutral sense-datum, floating in nothing, but a sense-datum that is deeply coloured by MY interests, interpretations and values. |
| 1333 | Memory only reveals personal identity, by showing cause and effect [Hume] |
| Full Idea: Memory does not so much produce as discover personal identity, by showing us the relation of cause and effect among our different perceptions. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: This is a rather strained proposal, as the revelation of a network of cause and effect seems to have no implications for personal identity (unless only 'I' could be the cause). |
| 1332 | We use memory to infer personal actions we have since forgotten [Hume] |
| Full Idea: We can extend the chain of causes acquired from memory, and consequently the identity of our persons beyond our memory, and can comprehend times, and circumstances, and actions, which we have entirely forgot. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: If the principle is just that 'I am my consciousness' (including of my past), then why should not my consciousness of other people's pasts by included in my identity. How do I know that images in my consciousness are MY memories? |
| 21305 | Memory not only reveals identity, but creates it, by producing resemblances [Hume] |
| Full Idea: The memory not only discovers the identity [of the mind], but also contributes to its production, by producing the relation of resemblance among the perceptions | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: This is Hume battling to explain personal identity by his principles of association. He discount 'contiguity'. He doesn't explain how memory creates resemblances. Is not resemblance of idea to fact required in order to remember? |
| 21307 | Who thinks that because you have forgotten an incident you are no longer that person? [Hume] |
| Full Idea: Who will affirm, because he has entirely forgot the incidents of past days, that the present self is not the same person with the self of that time? And by that means overturn all the most established notions of personal identity? | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: This is a swipe at one of Locke's most controversial claims (especially when applied to incidents of criminal behaviour). Hume says memory constitutes this identity, but Locke's view says it merely reveals identity. |
| 21306 | Causation unites our perceptions, by producing, destroying and modifying each other [Hume] |
| Full Idea: As to causation, the true idea of the human mind is to consider it as a system of different perceptions, which are linked together by the relation of cause and effect, and mutually produce, destroy, influence and modify each other. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: He suggests that the associations of memory and causation might be sufficient to produce identity of the mind, and he gives the priority to memory. Eventually the good empiricist despairs because you cannot experience the links. |
| 21294 | A continuous lifelong self must be justified by a single sustained impression, which we don't have [Hume] |
| Full Idea: If any impression gives rise to the idea of self, that impression must continue invariably the same, through the whole course of our lives; since self is supposed to exist after that manner. But there is no impression constant and invariable. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: This is a rather dogmatic application of the requirement that all knowledge must be founded in experience. It fails to recognise that knowledge of the thing having the experiences is a rather special case. We must ask for the best explanation. |
| 21295 | When I introspect I can only observe my perceptions, and never a self which has them [Hume] |
| Full Idea: When I enter most intimately into myself I always stumble on some particular perception or other, of heat or cold, love or hatred, pain or pleasure. I never can catch myself at any time without a perception, and never observe any thing but the perception. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: It isn't like looking for your car in the car park. The prior question should be: assuming you do have a persisting self, what would you expect introspection to reveal about it? |
| 21298 | We pretend our perceptions are continuous, and imagine a self to fill the gaps [Hume] |
| Full Idea: We feign the continued existence of the perceptions of our senses, to remove their interruption; and run into the notion of a soul, and self, and substance, to disguise the variation. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Modern neuroscience (according to Dennett) endorses this, because the brain continually fills in gaps in experience (as it fills in the blindspot during normal vision). |
| 21304 | Identity in the mind is a fiction, like that fiction that plants and animals stay the same [Hume] |
| Full Idea: The identity we ascribe to the mind is only a fictitious one, and of a like kind with that we ascribe to vegetable and animal bodies. It cannot therefore have a different origin, but must proceed from a like operation of the imagination upon like objects. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: Sustained purpose is Hume's common factor. Is the identity over time ascribed to the body of a single animal nothing more than a fiction? It is a wise ascription, compared to stupid ascriptions to gerrymandered objects. |
| 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. |
| 20030 | If one event causes another, the two events must be wholly distinct [Hume, by Wilson/Schpall] |
| Full Idea: Hume's maxim is that if one event cause another, then the two events must be wholly distinct. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Wilson,G/Schpall,S - Action 3 | |
| A reaction: [Anyone know the original reference?] So we are not allowed to say that one part of an event caused another. The charged caused the victory, so they are two events, but in another context the whole battle is one event. |
| 6692 | For Hume, practical reason has little force, because we can always modify our desires [Hume, by Graham] |
| Full Idea: In Hume's account of action, practical reason is not a very forceful guide to conduct, since we can escape its demands by abandoning or modifying our desires. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Gordon Graham - Eight Theories of Ethics Ch.6 | |
| A reaction: Presumably a desire can be a good reason, and we can passionately desire to be rational, etc., so this is a rather complex issue. 'Pure reason' is not 'all-or-nothing', and neither is pure desire. |
| 8257 | Reason alone can never be a motive to any action of the will [Hume] |
