49 ideas
| 13736 | Quinean metaphysics just lists the beings, which is a domain with no internal structure [Schaffer,J on Quine] |
| Full Idea: The Quinean task in metaphysics is to say what exists. What exists forms the domain of quantification. The domain is a set (or class, or plurality) - it has no internal structure. In other words, the Quinean task is to list the beings. | |
| From: comment on Willard Quine (works [1961]) by Jonathan Schaffer - On What Grounds What 1.1 | |
| A reaction: I really warm to this thesis. The Quinean version is what you get when you think that logic is the best tool for explicating metaphysics. Schaffer goes on to say that the only real aim for Quine is the cardinality of what exists! |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| Full Idea: While truth can be defined in a relative way, as truth in one particular model, a non-relative notion of truth is implied, as truth in all models. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: [The article is actually discussing arithmetic] This idea strikes me as extremely important. True-in-all-models is usually taken to be tautological, but it does seem to give a more universal notion of truth. See semantic truth, Tarski, Davidson etc etc. |
| 3302 | Set theory is full of Platonist metaphysics, so Quine aimed to keep it separate from logic [Quine, by Benardete,JA] |
| Full Idea: Quine has showed us how set theory - now recognised to be positively awash in Platonistic metaphysics - can and should be prevented from infecting logic proper. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Intro |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| Full Idea: In standard ZFC ('Zermelo-Fraenkel with Choice') set theory we deal merely with pure sets, not with additional urelements. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: The 'urelements' would the actual objects that are members of the sets, be they physical or abstract. This idea is crucial to understanding philosophy of mathematics, and especially logicism. Must the sets exist, just as the urelements do? |
| 10211 | Quine wants V = L for a cleaner theory, despite the scepticism of most theorists [Quine, by Shapiro] |
| Full Idea: Quine suggests that V = L be accepted in set theory because it makes for a cleaner theory, even though most set theorists are skeptical of V = L. | |
| From: report of Willard Quine (works [1961]) by Stewart Shapiro - Philosophy of Mathematics Ch.1 | |
| A reaction: Shapiro cites it as a case of a philosopher trying to make recommendations to mathematicians. Maddy supports Quine. |
| 3336 | Two things can never entail three things [Quine, by Benardete,JA] |
| Full Idea: Two things can never entail three things. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.17 |
| 8453 | If we had to name objects to make existence claims, we couldn't discuss all the real numbers [Quine] |
| Full Idea: Since one wants to say that real numbers exist and yet one cannot name each of them, it is not unreasonable to relinquish the connection between naming an object and making an existence claim about it. | |
| From: Willard Quine (works [1961]), quoted by Alex Orenstein - W.V. Quine Ch.2 | |
| A reaction: One could say that same about people, such as 'the most recent citizen of Brazil'. Some sort of successful reference seems to be needed, such as 'the next prime beyond the biggest so far found'. Depends what your predicate is going to be. |
| 10311 | No sense can be made of quantification into opaque contexts [Quine, by Hale] |
| Full Idea: Quine says that no good sense can be made of quantification into opaque contexts. | |
| From: report of Willard Quine (works [1961]) by Bob Hale - Abstract Objects Ch.2 | |
| A reaction: This is because poor old Quine was trapped in a world of language, and had lost touch with reality. I can quantify over the things you are thinking about, as long as you are thinking about things that can be quantified over. |
| 10538 | Finite quantification can be eliminated in favour of disjunction and conjunction [Quine, by Dummett] |
| Full Idea: Quine even asserts that where we have no infinite domains, quantification can be eliminated in favour of finite disjunction and conjunction. | |
| From: report of Willard Quine (works [1961]) by Michael Dummett - Frege Philosophy of Language (2nd ed) Ch.14 | |
| A reaction: Thus ∃x is expressed as 'this or this or this...', and ∀ is expressed as 'this and this and this...' Dummett raises an eyebrow, but it sounds OK to me. |
| 10793 | Quine thought substitutional quantification confused use and mention, but then saw its nominalist appeal [Quine, by Marcus (Barcan)] |
| Full Idea: Quine at first regarded substitutional quantification as incoherent, behind which there lurked use-mention confusions, but has over the years, given his nominalist dispositions, come to notice its appeal. | |
