When is the dialectical method used?
Dialect Test
The Dialect Test was created by A.J. Ellis in February 1879, and was used in the fieldwork for his work "On Early English Pronunciation". It stands as one of the earliest methods of identifying vowel sounds and features of speech. The aim was to capture the main vowel sounds of an individual dialect by listening to the reading of a short passage. All the categories of West Saxon words and vowels were included in the test so that comparisons could be made with the historic West Saxon speech as well as with various other dialects.
Frankfurt School
Marx thus extensively relied on a form of dialectical analysis. This method—to know the truth by uncovering the contradictions in presently predominant ideas and, by extension, in the social relations to which they are linked—exposes the underlying struggle between opposing forces. For Marx, it is only by becoming aware of the dialectic (i.e., class consciousness) of such opposing forces, in a struggle for power, that individuals can liberate themselves and change the existing social order.
Criticisms of Marxism
Popper believed that Marxism had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. When Marx's predictions were not in fact borne out, Popper argues that the theory was saved from falsification by the addition of "ad hoc" hypotheses which attempted to make it compatible with the facts. By this means, a theory which was initially genuinely scientific degenerated into pseudoscientific dogma. Popper agreed on the general non-falsifiability of the social sciences, but instead used it as an argument against central planning and all-encompassing historiographical ideologies. Popper devoted much attention to dissecting the practice of using the dialectic in defence of Marxist thought, which was the very strategy employed by V.A. Lektorsky in his defence of Marxism against Popper's criticisms. Among Popper's conclusions was that Marxists used dialectic as a method of side-stepping and evading criticisms, rather than actually answering or addressing them: Hegel thought that philosophy develops; yet his own system was to remain the last and highest stage of this development and could not be superseded. The Marxists adopted the same attitude towards the Marxian system. Hence, Marx's anti-dogmatic attitude exists only in the theory and not in the practice of orthodox Marxism, and dialectic is used by Marxists, following the example of Engels' Anti-Dühring, mainly for the purposes of apologetics – to defend the Marxist system against criticism. As a rule critics are denounced for their failure to understand the dialectic, or proletarian science, or for being traitors. Thanks to dialectic the anti-dogmatic attitude has disappeared, and Marxism has established itself as a dogmatism which is elastic enough, by using its dialectic method, to evade any further attack. It has thus become what I have called reinforced dogmatism.
Chinese Marxist philosophy
Marxist philosophy was initially imported into China between 1900 and 1930, in translations from German, Russian and Japanese. This was before the formal dialectical materialism of the Communist Party, in which many independent radical intellectuals embraced Marxism. Many of them would later join the Party. Chinese Dialectical Materialism began to be formalized during the 1930s, under the influence of Mitin's New Philosophy. In the late 1930s, Chairman Mao Zedong would begin to develop his own sinified version of Dialectical Materialism that was independent of the Soviet Philosophy. Maoist Dialectics remained the dominant paradigm into the 1970s, and most debates were on technical questions of dialectical ontology. In the 1980s the Dengist reforms led to a large-scale translation and influence of works of Western Marxism and Marxist Humanism.
Roy Bhaskar
The 'second phase' of Critical Realism, the dialectic turn initiated in "Dialectic: the Pulse of Freedom" (1993) won some new adherents but drew criticism from some Critical Realists. It argued for the 'dialecticising' of CR, through an elaborate reading of Hegel and Marx. Arguing against Hegel and with Marx that dialectical connections, relations and contradictions are themselves ontological – objectively real – Bhaskar developed a concept of real absence which it was claimed could provide a more robust foundation for the reality and objectivity of values and criticism. He attempted to incorporate critical, rational human agency into the dialectic figure with his 'Fourth Dimension' of dialectic, thereby grounding a systematic model for rational emancipatory transformative practice.
Rhetoric
Aristotle (384–322 BC) was a student of Plato who famously set forth an extended treatise on rhetoric that still repays careful study today. In the first sentence of The Art of Rhetoric, Aristotle says that "rhetoric is the counterpart [literally, the antistrophe] of dialectic". As the "antistrophe" of a Greek ode responds to and is patterned after the structure of the "strophe" (they form two sections of the whole and are sung by two parts of the chorus), so the art of rhetoric follows and is structurally patterned after the art of dialectic because both are arts of discourse production. Thus, while dialectical methods are necessary to find truth in theoretical matters, rhetorical methods are required in practical matters such as adjudicating somebody's guilt or innocence when charged in a court of law, or adjudicating a prudent course of action to be taken in a deliberative assembly. The core features of dialectic include the absence of determined subject matter, its elaboration on earlier empirical practice, the explication of its aims, the type of utility and the definition of the proper function.
The Hiram Key
The authors make their case through the use of dialectics. The technique requires the reader to accept a basic premise, and then proceeds in a logical order; requiring the reader to weigh the merit of each step on the way to a conclusion. If the initial premise, and each of the steps in logic towards the conclusion have merit, the conclusion can represent a legitimate, possible explanation.
Dialectic
A dialectical method was fundamental to Marxist politics, e.g., the works of Karl Korsch, Georg Lukács and certain members of the Frankfurt School. Soviet academics, notably Evald Ilyenkov and Zaid Orudzhev, continued pursuing unorthodox philosophic study of Marxist dialectics; likewise in the West, notably the philosopher Bertell Ollman at New York University.
Discrete element method
Periodical
Discontinuous Galerkin method
Discontinuous Galerkin methods were first proposed and analyzed in the early 1970s as a technique to numerically solve partial differential equations. In 1973 Reed and Hill introduced a DG method to solve the hyperbolic neutron transport equation.
The Phenomenology of Spirit
The famous dialectical process of thesis-antithesis-synthesis has been controversially attributed to Hegel. 
Regardless of (ongoing) academic controversy regarding the significance of a unique dialectical method in Hegel's writings, it is true, as Professor Howard Kainz (1996) affirms, that there are "thousands of triads" in Hegel's writings. Importantly, instead of using the famous terminology that originated with Kant and was elaborated by J. G. Fichte, Hegel used an entirely different and more accurate terminology for dialectical (or as Hegel called them, 'speculative') triads.
Plato
The role of dialectic in Plato's thought is contested but there are two main interpretations: a type of reasoning and a method of intuition. Simon Blackburn adopts the first, saying that Plato's dialectic is "the process of eliciting the truth by means of questions aimed at opening out what is already implicitly known, or at exposing the contradictions and muddles of an opponent's position." A similar interpretation has been put forth by Louis Hartz, who suggests that elements of the dialectic are borrowed from Hegel. According to this view, opposing arguments improve upon each other, and prevailing opinion is shaped by the synthesis of many conflicting ideas over time. Each new idea exposes a flaw in the accepted model, and the epistemological substance of the debate continually approaches the truth. Hartz's is a teleological interpretation at the core, in which philosophers will ultimately exhaust the available body of knowledge and thus reach "the end of history." Karl Popper, on the other hand, claims that dialectic is the art of intuition for "visualising the divine originals, the Forms or Ideas, of unveiling the Great Mystery behind the common man's everyday world of appearances."
