triad method
the triad approach to decision - making for hazardous waste sites offers a technically defensible methodology for managing decision uncertainty that leverages innovative characterization tools and strategies. the triad refers to three primary components, systematic planning, dynamic work strategies, and real - time measurement systems. if you are unfamiliar with the triad, follow the links to learn more about what makes the triad different from traditional approaches, key triad concepts, requirements for successfully implementing a triad approach, and the benefits one can expect from implementing the triad. an epa publication ,
summary of the triad approach
( pdf, 38 kb) also provides an excellent synopsis of the triad .
the triad method is a book written for homeopaths, whatever their prescribing style, who are looking for a way to approach complex cases .
using case examples, she explains the triad method and demonstrates how it can be applied in your homeopathic practice, wherever you are working .
differentiating dark triad traits within and across interpersonal circumplex surfaces. - pubmed - ncbi
► the triad method was used for ecological risk assessment of a metal contaminated site. ► the integrated risk was calculated from three lines of evidence; chemistry, toxicology and ecology. ► the triad was considered appropriate for conducting improved ecological risk assessments .
the triad approach can accelerate project schedules, reduce overall project costs, and improve project outcomes .
together, hegel believes, these characteristics make his dialectical method genuinely scientific. as he says, “the dialectical constitutes the moving soul of scientific progression” (el remark to §81). he acknowledges that a description of the method can be more or less complete and detailed, but because the method or progression is driven only by the subject matter itself, this dialectical method is the “only true method” (sl - m 54; sl - dg 33) .
in the triad method she tells her story of setting up the maun homeopathy project clinics, describes her experience of treating people there and how she developed a way of prescribing that addresses the different layers of ill health and suffering she perceived .
the triad manages hazardous waste site decision - making uncertainty through systematic planning, dynamic work strategies, and real - time measurement technologies .
• these cognitions cause distortions in the way we see things; ellis suggested it is through irrational thinking, while beck proposed the cognitive triad .
• rebt uses different methods depending on the personality of the client, in beck’s cognitive therapy, the method is based upon the particular disorder .
overview: triad is a very unique tool that allows surveyors to best fit a map, deed or coordinate system to an unlimited number of known points in considerably less time than any other method. triad will perform an analysis of all points common to two coordinate systems accurately, easily and quickly. the more points in a solution, the better it works. triad is a powerful program that is simple to learn, organizes and documents the process of analyzing a survey retracement. the surveyor can focus on professional judgment, not the tedious task of crunching numbers and comparing record verses measured data. the results are summarized with statistics .
recent discussions surrounding the dark triad (narcissism, psychopathy, and machiavellianism) have centered on areas of distinctiveness and overlap. given that interpersonal dysfunction is a core feature of dark triad traits, the current study uses self - report data from 562 undergraduate students to examine the interpersonal characteristics associated with narcissism, psychopathy, and machiavellianism on four interpersonal circumplex (ipc) surfaces. the distinctiveness of these characteristics was examined using a novel bootstrapping methodology for computing confidence intervals around circumplex structural summary method parameters. results suggest that dark triad traits exhibit distinct structural summary method parameters with narcissism characterized by high dominance, psychopathy characterized by a blend of high dominance and low affiliation, and machiavellianism characterized by low affiliation on the problems, values, and efficacies ipc surfaces. additionally, there was some heterogeneity in findings for different measures of psychopathy. gender differences in structural summary parameters were examined, finding similar parameter values despite mean - level differences in dark triad traits. finally, interpersonal information was integrated across different ipc surfaces to create profiles associated with each dark triad trait and to provide a more in - depth portrait of associated interpersonal dynamics .
there are a number of factors (e. g. , appropriate qa / qc, flexible contracting, stakeholder concurrence, etc .) that contribute to successful triad implementations .
v. a. terekhova, m. a. pukalchik, and a. s. yakovlev, “the triad approach to ecological assessment of urban soils, ” eurasian soil sci .
technological advances in field analytical methods combined with experiences gained from historical hazardous waste site cleanup work have led to the epa' s triad approach to hazardous waste site characterization, remediation, and closure .
knowledge of the genetic relatedness among individuals is essential in diverse research areas such as behavioural ecology, conservation biology, quantitative genetics and forensics. how to estimate relatedness accurately from genetic marker information has been explored recently by many methodological studies. in this investigation i propose a new likelihood method that uses the genotypes of a triad of individuals in estimating pairwise relatedness (r). the idea is to use a third individual as a control (reference) in estimating the r between two other individuals, thus reducing the chance of genes identical in state being mistakenly inferred as identical by descent. the new method allows for inbreeding and accounts for genotype errors in data. analyses of both simulated and human microsatellite and snp datasets show that the quality of r estimates (measured by the root mean squared error, rmse) is generally improved substantially by the new triadic likelihood method (tl) over the dyadic likelihood method and five moment estimators. simulations also show that genotyping errors / mutations, when ignored, result in underestimates of r for related dyads, and that incorporating a model of typing errors in the tl method improves r estimates for highly related dyads but impairs those for loosely related or unrelated dyads. the effects of inbreeding were also investigated through simulations. it is concluded that, because most dyads in a natural population are unrelated or only loosely related, the overall performance of the new triadic likelihood method is the best, offering r estimates with a rmse that is substantially smaller than the five commonly used moment estimators and the dyadic likelihood method .
