76 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. |
| 1627 | Any statement can be held true if we make enough adjustment to the rest of the system [Quine] |
| Full Idea: Any statement can be held true come what may, if we make drastic enough adjustments elsewhere in the system. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.43) |
| 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? |
| 1623 | Definition rests on synonymy, rather than explaining it [Quine] |
| Full Idea: Definition rests on synonymy, rather than explaining it. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.26) |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naïve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naïve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 9204 | Quine's arguments fail because he naively conflates names with descriptions [Fine,K on Quine] |
| Full Idea: Quine's logical argument against modality presupposes a naïve view of singular terms under which no significant distinction is to be drawn between the use of names and descriptions. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Kit Fine - Intro to 'Modality and Tense' p. 6 | |
| A reaction: See Idea 9201 for Quine's argument. The question is whether '9' and 'the number of planets' are names or descriptions. The 'number of planets' is not remotely descriptive of 9, so it must be referential. So '9' is a name? Hm. |
| 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) |
| 17738 | Quine blurs the difference between knowledge of arithmetic and of physics [Jenkins on Quine] |
| Full Idea: Quine cannot deal with the intuition that there is a difference in kind between our knowledge of arithmetic and our knowledge of physics. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Carrie Jenkins - Grounding Concepts 7.5 | |
| A reaction: The endorses this criticism, which she says is widespread. I'm not convinced that there is a clear notion of 'difference in kind' here. Jenkins gets arithmetic from concepts and physics from the world. Is that a sharp distinction? |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 19492 | Quine is hopeless circular, deriving ontology from what is literal, and 'literal' from good ontology [Yablo on Quine] |
| Full Idea: Quine's advice is to countenance numbers iff the literal part of our theory quantifies over them; and to count the part of our theory that quantifies over numbers literal iff there turn out really to be numbers. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Stephen Yablo - Does Ontology Rest on a Mistake? XIII | |
| A reaction: This sounds a bit devastating. Presumably it is indeed the choice of a best theory which results in the ontological commitment, so it is not much help to then read off the ontology from the theory. |
| 1628 | If physical objects are a myth, they are useful for making sense of experience [Quine] |
| Full Idea: The myth of physical objects is epistemologically superior to most in that it has proved more efficacious than other myths as a device for working a manageable structure into the flux of experience. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.44) |
| 16625 | In hylomorphism all the explanation of actions is in the form, and the matter doesn't do anything [Bacon] |
| Full Idea: Prime, common matter seems to be a kind of accessory and to stand as a substratum, whereas any kind of action seems to be a mere emanation of form. So it is that forms are given all the leading parts. | |
| From: Francis Bacon (Philosophical Studies 1611-19 [1617], p.206), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.2 | |
| A reaction: This is a very striking criticism of hylomorphism. The revolution was simple - that actually matter seems to do all the real work, and the form can take a back seat. |
| 10929 | Aristotelian essence of the object has become the modern essence of meaning [Quine] |
| Full Idea: The Aristotelian notion of essence was the forerunner of the modern notion of intension or meaning. ...Meaning is what essence becomes when it is divorced from the object of reference and wedded to the word. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], §1) | |
| A reaction: Quine first wants to jettison de re necessity (essence of the object), by shifting it to de dicto necessity (necessity in meaning), but he subsequently rejects that as well, presumably because he doesn't even believe in meanings. |
| 12188 | Contrary to some claims, Quine does not deny logical necessity [Quine, by McFetridge] |
| Full Idea: Nothing in Quine's argument seems to be said directly against the view that the propositions of logic are necessary truths, ..though Crispin Wright has represented him as saying this at the end of 'Two Dogmas'. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Ian McFetridge - Logical Necessity: Some Issues §3 | |
| A reaction: Quine famously denies that logical truths are merely a matter of convention, so the question is, if he believes in logical necessity, what does he think is the basis of it? Answers, as always, on a postcard. |
| 15090 | Quine's attack on the analytic-synthetic distinction undermined necessary truths [Quine, by Shoemaker] |
| Full Idea: Quine's attack on the analytic-synthetic distinction sought to contract, if not to empty, the class of truths that are called necessary. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Sydney Shoemaker - Causal and Metaphysical Necessity I | |
| A reaction: The thought was that absolutely everything, including, for example, basic logic, became potentially revisable. See the last section of Quine's paper. |
| 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. |
| 9383 | Metaphysical analyticity (and linguistic necessity) are hopeless, but epistemic analyticity is a priori [Boghossian on Quine] |
| Full Idea: Quine showed the vacuity of the metaphysical concept of analyticity and the futility of the underwritten project - the linguistic theory of necessity. But that doesn't effect the epistemic notion of analyticity needed for a priori knowledge. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Boghossian - Analyticity Reconsidered Concl | |
