intellectual themes back to index. |

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

diagonal.

However, this is not precisely the case. For a standard categorical

deduction does not represent a paradox at all, nor a contradiction,

but rather,

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,

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.