| From: report of Willard Quine (works [1961]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.166 |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| Full Idea: In second-order logic there are three kinds of variables, for objects, for functions, and for predicates or sets. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: It is interesting that a predicate seems to be the same as a set, which begs rather a lot of questions. For those who dislike second-order logic, there seems nothing instrinsically wicked in having variables ranging over innumerable multi-order types. |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| Full Idea: 'Analysis' is the theory of the real numbers. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: 'Analysis' began with the infinitesimal calculus, which later built on the concept of 'limit'. A continuum of numbers seems to be required to make that work. |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| Full Idea: The difficulties for a nominalistic mereological approach to arithmetic is that an infinity of physical objects are needed (space-time points? strokes?), and it must define functions, such as 'successor'. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: Many ontologically austere accounts of arithmetic are faced with the problem of infinity. The obvious non-platonist response seems to be a modal or if-then approach. To postulate infinite abstract or physical entities so that we can add 3 and 2 is mad. |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| Full Idea: A common formulation of Peano Arithmetic uses 2nd-order logic, the constant '1', and a one-place function 's' ('successor'). Three axioms then give '1 is not a successor', 'different numbers have different successors', and induction. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: This is 'second-order' Peano Arithmetic, though it is at least as common to formulate in first-order terms (only quantifying over objects, not over properties - as is done here in the induction axiom). I like the use of '1' as basic instead of '0'! |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| Full Idea: The merits of basing an account of mathematics on set theory are that it allows for a comprehensive unified treatment of many otherwise separate branches of mathematics, and that all assumption, including existence, are explicit in the axioms. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I am forming the impression that set-theory provides one rather good model (maybe the best available) for mathematics, but that doesn't mean that mathematics is set-theory. The best map of a landscape isn't a landscape. |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| Full Idea: Structuralism has emerged from the development of abstract algebra (such as group theory), the creation of axiom systems, the introduction of set theory, and Bourbaki's encyclopaedic survey of set theoretic structures. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §2) | |
| A reaction: In other words, mathematics has gradually risen from one level of abstraction to the next, so that mathematical entities like points and numbers receive less and less attention, with relationships becoming more prominent. |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| Full Idea: Relativist Structuralism simply picks one particular model of axiomatised arithmetic (i.e. one particular interpretation that satisfies the axioms), and then stipulates what the elements, functions and quantifiers refer to. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: The point is that a successful model can be offered, and it doesn't matter which one, like having any sort of aeroplane, as long as it flies. I don't find this approach congenial, though having a model is good. What is the essence of flight? |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| Full Idea: The term 'structure' has two uses in the literature, what can be called 'particular structures' (which are particular relational systems), but also what can be called 'universal structures' - what particular systems share, or what they instantiate. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §6) | |
| A reaction: This is a very helpful distinction, because it clarifies why (rather to my surprise) some structuralists turn out to be platonists in a new guise. Personal my interest in structuralism has been anti-platonist from the start. |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| Full Idea: According to 'pattern' structuralism, what we study are not the various particular isomorphic models of arithmetic, but something in addition to them: a corresponding pattern. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §7) | |
| A reaction: Put like that, we have to feel a temptation to wield Ockham's Razor. It's bad enough trying to give the structure of all the isomorphic models, without seeking an even more abstract account of underlying patterns. But patterns connect to minds.. |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| Full Idea: There are four main variants of structuralism in the philosophy of mathematics - formalist structuralism, relativist structuralism, universalist structuralism (with modal variants), and pattern structuralism. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §9) | |
