Traditional essay-writing methods focus on a thesis statement, supporting arguments, and secondary points. The general effect of this is that this essay format is not anywhere beyond set theory. Some would say this is not a big limitation, because set theory is a meaningful application in mathematics and linguistics. However, the following criticisms can be raised to the 'Set Theory' approach:
1. Answers are not contained, leading to ad absurdist elaboration of an initial concept, especially when that concept is not well-defined.
2. Infinite extension poses the problem of non-exclusive terms, limiting the function of the initial definition, however perfect.
3. The infinite extension of ideas poses a rhetorical problem, because whenever an additional term can be proposed, there is no limit on the number of criticisms that can be raised against an argument.
The overall effect is a very flawed approach, when it is considered that 1. the definition may be flawed, 2. the method relies on exhaustion, without proposing a solution to exhaustion, and 3. the rhetoric has unlimited opponents.
The Basis of a Dimensional MethodEdit
In opposition to the view that a single thesis should be developed, a dimensional method proposes that multiple equivalent theses should be developed. This is in contradiction to the hieratic method developed by Aristotle, in which one thesis should support another. However, there are good reasons for having equivalent theses.
1. Equivalent theses set a standard for the value of the argument. If one thesis is weak, it become standard to reject the entire argument. This creates a high standard of relevance for highly qualified arguments which involve multiple relevant theses.
2. Equivalent theses can be categorically related, creating logical coherence. For example, the use of opposite word pairs between two theses creates organizational structure, and encourages results that can be corroborated.
3. Equivalent theses have a similar or identical scale, which allows the reader of a paper to gauge the importance of a subject, and the referential importance of positions that are taken. When no inference can be logically pinned to the thesis statements, it is assumed that the language is weak, rather than the nature of the debate. This has the effect of strengthening theses which the writer does not adopt, which ordinarily would suffer under the fallacious assumption that a weak argument means a poor debate.
In these points, I have outlined several secrets to the nature of the dimensional method:  Using opposite pairs to structure reasoning,  Standardized debate,  Automatic understanding of an absence of validity for weak arguments, that use weak language.
A further advantage is the notion of quantification. Statements can use multiple opposite concepts, and multiple contexts in which the opposites appear. If it is seen that an application of a concept itself has an application, suddenly we are dealing with a three-dimensional process of analysis. This is not entirely prohibitive, because the method is the same.
The Use of Extended AnalysisEdit
It may be noted that once organization of theses develops, it appears there is little to do. It is as though the theses have already spoken for themselves. This is especially the case when categorical deduction is used (see The Dimensional Philosopher's Toolkit).
However, it is possible to reach for extended analysis when the subject of opposites is in question, when the context of the subject comparison is in question, or when it is necessary to reach for a translation of the thesis.
I. When the Subject is in Question
The question of the subject in dimensional analysis is the question of several things: [a] whether opposites are being used, for example, in all non-neutral contexts (the question of neutrality), [b] the question of the validity of an opposite pair, for example, 'is a dog really the opposite of a cat? No, they are both animals', [c] the question of the validity of the context as referred to as the subject, for example, questioning the subject by accepting the context: 'Jill is not the modal opposite of Jack because the context is school; they are both students, what is the opposite if a student? Jack is not a professor, etc. / I want to change the context' At that point there are two choices: to change the problem, or to identify what specifically about the original subject can be explained in opposite terms. For example, maybe Jack loves to travel, but Jill hates staying at home. In that case, we can deduce that Jack's airplane loves to 'stay at home': it loves to be the method of travel. We can also deduce that if Jill wanted to stay at home, she wouldn't like airplanes. The context can be described as Travel versus Home and Hate versus Love. Forming a thesis statement would simply be about a context and a subject, such as 'do we love travel? and secondly, do we hate being at home?' The result is to produce validity or contradiction. But equally an initial subject can refer to a complex situation involving two opposite isms, such as formalism versus substantivism, or psychological idealism versus material determinism.
II. When the Context of the Subject is in Question
Accepting an initial subject of opposites such as the hypothesis that time and location are opposed produces some necessary relationships in a second relationship of opposites called a 'context'. What is implied is generally that the context relates in terms of unrelated terms, and specifically opposite terms, and specifically the opposite terms of the subject. It becomes easier to choose abstract terms in an abstract context, and tangible terms in a tangible context. For example, in stimulation versus insensibility, someone might choose a hospital versus a home, or a sadist versus a masochist. These are somewhat tangible, and somewhat abstract, just like the subject.
Choosing unrelated terms is a smaller problem than choosing non-opposite terms, because most opposite terms, as demanded by the method, must relate to some degree with other opposites. The fact of their being opposites commands some degree of exclusion, which means that the context is as relevant as the subject.
Here are some problems that might emerge with the (second) context, called the context axis: [a] the person conducting the study or constructing the dimensional analysis does not accept the logic involved in the analysis, that is he or she does not accept that the context and subject themselves create the sphere of valid correspondences, [b] the person conducting the study does not accept the very existence of one of the terms being used in the analysis, such as love or war, not only limiting the idea of associations, but creating a denial of the very basis for the study. This is essentially a denial of relativism, which would itself render the categories acceptable in an objective way, [c] otherwise, an earlier problem may be raised again, that the terms do not constitute opposites, otherwise [d] it is possible that the dynamic relationship between the categories is invalid, but this is sometimes a rejection of the thesis outright. An example of this is when the context belongs to a different majesteria as the subject, as when heaven and hell are opposites, and the context is change and the eternal. We are left with the conclusion that the changing hell is the eternal heaven, and the eternal hell is the changing heaven, which seems to question the idea that both heaven and hell are eternal. Perhaps this is true, but if so, it may be that heaven and hell are not opposite in scale, or that one or both terms are not actually real. So where we began by questioning logic, we ended by questioning reality. The result is that the method remains logically valid.
III. When it is Necessary to Translate the Thesis
In translating the thesis, the standard concept is standardization. That is, if one category of four is translated, the new opposite term is the opposite of the new category. In some cases, the opposite may be selected to be only similar to the opposite, under the thesis that not all opposite pairs are traditionally correct (that they represent 'generalities of relation'). The important theme here is that the context remains as complex as the subject, because the complexity or simplicity of the adopted thesis is a reflection of the theme of universal specialism within the work, which is inescapable.
Translation becomes the most common method for extended analysis, because it allows a relatively rapid change of ideas in a logical way. However, the central content of analysis tends to be contingent, in the sense of relating to a volume of categories as explained under 'subject' and 'context'.
General Method of ElaborationEdit
It may be important to convey a further secret, that is, how to expand a dimensional analysis to have not valid, but valuable arguments, and points of contention, etc.
It is important to note at this point that this largely depends on the choice of subject, that is, the genus of the study itself, and also the familiarity with the subject that the student or researcher may possess.
It is important to have a strong and varied vocabulary to convey the ideas, and to be familiar with the opposites.
It may be central to choose philosophy, literature, history, or some other general subject before making a serious inquiry into dimensional analysis.
Those who make these studies may even find that what is required is a slight degree of eccentricity, which runs the risk of making the study unbelievable. But the alternative, that the material is dry or obvious, is also not desirable.
An effective technique may be to mix terms, words, or statements that are eccentric and by turns obvious or ordinary. When these two types of statements are interrelated with eachother logically, there is an inroad to a powerful method of reasoning. It promises to bind obscure subjects very quickly to the central body of reference, primarily by making the intermediate areas also primary to analysis.
At this point, it is easy to imagine how the subject might also relate to psychology, politics, anthropology, or poetry.