forster, michael, 1993, “hegel’s dialectical method”, in the cambridge companion to hegel, frederick c. beiser (ed .), cambridge: cambridge university press, pp. 130–170 .
summary: triad is used when it is necessary to relate different coordinate systems with two or more points in common. triad provides a rigorous approach for an accurate conversion of local coordinates to a different system or, state plane coordinates from nad27 to nad83. for control surveys, use it to compare the new measured positions with previous coordinates to get
tied - in
to an existing survey instantly with confidence based on the residuals listed for each point in the solution. use it to estimate the compass and chain index necessary for retracement of ancient glo surveys. in gis applications, it is great for hooking record maps together to build a mosaic. triad has been in wide use in the us and around the world since 1991. developed by a gps / gnss consultant, geodesist and licensed boundary surveyor with over 30 years' experience. there is no exaggeration to the statement that an analysis performed with triad will accomplish in seconds, what otherwise can take hours! .
fifth, because the determination in the speculative moment grasps the unity of the first two moments, hegel’s dialectical method leads to concepts or forms that are increasingly comprehensive and universal. as hegel puts it, the result of the dialectical process
winfield, richard dien, 1990, “the method of hegel’s science of logic ”, in essays on hegel’s logic, george di giovanni (ed .), albany, ny: state university of new york, pp. 45–57 .
worries that hegel’s arguments fail to fit his account of dialectics have led some interpreters to conclude that his method is arbitrary or that his works have no single dialectical method at all (findlay 1962: 93; solomon 1983: 21). these interpreters reject the idea that there is any logical necessity to the moves from stage to stage. “ [ t ] he important point to make here, and again and again”, robert c. solomon writes, for instance ,
the cognitive triad are three forms of negative (i. e helpless and critical) thinking that are typical of individuals with depression: namely negative thoughts about the self, the world and the future. these thoughts tended to be automatic in depressed people as they occurred spontaneously .
the displacement equations for trials with motion generation and prescribed timing capabilities are developed and cast in polynomial forms. these equations are solved for five precision points using a continuation method. a detailed description of the method used to generate the solution curves is provided in the paper. two infinities of solutions can be obtained for the problem under consideration as we are solving four equations in six unknowns. the solution procedure discussed is applied to synthesize a four - bar function generating mechanisms and a six - bar mechanism .
subbian tt, flugrad dr, jr. . five position triad synthesis with applications to four - and six - bar mechanisms. asme. j. mech. des. 1993; 115 (2): 262 - 268. doi: 10. 1115 / 1. 2919186 .
the data on the pollutant content, ecological toxicity, and structural and functional specifics of soil microbial communities in urbanozem sampled in the city of kirov were used to describe the remediation effect of humic substances (lignohumate and nanomagnetitohumate). the integral index of environmental risk on contaminated and background soil sites was calculated using the triad method. based on varying chemical risk index, ecotoxicological risk index, and ecological risk index, this method proved that humic substances are able to reduce ecological toxicity and transform the ecophysiological indices of biota in urban soils. the most vivid effect of humic products has been revealed on introduction of 0. 0025 and 0. 01% mass. the biological activity of nanomagnetitohumate and lignohumate, rather than their ability to bind toxicants, is apparently the principal factor controlling their remediating effect .
this volume presents recent advances in the field of matrix analysis based on contributions at the mat - triad 2015 conference. topics covered include interval linear algebra and computational complexity, birkhoff polynomial basis, tensors, graphs, linear pencils, k - theory and statistic inference, showing the ubiquity of matrices in different mathematical areas .
error trapping: the preference in retracing another survey is to quickly identify acceptable monuments. a unique feature of triad is its optimized blunder detection routine. this routine will instantaneously identify individual points contributing the greatest errors when fitting one system of coordinates with common points to another. simply remove the unacceptable points to obtain the best solution .
when i started visiting botswana and set up the maun homeopathy project in 2002 i faced the challenge of treating people living with hiv and aids. there i developed the “triad method of prescribing” which addresses three main layers of health to give as much homeopathic healing support as possible to clients who were struggling with a life - threatening condition. this approach does not attempt to cure hiv or aids but rather aims to support the individual living with the many stresses of this debilitating disease. the maun homeopathy project has now been running for 10 years and along with the other volunteer homeopaths we have treated over 3, 000 people there .