Paradox psychology
While the paradoxical method was documented by Adler as early as the 1920s, its counter-intuitive style has always been difficult to explain. Adler once described the method as "spitting in the patient's soup"; meaning that the method had the ability to impact behavior without 'convincing or rewarding' the patient to change.
Numerical methods for ordinary differential equations
Starting with the differential equation (1), we replace the derivative "y"' by the finite difference approximation
which when re-arranged yields the following formula
and using (1) gives:
This formula is usually applied in the following way. We choose a step size "h", and we construct the sequence "t", "t" = "t" + "h", "t" = "t" + 2"h", … We denote by "y" a numerical estimate of the exact solution "y"("t"). Motivated by (3), we compute these estimates by the following recursive scheme 
This is the "Euler method" (or "forward Euler method", in contrast with the "backward Euler method", to be described below). The method is named after Leonhard Euler who described it in 1768.
Deliberative democracy
The deliberative element of democracy was not widely studied by academics until the late 20th century. Although some of the seminal work was done in the 1970s and 80s, it was only in 1990 that deliberative democracy began to attract substantial attention from political scientists. According to Professor John Dryzek, early work on Deliberative Democracy was part of efforts to develop a theory of Democratic legitimacy. Theorists such as Carne Ross advocate deliberative democracy as a complete alternative to representative democracy. The more common view, held by contributors such as James Fishkin, is that direct deliberative democracy can be complementary to traditional representative democracy. Since 1994, hundreds of implementations of direct deliberative democracy have taken place throughout the world. For example, lay citizens have used deliberative democracy to determine local budget allocations in various cities and to undertake major public projects, such as the rebuilding of New Orleans after Hurricane Katrina.
Historical linguistics
The principal tools of research in diachronic linguistics are the comparative method and the method of internal reconstruction. Less-standard techniques, such as mass lexical comparison, are used by some linguists to overcome the limitations of the comparative method, but most linguists regard them as unreliable.
K. M. Petyt
He was one of the first to apply Labovian methods in Britain with his research in 1970-1 on the speech of Bradford, Halifax and Huddersfield. He concluded that the speech detailed in most of dialectology (e.g. A. J. Ellis, the Survey of English Dialects) had virtually disappeared, having found only one speaker out of his sample of 106 speakers who regularly used dialect. However, he found that differences in speech persisted as an indicator of social class, age and gender. This PhD dissertation was later adapted into a book, "Dialect and Accent in Industrial West Yorkshire". The work was criticised by Graham Shorrocks on the grounds that the sociolinguistic methods used were inappropriate for recording the traditional vernacular and that there was an inadequate basis for comparison with earlier dialect studies in West Yorkshire.
Comparative method
The comparative method was developed over the 19th century. Key contributions were made by the Danish scholars Rasmus Rask and Karl Verner and the German scholar Jacob Grimm. The first linguist to offer reconstructed forms from a proto-language was August Schleicher, in his "Compendium der vergleichenden Grammatik der indogermanischen Sprachen", originally published in 1861. Here is Schleicher's explanation of why he offered reconstructed forms:
In the present work an attempt is made to set forth the inferred Indo-European original language side by side with its really existent derived languages. Besides the advantages offered by such a plan, in setting immediately before the eyes of the student the final results of the investigation in a more concrete form, and thereby rendering easier his insight into the nature of particular Indo-European languages, there is, I think, another of no less importance gained by it, namely that it shows the baselessness of the assumption that the non-Indian Indo-European languages were derived from Old-Indian (Sanskrit).
Dialectic
Hegelian dialectic, usually presented in a threefold manner, was stated by Heinrich Moritz Chalybäus as comprising three dialectical stages of development: a thesis, giving rise to its reaction; an antithesis, which contradicts or negates the thesis; and the tension between the two being resolved by means of a synthesis. In more simplistic terms, one can consider it thus: problem → reaction → solution. Although this model is often named after Hegel, he himself never used that specific formulation. Hegel ascribed that terminology to Kant. Carrying on Kant's work, Fichte greatly elaborated on the synthesis model and popularized it.
History of scientific method
Some of the most important debates in the history of scientific method center on: rationalism, especially as advocated by René Descartes; inductivism, which rose to particular prominence with Isaac Newton and his followers; and hypothetico-deductivism, which came to the fore in the early 19th century. In the late 19th and early 20th centuries, a debate over realism vs. antirealism was central to discussions of scientific method as powerful scientific theories extended beyond the realm of the observable, while in the mid-20th century some prominent philosophers argued against any universal rules of science at all.
MacCormack method
In computational fluid dynamics, the MacCormack method is a widely used discretization scheme for the numerical solution of hyperbolic partial differential equations. This second-order finite difference method was introduced by Robert W. MacCormack in 1969. The MacCormack method is elegant and easy to understand and program.
Demotic Greek
Demotic Greek (, "dimotikí glóssa" , "language of the people") or dimotiki (, "dimotikí"), is the modern vernacular form of the Greek language. The term has been in use since 1818. "Demotic" refers particularly to the form of the language that evolved naturally from Ancient Greek, in opposition to the artificially archaic Katharevousa, which was the official standard until 1976. The two complemented each other in a typical example of diglossia until the resolution of the Greek language question in favour of Demotic.
Partial differential algebraic equation
Semi-discretization is a common method for solving PDAEs whose independent variables are those of time and space, and has been used for decades. This method involves removing the spatial variables using a discretization method, such as the finite volume method, and incorporating the resulting linear equations as part of the algebraic relations. This reduces the system to a DAE, for which conventional solution methods can be employed.
Ellipsoid method
where
Differential display
Differential display (also referred to as DDRT-PCR or DD-PCR) is a laboratory technique that allows a researcher to compare and identify changes in gene expression at the mRNA level between two or more eukaryotic cell samples. It was the most commonly used method to compare expression profiles of two eukaryotic cell samples in the 1990s. By 2000, differential display was superseded by DNA microarray approaches.
Interpersonal communication
A dialectical approach to interpersonal communication was developed by scholars Leslie Baxter and Barbara Montgomery. Their dialectical approach revolves around the notions of contradiction, change, praxis, and totality. Influenced by Hegel, Marx, and Bakhtin, the dialectical approach is informed by an epistemology that refers to a method of reasoning by which one searches for understanding through the tension of opposing arguments. Utilizing the dialectical approach, Baxter and Montgomery developed two types of dialectics that function in interpersonal relationships: internal and external. These include autonomy-connection, novelty-predictability, openness-closedness.
