86 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. |
| 22309 | An idea can only be like another idea [Berkeley] |
| Full Idea: An idea can be like nothing but an idea. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §08), quoted by Michael Potter - The Rise of Analytic Philosophy 1879-1930 43 'Mean' | |
| A reaction: I take this to be relevant to the correspondence theory, but also to be one of Berkeley's best observations. We understand ideas, but we can't map them onto the world (because they are not maps!). ...But then how is one idea like another? Hm. |
| 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 | 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. |
| 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) |
| 1635 | Mathematics reduces to set theory (which is a bit vague and unobvious), but not to logic proper [Quine] |
| Full Idea: Mathematics reduces only to set theory, and not to logic proper… but set theory cannot claim the same firmness and obviousness as logic. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.69-70) |
| 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) |
| 6717 | Abstract ideas are impossible [Berkeley] |
| Full Idea: We have, I think, shown the impossibility of Abstract Ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §21) | |
| A reaction: He achieves this by an attack on universals, offering the nominalist view that there are only particulars. There seems to be a middle ground, where universals don't actually exist, but there are settled conventional abstraction, beyond particulars. |
| 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. |
| 18876 | Berkeley does believe in trees, but is confused about what trees are [Berkeley, by Cameron] |
| Full Idea: I think that we should consider Berkeley as believing in trees; we should simply claim that he has false beliefs about what trees are. | |
| From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Ross P. Cameron - Truthmakers, Realism and Ontology 'Realism' | |
| A reaction: I can be realist about spots before my eyes, or a ringing in my ears, but be (quite sensibly) unsure about what they are, so Cameron's suggestion sounds plausible. |
| 6715 | Universals do not have single meaning, but attach to many different particulars [Berkeley] |
| Full Idea: There is no such thing as one precise and definite signification annexed to any general name, they all signifying indifferently a great number of particular ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §18) | |
| A reaction: The term 'red' may be assigned to a range of colours, but we also recognise the precision of 'that red'. For 'electron', or 'three', or 'straight', the particulars are indistinguishable. |
| 6719 | No one will think of abstractions if they only have particular ideas [Berkeley] |
| Full Idea: He that knows he has no other than particular ideas, will not puzzle himself in vain to find out and conceive the abstract idea annexed to any name. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §24) | |
| A reaction: A nice point against universals. Maybe gods only think in particulars. One particular on its own could never suggest a universal. How are you going to spot patterns if you don't think in universals? Maths needs patterns. |
| 6714 | Universals do not have any intrinsic properties, but only relations to particulars [Berkeley] |
| Full Idea: Universality, so far as I can comprehend it, does not consist in the absolute, positive nature or conception of anything, but in the relation it bears to the particulars signified or represented by it. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §15) | |
| A reaction: I always think it is a basic principle in philosophy that some sort of essence must precede relations (and functions). What is it about universals that enables them to have a relation to particulars? |
| 6729 | Material substance is just general existence which can have properties [Berkeley] |
| Full Idea: The most accurate philosophers have no other meaning annexed to 'material substance' but the idea of being in general, together with the relative notion of its supporting accidents. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §17) | |
| A reaction: This is part of the attack on Aristotle's concept of 'substance', and is a nice way of dissolving the concept. 'Substance' will never reappear in physics, but modern philosopher have returned to it, as possibly inescapable in metaphysics. |
| 16636 | A die has no distinct subject, but is merely a name for its modes or accidents [Berkeley] |
| Full Idea: To me a die seems to be nothing distinct from those things which are termed its modes or accidents. And to say a die is hard, extended and square is not to attribute those qualities to a distinct subject, but only an explication of the word 'die'. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], n 49) | |