lauer warns us against dismissing the idea that there is any implication or necessity in hegel’s method at all (lauer 1976: 3). (other scholars who also believe there is a logical necessity to the dialectics of the phenomenology include hyppolite 1974: 78–9 and h. s. harris 1997: xii. )
there are several features of this account that hegel thinks raise his dialectical method above the arbitrariness of plato’s dialectics to the level of a genuine science. first, because the determinations in the moment of understanding sublate themselves, hegel’s dialectics does not require some new idea to show up arbitrarily. instead, the movement to new determinations is driven by the nature of the earlier determinations. indeed, for hegel, the movement is driven by necessity (see, e. g. , el remarks to §§12, 42, 81, 87, 88). the nature of the determinations themselves drives or forces them to pass into their opposites. this sense of necessity —the idea that the method involves being forced from earlier moments to later ones—leads hegel to regard his dialectics as a kind of logic. as he says in the phenomenology, the method’s “proper exposition belongs to logic” (phg §48). necessity—the sense of being driven or forced to conclusions—is the hallmark of “logic” in western philosophy .
a. dagnino, s. sforzini, f. dondero, s. fenoglio, e. bona, j. jensen, and a. viarengo, “a “weight - of - evidence” approach for the integration of environmental “triad” data to assess ecological risk and biological vulnerability, ” integr. environ. assess. manage. , no. 4, 314–326 (2008) .
strengthened by my experience in botswana i started to use the triad method of prescribing for my clients in the uk. with this method i specialise in treating people with complex health issues for example layers including a chronic physical health problem, stress / emotional trauma and / or a history of taking conventional medications. in essence three remedies are given at each consultation to address three main layers of your health. the first layer is your main complaint, the most acute problem that is bothering you. the second layer is the whole picture of your health including any stresses and mood or emotional imbalances – this is known as the ‘constitutional’ or ‘fundamental’ layer and is the only prescription that classical homeopaths make. the third layer is the miasmatic layer. miasms are an aspect of homeopathic philosophy which explains why we are susceptible to particular illnesses or diseases. they are mostly inherited susceptibilities so in your consultation i will ask about your family medical history to gain an overview of which miasms need addressing. the miasmatic prescription underpins the other two prescriptions as well as aiming to strengthen your core health and vitality – your
with a greater focus on soil protection in the eu, the need for ecological risk assessment tools for cost - effective characterization of site contamination is increasing. one of the challenges in assessing the risk of soil contaminants is to accurately account for changes in mobility of contaminants over time, as a result of ageing. improved tools for measuring the bioavailable and mobile fraction of contaminants is therefore highly desirable. in this study the triad method was used to perform a risk characterization of a former surface treatment and metal industry in eskilstuna, sweden. the risk assessment confirmed the environmental risk of the most heavily contaminated sample and showed that the toxic effect was most likely caused by high metal concentrations. the assessment of the two soil samples with low to moderate metal contamination levels was more complex, as there was a higher deviation between the results from the three lines of evidence; chemistry, (eco) toxicology and ecology. for the slightly less contaminated sample of the two, a weighting of the results from the ecotoxicological loe would be recommended in order to accurately determine the risk of the metal contamination at the sampling site as the toxic effect detected in the microtox ® test and ostracodtoxkit™ test was more likely to be due to oil contamination. the soil sample with higher total metal concentrations requires further ecotoxicological testing, as the integrated risk value indicated an environmental risk from metal contamination. the applied methodology, the triad method, is considered appropriate for conducting improved environmental risk assessments in order to achieve sustainable remediation processes .
“hegel’s dialectics” refers to the particular dialectical method of argument employed by the 19th century german philosopher, g. w. f. hegel (see entry on hegel), which, like other “dialectical” methods, relies on a contradictory process between opposing sides. whereas plato’s “opposing sides” were people (socrates and his interlocutors), however, what the “opposing sides” are in hegel’s work depends on the subject matter he discusses. in his work on logic, for instance, the “opposing sides” are different definitions of logical concepts that are opposed to one another. in the phenomenology of spirit, which presents hegel’s epistemology or philosophy of knowledge, the “opposing sides” are different definitions of consciousness and of the object that consciousness is aware of or claims to know. as in plato’s dialogues, a contradictory process between “opposing sides” in hegel’s dialectics leads to a linear evolution or development from less sophisticated definitions or views to more sophisticated ones later. the dialectical process thus constitutes hegel’s method for arguing against the earlier, less sophisticated definitions or views and for the more sophisticated ones later. hegel regarded this dialectical method or “speculative mode of cognition” (pr §10) as the hallmark of his philosophy, and used the same method in the phenomenology of spirit [ phg ], as well as in all of the mature works he published later—the entire encyclopaedia of philosophical sciences (including, as its first part, the “lesser logic” or the encyclopaedia logic [ el ]), the science of logic [ sl ], and the philosophy of right [ pr ] .
