Sion's statement does not clarify how to use this
principle of negation to reach logic sentences. Nor does
it hint at any principle of exponential efficiency. As Sion
says, he is merely following in the footsteps of Aristotle.
DIMENSIONISM
Quotes, Etc.

ABOVE: THE LOGO OF THE
DIMENSIONAL ENCYCLOPEDIA
"The function f is real-valued if and only if
the Fourier transform of f is Hermitian. The
function f is Hermitian if and only if the
Fourier transform of f is real-valued"
http://en.wikipedia.org/wiki/Hermitian_symmetry
A method similar to categorical deduction is used on
Wikipedia in one place. Understandably, the topic is
math rather than general properties of language or
wisdom. Also, it is not used in this case to support
coherent sentences:
"If an affirmation is true, then its denial is
false; if the denial is true, then the
affirmation is false"

Sion, Avi.
Future Logic, [Chapter 3.4.
Axioms of Logic, B. The Law of
Outside of generalizations, I have found occasional
traces of dimensional axioms in a few obscure works.
Such as Avi Sion's treatise entitled Future Logic:
"It's unconscious or transcendental
'spontaneity' is perhaps to be
conceived figuratively upon analogy.
We can attempt to give sense to the
idea, as we extend and modify the
conception of a barrier or network (or
set of 'schemata')..." ---Iris Murdoch,
Metaphysics as a Guide to Morals, p.
309.
The method of categorical deduction, which grants
dimensionism its exponential property, is
pre-figured in several major philosophical works:
(1) "The idea of foundation is rather that which secures the
equivalence and convergence of the ways (logical, Cartesian,
psychological, historico-teleological, etc.)" (Part I, section 1,
parentheses his) (Phen. Reader, p. 580).

(2) "Thus elucidation... requries that meaning be submitted to a
genuine form of work" (Part II, section 2) (Phen. Reader p. 594).

(3) Ricoeur quotes Husserl about "sustaining a universal" and then
goes on to talk about how "this interpretive core assures the
'representative' commonality of the two intended meanings." (Part II.
sec. 2) (Phen. Reader, p. 595).

(4).  "Hence the fixed meanings and the contents of stable
expressions must be substituted for fluctuating meanings and
subjective expressions. The task is dictated by the ideal of univocity
and governed by the axiom of the UNBOUNDED RANGE OF OBJECTIVE
REASON" (italics originally) (Part II, section 2) (Phen. Reader, p. 596).
Paul Ricoeur, a critic of
phenomenology, says:
With similar tones of secretness,
David Antin (a poet), writes:
"Don Wellman wrote asking me if i would write
something do something ... on or rather
a sensible way [of] taking pieces of language
that had been parts of continuous discourses
and assembling and disassembling them
putting them down next to eachother one after
another in accordance with what I would call
collage strategies (p. 227) ...to consider this
kind of organization... to restore the missing
parts or merely take pleasure in the
juxtaposition and collision of these fragments
of otherwise unrelated or arbitrarily related
things that are now parts of some new and
totally unfamiliar yet partially familiar thing (p.
235)" ----Antin, David.
(1966-2005)
"It's unconscious or transcendental
'spontaneity' is perhaps to be conceived
figuratively upon analogy. We can attempt
to give sense to the idea, as we extend and
modify the conception of a barrier or
network (or set of 'schemata')..."

---Murdoch, Iris.
Metaphysics as a Guide to
Morals
, p. 309
"Dimensionism is no longer merely
perspective art, it is a movement with
roots in a philosophical system..."
Since the date of the article is recent, it
seems possible that the comparison is
either an unconscious revelation of the
method, or was constructed at a later date
than key examples of the categorical
deduction, as demonstrated at Yahoo
"[M]uch to my chagrin, whatever God this age held
demanded that the answer was a square! (p. 12)...
The dialectical circle could be used as a form of
logic! (p. 13)... I decided that if something could be
eliminated, it was the concept of neutrality..... Thus, I
theorized that I had solved the problem of reduction
(p. 14)...This was, fundamentally, an objective system
(p. 17)."

---Coppedge, Nathan.
The Dimensional
Philosopher's Toolkit
, new introduction.
"Dimensional philosophy may be seen as
composed of a number of sub-categories,
including proto-mathematics, coherentist
philosophy, categorical philosophy, and
metaphysical criticism." ---Nathan
Coppedge, January 31st, 2015
"The major alternatives to categorical
dimensionism include aesthetic theories,
mathematical theories, and social
criticism." ---Nathan Coppedge, January
31st, 2015