I will give a full example of a means to formulate categorical deductions on a sixteen-category diagram. This will allow me (hopefully) to progenitate the method in light of disappointing book sales.

Also, I make the excuse that this expansion of the system is not present in the published book, and deserves recording somewhere. It seems unlikely at this point that I will have the opportunity to publish a condensed version of the methods, as I very much would like to. So here is a way of meeting the prospective reader half-way.

There is an initial context of sixteen categories. I will show how these reduce to four. The method has none of the weaknesses of permutation. The categories are listed in order of closest approximate axialarity, from the beginning point to the oppositemost point.

D, C, B, A

H, G, F, E

L, K, J, I

P, O, N, M

A-B-F-E is taken to be one category box (quadra diagram), say CC: Quantity, Texture, Quality, Amorphous.

C-D-H-G is taken to be one quadra, say Physics, Coherency, Abstraction, Correspondence.

K-L-P-O is taken to be one quadra, say Pessimist, Permanent, Optimist, Temporary.

I-J-N-M is taken to be a final quadra, say Perfect, Subject, Complex, Context.

First, a method yields the following for the first quadra:

Quantity-texture is an amorphous quality, or

Amorphous quantity is texture quality

Second, the same method yields the following for quadra number two:

Physics coherency is abstract correspondence, or

Physical correspondence is abstract coherency

Thirdly, the same method yields the following for quadra number three:

Pessimistic permanence is optimistically temporary, or

Temporary pessimism is permanent optimism

Fourthly, the method yields the following for the fourth quadra:

Perfect subjects are complex contexts, or

Perfect contexts are complex subjects

Since only opposites combine [If, as in the sub-methods, the four macro-categories express opposites, something I was not careful to ensure this time, but which is securable in many cases], and there are two choices for every four opposites when it is determined that the relationship is non-arbitrary by virtue of oppositeness, then there are four large categories produced from the initial sixteen categories:

A. Quantitative texture is an amorphous quality so that temporary pessimism is permanent optimism when physics coherency is abstract correspondence so that perfect contexts are complex subjects.

B. Quantity texture is an amorphous quality so that temporary pessimism is permanent optimism when physical correspondence is abstract coherency so that perfect subjects are complex contexts.

C. Meaningless quantity is texture quality so that pessimistic permanence is optimistically temporary when physics coherency is abstract correspondence so that perfect contexts are complex subjects.

D. Meaningless quantity is texture quality so that pessimistic permanence is optimistically temporary when physical correspondence is abstract coherency so that perfect subjects are complex contexts.

These simply go to demonstrate the method. They would be more rational if opposite macro-categories had been chosen, such as if 1.3 were a suitable but separate opposite from 3.1 (vs. 3.3). The numbers provide a foundation for organizing the properties of the boxes.

Notice again, that the product is four from sixteen, made possible because of the double-tier of oppositeness, a kind of effect in which it is determined that there is one and not two layers of significance. This is not the same as a failed method in which only a fraction of the categories are compared, or in which fallaciously opposites are only compared to opposites, or in which fallaciously any detail is reiterated.

The general form of categorical deduction seems to follow the formula "the

*n*th root of n-dimensions", so 4 = 2, 9 = 3, 16 = 4. If this is the case, it could be considered flat and vastly efficient. This is essentially possible because the property of opposites is protracted over every dimension of the hierarchy.

A simpler example in the extreme is the case of the beautiful stoic, who is said to be sensitive to ugliness.

For those using this article, I highly recommend citing the author, Nathan Coppedge. Further information about how to operate categorical methods may be found in The Dimensional Philosopher's Toolkit (2013), available from Amazon.