other sections of hegel’s philosophy do not fit the triadic, textbook example of being - nothing - becoming at all, as even interpreters who have supported the traditional reading of hegel’s dialectics have noted. after using the being - nothing - becoming example to argue that hegel’s dialectical method consists of “triads” whose members “are called the thesis, antithesis, synthesis” (stace 1955 [ 1924 ]: 93), w. t. stace, for instance, goes on to warn us that hegel does not succeed in applying this pattern throughout the philosophical system. it is hard to see, stace says, how the middle term of some of hegel’s triads are the opposites or antitheses of the first term, “and there are even ‘triads’ which contain four terms! ” (stace 1955 [ 1924 ]: 97). as a matter of fact, one section of hegel’s logic—the section on cognition—violates the thesis - antithesis - synthesis pattern because it has only two sub - divisions, rather than three. “the triad is incomplete”, stace complains. “there is no third. hegel here abandons the triadic method. nor is any explanation of his having done so forthcoming” (stace 1955 [ 1924 ]: 286; cf. mctaggart 1964 [ 1910 ]: 292) .
typical boundary re - tracement application: it is a well - known principal that the intent of a boundary retracement is to re - establish the lines and corners of a prior survey in their most probable original locations. a common method of analysis uses coordinates to compute the inverses or connections between found monuments and compare the inversed bearings and distances with the corresponding inverses on a plat or map. if the inverses are consistent in rotation and distance then those monuments may be acceptable for re - establishing the boundary. this process becomes more difficult to organize and quantify as the number of points increase. for example, four points have six possible inverses. eight points have 28, doubling to 56 inverses when comparing the map points with the field points. the time spent analyzing found monuments in this way is time consuming and costly. triad is a productive and efficient solution for handling this problem .
so far, we have seen how hegel describes his dialectical method, but we have yet to see how we might read this method into the arguments he offers in his works. scholars often use the first three stages of the logic as the “textbook example” (forster 1993: 133) to illustrate how hegel’s dialectical method should be applied to his arguments. the logic begins with the simple and immediate concept of pure being, which is said to illustrate the moment of the understanding. we can think of being here as a concept of pure presence. it is not mediated by any other concept—or is not defined in relation to any other concept—and so is undetermined or has no further determination (el §86; sl - m 82; sl - dg 59). it asserts bare presence, but what that presence is like has no further determination. because the thought of pure being is undetermined and so is a pure abstraction, however, it is really no different from the assertion of pure negation or the absolutely negative (el §87). it is therefore equally a nothing (sl - m 82; sl - dg 59). being’s lack of determination thus leads it to sublate itself and pass into the concept of nothing (el §87; sl - m 82; sl - dg 59), which illustrates the dialectical moment .
note that, while hegel was clearly influenced by fichte’s work, he never adopted fichte’s triadic “thesis—antithesis—synthesis” language in his descriptions of his own philosophy (mueller 1958: 411–2; solomon 1983: 23), though he did apparently use it in his lectures to describe kant’s philosophy (lhp iii: 477). indeed, hegel criticized formalistic uses of the method of “ triplicity [ triplizität ] ” (phg §50; alternative translation) inspired by kant—a criticism that could well have been aimed at fichte. hegel argued that kantian - inspired uses of triadic form had been reduced to “a lifeless schema” and “an actual semblance [ eigentlichen scheinen ] ” (phg §50; alternative translation) that, like a formula in mathematics, was simply imposed on top of subject matters. instead, a properly scientific use of kant’s “triplicity” should flow—as he said his own dialectical method did (see section 1) —out of “the inner life and self - movement” (phg §51) of the content .
since the analytical method leads to oppositions or contradictions, he argued, if we use only analytic judgments, “we not only do not get very far, as kant says; we do not get anywhere at all” (the science of knowledge, i: 113; fichte 1982: 112). without the synthetic concepts or judgments, we are left, as the classic reductio ad absurdum argument suggests, with nothing at all. the synthetic concepts or judgments are thus necessary to get beyond contradiction without leaving us with nothing .
how it works: triad works by determining the four parameters of a two - dimensional transformation: rotation, scale and translation. these are solved simultaneously by best fitting the points in one coordinate system to the same points in a second coordinate system. the points in the first system are treated like a figure, the angular relationship between points is retained while the figure is scaled, rotated and shifted to best fit all the points in the second system. new coordinates can be computed for the boundary based on a best fit of all acceptable monuments. alternately, if one prefers, the two best points can be fixed. a summary report is created for the job file .
