## Saturday, June 29, 2013

### A More Careful Variation: Coherent Logic with Sixteen Categories

Using the same sixteen-category method:

D, C, B, A
H, G, F, E
L, K, J, I
P, O, N, M

Initially, the categories are reset to correspond with the numeric constituencies:

A-B-F-E is taken to be one category box (quadra diagram), say CC: [1.1] Purity, [1.2] Simplicity, [2.2] Reduction, [2.1] Nothing.

C-D-H-G is taken to be one quadra, say [1.3] Complexity, [1.4] Chaos, [2.4] Paradigmatics, [2.3] Usefulness.

K-L-P-O is taken to be one quadra, say [3.3] Perfection, [3.4] Order, [4.4] Architecture, [4.3] Justice.

I-J-N-M is taken to be a final quadra, say [3.1] Construction, [3.2] Ugliness, [4.2] Injustice, [4.1] Destruction.

Here are the results for the four either-or comparisons:

Simple purity is reduced to nothing, or
Nothing pure is reduced to simplicity

Chaotic complexity has paradigmatic usefulness, or

Perfect order is the justice of architecture, or
Perfect justice is the architecture of order

Constructed ugliness is injustly destroyed, or
Constructed destruction is an ugly injustice

Now, I use the same balanced method, in which 1 must be abverse of 3, and 2 must be abverse of 4. This time, however, the result is more balanced in terms of the macro-level oppositeness:

A. Simple purity is reduced to nothing so that perfect justice is the architecture of order, when chaotic complexity has paradigmatic usefulness so that constructed destruction is an ugly injustice

B. Simple purity is reduced to nothing so that perfect justice is the architecture of order, when useful complexity is paradigmatic chaos so that constructed ugliness is injustly destroyed

C. Nothing pure is reduced to simplicity so that perfect order is the justice of architecture, when chaotic complexity has paradigmatic usefulness so that constructed destruction is an ugly injustice

D. Nothing pure is reduced to simplicity so that perfect order is the justice of architecture, when useful complexity is paradigmatic chaos so that constructed ugliness is injustly destroyed

Remember that, miraculously, sixteen categories have been reduced to four. There are two primary methods for interpreting the validity of the aphorisms. One is the value method, and the other is the equivalency method. In the value method, it is assumed or determined that one or another end has an advantage in defending a particular set of principles, typically the principles laid out by that description (say, A .or D.). The categories can be re-arranged by cycling them in the same linear positions, if a different value system is desired. The second method, equivalency, involves comparing the aphorisms for differential values. The equivalent sectors are accepted as the standard for comparing the two aphorisms, and the remaining descriptions are used as the primary character of judgment. Axioms can be used of the form that 'the terms differ by the degrees of separation' [in which D. is 1-degree different from A. and 2-degrees different from B.]

Note that, by using the words as variables which have assumed quantifiability, both the opposite subjects A-C and the opposite contexts B-D provide a ground for determining many truths on subjects related to the terms. However, in the case of a sixteen-box diagram, the following assumptions must be made:

A. Two opposites express the entire range of a given notional meaning.
B. What is not an opposite term for anything is determined to be a meaningless context. Note that oppositeness can exist in degrees and still fit into the system.
A. Modal variation allows for multiple opposites for a given term.
B. The terms chosen are in fact opposites, both on a sub-quadra and on a macro-quadra level. E.g. 1.1 opposes both 1.3 and 3.3, 2.4 opposes both 2.1 and 4.1, etc.

With that, it should be possible to assess the validity of the system. Purchases of the Dimensional Philosopher's Toolkit are encouraged for additional insight and organization.