| A reaction: I'm not sure where Chihara's later book fits into this, though it is at the nominalist end of the spectrum. Shapiro and Resnik do patterns (the latter more loosely); Hellman does modal universalism; Quine does the relativist version. Dedekind? |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| Full Idea: Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3) | |
| A reaction: [very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations. |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| Full Idea: It is tempting to take a modal turn, and quantify over all possible objects, because if there are only a finite number of actual objects, then there are no models (of the right sort) for Peano Arithmetic, and arithmetic is vacuously true. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: [compressed; Geoffrey Hellman is the chief champion of this view] The article asks whether we are not still left with the puzzle of whether infinitely many objects are possible, instead of existent. |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| Full Idea: Universalist Structuralism is a semantic thesis, that an arithmetical statement asserts a universal if-then statement. We build an if-then statement (using quantifiers) into the structure, and we generalise away from any one particular model. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: There remains the question of what is distinctively mathematical about the highly generalised network of inferences that is being described. Presumable the axioms capture that, but why those particular axioms? Russell is cited as an originator. |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| Full Idea: Universalist Structuralism is eliminativist about abstract objects, in a distinctive form. Instead of treating the base element (say '1') as an ambiguous referring expression (the Relativist approach), it is a variable which is quantified out. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §5) | |
| A reaction: I am a temperamental eliminativist on this front (and most others) so this is tempting. I am also in love with the concept of a 'variable', which I take to be utterly fundamental to all conceptual thought, even in animals, and not just a trick of algebra. |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| Full Idea: Relativist Structuralism must first assume the existence of an infinite set, otherwise there would be no model to pick, and arithmetical terms would have no reference. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: See Idea 10169 for Relativist Structuralism. They point out that ZFC has an Axiom of Infinity. |
| 8466 | For Quine, intuitionist ontology is inadequate for classical mathematics [Quine, by Orenstein] |
| Full Idea: Quine feels that the intuitionist's ontology of abstract objects is too slight to serve the needs of classical mathematics. | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: Quine, who devoted his life to the application of Ockham's Razor, decided that sets were an essential part of the ontological baggage (which made him, according to Orenstein, a 'reluctant Platonist'). Dummett defends intuitionism. |
| 8467 | Intuitionists only admit numbers properly constructed, but classical maths covers all reals in a 'limit' [Quine, by Orenstein] |
| Full Idea: Intuitionists will not admit any numbers which are not properly constructed out of rational numbers, ...but classical mathematics appeals to the real numbers (a non-denumerable totality) in notions such as that of a limit | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.3 | |
| A reaction: (See Idea 8454 for the categories of numbers). This is a problem for Dummett. |
| 10667 | A logically perfect language could express all truths, so all truths must be logically expressible [Quine, by Hossack] |
| Full Idea: Quine's test of ontological commitment says that anything that can be said truly at all must be capable of being said in a logically perfect language, so there must be a paraphrase of every truth into the language of logic. | |
| From: report of Willard Quine (works [1961]) by Keith Hossack - Plurals and Complexes 2 | |
| A reaction: A very nice statement of the Quinean view, much more persuasive than other statements I have encountered. I am suddenly almost converted to a doctrine I have hitherto despised. Isn't philosophy wonderful? |
| 16021 | Quine says we can expand predicates easily (ideology), but not names (ontology) [Quine, by Noonan] |
| Full Idea: The highly intuitive methodological programme enunciated by Quine says that as our knowledge expands we should unhesitatingly expand our ideology, our stock of predicables, but should be much more wary about ontology, the name variables. | |
| From: report of Willard Quine (works [1961]) by Harold Noonan - Identity §3 | |
| A reaction: I suddenly embrace this as a crucial truth. This distinction allows you to expand on truths without expanding on reality. I would add that it is also crucial to distinguish properties from predicates. A new predicate isn't a new property. |
| 3325 | For Quine everything exists theoretically, as reference, predication and quantification [Quine, by Benardete,JA] |