Dialectic
Within Hegelianism, the word "dialectic" has the specialised meaning of a contradiction between ideas that serves as the determining factor in their relationship. Dialectic comprises three stages of development: first, a thesis or statement of an idea, which gives rise to a second step, a reaction or antithesis that contradicts or negates the thesis, and third, the synthesis, a statement through which the differences between the two points are resolved. Dialectical materialism, a theory or set of theories produced mainly by Karl Marx and Friedrich Engels, adapted the Hegelian dialectic into arguments regarding traditional materialism.
Lexical approach
The lexical approach is a method of teaching foreign languages described by Michael Lewis in the early 1990s. The basic concept on which this approach rests is the idea that an important part of learning a language consists of being able to understand and produce lexical phrases as chunks. Students are thought to be able to perceive patterns of language (grammar) as well as have meaningful set uses of words at their disposal when they are taught in this way.
Pragma-dialectics
To allow for the systematic integration of the pragmatic and dialectical dimensions in the study of argumentation, the pragma-dialectical theory uses four meta-theoretical principles as its point of departure: functionalization, socialization, externalization and dialectification. Functionalization is achieved by treating discourse as a purposive act. Socialization is achieved by extending the speech act perspective to the level of interaction. Externalization is achieved by capturing the propositional and interactional commitments created by the speech acts performed. And dialectification is achieved by regimenting the exchange of speech acts to an ideal model of a critical discussion. (see Van Eemeren & Grootendorst, 2004, pp.52-53).
Dialectical research
Dialectical research may also be thought of as the opposite of empirical research, in that the researcher is working with arguments and ideas, rather than data. Indeed Bertell Ollman (1993) argues that all research is either dialectical or nondialectical. Dialectical research may be applied to a range of problems. For instance, Eli Berniker and David McNabb (2006) argue for the application of dialectical research for the study of organizational processes, and James Page (2008) has used a dialectical research method to develop a philosophy of peace education.
Dialectician
A dialectician is a philosopher who views the world in terms of complementary opposites and the interactions thereof. In popular usage, the central feature of dialectic is the concept of "thesis, antithesis, synthesis" - when an idea or phenomenon (thesis) arises, it carries within itself the seed of its opposite (antithesis), and the interplay of these polarities leads to a synthesis which is somehow beyond the scope of either polarity alone. In turn, the synthesis is now itself a new thesis, and the entire process can begin again.
Delta method
The delta method is often used in a form that is essentially identical to that above, but without the assumption that or "B" is asymptotically normal. Often the only context is that the variance is "small". The results then just give approximations to the means and covariances of the transformed quantities. For example, the formulae presented in Klein (1953, p. 258) are:
Lutheran scholasticism
Some Lutheran scholastic theologians, for example, Johann Gerhard, used exegetical theology along with Lutheran scholasticism. However, in Calov, even his exegesis is dominated by his use of the analytic method With Johann Friedrich König and his student Johannes Andreas Quenstedt, scholastic Lutheran theology reached its zenith. However the 20th century Lutheran scholar Robert Preus was of the opinion that König went overboard with the scholastic method by overloading his small book, "Theologia Positiva Acroamatica" with Aristotelian distinctions. He noted that the scholastic method was inherently loaded with pitfalls. In particular, dogmaticians sometimes established cause and effect relationships without suitable links. When dogmaticians forced mysteries of the faith to fit into a strict cause and effect relationships, they created "serious inconsistencies". In addition, sometimes they drew unneeded or baseless conclusions from the writings of their opponents, which not only was unproductive, but also harmed their own cause more than that of their rivals. Later orthodox dogmaticians tended to have an enormous number of artificial distinctions.
Dialogical analysis
Dialogical analysis, or more precisely dialogical interaction analysis, refers to a way of analyzing human communication which is based on the theory of dialogism. The approach has been developed based on the theoretical work of George Herbert Mead and Bakhtin.
Critical communicative methodology
This methodology has been used in international research projects such as Workaló (2001–2004); which is a Research and Technological Development (RTD) that forms part of the Fifth European Union Framework Programme; or INCLUD-ED (2006–2011), which is an Integrated Project of the Sixth Framework Programme.The main results of the Workaló project as well as different proposals with the objective of defining strategies for the inclusion of cultural minorities focusing on the Romani Community; were presented on 29 September 2004 in the Workaló Conference in Brussels. More recently, the results of the INCLUD-ED project, were disseminated across Europe, on 18 November 2009, in a Conference at the European Parliament, in Brussels, as well.
In addition, the critical communicative methodology was introduced in the First International Congress of Quality Inquiry (May 2005) celebrated in the University of Illinois at Urbana- Champaign in May, 2010. The last edition (2010) has incorporated a round table about this methodology.
Dialectical behavior therapy
A Duke University study of compared treatment of depression by antidepressant medication to treatment by antidepressants and dialectical behavior therapy. A total of 34 chronically depressed individuals over age 60 were treated for 28 weeks. Six months after treatment, statistically-significant differences were noted in remission rates between groups, with a greater percentage of patients treated with antidepressants and dialectical behavior therapy in remission.
Relationship aspect
Within the argumentation, the relationship to the use of the relationship aspect is based on emotional arguments which are supported by preconceptions, personal references, experience and the credibility of the speaker. The logically valid deductive reasoning on the other hand completely excludes the relationship aspect between speaker and audience. Since Plato, dialectics has established itself as a school of argumentation. Dialectics aims to promote an inner understanding and willingness to compromise, comprising three stages of development: a thesis, an antithesis and a synthesis.
Peter Trudgill
Trudgill is a well-known authority on dialects, as well as being one of the first to apply Labovian sociolinguistic methodology in the UK, and to provide a framework for studying dialect contact phenomena.
Dialogic pedagogy
Although modern interest in dialogic pedagogy seems to emerge only in the 1960s, it was a very old and probably widespread educational practice. Perhaps one of the best known examples of dialogic pedagogy in the Ancient times is the Socratic method described by his student Plato. However, dialogic practices and dialogic pedagogy existed in Ancient Greece, before, during, and after Socrates' time, possibly in other forms than those depicted by Plato. There has been a long tradition of dialogic pedagogy, called Chavruta/Chavrusa/Havruta, in Jewish Yeshivas, involving dialogic studies of Talmudic texts, that goes back to the eras of the Tannaim (Rabbis of the Mishnaic period, 10-220 CE). Economist Amartya Sen argues that dialogic pedagogy has been well situated within the Indian religious and civic traditions and spread across Asia with the rise of Buddhism.