but why does hegel come to define reason in terms of dialectics, and hence adopt a dialectical method? we can begin to see what drove hegel to adopt a dialectical method by returning once again to plato’s philosophy. plato argued that we can have knowledge of the world only by grasping the forms, which are perfectly universal, rational concepts or ideas. because things in the world are so imperfect, however, plato concluded that the forms are not in this world, but in a realm of their own. after all, if a human being were perfectly beautiful, for instance, then he or she would never become not - beautiful. but human beings change, get old, and die, and so can be, at best, imperfect copies of the form of beauty—though they get whatever beauty they have by participating in that form. moreover, for plato, things in the world are such imperfect copies that we cannot gain knowledge of the forms by studying things in the world, but only through reason, that is, only by using our rationality to access the separate realm of the forms (as plato argued in the well - known parable of the cave; republic, book 7, 514–516b) .
hegel provides the most extensive, general account of his dialectical method in part i of his encyclopaedia of philosophical sciences, which is often called the encyclopaedia logic [ el ]. the form or presentation of logic, he says, has three sides or moments (el §79). these sides are not parts of logic, but, rather, moments of “every logical concept”, as well as “of everything true in general” (el remark to §79; we will see why hegel thought dialectics is in everything in section 4). the first moment—the moment of the understanding—is the moment of fixity, in which concepts or forms have a seemingly stable definition or determination (el §80) .
my approach is flexible: at the end of your consultation i will give you 3 different remedies to take alternating either daily or weekly depending on the intensity of your complaint. this prescription will cover you for a month. when starting treatment with me i like to suggest that you commit to three consultations (another triad !) every 4 - 6 weeks as this gives our healing partnership its best chance to work deeply and long lastingly. after that you can chose to have regular consultations with me if you have a long - standing, deep - seated complaint and / or are going through a particularly stressful time. or you can chose to book in to see me in the future if and when you need to do so. i am also available via the phone and email between appointments if you need any extra advice or support. and if you are on the move i can offer full consultations by phone or skype too .
interpreters have offered various solutions to the complaint that hegel’s dialectics sometimes seems to violate the triadic form. some scholars apply the triadic form fairly loosely across several stages (e. g. burbidge 1981: 43–5; taylor 1975: 229–30). others have applied hegel’s triadic method to whole sections of his philosophy, rather than to individual stages. for g. r. g. mure, for instance, the section on cognition fits neatly into a triadic, thesis - antithesis - synthesis account of dialectics because the whole section is itself the antithesis of the previous section of hegel’s logic, the section on life (mure 1950: 270). mure argues that hegel’s triadic form is easier to discern the more broadly we apply it. “the triadic form appears on many scales”, he says, “and the larger the scale we consider the more obvious it is” (mure 1950: 302) .
note that, although hegel acknowledged that his dialectical method was part of a philosophical tradition stretching back to plato, he criticized plato’s version of dialectics. he argued that plato’s dialectics deals only with limited philosophical claims and is unable to get beyond skepticism or nothingness (sl - m 55–6; sl - dg 34–5; pr, remark to §31). according to the logic of a traditional reductio ad absurdum argument, if the premises of an argument lead to a contradiction, we must conclude that the premises are false—which leaves us with no premises or with nothing. we must then wait around for new premises to spring up arbitrarily from somewhere else, and then see whether those new premises put us back into nothingness or emptiness once again, if they, too, lead to a contradiction. because hegel believed that reason necessarily generates contradictions, as we will see, he thought new premises will indeed produce further contradictions. as he puts the argument, then ,
in conclusion, the study presents a useful way of differentiating neurochemical subsystems involved in the processing of emotional information by combining functional imaging during an emotional task with an acute and specific pharmacological enhancement of serotonergic and noradrenergic neurotransmission in healthy subjects. this differentiation revealed common influences of both neurotransmitters (with a slight overweight of serotonergic effects) in medial and dorsolateral prefrontal regions during the anticipation of negatively and ‘unknown’ (ambiguously) cued emotional stimuli. the bilateral medial thalamic region was selectively affected by noradrenergic modulation, unlike medial and dorsolateral prefrontal regions, which were primarily modulated by serotonergic enhancement. this combined method of pharmaco - fmri points to regions, which in future could possibly be used to detect endophenotypes of depressive syndromes in patients responding primarily to serotonergic - or noradrenergic - acting antidepressants. next steps in the development of a neurobiologically based administration of differential therapy in depression will be the application of these findings to depressed patients with a prospective view concerning the response to more noradrenergic or serotonergic acting antidepressants .
