Dear Reader,
Wanted to share with you 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 --
http://www.dialectics.info/Primer_files/3_F.E.D.%20Intro.%20Letter,%20Supplement%20A-1_OCR.pdf
-- and in their "Meta-Briefing", pages I-122 through I-128 --
http://www.dialectics.info/dialectics/Dialectic_Ideography_files/7_Dialectics-Part1c-MetaBrief_OCR.pdf
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.
Wanted to share with you 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 --
http://www.dialectics.info/Primer_files/3_F.E.D.%20Intro.%20Letter,%20Supplement%20A-1_OCR.pdf
-- and in their "Meta-Briefing", pages I-122 through I-128 --
http://www.dialectics.info/dialectics/Dialectic_Ideography_files/7_Dialectics-Part1c-MetaBrief_OCR.pdf
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.
For more
information regarding these
Seldonian insights, please see --
For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as illustrated
books by the F.E.D. Press, see --
https://www.etsy.com/shop/DialecticsMATH
¡ENJOY!
Regards,
Miguel Detonacciones,
Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];
Elected Member, F.E.D. General Council;
Participant, F.E.D. Special Council for Public Liaison;
Officer, F.E.D. Office of Public Liaison.
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