Georg Simmel
A dialectical approach is multicausal, multidirectional, integrates facts and value, rejects the idea that there are hard and fast dividing lines between social phenomena, focuses on social relations, looks not only at the present but also at the past and future, and is deeply concerned with both conflicts and contradictions. Simmel’s sociology was concerned with relationships—especially interaction—and was known as a “methodological relationist”. This approach is based on the idea that interactions exist between everything. Overall, he was mostly interested in dualisms, conflicts, and contradictions in whatever realm of the social world he happened to be working on.
Jacobi method
In numerical linear algebra, the Jacobi method is an iterative algorithm for determining the solutions of a diagonally dominant system of linear equations. Each diagonal element is solved for, and an approximate value is plugged in. The process is then iterated until it converges. This algorithm is a stripped-down version of the Jacobi transformation method of matrix diagonalization. The method is named after Carl Gustav Jacob Jacobi.
Naive dialecticism
Naïve dialecticism research has arisen primarily out of the holistic/ analytic tradition of cultural research, which compares cultures on the basis of cognitive styles. These cognitive styles are general ways of interpretation that are adopted, and often similar within a culture. Holism is a characteristic that is generally applied to East Asian cultures, while Western cultures are more often characterized by analytic thinking. This means that Westerners tend to deconstruct something into parts to understand it, while East Asians tend to look at the entire phenomena as a whole and attempt to understand the relationships that bind each facet to every other and to the phenomena as a whole.
René Debrie
Debrie began his research career in 1950. In the years 1960-1980, it is one of the masters of dialectology of Picard whom he greatly enriched by his work. He has published numerous books and lexicons of dialectology. 
He is an assistant professor in 1975 at the University of Picardie and professor in 1979.
Explicit and implicit methods
Since the implicit method cannot be carried out for each kind of differential operator, it is sometimes advisable to make use of the so called operator splitting method, which means that the differential operator is rewritten as the sum of two complementary operators
while one is treated explicitly and the other implicitly.
For usual applications the implicit term is chosen to be linear while the explicit term can be nonlinear. This combination of the former method is called Implicit-Explicit Method (short IMEX ).
Dialectician
Historically, dialecticians and dialectical thought have been primarily associated with Marxism, as the philosophical grounding of Marxism is based on a materialist interpretation of Hegelian dialectic. However, individuals widely recognized as dialecticians exist outside of Marxism. Indeed, dialectic is at least as old as Plato, who argues that it is the process by which one ascends the divided line (cf. "Republic" book VI) to reach the "unhypothetical first principle of everything." Plotinus, too, argued that dialectic was necessary in order to become Intellect, the second hypostasis, in the soul's search for the One.
Diasystem
The term "diasystem" was coined by linguist and dialectologist Uriel Weinreich in a 1954 paper as part of an initiative in exploring how to extend advances in structuralist linguistic theory to dialectology to explain linguistic variation across dialects. Weinreich's paper inspired research in the late 1950s to test the proposal. However, the investigations soon showed it to be generally untenable, at least under structuralist theory. With the advent of generative theory in the 1960s, researchers tried applying a generative approach in developing diasystemic explanations; this also fell short.
Development communication
Melafopulos (2008) presented two modes or approaches to development communication: the monologic mode and the dialogic mode. The monologic mode is linked to the standpoint of 'diffusion' following the one-way model of communication. The purpose of this mode is to disseminate information and messages to persuade its recipients about the intended change. In short, communication is positioned to (1) inform and (2) persuade. In this model, the feedback is enhanced and canned allowing the sender to refine its persuasive message. On the other hand, dialogic mode is related with the participatory paradigm which follows a two-way communication model. It seeks to create a conducive environment where stakeholders are involved in all stages of the project from the definitions down to the implementation of solutions. This model seeks to make use of communication (1) to assess and (2) to empower. The use of dialogic communication paves the way for building of trust and understanding which is the key to participation and eventually for the empowerment of the people in the grassroots.
Thesis, antithesis, synthesis
The relation between the three abstract terms of the triad, also known as the dialectical method, is summarized in the following way in the "Encyclopedia of Sciences and Religions":
(1) a beginning proposition called a thesis, (2) a negation of that thesis called the antithesis, and (3) a synthesis whereby the two conflicting ideas are reconciled to form a new proposition.
Dialectometry
Dialectometry is the quantitative and computational branch of dialectology, the study of dialect. This sub-field of linguistics studies language variation using the methods of statistics; it arose in the 1970s and 80s as a result of seminal work by J. Séguy and H. Goebl.
Newton's method
with derivative
Dialectical materialism
Some evolutionary biologists, such as Richard Lewontin and the late Stephen Jay Gould, have tried to employ dialectical materialism in their approach. They view dialectics as playing a precautionary heuristic role in their work. From Lewontin's perspective, we get this idea:
Dialectical materialism is not, and never has been, a programmatic method for solving particular physical problems. Rather, a dialectical analysis provides an overview and a set of warning signs against particular forms of dogmatism and narrowness of thought. It tells us, "Remember that history may leave an important trace. Remember that being and becoming are dual aspects of nature. Remember that conditions change and that the conditions necessary to the initiation of some process may be destroyed by the process itself. Remember to pay attention to real objects in time and space and not lose them in utterly idealized abstractions. Remember that the qualitative effects of context and interaction may be lost when phenomena are isolated". And above all else, "Remember that all the other caveats are only reminders and warning signs whose application to different circumstances of the real world is contingent."
Gould shared similar views regarding a heuristic role for dialectical materialism. He wrote that:
Frankfurt School
For their part, Frankfurt School theorists quickly came to realize that a dialectical method could only be adopted —that is to say, if they adopted a self-correcting method—a dialectical method that would enable them to correct previous false dialectical interpretations. Accordingly, critical theory rejected the historicism and materialism of orthodox Marxism. Indeed, the material tensions and class struggles of which Marx spoke were no longer seen by Frankfurt School theorists as having the same revolutionary potential within contemporary Western societies—an observation that indicated that Marx's dialectical interpretations and predictions were either incomplete or incorrect.
Discontinuous Galerkin method
The origin of the DG method for elliptic problems cannot be traced back to a single publication as features such as jump penalization in the modern sense were developed gradually. However, among the early influential contributors were Babuška, J.-L. Lions, Nitsche and Miloš Zlámal. DG methods for elliptic problems were already developed in a paper by Baker in the setting of 4th order equations in 1977. A more complete account of the historical development and an introduction to DG methods for elliptic problems is given in a publication by Arnold, Brezzi, Cockburn and Marini. A number of research directions and challenges on DG methods are collected in the proceedings volume edited by Cockburn, Karniadakis and Shu.