| A reaction: This summarise Boghossian's view, that a priori knowledge is still analytic, once we get clear about analyticity. See Idea 9368 for his two types of analyticity. Horwich attacks the view. |
| 12424 | Quine challenges the claim that analytic truths are knowable a priori [Quine, by Kitcher] |
| Full Idea: The last section of Quine's article challenges the claim that analytic truths are knowable a priori. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Philip Kitcher - The Nature of Mathematical Knowledge 04.5 | |
| A reaction: That is, Quine does not deny that there are truths which rest entirely on meaning. It is a 'dogma of empiricism' that the a priori can be equated with the analytic (and the necessary). |
| 9338 | Quine's objections to a priori knowledge only work in the domain of science [Horwich on Quine] |
| Full Idea: Quine's arguments provide no reason to doubt the existence of a priori knowledge outside the domain of science. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §10 | |
| A reaction: This rather ignores Quine's background view of thoroughgoing physicalism, so that the domain of science is the domain of nature, which is the domain of everything. See his naturalising of epistemology, for example. Maths is part of his science. |
| 9337 | Science is empirical, simple and conservative; any belief can hence be abandoned; so no a priori [Quine, by Horwich] |
| Full Idea: Quine says scientific beliefs follow empirical adequacy, simplicity and conservatism; science and rationality support this view; hence any hypothesis can be abandoned to increase simplicity; so no scientific belief is a priori. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §10 | |
| A reaction: [Compressed] I just don't accept this claim. If science wants to drop simple arithmetic or the laws of thought, so much the worse for science - they've obviously taken a wrong turning somewhere. We must try to infer God's logic. |
| 9340 | Logic, arithmetic and geometry are revisable and a posteriori; quantum logic could be right [Horwich on Quine] |
| Full Idea: I think logic, arithmetic and geometry are subject to Quine's empirical revisability argument: quantum logic may turn out to be the best overall theory; so these things are justified a posteriori. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Horwich - Stipulation, Meaning and Apriority §11 | |
| A reaction: Not much of an argument, because 'quantum logic' may also turn out to be a will-o'-the-whisp. Until it is established (which I doubt, because quantum theory is so poorly understood), I think we should be highly suspicious of the Quinean view. |
| 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. |
| 1620 | Empiricism makes a basic distinction between truths based or not based on facts [Quine] |
| Full Idea: One dogma of empiricism is that there is some fundamental cleavage between truths that are analytic, or grounded in meanings independently of facts, and truths which are synthetic, or grounded in fact. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.20) |
| 1629 | Our outer beliefs must match experience, and our inner ones must be simple [Quine] |
| Full Idea: The outer edge of our empirical system must be kept squared with experience; the rest, with all its elaborate myths and fictions, has as its objective the simplicity of laws. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.45) |
| 19488 | The second dogma is linking every statement to some determinate observations [Quine, by Yablo] |
| Full Idea: Quine's second dogma of empiricism is the reductionism that finds every statement to be linkable by fixed correspondence rules to a determinate range of confirming observations. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Stephen Yablo - Does Ontology Rest on a Mistake? V | |
| A reaction: Quine's response to this is to embrace holism about theories, instead of precise connections with Humean impressions. I'm thinking that Lewis disagrees with Quine, when his Humean supervenience rests on a 'mosaic' of small qualities. |
| 1625 | Statements about the external world face the tribunal of sense experience as a corporate body [Quine] |
| Full Idea: My suggestion, following Carnap, is that our statements about the external world face the tribunal of sense experience not individually but only as a corporate body. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.41) |
| 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. |
| 1626 | It is troublesome nonsense to split statements into a linguistic and a factual component [Quine] |
| Full Idea: My present suggestion is that it is nonsense, and the root of much nonsense, to speak of a linguistic component and a factual component in the truth of any individual statement. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.42) | |
| A reaction: I take the language and its subject matter to be obviously separate, but it is right that we can't separate these two components within a sample of language. |
| 7317 | 'Renate' and 'cordate' have identical extensions, but are not synonymous [Quine, by Miller,A] |
| Full Idea: It is easy to see that intersubstitutability salva veritate is not a sufficient condition for synonymy. 'Renate' (with kidney) and 'cordate' (with heart) can be substituted in a purely extensional language, but are plainly not synonymous. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Alexander Miller - Philosophy of Language 4.2 | |
| A reaction: This seems to be a key example (along with Hesperus, and many others) in mapping out synonymy, meaning, analyticity, sense, reference, extension, intension, and all that stuff. |
| 1621 | Once meaning and reference are separated, meaning ceases to seem important [Quine] |