| Full Idea: Theoretical entities (which is everything, according to Quine) are postulated by us in a threefold fashion as an object (1) to which we refer, (2) of which we predicate, and (3) over which we quantify. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.12 |
| 8534 | Quine says the predicate of a true statement has no ontological implications [Quine, by Armstrong] |
| Full Idea: Quine's doctrine is that the predicate of a true statement carries no ontological implications. | |
| From: report of Willard Quine (works [1961]) by David M. Armstrong - Properties §1 | |
| A reaction: Quine is ontologically committed to the subject of the statement (an object). The predicate seems to be an inseparable part of that object. Quine is, of course, a holist, so ontological commitment isn't judged in single statements. |
| 10295 | Quine suggests that properties can be replaced with extensional entities like sets [Quine, by Shapiro] |
| Full Idea: Quine doubts the existence of properties, and, trying to be helpful, suggests that variables ranging over properties be replaced with variables ranging over respectable extensional entities like sets, so we can 'identify' a property with a singleton set. | |
| From: report of Willard Quine (works [1961]) by Stewart Shapiro - Higher-Order Logic 2.1 | |
| A reaction: This strikes me as a classic modern heresy, a slippery slope that loses all grip on what a property is, replacing it with entities that mean nothing, but make the logic work. |
| 3322 | Quine says that if second-order logic is to quantify over properties, that can be done in first-order predicate logic [Quine, by Benardete,JA] |
| Full Idea: Quine assures us that if the specific mission of second-order logic is quantifying over properties, the task can readily be performed by first-order predicate logic, as in (Ex) x is a property, and (y) y has x. | |
| From: report of Willard Quine (works [1961]) by José A. Benardete - Metaphysics: the logical approach Ch.10 |
| 6078 | Quine brought classes into semantics to get rid of properties [Quine, by McGinn] |
| Full Idea: Quine brought classes into semantics in order to oust properties. | |
| From: report of Willard Quine (works [1961]) by Colin McGinn - Logical Properties Ch.3 | |
| A reaction: Quine's view has always struck me as odd, as I don't see how you can decide what set something belongs to if you haven't already decided its properties. But then I take it that nature informs you of most properties, and set membership is not arbitrary. |
| 8479 | Don't analyse 'red is a colour' as involving properties. Say 'all red things are coloured things' [Quine, by Orenstein] |
| Full Idea: Quine proposes that 'red is a colour' does not require analysis, such as 'there is an x which is the property of being red and it is a colour' which needs an ontology of properties. We can just say that all red things are coloured things. | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.6 | |
| A reaction: The question of the ontology of properties is here approached, in twentieth century style, as the question 'what is the logical form of property attribution sentences?' Quine's version deals in sets of prior objects, rather than abstract entities. |
| 3751 | Universals are acceptable if they are needed to make an accepted theory true [Quine, by Jacquette] |
| Full Idea: Abstract entities (universals) are admitted to an ontology by Quine's criterion if they must be supposed to exist (or subsist) in order to make the propositions of an accepted theory true. | |
| From: report of Willard Quine (works [1961]) by Dale Jacquette - Abstract Entity p.3 |
| 7970 | Quine is committed to sets, but is more a Class Nominalist than a Platonist [Quine, by Macdonald,C] |
| Full Idea: Armstrong dubs Quine an 'Ostrich Nominalist' (what problem??), but Quine calls himself a Platonist, because he is committed to classes or sets as well as particulars. He is not an extreme nominalist, and might best be called a Class Nominalist. | |
| From: report of Willard Quine (works [1961], Ch.6 n15) by Cynthia Macdonald - Varieties of Things | |
| A reaction: For someone as ontologically austere as Quine to show 'commitment' to sets deserves some recognition. If he wants to be a Platonist, I say that's fine. What on earth is a set, apart from its members? |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| Full Idea: One way for a nominalist to reject appeal to all abstract objects, including sets, is to only appeal to nominalistically acceptable objects, including mereological sums. | |
| From: E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §4) | |
| A reaction: I'm suddenly thinking that this looks very interesting and might be the way to go. The issue seems to be whether mereological sums should be seen as constrained by nature, or whether they are unrestricted. See Mereology in Ontology...|Intrinsic Identity. |
| 15783 | Definite descriptions can't unambiguously pick out an object which doesn't exist [Lycan on Quine] |
| Full Idea: Meinong characteristically refers to his Objects using definite descriptions, such as 'the golden mountain'. But on his view there are many golden mountains, with different features. How can 'the golden mountain' then succeed in denoting a single Object? | |