Dialectical monism
Dialectical monism has been mentioned in Western literature, although infrequently. Jean-Paul Sartre used the term on at least one occasion. Sartre may have used the term "dialectical monism" to when inferring what he saw as absurd in the dogma of a Marxist–Leninist non-dualistic interpretation of the dialectic, in which any oppositional view point was claimed to be non-dialectical rather than part of the dialectic itself.
Didactic method
With the advent of globalisation at the beginning of the 20th century, however, the arguments for such relative philosophical aspects in the methods of teaching started to diminish somewhat. It is therefore possible to categorise didactics and pedagogy as a general analytic theory on three levels:Didactic method provides students with the required theoretical knowledge. It is an effective method used to teach students who are unable to organize their work and depend on the teachers for instructions. It is also used to teach basic skills of reading and writing. The teacher or the literate is the source of knowledge and the knowledge is transmitted to the students through didactic method.
Discourse grammar
Being a relatively young framework, DG has so far found only limited applications. Work has focused mainly on comment clauses, discourse markers, final particles, and insubordination. Furthermore, DG as a descriptive tool has for the most part been restricted to the study of English. Analysis within this framework is now being extended to non-European languages. More detailed research has been carried out already on Akie, a traditional hunter-gatherer language of the Nilotic family spoken in north-central Tanzania. A grammar of this language based on DG has been published, the use of theticals in the organization of texts has been studied, and institutional frames surfacing from the analysis of Akie texts have been identified using Thetical Grammar as a basis.
Pragma-dialectics
In pragma-dialectics, argumentation is viewed as a communicative and interactional discourse phenomenon that is to be studied from a normative as well as a descriptive perspective. The dialectical dimension is inspired by normative insights from “critical rationalism” and formal dialectics, the pragmatic dimension by descriptive insights from speech act theory, Gricean language philosophy and discourse analysis.
Dialectic
Neo-orthodoxy, in Europe also known as theology of crisis and dialectical theology, is an approach to theology in Protestantism that was developed in the aftermath of the First World War (1914–1918). It is characterized as a reaction against doctrines of 19th-century liberal theology and a more positive reevaluation of the teachings of the Reformation, much of which had been in decline (especially in western Europe) since the late 18th century. It is primarily associated with two Swiss professors and pastors, Karl Barth (1886–1968) and Emil Brunner (1899–1966), even though Barth himself expressed his unease in the use of the term.
Dialectology
The first comparative dialect study in Germany was "The Dialects of Bavaria" by Johann Andreas Schmeller, which included a linguistic atlas. In 1876, Georg Wenker sent postal questionnaires out over Northern Germany. These postal questionnaires contained a list of sentences written in Standard German. These sentences were then transcribed into the local dialect, reflecting dialectal differences. Many studies proceeded from this, and over the next century dialect studies were carried out all over the world. Joseph Wright produced the six-volume "English Dialect Dictionary" in 1905.
Traditional studies in Dialectology were generally aimed at producing dialect maps, whereby imaginary lines were drawn over a map to indicate different dialect areas. The move away from traditional methods of language study however caused linguists to become more concerned with social factors. Dialectologists therefore began to study social, as well as regional variation. The "Linguistic Atlas of the United States" (1930s) was amongst the first dialect studies to take social factors into account.
Speech shadowing
The speech shadowing technique is used in dichotic listening tests. The first one to apply this technique was E. Colin Cherry in 1953. During dichotic listening tests, subjects are presented with two different messages, one in their right ear and one in their left. The participants are often asked to focus on only one of the different messages and this is where the speech shadowing technique is used. Participants are instructed to shadow the attended message by repeating it out loud with a delay of a few seconds between hearing a word and repeating the word. The speech shadowing technique is significant for these experiments because it ensures that the subjects are attending to the desired message. Various other stimuli are then presented to the other ear, and subjects are afterwards queried on what they can recall from the other message.
Historical materialism
In the early years of the 20th century, historical materialism was often treated by socialist writers as interchangeable with dialectical materialism, a formulation never used by Marx or Engels. According to many Marxists influenced by Soviet Marxism, historical materialism is a specifically sociological method, while dialectical materialism refers to the more general, abstract philosophy underlying Marx and Engels' body of work. This view is based on Joseph Stalin's pamphlet "Dialectical and Historical Materialism", as well as textbooks issued by the Institute of Marxism-Leninism of the Central Committee of the Communist Party of the Soviet Union.
Socratic method
Plato famously formalized the Socratic elenctic style in prose—presenting Socrates as the curious questioner of some prominent Athenian interlocutor—in some of his early dialogues, such as "Euthyphro" and "Ion", and the method is most commonly found within the so-called "Socratic dialogues", which generally portray Socrates engaging in the method and questioning his fellow citizens about moral and epistemological issues. But in his later dialogues, such as Theaetetus or Sophist, Plato had a different method to philosophical discussions, namely dialectic.
Reflectance difference spectroscopy
The method was introduced in 1956 for the study optical properties of the cubic semiconductors silicon and germanium. Due to its high surface sensitivity and independence of ultra-high vacuum, its use has been expanded to in situ monitoring of epitaxial growth or the interaction of surfaces with adsorbates. To assign specific features in the signal to their origin in morphology and electronic structure, theoretical modelling by density functional theory is required.
Critical communicative methodology
Research methodology based on intersubjective dialogue and an egalitarian relationship between the research team and those being researched (Gomez & Latorre, 2005).Current societies are characterized for using dialogue in different domains, seeing it as necessary for social progress and for avoiding different social conflicts (Castells 1996; Flecha, Gómez & Puigvert, 2003; Habermas, 2000). Critical communicative methodology is characterized for its dialogic orientation in different aspects of the research (Gomez & Flecha, 2004).
Mindfulness
Mindfulness is a "core" exercise used in dialectical behavior therapy (DBT), a psychosocial treatment Marsha M. Linehan developed for treating people with borderline personality disorder. DBT is dialectic, explains Linehan, in the sense of "the reconciliation of opposites in a continual process of synthesis." As a practitioner of Buddhist meditation techniques, Linehan says:
Mode deactivation therapy (MDT) is a treatment methodology that is derived from the principles of cognitive behavioral therapy and incorporates elements of Acceptance and commitment therapy, Dialectical behavior therapy, and mindfulness techniques. Mindfulness techniques such as simple breathing exercises are applied to assist the client in awareness and non-judgmental acceptance of unpleasant and distressing thoughts and feelings as they occur in the present moment. Mode Deactivation Therapy was developed and is established as an effective treatment for adolescents with problem behaviors and complex trauma-related psychological problems, according to recent publications by Jack A. Apsche and Joan Swart.
Didactic method
A didactic method ( "didáskein", "to teach") is a teaching method that follows a consistent scientific approach or educational style to present information to students. The didactic method of instruction is often contrasted with dialectics and the Socratic method; the term can also be used to refer to a specific didactic method, as for instance constructivist didactics.