“dialectics” is a term used to describe a method of philosophical argument that involves some sort of contradictory process between opposing sides. in what is perhaps the most classic version of “dialectics”, the ancient greek philosopher, plato (see entry on plato), for instance, presented his philosophical argument as a back - and - forth dialogue or debate, generally between the character of socrates, on one side, and some person or group of people to whom socrates was talking (his interlocutors), on the other. in the course of the dialogues, socrates’ interlocutors propose definitions of philosophical concepts or express views that socrates challenges or opposes. the back - and - forth debate between opposing sides produces a kind of linear progression or evolution in philosophical views or positions: as the dialogues go along, socrates’ interlocutors change or refine their views in response to socrates’ challenges and come to adopt more sophisticated views. the back - and - forth dialectic between socrates and his interlocutors thus becomes plato’s way of arguing against the earlier, less sophisticated views or positions and for the more sophisticated ones later .
two further journeys into the history of philosophy will help to show why hegel chose dialectics as his method of argument. as we saw, hegel argues against kant’s skepticism by suggesting that reason is not only in our heads, but in the world itself. to show that reason is in the world itself, however, hegel has to show that reason can be what it is without us human beings to help it. he has to show that reason can develop on its own, and does not need us to do the developing for it (at least for those things in the world that are not human - created). as we saw (cf. section 1), central to hegel’s dialectics is the idea that concepts or forms develop on their own because they “self - sublate”, or sublate (cancel and preserve) themselves, and so pass into subsequent concepts or forms on their own accounts, because of their own, dialectical natures. thus reason, as it were, drives itself, and hence does not need our heads to develop it. hegel needs an account of self - driving reason to get beyond kant’s skepticism .
these sorts of considerations have led some scholars to interpret hegel’s dialectics in a way that is implied by a more literal reading of his claim, in the encyclopaedia logic, that the three “sides” of the form of logic—namely, the moment of understanding, the dialectical moment, and the speculative moment—“are moments of each [ or every; jedes ] logically - real, that is each [ or every; jedes ] concept” (el remark to §79; this is an alternative translation). the quotation suggests that each concept goes through all three moments of the dialectical process—a suggestion reinforced by hegel’s claim, in the phenomenology, that the result of the process of determinate negation is that “a new form has thereby immediately arisen” (phg §79). according to this interpretation, the three “sides” are not three different concepts or forms that are related to one another in a triad—as the textbook being - nothing - becoming example suggests—but rather different momentary sides or “determinations” in the life, so to speak, of each concept or form as it transitions to the next one. the three moments thus involve only two concepts or forms: the one that comes first, and the one that comes next (examples of philosophers who interpret hegel’s dialectics in this second way include maybee 2009; rosen 2014: 122, 132; and winfield 1990: 56) .
the second moment—the “ dialectical ” (el §§79, 81) or “ negatively rational ” (el §79) moment—is the moment of instability. in this moment, a one - sidedness or restrictedness (el remark to §81) in the determination from the moment of understanding comes to the fore, and the determination that was fixed in the first moment passes into its opposite (el §81). hegel describes this process as a process of “self - sublation” (el §81). the english verb “to sublate” translates hegel’s technical use of the german verb aufheben, which is a crucial concept in his dialectical method. hegel says that aufheben has a doubled meaning: it means both to cancel (or negate) and to preserve at the same time (phg §113; sl - m 107; sl - dg 81–2; cf. el the addition to §95). the moment of understanding sublates itself because its own character or nature—its one - sidedness or restrictedness—destabilizes its definition and leads it to pass into its opposite. the dialectical moment thus involves a process of self - sublation, or a process in which the determination from the moment of understanding sublates itself, or both cancels and preserves itself, as it pushes on to or passes into its opposite .
fichte’s account of the synthetic method provides hegel with the key to moving beyond kant. fichte suggested that a synthetic concept that unifies the results of a dialectically - generated contradiction does not completely cancel the contradictory sides, but only limits them. as he said, in general, “ [ t ] o limit something is to abolish its reality, not wholly, but in part only” (the science of knowledge, i: 108; fichte 1982: 108). instead of concluding, as a reductio ad absurdum requires, that the two sides of a contradiction must be dismissed altogether, the synthetic concept or judgment retroactively justifies the opposing sides by demonstrating their limit, by showing which part of reality they attach to and which they do not (the science of knowledge, i: 108–10; fichte 1982: 108–9), or by determining in what respect and to what degree they are each true. for hegel, as we saw (cf. section 1), later concepts and forms sublate—both cancel and preserve —earlier concepts and forms in the sense that they include earlier concepts and forms in their own definitions. from the point of view of the later concepts or forms, the earlier ones still have some validity, that is, they have a limited validity or truth defined by the higher - level concept or form .