| A reaction: This is apparently a reaction to Locke, and a final rejection of the medieval idea of a 'substance'. Unfortunately it leaves Berkeley with a 'bundle' view of objects (a typical empiricist account), which is even worse. |
| 6722 | Perception is existence for my table, but also possible perception, by me or a spirit [Berkeley] |
| Full Idea: The table I write on I say exists, that is, I see and feel it; and if I were out of my study I should say it existed - meaning thereby that if I was in my study I might perceive it, or that some other spirit actually does perceive it. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §3) | |
| A reaction: Berkeley is always (understandably) labelled as an 'idealist', but this seems to be what we call 'phenomenalism', because it allows possible experiences as well as actual ones. See Ideas 5170 and 6522. |
| 6724 | The only substance is spirit, or that which perceives [Berkeley] |
| Full Idea: It is evident that there is not any other Substance than spirit, or that which perceives. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §7) | |
| A reaction: Weird. To say that this is 'evident' seems to be begging the question. Why should he assume that there is nothing more to reality than his perception of it? He seems strangely unimaginative. |
| 6723 | The 'esse' of objects is 'percipi', and they can only exist in minds [Berkeley] |
| Full Idea: The absolute existence of unthinking things with no relation to their being perceived is unintelligible to me; their 'esse' is 'percipi', nor is it possible they should have any existence out of the minds or thinking things which perceive them. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §3) | |
| A reaction: "Esse est percipi" (to be is to be perceived) is the well-known slogan associated with Berkeley. I cannot see how Berkeley can assert that the separate existence of things is impossible. He is the classic confuser of epistemology and ontology. |
| 6732 | When I shut my eyes, the things I saw may still exist, but in another mind [Berkeley] |
| Full Idea: When I shut my eyes, the things I saw may still exist, but it must be in another mind. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §90) | |
| A reaction: This strikes me as ridiculous. What kind of theory says that a table goes out of existence when someone forgets to look at it for a moment, but is then recreated in identical form? Epistemology is not ontology. |
| 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. |
| 6726 | No one can, by abstraction, conceive extension and motion of bodies without sensible qualities [Berkeley] |
| Full Idea: I desire any one to reflect and try whether he can, by any abstraction of thought, conceive the extension and motion of a body without any sensible qualities. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §10) | |
| A reaction: The rather geometrical view of objects found in Descartes and Russell is an attempt to do this. I don't think the fact that we can't really achieve it matters much. We divide primary from secondary qualities in our understanding, not in experience. |
| 6728 | Motion is in the mind, since swifter ideas produce an appearance of slower motion [Berkeley] |
| Full Idea: Is it not reasonable to say that motion is not without the mind, since if the succession of ideas in the mind become swifter the motion, it is acknowledged, shall appear slower without any alteration in any external object. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §14) | |
| A reaction: An intriguing argument, based on what is now the principle of slow-motion photography. Fast minds slow down movement, like great tennis players. By what right does Berkeley say that the external subject is unaltered? |
| 6727 | Figure and extension seem just as dependent on the observer as heat and cold [Berkeley] |
| Full Idea: If heat and cold are only affections of the mind (since the same body seems cold to one hand and warm to the other), why may we not argue that figure and extension also appear different to the same eye at different stations? | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §14) | |
| A reaction: If the assessment of the qualities of an object is entirely a matter of our experiences of it, there is no denying Berkeley on this. However, judgement goes beyond experience, into speculations, inferences, and explanations. |
| 6495 | Berkeley's idealism resulted from fear of scepticism in representative realism [Robinson,H on Berkeley] |
| Full Idea: It was fear of scepticism based upon representative realism that motivated Berkeley's idealism. | |
| From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception II.1 | |
| A reaction: Personally I side with Russell, who accepts representative realism, and also accepts that some degree of scepticism is unavoidable, but without getting excited about it. The key to everything is to be a 'fallibilist' about knowledge. |