| From: comment on Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01 | |
| A reaction: Use of definite descriptions doesn't seem obligatory in this situation. 'Think of a golden mountain' - 'which one?' - 'never mind which one!'. |
| 15782 | Quine wants identity and individuation-conditions for possibilia [Quine, by Lycan] |
| Full Idea: Quine notoriously demands identity and individuation-conditions for mere possibilia. | |
| From: report of Willard Quine (works [1961]) by William Lycan - The Trouble with Possible Worlds 01 | |
| A reaction: Demanding individuation before speaking of anything strikes me as dubious. 'Whoever did this should own up'. 'There must be something we can do'. Obviously you need some idea of what you are talking about - but not much. |
| 2796 | For Quine the only way to know a necessity is empirically [Quine, by Dancy,J] |
| Full Idea: Quine argues that no necessity can be known other than empirically. | |
| From: report of Willard Quine (works [1961]) by Jonathan Dancy - Intro to Contemporary Epistemology 14.6 |
| 8450 | Quine's empiricism is based on whole theoretical systems, not on single mental events [Quine, by Orenstein] |
| Full Idea: Traditional empiricism takes impressions, ideas or sense data as the basic unit of empirical thought, but Quine takes account of the theoretical as well as the observational; the unit of empirical significance is whole systems of belief. | |
| From: report of Willard Quine (works [1961]) by Alex Orenstein - W.V. Quine Ch.1 | |
| A reaction: This invites either the question of what components make up the whole systems, or (alternatively) what sort of mental events decide to accept a system as a whole. Should Quine revert either to traditional empiricism, or to rationalism? |
| 3868 | To proclaim cultural relativism is to thereby rise above it [Quine, by Newton-Smith] |
| Full Idea: Truth, says the cultural relativist, is culture-bound. But if it were, then he, within his own culture, ought to see his own culture-bound truth as absolute. He cannot proclaim cultural relativism without rising above it. | |
| From: report of Willard Quine (works [1961]) by W.H. Newton-Smith - The Rationality of Science VII.10 |
| 4713 | For Quine, theories are instruments used to make predictions about observations [Quine, by O'Grady] |
| Full Idea: Quine's epistemological position is instrumentalist. Our theories are instruments we use to make predictions about observations. | |
| From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3 | |
| A reaction: This is the pragmatist in Quine. It fits the evolutionary view to think that the bottom line is prediction. My theory about the Pelopponesian War seems an exception. |
| 4712 | Quine says there is no matter of fact about reference - it is 'inscrutable' [Quine, by O'Grady] |
| Full Idea: Quine holds the doctrine of the 'inscrutability of reference', which means there is no fact of the matter about reference. | |
| From: report of Willard Quine (works [1961]) by Paul O'Grady - Relativism Ch.3 | |
| A reaction: Presumably reference depends on conventions like pointing, or the functioning of words like "that", or the ambiguities of descriptions. If you can't define it, it doesn't exist? I don't believe him. |
| 7330 | The principle of charity only applies to the logical constants [Quine, by Miller,A] |
| Full Idea: Quine takes to the principle of charity to apply only to the translation of the logical constants. | |
| From: report of Willard Quine (works [1961]) by Alexander Miller - Philosophy of Language 8.7 | |
| A reaction: Given how weird some people's view of the world seems to be, this very cautious approach has an interesting rival appeal to Davidson't much more charitable view, that people mostly speak truth. It depends whether you are discussing lunch or the gods. |
| 4050 | We only allow voluntary euthanasia to someone who is both sane and crazed by pain [Kamisar] |
| Full Idea: It seems that voluntary euthanasia can only be carried out by someone who is both sane, and crazed by pain. | |
| From: Yale Kamisar (Against Euthanasia [1958], p.77) | |
| A reaction: A fair point, despite its obvious exaggeration. How much pain must someone experience before we permit them to choose euthanasia? |
| 4051 | People will volunteer for euthanasia because they think other people want them dead [Kamisar] |
| Full Idea: In the process of voluntary euthanasia we will sweep up some who are not really tired of life, but think others are tired of them. | |
| From: Yale Kamisar (Against Euthanasia [1958], p.78) | |
| A reaction: We could permit such choices. Or set up systems to eliminate such cases. |
| 17862 | Essence gives an illusion of understanding [Quine, by Almog] |
| Full Idea: Essence engenders a mere illusion of understanding | |
| From: report of Willard Quine (works [1961]) by Joseph Almog - Nature Without Essence Intro | |
| A reaction: [Almog quotes Quine, but doesn't give a reference] This is roughly the same as Popper's criticism of essentialism. |