Rudolf Podgornik
Podgornik and coworkers discovered the line hexatic phase in the phase diagram of the concentrated long fragment DNA solutions . The line hexatic mesophase appears to be the preferred packing form of long DNA in bacteriophages. He is the author of more than two hundred scientific papers  and a coeditor of books: "Electrostatic Effects in Soft Matter"  (Proceedings of the NATO Advanced Study Institute, Les Houches, France, 1–13 October 2000, Series: NATO Science Series II: Mathematics, Physics and Chemistry, Vol. 46 ), together with Christian Holm and Patrick Kekicheff and "Electrostatics of Soft and Disordered Matter"  (Pan Stanford Publishing, March 31, 2014) with 
David S. Dean, Jure Dobnikar and Ali Naji. Together with D. Harries, J. DeRouchey, H. H. Strey, and V. A. Parsegian, he coauthored the chapter "Interactions in Macromolecular Complexes Used as Nonviral Vectors for Gene Delivery", in the leading textbook of gene therapy: "Gene Therapy: Therapeutic Mechanisms and Strategies" , N. Smyth – Templeton, Marcel Dekker, New York (2008), Third Edition.
Self-compassion
Dialectical behavior therapy (DBT), is a derivative of cognitive behavior therapy that incorporates Eastern meditative practice. DBT is based on a dialectical world view that incorporates the balance and integration of opposing beliefs, particularly in acceptance and change. We accept ourselves as good enough, and we recognize the need for all of us to change and grow. Unlike MBCT and MBSR therapies, dialectical behavior therapy does not use meditation but less formal exercises, such as individual therapy sessions and group skill sessions. In general last for approximately a year where participants will engage in weekly individual skill therapy sessions and group skill sessions. The skills therapy sessions include four segments; core mindfulness, interpersonal effectiveness, emotion regulation, and distress tolerance skills. Dialectical behaviour therapist recommend developing self-compassion. The basic premise of using self-compassion therapies in DBT is to cultivate a compassionate mind state, defined by feelings of warmth, safety, presence and interconnectedness that can in turn relieve emotional dysregulation.
Dialectique de la dialectique
It called for the preservation of the surrealist movement in a "constantly revolutionary state" to counter the decline of the movement. It begins by criticising the then movement's "artistic deviation" and "the petrification of its revolutionary effort". Following this it makes a statement as to how artist's can counter this: by "constantly surpass[ing] itself". Love is declared to be the "principal method of knowledge and action" for the artists. Finally the artists declare the need to ""revolt against nature and dissolving the oedipal complex in order to liberate love"".
Nothing
Georg Wilhelm Friedrich Hegel (1770–1831) is the philosopher who brought the dialectical method to a new pinnacle of development. According to Hegel in "Science of Logic", the dialectical methods consists of three steps. First, a thesis is given, which can be any proposition in logic. Second, the antithesis of the thesis is formed and, finally, a synthesis incorporating both thesis and antithesis. Hegel believed that no proposition taken by itself can be completely true. Only the whole can be true, and the dialectical synthesis was the means by which the whole could be examined in relation to a specific proposition. Truth consists of the whole process. Separating out thesis, antithesis, or synthesis as a stand-alone statement results in something that is in some way or other untrue. The concept of "nothing" arises in Hegel right at the beginning of his "Logic". The whole is called by Hegel the "Absolute" and is to be viewed as something spiritual. Hegel then has:
Derek Brueckner
Specifically the dialectic explores a reaffirmation of painting/drawing involving either in collaboration or against technology and this dialectic’s relation to the body and modes of interpretation and depiction of imagery. Currently Brueckner is an instructor at the University of Manitoba. View work by Brueckner's students at http://www.derekbrueckner.com/courses. Lectures and panel discussions include a panel discussion at the 2008 College Art Association Conference in Dallas (The Search for Vision's Body: The Role of Touch in the Practice of Painting and Architecture
Wednesday, February 20, 2008, 2:30 PM–5:00 PM session). As well Brueckner co-hosts and curates an arts talk radio show in Winnipeg at CKUW 95.9 FM.
He has a Master of Fine Arts from Hunter College City University of New York Department of Art.
Dialectic
Moreover, the term "dialectic" owes much of its prestige to its role in the philosophies of Socrates and Plato, in the Greek Classical period (5th to 4th centuries BCE). Aristotle said that it was the pre-Socratic philosopher Zeno of Elea who invented dialectic, of which the dialogues of Plato are the examples of the Socratic dialectical method.
Essay
In the dialectic form of the essay, which is commonly used in philosophy, the writer makes a thesis and argument, then objects to their own argument (with a counterargument), but then counters the counterargument with a final and novel argument. This form benefits from presenting a broader perspective while countering a possible flaw that some may present. This type is sometimes called an ethics paper.
Catuṣkoṭi
Wayman (1977) proffers that the Catuṣkoṭi may be employed in different ways and often these are not clearly stated in discussion nor the tradition. Wayman (1977) holds that the Catuṣkoṭi may be applied in suite, that is all are applicable to a given topic forming a paradoxical matrix; or they may be applied like trains running on tracks (or employing another metaphor, four mercury switches where only certain functions or switches are employed at particular times). This difference in particular establishes a distinction with the Greek tradition of the Tetralemma. Also, predicate logic has been applied to the Dharmic Tradition, and though this in some quarters has established interesting correlates and extension of the logico-mathematical traditions of the Greeks, it has also obscured the logico-grammatical traditions of the Dharmic Traditions of Catuṣkoṭi within modern English discourse.
Dialectic
Dialectic or dialectics (, "dialektikḗ"; related to dialogue), also known as the dialectical method, is at base a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned arguments. Dialectic resembles debate, but the concept excludes subjective elements such as emotional appeal and the modern pejorative sense of rhetoric. Dialectic may be contrasted with the didactic method, wherein one side of the conversation teaches the other. Dialectic is alternatively known as minor logic, as opposed to major logic or critique.
Probabilistic method
when
Socratic method
The Socratic method, also known as maieutics, method of elenchus, elenctic method, or Socratic debate, is a form of cooperative argumentative dialogue between individuals, based on asking and answering questions to stimulate critical thinking and to draw out ideas and underlying presuppositions. It is a dialectical method, involving a discussion in which the defense of one point of view is questioned; one participant may lead another to contradict themselves in some way, thus weakening the defender's point. This method is named after the Classical Greek philosopher Socrates and is introduced by him in Plato's Theaetetus as midwifery (maieutics) because it is employed to bring out definitions implicit in the interlocutors' beliefs, or to help them further their understanding.