| 6720 | Knowledge is of ideas from senses, or ideas of the mind, or operations on sensations [Berkeley] |
| Full Idea: The objects of knowledge are either ideas imprinted on the senses, or passions and operations of the mind, or ideas (formed by memory and imagination) compounding, dividing or barely representing the original perceptions. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §1) | |
| A reaction: This is the germ of Hume's 'associations' (Idea 2189). There is not much room here for synthetic a priori knowledge, as the a priori part seems to merely know the mind. Most of Russell's epistemology is contained in the last part of the sentence. |
| 7627 | You can't reduce epistemology to psychology, because that presupposes epistemology [Maund on Quine] |
| Full Idea: There is something seriously misguided about Quine's project of reducing epistemology to psychology, since psychology, like any of the natural sciences, presupposes an epistemology. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Barry Maund - Perception Ch.1 | |
| A reaction: I wonder if epistemology presupposes psychology? Belief, for example, is a category of folk psychology, which could be challenged. There is a quiet battle going on between philosophy and science. |
| 8871 | We should abandon a search for justification or foundations, and focus on how knowledge is acquired [Quine, by Davidson] |
| Full Idea: Quine is suggesting that philosophy should abandon the attempt to provide a foundation for knowledge, or otherwise justify it, and should instead give an account of how knowledge is acquired. | |
| From: report of Willard Quine (Epistemology Naturalized [1968]) by Donald Davidson - Epistemology Externalized p.193 | |
| A reaction: If you are going to explain how 'knowledge' is acquired, you'd better know what knowledge is. My suspicion is that Quine would be quite happy (in the pragmatist tradition) to just focus on belief, and forget about knowledge entirely. |
| 8826 | If we abandon justification and normativity in epistemology, we must also abandon knowledge [Kim on Quine] |
| Full Idea: Quine asks us to set aside the entire framework of justification-centered epistemology, ..and repudiate normativity. ..But then knowledge itself drops out of epistemology, for our concept of knowledge is inseparably tied to that of justification. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.305 | |
| A reaction: Presumably this would not bother Quine, who wants to hand so-called 'epistemology' over to the psychologists. A psychological account of belief seems plausible. Presumably false beliefs could only be pragmatically characterised. |
| 8827 | Without normativity, naturalized epistemology isn't even about beliefs [Kim on Quine] |
| Full Idea: If normativity is wholly excluded from naturalized epistemology it cannot even be thought of as being about beliefs. | |
| From: comment on Willard Quine (Epistemology Naturalized [1968]) by Jaegwon Kim - What is 'naturalized epistemology'? p.306 | |
| A reaction: And if it doesn't refer to beliefs, it certainly doesn't refer to knowledge. One might try to subsume normativity under evolutionary pragmatic 'drives', or something. Quine's project would then become wildly speculative, and hence boring. |
| 8899 | Epistemology is a part of psychology, studying how our theories relate to our evidence [Quine] |
| Full Idea: Epistemology falls into place as a chapter of psychology, and hence of natural science. ..We study meagre input and torrential output, to see how evidence relates to theory, and in what ways one's theory of nature transcends any available evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.83) | |
| A reaction: It depends what you are interested in. If you just want to know what makes humans tick, then Quine is your man, but if you want to know things in general, and want to know how to get it right, then the normative side of epistemology is unavoidable. |
| 23636 | Berkeley's idealism gives no grounds for believing in other minds [Reid on Berkeley] |
| Full Idea: I can find no principle in Berkeley's system, which affords me even probable ground to conclude that there are other intelligent beings, like myself. | |
| From: comment on George Berkeley (The Principles of Human Knowledge [1710]) by Thomas Reid - Essays on Intellectual Powers 2: Senses 10 | |
| A reaction: I agree, which means that Berkeley's position seems to entail solipsism, unless God is the Cartesian deus ex machina who rescues him from this wall of ignorance. |
| 6736 | I know other minds by ideas which are referred by me to other agents, as their effects [Berkeley] |
| Full Idea: The knowledge I have of other spirits is not immediate, as is the knowledge of my ideas; but depending on the intervention of ideas, by me referred to agents or spirits distinct from myself, as effects or concomitant signs. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §145) | |
