THE METHOD OF CATEGORICAL DEDUCTION
Categorical deduction is a method I invented for formulating coherent knowledge using an n-dimensional typology. For most purposes it only operates in four square categories ('quadra') lying inside a bounded Cartesian Coordinate System ('axes').
Deductions are produced when opposite terms or labels, each being of any length, and occupying separate boxes, are arranged to form statements that are said to express all the data that could be expressed----because the words are analogous to everything contained by the concepts.
The words must be opposites opposed along the diagonal, and arranged with an order preference given to categories A and B, which are taken to be the subject of the individual analysis.
Coherent statements are then expressed as "AB:CD and AD:CB" in terms of A.
Since B and D are switched as part of the operation of the deduction, the preference of B over D is actually unnecessary, although the content is not arbitrary, as it expresses a certain relation of judgment axis B-D with judgment axis A-C.
Examples that don't work:
"Bad women make good men." You may think this is sound reasoning, but it does not logically follow, because if man is the opposite of woman, they cannot both be human. The opposite of human is at least not human.
Examples that do work:
However, you could argue bad is the opposite of good, and the opposite of love is hate, now you can conclude that "bad hate makes good love." That would be logically sound, because it serves as a definition, and we know that it is not contradictory. Of course, other types of exceptions still exist which restrain the ultimate significance both of good and bad, and of love and hate. The statement does not say that it is true in every possible way, but only that it is a logically true definition which measures the extent of validity for that exact case, insofar as the words are accurate representations. If we want it to be measurably true, and not just logically true, then we have to assume that the opposite properties are measurable. And, unless they are absolute, there is no way to be certain that the statement is coherent. However, using similar rules, we can make more complex statements that are equally valid, such as: "good problems with hate produce bad solutions in love." Although more entities are involved, the more complex statements do not have to assume the entities are real or measurable to be logically valid. The deductions also don't depend on the idea of cause and effect, hence the concept of 'non-linear inference'.
Consider the example of beauty versus ugliness, and a sensitive person versus a stoic. We don't argue that any of these entities or qualities don't exist for some person or other. Now, we can't compare opposites directly because that would create a contradiction. So, we compare non-opposites. There is no rule which says that stoics can't be ugly, or that sensitive people can't be beautiful or ugly, etc. In fact, the only thing that would contradict sensitivity is being stoical, and the only thing that would contradict beauty is ugliness. (The only exception to this is irrationality).
Now, we are not saying that stoic and sensitivity or beauty and ugliness cannot be compared to other things, so there is no contradiction in selecting something specific. At this point there is no contradiction. We are comparing non-opposites, because that is not contradictory. It is a possibility, so it can express something about the world. Since the concepts can be defined as the only words that represent the exact same concept, or the identical concepts are interchangeable and have only one opposite, therefore the comparison of non-opposites represents the only available knowledge on whatever topic the terms concern. Since it is the only available knowledge, it is the best knowledge, and where opposite terms are exclusive of all possible descriptions, it is also universal knowledge. Now it follows that 'a beautiful stoic is ugly sensitively' and, under different conditions, 'an ugly stoic is beauty-sensitive'. Otherwise, the terms are not opposites, the process is resolved differently, the interpretation is naive realist, or there is a paradox, irrationality, or incoherence. In sheerly objective terms the only exceptions I know of are naive realism, paradoxes, irrationality, and incoherence. There are also several other trivial exceptions, such as when formal tools are rejected out of hand, or when an informal tool is assumed to be more important.
What is potentially unique about the system is not just its sense of double relativism which I call relative absoluteness, but the way it works across language, and for any extreme concept.
However, things like 'cat and dog' or 'man and woman' don't work except in what is called a 'modal sense'. The modal sense is the same sense as 'this lamp post to that street over there' --- it may not in fact be opposite. However, terms like cat and dog can be lumped into categories like animal and human, and opposites can be imagined for them, like 'dead human' and maybe 'nativity water' for 'alien flame' or the like. These sorts of concepts at least set up a relationship for logical comparison coherently, providing a meaningful standard for correspondence that was not previously imaginable outside of science fiction and Alien Phenomenology.
----Nathan Larkin Coppedge, 2016/11/18