Constructive developmental framework
Kegan (1982) described five stages of development, of which the latter four are progressively attained only in adulthood. Basseches (1984) showed that adults potentially transcend formal logical thinking by way of dialectical thinking, in four phases, measurable by a fluidity index. Both Kegan's and Basseches' findings were updated and refined by Laske in 2005 and 2008 respectively. In 2008 and 2015, Laske proposed that dialectical thought forms are an instantiation of Bhaskar's "four moments of dialectic" (MELD; Bhaskar 1993), and that these ontological moments form a sequence M→E→L→D that underlies individual cognitive development (Laske 2015), providing a basis for a dialectical cognitive science as well as a cognitively oriented management science. Based on the concept of 'dialogical dialectic', Laske stressed the need for a dialogical, in contrast to a monological, social science.The CDF methodology involves three separate instruments that respectively measure a person's social–emotional stage ('what should I do and for whom?'), cognitive level of development ('what can I know and what therefore are my options?'), and psychological profile ('how am I doing right now?'). The first two tools (ED, CD) provide an epistemological, the third (NP) a psychological, perspective on a person or team. See the list of references below.
Socrates
An alternative interpretation of the dialectic is that it is a method for direct perception of the Form of the Good. Philosopher Karl Popper describes the dialectic as "the art of intellectual intuition, of visualising the divine originals, the Forms or Ideas, of unveiling the Great Mystery behind the common man's everyday world of appearances." In a similar vein, French philosopher Pierre Hadot suggests that the dialogues are a type of spiritual exercise. Hadot writes that "in Plato's view, every dialectical exercise, precisely because it is an exercise of pure thought, subject to the demands of the Logos, turns the soul away from the sensible world, and allows it to convert itself towards the Good."
Dynamic debugging technique
The first version of DDT was developed at MIT for the PDP-1 computer in 1961, but newer versions on newer platforms continued to use the same name. After being ported to other vendor's platforms and changing media, the name was changed to the less DEC-centric version.
Johann Heinrich Alsted
Q. Is it true that the seven dialectical theories of method in use today, to wit, i) the Aristotelian, 2) the Lullian, 3) the Ramistic, 4) the Mixt, whether indeed in the manner of Keckermann or of Alsted, 5) the Forensic of Hotman, 6) the Jesuitic, and 7) the Socinian, differ mostly in respect to manner of treatment, not in respect to 
purpose?
Frankfurt School
The Institute also attempted to reformulate dialectics as a concrete method. The use of such a dialectical method can be traced back to the philosophy of Hegel, who conceived dialectic as the tendency of a notion to pass over into its own negation as the result of conflict between its inherent contradictory aspects. In opposition to previous modes of thought, which viewed things in abstraction, each by itself and as though endowed with fixed properties, Hegelian dialectic has the ability to consider ideas according to their movement and change in time, as well as according to their interrelations and interactions.
Domain decomposition methods
In non-overlapping methods, the subdomains intersect only on their interface. In primal methods, such as Balancing domain decomposition and BDDC, the continuity of the solution across subdomain interface is enforced by representing the value of the solution on all neighboring subdomains by the same unknown. In dual methods, such as FETI, the continuity of the solution across the subdomain interface is enforced by Lagrange multipliers. The FETI-DP method is hybrid between a dual and a primal method.
Dialectic
In contradiction to Hegelian idealism, Marx presented his own dialectic method, which he claims to be "direct opposite" of Hegel's method:
Dialectic
In Marxism, the dialectical method of historical study became intertwined with historical materialism, the school of thought exemplified by the works of Marx, Engels, and Vladimir Lenin. In the USSR, under Joseph Stalin, Marxist dialectics became "diamat" (short for dialectical materialism), a theory emphasizing the primacy of the material way of life; social "praxis" over all forms of social consciousness; and the secondary, dependent character of the "ideal". The term "dialectical materialism" was coined by the 19th-century social theorist Joseph Dietzgen who used the theory to explain the nature of socialism and social development. The original populariser of Marxism in Russia, Georgi Plekhanov used the terms "dialectical materialism" and "historical materialism" interchangeably. For Lenin, the primary feature of Marx's "dialectical materialism" (Lenin's term) was its application of materialist philosophy to history and social sciences. Lenin's main input in the philosophy of dialectical materialism was his theory of reflection, which presented human consciousness as a dynamic reflection of the objective material world that fully shapes its contents and structure. Later, Stalin's works on the subject established a rigid and formalistic division of Marxist–Leninist theory in the dialectical materialism and historical materialism parts. While the first was supposed to be the key method and theory of the philosophy of nature, the second was the Soviet version of the philosophy of history.
Schwarz alternating method
In the 1950s Schwarz's method was generalized in the theory of partial differential equations to an iterative method for finding the solution of a elliptic boundary value problem on a domain which is the union of two overlapping subdomains. It involves solving the boundary value problem on each of the two subdomains in turn, taking always the last values of the approximate solution as the next boundary conditions. In numerical analysis, a modification of the method, known as the additive Schwarz method, has become a practical domain decomposition method. An abstract formulation of the original method is then referred to as the multiplicative Schwarz method.
Balancing domain decomposition method
In numerical analysis, the balancing domain decomposition method (BDD) is an iterative method to find the solution of a symmetric positive definite system of linear algebraic equations arising from the finite element method. In each iteration, it combines the solution of local problems on non-overlapping subdomains with a coarse problem created from the subdomain nullspaces. BDD requires only solution of subdomain problems rather than access to the matrices of those problems, so it is applicable to situations where only the solution operators are available, such as in oil reservoir simulation by mixed finite elements. In its original formulation, BDD performs well only for 2nd order problems, such elasticity in 2D and 3D. For 4th order problems, such as plate bending, it needs to be modified by adding to the coarse problem special basis functions that enforce continuity of the solution at subdomain corners, which makes it however more expensive. The BDDC method uses the same corner basis functions as, but in an additive rather than multiplicative fashion. The dual counterpart to BDD is FETI, which enforces the equality of the solution between the subdomain by Lagrange multipliers. The base versions of BDD and FETI are not mathematically equivalent, though a special version of FETI designed to be robust for hard problems has the same eigenvalues and thus essentially the same performance as BDD.
Language education
Most books on language teaching list the various methods that have been used in the past, often ending with the author's new method. These new methods are usually presented as coming only from the author's mind, as the authors generally give no credence to what was done before and do not explain how it relates to the new method. For example, descriptive linguists seem to claim unhesitatingly that there were no scientifically based language teaching methods before their work (which led to the audio-lingual method developed for the U.S. Army in World War II). However, there is significant evidence to the contrary. It is also often inferred or even stated that older methods were completely ineffective or have died out completely, though in reality even the oldest methods are still in use (e.g. the Berlitz version of the direct method). Proponents of new methods have been so sure that their ideas are so new and so correct that they could not conceive that the older ones have enough validity to cause controversy. This was in turn caused by emphasis on new scientific advances, which has tended to blind researchers to precedents in older work.(p. 5)
Dialogical analysis
Dialogical analysis is an interpretative methodology which closely analyzes spoken or written utterances or actions for their embedded communicative significance. Questions typically asked during a dialogical analysis include: What does each interactant think about themselves, the other and what the other thinks of them? What do the given utterances and actions imply about the given activity or participants? Why was a given communicative act performed – why did it need to be said? What was the alternative that the utterance was trying to dispel? People are often borrowing words, phrases and ideas from other people, and accordingly, dialogical analysis often asks: who is doing the talking? Specifically, which voices and echoes are evident in the given utterance?