| A reaction: This strikes me as gross intellectual dishonesty, since the argument Berkeley uses to assert other minds could equally be used to assert the existence of tables ('by me referred to agents distinct from myself, as effects'). Be a solipsist or a realist. |
| 6713 | If animals have ideas, and are not machines, they must have some reason [Berkeley] |
| Full Idea: If the brutes have any ideas at all, and are not bare machines (as some would have them), we cannot deny them to have some reason. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §11) | |
| A reaction: It seems possible to imagine a low level of mind, where a few ideas (or concepts) float around, but hardly anything worth the name of reason. However, a Darwinian view suggests that concepts must bestow an advantage, so the two go together. |
| 6491 | Berkeley replaced intentionality with an anti-abstractionist imagist theory of thought [Berkeley, by Robinson,H] |
| Full Idea: By Berkeley - with his anti-abstractionism and imagist theory of thought - the classical sense-datum conception was firmly established, and intentionality had disappeared as an intrinsic property, not only of perceptual states, but of all mental contents. | |
| From: report of George Berkeley (The Principles of Human Knowledge [1710]) by Howard Robinson - Perception 1.6 | |
| A reaction: Intentionality was originally a medieval concept, and was revived by Brentano in the late nineteenth century. Nowadays intentionality is taken for granted, but I still suspect that we could drop it, and talk of nothing but brain states caused by reality. |
| 6711 | The mind creates abstract ideas by considering qualities separated from their objects [Berkeley] |
| Full Idea: We are told that the mind being able to consider each quality of things singly, or abstracted from those other qualities with which it is united, does by that means frame to itself abstract ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §7) | |
| A reaction: A helpful explanation of 'abstract' ideas. Berkeley gives colour and movement as examples. Fodor suggests that abstraction is the key strategy in empiricist epistemology. The difficulty is to decide whether the qualities are natural or conventional. |
| 10581 | I can only combine particulars in imagination; I can't create 'abstract' ideas [Berkeley] |
| Full Idea: Whether others can abstract their ideas, they best can tell. For myself, I find I have a faculty of imagining, or representing to myself, only the idea of those particular things I have perceived, and of compounding and dividing them. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], 10) | |
| A reaction: He is admitting mixing experiences, but always particulars, never abstract. His examples are 'man' and 'motion'. Compare Aristotle Idea 9067. Berkeley is, I think, trapped in a false imagistic view of thought. My image of Plato blurs young and old. |
| 6721 | Ideas are perceived by the mind, soul or self [Berkeley] |
| Full Idea: The thing which knows or perceives ideas is what I call mind, spirit, soul or myself. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §2) | |
| A reaction: The interest here is in making no distinction between 'mind' and 'self', which seems to ally Berkeley with Locke's view of personal identity, as continuity of consciousness. The addition of 'soul' tries to connect Locke to Christian thought. |
| 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. |
| 8898 | Inculcations of meanings of words rests ultimately on sensory evidence [Quine] |
| Full Idea: All inculcation of meanings of words must rest ultimately on sensory evidence. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.75) | |
| A reaction: This betrays Quine's behaviourist tendencies, and rules out introspection, definitions and inferences. Quine's conclusion is fairly total scepticism about meaning, but that is not surprising, given his external and meaningless starting point. |
| 6716 | Language is presumably for communication, and names stand for ideas [Berkeley] |
| Full Idea: It is a received opinion that language has no other end but the communicating our ideas, and that every significant name stands for an idea. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §19) | |
| A reaction: This attitude to language has been widely discredited, partly by the observation that 'idea' is very ambiguous, and partly by the fans of meaning-as-use. Truth conditions seem to be ideas, and so are speaker's intentions. |
| 6718 | I can't really go wrong if I stick to wordless thought [Berkeley] |
| Full Idea: So long as I confine my thoughts to my own ideas divested of words, I do not see how I can easily be mistaken. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], Intro §22) | |
| A reaction: I think it was one of the great errors of twentieth century philosophy to say that Berkeley cannot do this, because thought needs language. Personally I think language lags along behind most our thinking, tidying up the mess. I believe in propositions. |
