50 ideas
| 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) |
| 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) |
| 10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
| Full Idea: For a set to be 'well-ordered' it is required that every subset of the set has a first element. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10857 | Set theory made a closer study of infinity possible [Clegg] |
| Full Idea: Set theory made a closer study of infinity possible. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
| Full Idea: The idea of the 'power set' means that it is always possible to generate a bigger one using only the elements of that set, namely the set of all its subsets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
| Full Idea: Axiom of Extension: Two sets are equal if and only if they have the same elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
| Full Idea: Axiom of Pairing: For any two sets there exists a set to which they both belong. So you can make a set out of two other sets. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
| Full Idea: Axiom of Unions: For every collection of sets there exists a set that contains all the elements that belong to at least one of the sets in the collection. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
| Full Idea: Axiom of Infinity: There exists a set containing the empty set and the successor of each of its elements. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This is rather different from the other axioms because it contains the notion of 'successor', though that can be generated by an ordering procedure. |
| 10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
| Full Idea: Axiom of Powers: For each set there exists a collection of sets that contains amongst its elements all the subsets of the given set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: Obviously this must include the whole of the base set (i.e. not just 'proper' subsets), otherwise the new set would just be a duplicate of the base set. |
| 10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
| Full Idea: Axiom of Choice: For every set we can provide a mechanism for choosing one member of any non-empty subset of the set. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: This axiom is unusual because it makes the bold claim that such a 'mechanism' can always be found. Cohen showed that this axiom is separate. The tricky bit is choosing from an infinite subset. |
| 10871 | Axiom of Existence: there exists at least one set [Clegg] |
| Full Idea: Axiom of Existence: there exists at least one set. This may be the empty set, but you need to start with something. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
| Full Idea: Axiom of Specification: For every set and every condition, there corresponds a set whose elements are exactly the same as those elements of the original set for which the condition is true. So the concept 'number is even' produces a set from the integers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) | |
| A reaction: What if the condition won't apply to the set? 'Number is even' presumably won't produce a set if it is applied to a set of non-numbers. |
| 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. |
| 10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
| Full Idea: Three views of mathematics: 'pure' mathematics, where it doesn't matter if it could ever have any application; 'real' mathematics, where every concept must be physically grounded; and 'applied' mathematics, using the non-real if the results are real. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.17) | |
| A reaction: Very helpful. No one can deny the activities of 'pure' mathematics, but I think it is undeniable that the origins of the subject are 'real' (rather than platonic). We do economics by pretending there are concepts like the 'average family'. |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| Full Idea: You can think of an ordinal number as being defined by the set that comes before it, so, in the non-negative integers, ordinal 5 is defined as {0, 1, 2, 3, 4}. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
| Full Idea: With ordinary finite numbers ordinals and cardinals are in effect the same, but beyond infinity it is possible for two sets to have the same cardinality but different ordinals. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.13) |
| 10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
| Full Idea: The 'transcendental numbers' are those irrationals that can't be fitted to a suitable finite equation, of which π is far and away the best known. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
| Full Idea: The realisation that brought 'i' into the toolkit of physicists and engineers was that you could extend the 'number line' into a new dimension, with an imaginary number axis at right angles to it. ...We now have a 'number plane'. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.12) |
| 10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
| Full Idea: It is a chicken-and-egg problem, whether the lack of zero forced forced classical mathematicians to rely mostly on a geometric approach to mathematics, or the geometric approach made 0 a meaningless concept, but the two remain strongly tied together. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch. 6) |
| 10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
| Full Idea: As far as Kronecker was concerned, Cantor had built a whole structure on the irrational numbers, and so that structure had no foundation at all. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
| Full Idea: Paul Cohen showed that the Continuum Hypothesis is independent of the axioms of set theory. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.15) |
| 10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
| Full Idea: The 'continuum hypothesis' says that aleph-one is the cardinality of the rational and irrational numbers. | |
| From: Brian Clegg (Infinity: Quest to Think the Unthinkable [2003], Ch.14) |
| 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? |
| 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) |
| 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. |
| 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. |
| 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) |
| 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. |
| 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. |
| 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'. |
| 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. |
| 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. |
| 7294 | No crime and no punishment without a law [Roman law] |
| Full Idea: An ancient principle of Roman law states, nullum crimen et nulla poene sine lege, - there is no crime and no punishment without a law. | |
| From: [Roman law] (Roman Law [c.100]), quoted by A.C. Grayling - Among the Dead Cities Ch.6 | |
| A reaction: That there is no 'punishment' without law seems the basis of civilization. Suppose a strong person imposed firm punishment in order to forestall more brutal revenge by others? What motivates the creation of criminal laws? |