A FUTURE FOR CATEGORICAL KNOWLEDGE DRAFT Wittgenstein was a pessimist, and is often cited as the singular source for knowledge typing. The following article attempts to discredit the tradition, by establishing a stronger one. Interestingly, the context of this basis for study is no longer esoterics, instead it may pertain to the computer programmer. Necessity is relative, that is what I think many technologists have said. And if that is not true, I’m sure I could produce a convincing argument. But the proper subject of this comparison is, in my mind, categories. Continually categories are the reference point---however secretively---for advances in science. There is a temptation to believe that every new advancement is itself a “new category” of science, knowledge, or systematics. There is a value for categories. For example, the second zero. The second zero is not only a subset of the idea of ‘decimal system’ as it might be assumed. Instead, the second zero can incorporate its own definition. That seems adequate if it is in fact possible. So far so good. But if the definition is not possible, this has the potential to compromise the decimal system. But, with understanding, this is the most drastic possible result from a system of assumptions that often enough has not been tested in what I will call a ‘visual parsing method’. What I describe is the simplest method to a new understanding that is, finally, itself, quite simple. It is the correspondence to complex assumptions that remains daunting. The second zero is a basic typological concept, just like the ‘second degree’ of anything. We don’t have to assume that there are 360 degrees. Degrees might be unlimited. Or, in my view, degrees might be organized in iterations. Iterations have gained some notoriety since Boyd’s experimentation with fighter aircraft. What he determined was that iterations are the cheap and effective way to get quality results---what I prefer to call meaningful results. His law of iteration is stated that “The quality of iterations increases with the number of iterations, not the quality of iterations”. Essentially this is simply a value for iteration. Iteration became a concept with Boyd. What I would like to add is the rule of exclusivity: the more an iteration is exclusive, the more material has been ‘processed’. If this were not so, there would be a danger of a recursive loop returning to a point of static advantage. And thus independent of the quality of iteration (that is, once again) there are quality results with exclusive results. This is a kind of exponent on Boyd’s system, which I call Coppedge’s Law of Iteration: “Quality iteration increases with an increase in exclusivity”. But, as it turns out, iteration is a basic concept in the network of information processes which I call Categorix or Objective Coherentism. Interestingly, the intellectual guise of these concepts only seems inappropriate because often enough the intellectual tradition has had no real technical approach to knowledge systems. Arguments are considered rhetorical or deductive, but not even qua systematic. Arguments rarely attain the status of machines. Building on the iterative method and Coppedge’s Law, exclusivity can be grouped into typological categories. The simplest approach is to use opposites as a mode of exclusive organization. But, moreover, this is a theory of “four opposites” in a quadratic system, or actually 2^(n - 1) pairs of opposites in an n-dimensional typology. It is the beginnings of dimensional knowledge, which, for its realization, depends on actual linguistic descriptions of reality. If it is not objective, it is because it does not relate on a 1-to-1 basis with Everything that might be possible for data or experience. In short, there could be a schizophrenia between abstract systems as we know them today, and the factualities of real or desirable experiences, and their substantive categories. But that is getting ahead of myself. Not in this system. The important insight on the level of modalities (modes for short) is the use of a Cartesian coordinate system, to describe qualities. They are not simply positive and negative, because positive and negative ultimately describe only one property. What I am describing is what I call dimensional. When the qualities are opposites, their relationship is along a diagonal, such as A-C or B-D as shown in the diagram. This shows that they have n-categories/d-dimensions (or axes) number of comparative sets, equal to the number of subset categories within each sector of the diagram, and also equal to the number of diagonal correspondences which form the basis for a method of categorical deduction. The method of categorical deduction for a quadratic categorical diagram has six possible forms, which are not directly analogous to anything within the history of logic, since it makes use of a flexible context-oriented concept of exclusivity, which relates---relatively---to any practical solution, in the context of whether positive or negative definitions have been introduced. The six forms of categorical deduction are as follows: B of A :: D of C D of A :: B of C B of Not A :: D of Not C D of Not A :: B of Not C Not B of A :: Not D of C Not D of A :: Not B of C The following six methods are NOT valid in a balanced system: B of A Not :: D of C D of A Not :: B of C A of Not C :: B of Not D A of Not C :: Not B of D Not A of C :: B of Not D Not A of C :: Not B of D As a meaningful notation, there is a kind of artificial quantum effect between two opposite categories, according to my theory. Whenever one category displays one property, the opposite category displays the opposite property, to the extent that we posit that both categories are actual, and the context is logically balanced. What this means is not only do categorical diagrams express an optimal subject-context relationship in which duality has function, but the logical correspondence between categories in an axial system grows by a factor of two for every opposite comparison available in the entire universal set. I propose that these types of category deduction be applied to such various efforts as the organization of virtual landscapes, the functionality of monetary currency (categorical or variablist economics) and a wide range of knowledge and information-generation applications. Nathan Coppedge, SCSU Last modified 9/30/2013