we must be careful, however, not to apply this textbook example too dogmatically to the rest of hegel’s logic or to his dialectical method more generally (for a classic criticism of the thesis - antithesis - synthesis reading of hegel’s dialectics, see mueller 1958). there are other places where this general pattern might describe some of the transitions from stage to stage, but there are many more places where the development does not seem to fit this pattern very well. one place where the pattern seems to hold, for instance, is where the measure (el §107) —as the combination of quality and quantity—transitions into the measureless (el §107), which is opposed to it, which then in turn transitions into essence, which is the unity or combination of the two earlier sides (el §111). this series of transitions could be said to follow the general pattern captured by the “textbook example”: measure would be the moment of the understanding or thesis, the measureless would be the dialectical moment or antithesis, and essence would be the speculative moment or synthesis that unifies the two earlier moments. however, before the transition to essence takes place, the measureless itself is redefined as a measure (el §109) —undercutting a precise parallel with the textbook being - nothing - becoming example, since the transition from measure to essence would not follow a measure - measureless - essence pattern, but rather a measure - (measureless ?) - measure - essence pattern .
scholars who interpret hegel’s description of dialectics on a smaller scale—as an account of how to get from stage to stage—have also tried to explain why some sections seem to violate the triadic form. j. n. findlay, for instance—who, like stace, associates dialectics “with the triad, or with triplicity ”—argues that stages can fit into that form in “more than one sense” (findlay 1962: 66). the first sense of triplicity echoes the textbook, being - nothing - becoming example. in a second sense, however, findlay says, the dialectical moment or “contradictory breakdown” is not itself a separate stage, or “does not count as one of the stages”, but is a transition between opposed, “but complementary”, abstract stages that “are developed more or less concurrently” (findlay 1962: 66). this second sort of triplicity could involve any number of stages: it “could readily have been expanded into a quadruplicity, a quintuplicity and so forth” (findlay 1962: 66). still, like stace, he goes on to complain that many of the transitions in hegel’s philosophy do not seem to fit the triadic pattern very well. in some triads, the second term is “the direct and obvious contrary of the first”—as in the case of being and nothing. in other cases, however, the opposition is, as findlay puts it, “of a much less extreme character” (findlay 1962: 69). in some triads, the third term obviously mediates between the first two terms. in other cases, however, he says, the third term is just one possible mediator or unity among other possible ones; and, in yet other cases, “the reconciling functions of the third member are not at all obvious” (findlay 1962: 70) .
although the speculative moment negates the contradiction, it is a determinate or defined nothingness because it is the result of a specific process. there is something particular about the determination in the moment of understanding—a specific weakness, or some specific aspect that was ignored in its one - sidedness or restrictedness—that leads it to fall apart in the dialectical moment. the speculative moment has a definition, determination or content because it grows out of and unifies the particular character of those earlier determinations, or is “a unity of distinct determinations ” (el §82). the speculative moment is thus “truly not empty, abstract nothing, but the negation of certain determinations ” (el §82). when the result “is taken as the result of that from which it emerges”, hegel says, then it is “in fact, the true result; in that case it is itself a determinate nothingness, one which has a content” (phg §79). as he also puts it, “the result is conceived as it is in truth, namely, as a determinate negation [ bestimmte negation ]; a new form has thereby immediately arisen” (phg §79). or, as he says, “ [ b ] ecause the result, the negation, is a determinate negation [ bestimmte negation ], it has a content ” (sl - dg 33; cf. sl - m 54). hegel’s claim in both the phenomenology and the science of logic that his philosophy relies on a process of “ determinate negation [ bestimmte negation ] ” has sometimes led scholars to describe his dialectics as a method or doctrine of “determinate negation” (see entry on hegel, section on science of logic; cf. rosen 1982: 30; stewart 1996, 2000: 41–3; winfield 1990: 56) .
we can begin to see why hegel was motivated to use a dialectical method by examining the project he set for himself, particularly in relation to the work of david hume and immanuel kant (see entries on hume and kant). hume had argued against what we can think of as the naïve view of how we come to have scientific knowledge. according to the naïve view, we gain knowledge of the world by using our senses to pull the world into our heads, so to speak. although we may have to use careful observations and do experiments, our knowledge of the world is basically a mirror or copy of what the world is like. hume argued, however, that naïve science’s claim that our knowledge corresponds to or copies what the world is like does not work. take the scientific concept of cause, for instance. according to that concept of cause, to say that one event causes another is to say that there is a necessary connection between the first event (the cause) and the second event (the effect), such that, when the first event happens, the second event must also happen. according to naïve science, when we claim (or know) that some event causes some other event, our claim mirrors or copies what the world is like. it follows that the necessary, causal connection between the two events must itself be out there in the world. however, hume argued, we never observe any such necessary causal connection in our experience of the world, nor can we infer that one exists based on our reasoning (see hume’s a treatise of human nature, book i, section ii; enquiry concerning human understanding, §6). there is nothing in the world itself that our idea of cause mirrors or copies .
