Wednesday, August 24, 2011

Part 2 -- Some Help with "Getting a Handle" on F.E.D. Dialectics.

 [Note:  This topic will also be continued further in my next blog entry].

Dear Readers,

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.

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";

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";

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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