| Full Idea: Reason alone can never be a motive to any action of the will. | |
| From: David Hume (Treatise of Human Nature [1739], II.III.3) | |
| A reaction: This is Hume's notorious total rejection of Socratic intellectualism, a stilleto in the back of the 'age of reason'. Hume thinks desire is the motivator. He's probably right. Why should truth motivate? See Idea 4421. |
| 22374 | You can only hold people responsible for actions which arise out of their character [Hume] |
| Full Idea: Where actions proceed not from some cause in the characters and dispositions of the person who performed them, they infix not themselves upon him, and can neither redound to his honour if good, nor infamy if evil. The action in itself may be blameable. | |
| From: David Hume (Treatise of Human Nature [1739], II.III.2), quoted by Philippa Foot - Free Will as Involving Determinism p.70 | |
| A reaction: I agree with Foot that this is wrong. Uncharacteristic actions still reflect on the person. The last sentence is wrong too. If you ignore the agent of an action, it can't be distinguished from a flash of lightning. |
| 22382 | We cannot discover vice by studying a wilful murder; that only arises from our own feelings [Hume] |
| Full Idea: Examine wilful murder and see if you can find the matter of fact called vice. You only find certain passions, motives, volitions and thoughts. There is no matter of fact in the case. You can never find it till you turn your reflexion into your own breast. | |
| From: David Hume (Treatise of Human Nature [1739], III.I.2), quoted by Philippa Foot - Hume on Moral Judgement p.77 | |
| A reaction: [...In you breast you find 'disapprobation'] The question Foot asks is whether the facts of the case are relevant to the disapprobation. If they are not, as Hume implies, then it would be rational to feel the same disapprobation about drinking coffee. |
| 4008 | Modern science has destroyed the Platonic synthesis of scientific explanation and morality [Hume, by Taylor,C] |
| Full Idea: From our modern perspective, the Platonic synthesis of scientific explanation and moral insight lies irrecoverably shattered by the rise of natural science. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Charles Taylor - Sources of the Self §3.2 | |
| A reaction: Modern attempts to challenge Hume's separation of fact from value have failed, but a return to the Greek perspective presents a plausible alternative. |
| 8067 | The problem of getting to 'ought' from 'is' would also apply in getting to 'owes' or 'needs' [Anscombe on Hume] |
| Full Idea: Hume's objection to passing from 'is' to 'ought' would equally apply to passing from 'is' to 'owes' or from 'is' to 'needs'. | |
| From: comment on David Hume (Treatise of Human Nature [1739]) by G.E.M. Anscombe - Modern Moral Philosophy p.176 | |
| A reaction: Profound and important. The empirical and emotivist (nay, nihilist) clinging to the total independence of duties from facts crumbles when looking at facts of human nature or of social groups. Creatures ought to feed; societies ought to flourish. |
| 4578 | You can't move from 'is' to 'ought' without giving some explanation or reason for the deduction [Hume] |
| Full Idea: In many writers I find that instead of the usual propositions 'is' and 'is not', I then find no proposition that is not connected with an 'ought' or an 'ought not'. It is necessary that a reason be given for how one can be a deduction from the other. | |
| From: David Hume (Treatise of Human Nature [1739], III.1.1) | |
| A reaction: A huge claim, the basis of the value-free modern scientific world view. Possible escapes are Greek virtue theory, or Kantian principles, or some sort of a priori values (as in Charles Taylor). |
| 3650 | Total selfishness is not irrational [Hume] |
| Full Idea: It is not contrary to reason to prefer the destruction of the whole world to the scratching of my finger. | |
| From: David Hume (Treatise of Human Nature [1739], II.III.ii) | |
| A reaction: A famous idea, and the embodiment of moral nihilism. I say nothing could ever refute someone who held such a view. No moral theory can force someone to care, if they just don't. |
| 14301 | We have no good concept of solidity or matter, because accounts of them are all circular [Hume] |
| Full Idea: In order to form an idea of solidity, we must conceive two bodies pressing on each other without penetration. ..The ideas of secondary qualities are excluded, and the idea of motion depends on extension. This leaves us no just idea of solidity or matter. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.4), quoted by Stephen Mumford - Dispositions 02.3 | |
| A reaction: [compressed] For me these kind of strict empiricist arguments always recede when you accept the notion of an inference to be best explanation. We have some sort of notion of 'matter', but here the physicist seems to take over. |
| 8382 | For Hume a constant conjunction is both necessary and sufficient for causation [Hume, by Crane] |
| Full Idea: Hume held that constant conjunction between As and Bs is both necessary and sufficient for a causal relation. If As and Bs are conjoined that is sufficient for a causal relation; if A and B are causally related, necessarily they are constantly conjoined. | |
| From: report of David Hume (Treatise of Human Nature [1739]) by Tim Crane - Causation 1.2.2 | |
| A reaction: A helpful connection between Hume and the modern debate about conditions for causation (e.g. Mackie). It sounds as if, to spot the necessary condition, you need to independently see that A and B are causally related, which regularity does not allow. |
| 19274 | Hume seems to presuppose necessary connections between mental events [Kripke on Hume] |
| Full Idea: A well-known objection to Hume's analysis of causation is that he presupposes necessary connections between mental events in the theory. | |
| From: comment on David Hume (Treatise of Human Nature [1739]) by Saul A. Kripke - Wittgenstein on Rules and Private Language n 87 | |
| A reaction: Are these the associations that occur within the mind? I'm not clear about the objection, but record it for interest. |
| 21296 | If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume] |
| Full Idea: Were all my perceptions removed by death, and I could I neither think nor feel nor see nor love nor hate, after the dissolution of my body, I should be enitrely annihilated, nor do I conceive what is further requisite to make me a perfect non-entity. | |
| From: David Hume (Treatise of Human Nature [1739], I.IV.6) | |
| A reaction: 'A perfect non-entity'. How about that for an eighteenth century rejection of immortality of the soul? In the context, his point is that the has no enduring self, apart from this range of experiences. |