the work of johann gottlieb fichte (see entry on fichte) showed hegel how dialectics can get beyond kant—beyond the contradictions that, as kant had shown, reason (necessarily) develops on its own, beyond the reductio ad absurdum argument (which, as we saw above, holds that a contradiction leads to nothingness), and beyond kant’s skepticism, or kant’s claim that reason’s contradictions must be reined in by the understanding and cannot count as knowledge. fichte argued that the task of discovering the foundation of all human knowledge leads to a contradiction or opposition between the self and the not - self (it is not important, for our purposes, why fichte held this view). the kind of reasoning that leads to this contradiction, fichte said, is the analytical or antithetical method of reasoning, which involves drawing out an opposition between elements (in this case, the self and not - self) that are being compared to, or equated with, one another. while the traditional reductio ad absurdum argument would lead us to reject both sides of the contradiction and start from scratch, fichte argued that the contradiction or opposition between the self and not - self can be resolved. in particular, the contradiction is resolved by positing a third concept—the concept of divisibility—which unites the two sides (the science of knowledge, i: 110–11; fichte 1982: 108–110). the concept of divisibility is produced by a synthetic procedure of reasoning, which involves “discovering in opposites the respect in which they are alike ” (the science of knowledge, i: 112–13; fichte 1982: 111). indeed, fichte argued, not only is the move to resolve contradictions with synthetic concepts or judgments possible, it is necessary. as he says of the move from the contradiction between self and not - self to the synthetic concept of divisibility ,
notice, however, that plato’s conclusion that the forms cannot be in this world and so must be exiled to a separate realm rests on two claims. first, it rests on the claim that the world is an imperfect and messy place—a claim that is hard to deny. but it also rests on the assumption that the forms—the universal, rational concepts or ideas of reason itself—are static and fixed, and so cannot grasp the messiness within the imperfect world. hegel is able to link reason back to our messy world by changing the definition of reason. instead of saying that reason consists of static universals, concepts or ideas, hegel says that the universal concepts or forms are themselves messy. against plato, hegel’s dialectical method allows him to argue that universal concepts can “overgrasp” (from the german verb übergreifen) the messy, dialectical nature of the world because they, themselves, are dialectical. moreover, because later concepts build on or sublate (cancel, but also preserve) earlier concepts, the later, more universal concepts grasp the dialectical processes of earlier concepts. as a result, higher - level concepts can grasp not only the dialectical nature of earlier concepts or forms, but also the dialectical processes that make the world itself a messy place. the highest definition of the concept of beauty, for instance, would not take beauty to be fixed and static, but would include within it the dialectical nature or finiteness of beauty, the idea that beauty becomes, on its own account, not - beauty. this dialectical understanding of the concept of beauty can then overgrasp the dialectical and finite nature of beauty in the world, and hence the truth that, in the world, beautiful things themselves become not - beautiful, or might be beautiful in one respect and not another. similarly, the highest determination of the concept of “tree” will include within its definition the dialectical process of development and change from seed to sapling to tree. as hegel says, dialectics is “the principle of all natural and spiritual life” (sl - m 56; sl - dg 35), or “the moving soul of scientific progression” (el §81). dialectics is what drives the development of both reason as well as of things in the world. a dialectical reason can overgrasp a dialectical world .
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triad is one of the earliest and simplest solutions to the spacecraft attitude determination problem , due to harold black . black played a key role in the development of the guidance , navigation and control of the u.s. navy 's transit satellite system at johns hopkins applied physics laboratories . as evident from the literature , triad represents the state of practice in spacecraft attitude determination , well before the advent of the wahba 's problem and its several optimal solutions . given the knowledge of two vectors in the reference and body coordinates of a satellite , the triad algorithm obtains the direction cosine matrix relating both frames . covariance analysis for black 's classical solution was subsequently provided by markley . 
triad is one of the earliest and simplest solutions to the spacecraft attitude determination problem, due to harold black. black played a key role in the development of the guidance, navigation and control of the u.s. navy's transit satellite system at johns hopkins applied physics laboratories. as evident from the literature, triad represents the state of practice in spacecraft attitude determination, well before the advent of the wahba's problem and its several optimal solutions. given the knowledge of two vectors in the reference and body coordinates of a satellite, the triad algorithm obtains the direction cosine matrix relating both frames. covariance analysis for black's classical solution was subsequently provided by markley.
triad is one of the earliest and simplest solutions to the spacecraft attitude determination problem, due to harold black. black played a key role in the development of the guidance, navigation and control of the u.s. navy's transit satellite system at johns hopkins applied physics laboratories. as evident from the literature, triad represents the state of practice in spacecraft attitude determination, well before the advent of the wahba's problem and its several optimal solutions. given the knowledge of two vectors in the reference and body coordinates of a satellite, the triad algorithm obtains the direction cosine matrix relating both frames. covariance analysis for black's classical solution was subsequently provided by markley.