Saturday, November 12, 2011

Dialogue: "What Precedes "Step 0" in F.E.D.'s Dialectics-Algorithm?

Dialogue:  "What Precedes "Step 0" in F.E.D.'s Dialectics-Algorithm?

Dear Readers,

Wanted to share here a recent dialogue from elsewhere on an aspect of the earlier entry to this blog on the "simple side" of F.E.D. Dialectics --

Response to "Simple Side" Blog Entry: "Well said.

It can also be said that Step 0 is the synthesis of all pre-Step 0 self-"movement". ..."

Reply: Thank you for your substantive response!

Yes, I agree -- it seems to me also that the "arche'-ic", or <<arche'>>, of Step 0 is typically the final synthesis, the most advanced product, of a previous dialectical [self-]progression, although one which may exist in a qualitatively "different universe[-of-discourse]" from the later progression into which it feeds.

For example, in F.E.D.'s "meta-model" of the dialectical progression of the standard axioms-systems of arithmetic [N --> W --> Z --> Q --> R --> C --> H --> . . .], and also in their "meta-model" of their dialectical progression of the "non-standard", "dialectical", systems of arithmetic, the "Natural Numbers" axioms-system, for the numbers N = {1, 2, 3,...}, is the Step 0 system, the <<arche'>>, of both progressions [although, for the non-standard, "dialectical" arithmetics, that Step 0 axioms-system for N uses only "first-order" logic [and is therefore syntactically but not semantically Goedel-"incomplete"], whereas the N_ system axioms of Step 0 for the progression of the "standard" arithmetics uses higher-order logic, and is therefore more strongly "incomplete" ["incomplete" both syntactically and semantically] in the Goedelian sense].

But, as per your comment, the "Natural Numbers" have their own prehistory -- an anterior dialectical progression that led to the "Natural Numbers" as its final, highest product.

That same dialectical progression also gave rise to cuneiform, believed to be the origin, the <<arche'>>, of all written language in the ancient Mediterranean world!

That dialectical progression -- which begins with a 3-D micro-iconic "tokenology", and "meta-evolves", by stages, into a "tokenography", before giving rise to cuneiform fired-clay tables -- was discovered, via fired-clay token artifacts discovered in ancient Mesopotamian archeological assemblages, by Denise Schmandt-Besserat, and documented in her book "Before Writing: From Counting to Cuneiform".

F.E.D. formulates a "dialectical meta-model", using their "First Dialectical Arithmetic", of the historical-dialectical progression of systems of goods temple-tithes counting, and, later, of commodities [ac]counting, that Denise Schmandt-Besserat discovered, in Supplement A to their Introductory Letter, pages A-22 through A-28 --,%20Supplement%20A-1_OCR.pdf

-- and in their "Meta-Briefing", pages I-122 through I-128  --

So, as your comment suggests, the dialectical progression prior to the "Natural Numbers" -- the "pre-progression" that leads to the "Natural Numbers" only after protracted historical self-development of humanity and of its praxis of collective, societal self-reproduction -- exists in a different "universe of discourse" from that in which the "Natural Numbers", and the dialectical progression from them and after them -- to the Whole Numbers, the Integers, the Rational Numbers, the Real Numbers, the Complex Numbers, the Hamilton Quaternions, etc. -- exists.

Much of the prehistory of the "Natural Numbers" ensues in a "universe of discourse" of which even written language is not yet a part.



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