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Exceptional Knowledge

The general context of paradox may at first be assumed to consist
of just the sorts of relationships which occur within the schema of
categorical deduction: the bounded version of the Cartesian
Coordinate System, in which opposite qualities oppose along the

However, this is not precisely the case. For a standard categorical
deduction does not represent a paradox at all, nor a contradiction,
but rather,
a non-trivial case.

The case in which a paradoxical solution is needed are only cases
which are problematic. And that is not obvious, because ordinarily
all terms are necessary to create a categorical deduction.

So, it must be clarified that there is an exceptional  case which is
paradoxical even for the categorical deduction. But how could this
be the case?

The answer is that true opposites are always positive terms,
because they have content. What is paradoxical is simply the
existence of a concept solely as the negation of its opposite,
kind of contention with zero

We can see, for example, that in categorical deduction...
A. Arbitrary solutions have non-arbitrary problems, AND
B. Arbitrary problems have non-arbitrary solutions.

...that both 'non-arbitrary' and potentially 'problems' pose Type 3
weaknesses, that is, weaknesses involving the assertability of
single subset categories*

*(Each of the opposites is a subset category. For four categories
there are two deductions, rendering it exponential or efficient).

Since there are two weaknesses, it is possible to see a solution to
the problem through paroxysm: while one missing category is
incoherent, two missing categories means there is a problem.

If there is a problem, however, there is a solution!

The solution in this case is simply to ignore the problematic
categories, and accept that the remaining categories are coherent
by themselves.

For example, the paroxysm of non-arbitrary problems involves
arbitrary solutions. The paroxysm of problematic non-arbitration
involves a solution to arbitrariness.

But although these paroxysms are helpful with incoherent cases in
which positive data has gone missing, they are not so helpful with
actual opposites, at least coherently!

For example, we would find it less helpful to realize that the
paroxysm of  the arbitrary solution to non-arbitrary problems is the
non-arbitrary problem of arbitrary solutions!

The explanation for the exception in which paroxysm is used
instead of categorical deduction has two parts: 1. The data
expressed is already coherent, and 2. The limit of the data has
been reached. But in the vocabulary of coherent philosophy, these
two explanations mean the same thing!

In general, what I have described is a group of methods related to
the topic of exceptional knowledge.