| 8900 | In observation sentences, we could substitute community acceptance for analyticity [Quine] |
| Full Idea: Perhaps the controversial notion of analyticity can be dispensed with, in our definition of observation sentences, in favour of the straightforward attitude of community-wide acceptance. | |
| From: Willard Quine (Epistemology Naturalized [1968], p.86) | |
| A reaction: That might be a reasonable account of 'bachelors'. If the whole community accepts 'God exists', does that make it analytic? If a whole (small!) community claims to actually observe a ghost or a flying saucer, is that then analytic? |
| 6731 | No one can explain how matter affects mind, so matter is redundant in philosophy [Berkeley] |
| Full Idea: How matter should operate on a spirit, or produce any idea in it, is what no philosopher will pretend to explain; it is therefore evident there can be no use of matter in natural philosophy. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §50) | |
| A reaction: An intriguing argument for idealism, which starts in Cartesian dualism, but then discards the physical world because of the notorious interaction problem. Of course, if he had thought that matter and spirit were one (Spinoza) the problem vanishes. |
| 6730 | We discover natural behaviour by observing settled laws of nature, not necessary connections [Berkeley] |
| Full Idea: That food nourishes, sleep refreshes, and fire warms us; all this we know, not by discovering any necessary connexion between our ideas, but only by the observation of the settled laws of nature. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §31) | |
| A reaction: Hume is famous for this idea, but it is found in Hobbes too (Idea 2364), and is the standard empiricist view of causation. The word 'settled' I take to imply that the laws are contingent, because they could become unsettled at any time. |
| 15861 | The laws of nature are mental regularities which we learn by experience [Berkeley] |
| Full Idea: The set rules or established methods wherein the Mind we depend on excites in us the ideas of sense, are called the 'laws of nature'; and these we learn by experience, which teaches us that such and such ideas are attended with certain other ideas. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], 33) | |
| A reaction: He observes that the ideas of sense are more regular than other mental events, and attributes the rules to an Author. He is giving the standard empirical Humean view, with his own quirky idealist slant. |
| 6734 | If properties and qualities arise from an inward essence, we will remain ignorant of nature [Berkeley] |
| Full Idea: An inducement to pronouncing ourselves ignorant of the nature of things is the opinion that everything includes within itself the cause of its properties; or that there is in each object an inward essence which is the source whence its qualities flow. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §102) | |
| A reaction: This remains a good objection to essentialism - that while it remains quite a plausible picture of how nature operates, it makes the task of understanding nature hopeless. We can grasp imposed regular laws, but not secret inner essences. |
| 6735 | All motion is relative, so a single body cannot move [Berkeley] |
| Full Idea: There cannot be any motion other than relative; …if there was one only body in being it could not possibly move. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §112) | |
| A reaction: This seems to agree with with Leibniz in denying the Newton-Clarke idea of absolute space. See Idea 2100. Suppose there were two bodies racing towards one another, when one of them suddenly vanished? |
| 6733 | I cannot imagine time apart from the flow of ideas in my mind [Berkeley] |
| Full Idea: Whenever I attempt to frame a simple idea of time, abstracted from the succession of ideas in my mind, which flows uniformly and is participated in by all beings, I am lost and embrangled in inextricable difficulties. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §98) | |
| A reaction: 'Embrangled'! A nice statement of the idealist view of time, as entirely mental. I know what he means. However, surely he can manage to imagine a movement which continues when he shuts he eyes? Try blinking during a horse race. |
| 6737 | Particular evils are really good when linked to the whole system of beings [Berkeley] |
| Full Idea: Those particular things which, considered in themselves, appear to be evil, have the nature of good, when considered as linked with the whole system of beings. | |
| From: George Berkeley (The Principles of Human Knowledge [1710], §153) | |
| A reaction: This wildly contradicts the rest of Berkeley's philosophy, which is strictly empiricist, and rests wholly on actual experience. What experience does he have of the 'whole system of beings', and its making evil into actual good? |