[Note: This topic will also be continued further in my next blog entry].
Dear Reader,
Below, we use '(---]' as the assignment-relation symbol, to signify the assignment -- "generic symbol (---] specific symbol", e.g., q/n (---] q/X, and '=' signifies "is equal to by definition".
We also use a standard partitioning of visible-light-spectrum-order color-coding to call attention to dialectical, qualitative ordinalities: red, orange, yellow, green, blue, indigo, violet.
The F.E.D. presentation of their "meta-system" of Dialectical Arithmetic, which they model, in "bootstrap" fashion -- using the very second system of dialectical arithmetic in that meta-system itself, the NQ system in that multi-system progression, unfolds as follows, through its 4th step [i.e., through its (2^4)th = 16th system of arithmetic] [wherein I am doing my best to render the "syntactics" of the various, ever-richer "meta-numeralic" units, or <<monads>>, of the "spaces" , or "sets", basing these successive axiomatic systems of dialectical arithmetic, although with a fraction of the innovative typographical facilities that F.E.D. has at its disposal] --
)-|-(s = (N_)^(2^s):
)-|-(step = 4 = (N_)^(2^4) =
q/1 (---] N_ =
the <<arche'>>-system of the purely-quantitative "Natural" Numbers as a system of "pure, unqualified quantifiers";
space N = { 1, 2, 3, 4, ... };
+
q/2 (---] Nq/NN = Nq/Q = NQ_ =
the first "contra-system" to the <<arche'>>-system; the N-based arithmetical system of the "purely-qualitative" dialectical "meta-Natural meta-Numbers" as "pure, unquantifiable ordinal/ontological qualifiers";
space NQ = { q/1, q/2, q/3, q/4, . . .} = { q1, q2, q3, q4, ... }
[Example(s) of this dialectical arithmetic in use --
A Systematic Dialectics Model: http://www.adventures-in-dialectics....y-PartII_D.pdf
An Historical Dialectics Model: http://www.adventures-in-dialectics....-PartIII_A.pdf
-- et passim.];
+
q/3 (---] Nq/QN = Nq/U = NU_ ...
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