| Full Idea: Once theory of meaning and of reference are separated it is a short step to recognising as the primary business of theory of meaning simply the synonymy of linguistic forms and analyticity of statements; meanings themselves may be abandoned. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.22) | |
| A reaction: I can't buy the abandonment of meaning, because when I introspect my own speech there is clearly what I want to say formulating in my mind before the words are settled. |
| 9371 | Analytic statements are either logical truths (all reinterpretations) or they depend on synonymy [Quine] |
| Full Idea: Analytic statements fall into two classes: 'no unmarried man is married' typifies the first class, of logical truths; it remains true under all reinterpretations. 'No bachelor is married' is analytic if synonyms replace synonyms, and there's the problem. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], §1) | |
| A reaction: Boghossian emphasises this passage. In other papers Quine argues that logical truths also cannot be purely analytic, although he does not deny that there are logical truths. |
| 1622 | Did someone ever actually define 'bachelor' as 'unmarried man'? [Quine] |
| Full Idea: How do we find that 'bachelor' is defined as unmarried man? Who defined it thus, and when? Not the lexicographer, who is a scientist recording antecedent facts. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.24) | |
| A reaction: All mid-20th C philosophy of language is too individualistic in its strategy. Eventually later Wittgenstein sank in, and socially agreed meanings for 'water' and 'elm'. |
| 9366 | Quine's attack on analyticity undermined linguistic views of necessity, and analytic views of the a priori [Quine, by Boghossian] |
| Full Idea: Quine's attack on analyticity devastated the philosophical programs that depend upon a notion of analyticity - specifically, the linguistic theory of necessary truth, and the analytic theory of a priori knowledge. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Paul Boghossian - Analyticity Reconsidered §I | |
| A reaction: Note that much more would be needed to complete Quine's aim of more or less eliminating both necessity and the a priori from his scientific philosophy. Quine was trying to complete a programme initiated by C.I. Lewis (q.v.). |
| 14473 | Quine attacks the Fregean idea that we can define analyticity through synonyous substitution [Quine, by Thomasson] |
| Full Idea: Quine's attack argues against the Fregean attempt to define 'analyticity' in terms of synonymy - where analytical truths are logical truths ('unmarried men are unmarried'), or become logical truths by synonymous replacement ('bachelors are unmarried'). | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Amie L. Thomasson - Ordinary Objects 02.1 | |
| A reaction: This is a very helpful explanation of what is going on in Quine. Why won't philosophers explain clearly what they are attacking, before they attack it? |
| 7321 | The last two parts of 'Two Dogmas' are much the best [Miller,A on Quine] |
| Full Idea: The arguments of the final two sections of 'Two Dogmas' have received more acceptance than the arguments of the first four sections, which are now generally acknowledged to be unsuccessful. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Alexander Miller - Philosophy of Language 4 Read | |
| A reaction: The early sections are the 'circular' argument against analyticity; the later parts are further discussions of the concept. We don't have to take Miller's word for this, but it is a useful pointer when reading the paper. |
| 8803 | Erasing the analytic/synthetic distinction got rid of meanings, and saved philosophy of language [Davidson on Quine] |
| Full Idea: Erasing the line between the analytic and the synthetic saved philosophy of language as a serious subject by showing how it could be pursued without what there cannot be: determinate meanings. | |
| From: comment on Willard Quine (Two Dogmas of Empiricism [1953]) by Donald Davidson - Coherence Theory of Truth and Knowledge p.158 | |
| A reaction: Note that this comes from the most famous modern champion of one of the main theories of meaning (as truth-conditions). Did anyone ever believe in reified objects called 'meanings'? |
| 17737 | The analytic needs excessively small units of meaning and empirical confirmation [Quine, by Jenkins] |
| Full Idea: Quine rejects the analytic on the grounds that it assumes a smaller unit of meaning than a total theory, and he does not think it makes sense to talk about such smaller units of meaning because there are no smaller units of empirical confirmation. | |
| From: report of Willard Quine (Two Dogmas of Empiricism [1953]) by Carrie Jenkins - Grounding Concepts 7.5 | |
| A reaction: A very helpful account of the famous Quine argument, showing how it arises out of his particular holistic view of empiricism. |
| 1624 | If we try to define analyticity by synonymy, that leads back to analyticity [Quine] |
| Full Idea: In defining analyticity an appeal to meanings seems natural, but that reduces to synonymy or definition. Definition is a will-o'-the-wisp, and synonymy is best understood by a priori appeal to analyticity, so we are back at the problem of analyticity. | |
| From: Willard Quine (Two Dogmas of Empiricism [1953], p.32) | |
| A reaction: Quine is full of these over-neat sceptical arguments, saying everything is circular, or can never get started. Compare Aristotle's benign circle of virtuous people and virtuous actions. |
| 16624 | Stripped and passive matter is just a human invention [Bacon] |
| Full Idea: Stripped and passive matter seems nothing more than an invention of the human mind. | |
| From: Francis Bacon (Philosophical Studies 1611-19 [1617], p.206), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 07.2 | |
| A reaction: Bacon seems to me to get too little credit in the history of philosophy, because he is just seen as a progenitor of science. His modern views predate most radical 17th C thought by 20 years. |