Nausiphanes
The man who employs continuous discourse will be best able to employ the dialectic method and vice versa, because both depend on an accurate judgement of how to lead pupils from the known to the unknown; that is, they depend upon a knowledge of the 'right time' and 'right measure' in speaking.
Perceptual dialectology
Historical perceptual dialectology allows linguists to examine how and why dialects in the past gained popularity. Linguists gain the chance to examine how the perceptual dialectology of certain dialects of languages have evolved over a given time. The principal scholar examining perceptual dialectology is Dennis Preston, and his methodology involves interview-based techniques. Applying the initial methodology used in the field of perceptual dialectology would be impossible when examining the dialects of the past.
Dialectic
Dialectic tends to imply a "process" of evolution and so does not naturally fit within formal logic (see logic and dialectic). This process is particularly marked in Hegelian dialectic and even more so in Marxist dialectic which may rely on the evolution of ideas over longer time periods in the real world; dialectical logic attempts to address this.
Perceptual dialectology
Perceptual dialectology studies in Japan were also taking place during the early 20th century. Japanese methodology was fundamentally different from the Netherlands' in that informants were asked to judge differences between dialects on degrees of difference (for example, from 'not different' to 'incomprehensible'). Data was thus analyzed by drawing lines between areas to indicate a scale of difference, and was the first method in 'calculating' perceptual boundaries.
Abram Deborin
In 1931, Joseph Stalin decided the issue of the debate between dialecticians and mechanists by publishing a decree which identified dialectical materialism as pertaining solely to Marxism-Leninism. He then codified it in "Dialectical and Historical Materialism" (1938) by enumerating the "laws of dialectics", which are the grounds of particular disciplines and in particular of the science of history, and which guarantees their conformity to the "proletarian conception of the world". Thus, "diamat" was imposed on most Communist parties affiliated to the Third International. Diamat became the official philosophy of the Soviet Union and remained as such until its dissolution. When Stalin decided in favor of dialectical materialism, Deborin made a show of support for Stalin's position. For some years afterwards, Deborin kept a low profile, and most of his writings were suppressed. However, he lived long enough to see all of his works republished in the Soviet Union during the "thaw" under Nikita Khrushchev.
Perceptual dialectology
The little arrow method is an early method for comparing regional dialects. In the little arrows method, researchers begin with a general map of a region, often with traditional linguistic dialect boundaries indicated for reference. Then, informants from several sites are asked how similar they believe the language of other sites is to their own. Sites which participants indicate as being extremely similar are connected by a "little arrow." By gathering responses from several informants and sites, these "little arrows" connect to form networks of related languages. From this information, information on perceptual dialectical boundaries can be drawn. Perceptual dialect categories consist of areas linked together by the "little arrows," and dialect borders are indicated when there are no connections between sites. These informant-perceived categories can then be compared to more traditional linguistic boundaries for further analysis.
Dialectical logic
During the Sino-Soviet split, dialectical logic was used in China as a symbol of Marxism–Leninism against the Soviet rehabilitation of formal logic.
Dialectical materialism
For Marx, dialectics is not a formula for generating predetermined outcomes but is a method for the empirical study of social processes in terms of interrelations, development, and transformation. In his introduction to the Penguin edition of Marx's "Capital", Ernest Mandel writes, "When the dialectical method is applied to the study of economic problems, economic phenomena are not viewed separately from each other, by bits and pieces, but in their inner connection as an integrated totality, structured around, and by, a basic predominant mode of production."
Meshfree methods
In the 1990s a new class of meshfree methods emerged based on the Galerkin method. This first method called the diffuse element method (DEM), pioneered by Nayroles et al., utilized the MLS approximation in the Galerkin solution of partial differential equations, with approximate derivatives of the MLS function. Thereafter Belytschko pioneered the Element Free Galerkin (EFG) method, which employed MLS with Lagrange multipliers to enforce boundary conditions, higher order numerical quadrature in the weak form, and full derivatives of the MLS approximation which gave better accuracy. Around the same time, the reproducing kernel particle method (RKPM) emerged, the approximation motivated in part to correct the kernel estimate in SPH: to give accuracy near boundaries, in non-uniform discretizations, and higher-order accuracy in general. Notably, in a parallel development, the Material point methods were developed around the same time which offer similar capabilities. Material point methods are widely used in the movie industry to simulate large deformation solid mechanics, such as snow in the movie Frozen. RKPM and other meshfree methods were extensively developed by Chen, Liu, and Li in the late 1990s for a variety of applications and various classes of problems . During the 1990s and thereafter several other varieties were developed including those listed below.
Comparative linguistics
The earliest method of this type was the comparative method, which was developed over many years, culminating in the nineteenth century. This uses a long word list and detailed study. However, it has been criticized for example as being subjective, being informal, and lacking testability. The comparative method uses information from two or more languages and allows reconstruction of the ancestral language. The method of internal reconstruction uses only a single language, with comparison of word variants, to perform the same function. Internal reconstruction is more resistant to interference but usually has a limited available base of utilizable words and is able to reconstruct only certain changes (those that have left traces as morphophonological variations).
Paradox psychology
Even though the method was documented to be successful when working with treatment-resistance, paradoxical interventions lost favor in the late 1980s and '90s. This was due to the fact that the psychology field desired to present itself as science oriented, and pushed for 'evidence based' approaches. Since the underlying theory and mechanism for the paradoxical approach had remained an 'unsolved mystery', there was no way to promote the method in a concise and logical manner.
Dialectic
The Socratic dialogues are a particular form of dialectic known as the method of elenchus (literally, "refutation, scrutiny") whereby a series of questions clarifies a more precise statement of a vague belief, logical consequences of that statement are explored, and a contradiction is discovered. The method is largely destructive, in that false belief is exposed and only constructive in that this exposure may lead to further search for truth. The detection of error does not amount to a proof of the antithesis; for example, a contradiction in the consequences of a definition of "piety" does not provide a correct definition. The principal aim of Socratic activity may be to improve the soul of the interlocutors, by freeing them from unrecognized errors; or indeed, by teaching them the spirit of inquiry.