An Easy Take on F.E.D.'s 1st Dialectical Ideography
Dear Readers,
Preface. This blog entry is my attempt at a low-detail take on the essence of the F.E.D. "first dialectical arithmetic".
[Almost] "No Math.", "No Frills" Intro. to the first Dialectical Ideography. The dialectical ideograms of the F.E.D. "first dialectical ideography" can be used, as follows below, to discover [to reconstruct] the past, and [to "pre-construct"] the future, of various human-natural, and pre-human-natural, self-formation-processes, or systems, as well as to illuminate, in systematic fashion, the present "meta-anatomy" and "meta-physiology" of presently thriving systems -- the organizational processes by which they reproduce, or maintain, and expand, their processes, their organization, and their substantiality, illuminating the progress[ions] of nature / of natural systems, and/or the progress[ions] of human idea-systems.
It is all a matter of the "squaring with itself" of each single category, or of each "cumulum" of more than a single category, and of the cumulative effect of all of these "anded" categorial qualities / qualifiers / intensions / connotations on the human mind -- on that of the user, and on those of the user's audience(s).
cumulum, pl. cumula
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
Step-by-Step Application of the F.E.D. Dialectical Method at Its First [Minimal] Level of Richness.
Step a. In step a., the user of this ideographical method/algorithm decides what is the best starting point category -- for example, the ontological category of "quarks", and such, for the dialectic of nature, and that of commodities, or, more deeply, that of "the elementary form of value", for Marx's dialectical presentation of the capitals-system -- and simply "posits" that beginning:
step = a. "thesis".
Step b. Next, to get to step b., the user "squares", or "self-multiplies", or "self-interacts", or "self-operate", or "self-applies", or "self-confronts" the content/result of step a., and considers the meaning of the result thereof:
step = b.
Preface. This blog entry is my attempt at a low-detail take on the essence of the F.E.D. "first dialectical arithmetic".
[Almost] "No Math.", "No Frills" Intro. to the first Dialectical Ideography. The dialectical ideograms of the F.E.D. "first dialectical ideography" can be used, as follows below, to discover [to reconstruct] the past, and [to "pre-construct"] the future, of various human-natural, and pre-human-natural, self-formation-processes, or systems, as well as to illuminate, in systematic fashion, the present "meta-anatomy" and "meta-physiology" of presently thriving systems -- the organizational processes by which they reproduce, or maintain, and expand, their processes, their organization, and their substantiality, illuminating the progress[ions] of nature / of natural systems, and/or the progress[ions] of human idea-systems.
It is all a matter of the "squaring with itself" of each single category, or of each "cumulum" of more than a single category, and of the cumulative effect of all of these "anded" categorial qualities / qualifiers / intensions / connotations on the human mind -- on that of the user, and on those of the user's audience(s).
cumulum, pl. cumula
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Cumulum/Cumulum.htm
Step-by-Step Application of the F.E.D. Dialectical Method at Its First [Minimal] Level of Richness.
Step a. In step a., the user of this ideographical method/algorithm decides what is the best starting point category -- for example, the ontological category of "quarks", and such, for the dialectic of nature, and that of commodities, or, more deeply, that of "the elementary form of value", for Marx's dialectical presentation of the capitals-system -- and simply "posits" that beginning:
step = a. "thesis".
Step b. Next, to get to step b., the user "squares", or "self-multiplies", or "self-interacts", or "self-operate", or "self-applies", or "self-confronts" the content/result of step a., and considers the meaning of the result thereof:
step = b.
"thesis" "times" "thesis" =
"thesis" "of" "thesis" =
"thesis" & "anti-thesis".
Step c. Next, to get to step c., the user "squares" again, but this time "squares", or "[re-]self-reflects", the result of "squaring" the step a. result, that result being the content of step b., namely, the "cumulum" content
Step c. Next, to get to step c., the user "squares" again, but this time "squares", or "[re-]self-reflects", the result of "squaring" the step a. result, that result being the content of step b., namely, the "cumulum" content
--
"thesis" & "anti-thesis":
step = c.
step = c.
("thesis" & "anti-thesis") "times"
("thesis" & "anti-thesis") =
("thesis" & "anti-thesis") "of"
("thesis" & "anti-thesis") =
"thesis" & "anti-thesis" & "syn-thesis" &
"second anti-thesis".
Step d. Next, to get to step d., the user would "square" again, this time "squaring", or "[re-]self-reflecting", the result of "squaring" the step b. result, that result being the content of step c., namely, the "cumulum" content --
("thesis" & "anti-thesis") =
("thesis" & "anti-thesis") "of"
("thesis" & "anti-thesis") =
"thesis" & "anti-thesis" & "syn-thesis" &
"second anti-thesis".
Step d. Next, to get to step d., the user would "square" again, this time "squaring", or "[re-]self-reflecting", the result of "squaring" the step b. result, that result being the content of step c., namely, the "cumulum" content --
"thesis" & "anti-thesis" & "syn-thesis" &
"second anti-thesis"
"second anti-thesis"
-- and so on, for as many subsequent steps -- for as long -- as the succeeding result / content / "cumula" of symbolized categories makes sense, to the user, for the application at hand.
Commentary. All of the rules ["axioms"] of the F.E.D. "first dialectical ideography" rules-system ["axioms-system"], whose main rules were presented to this thread in a previous blog-entry, entry # 4 --
Commentary. All of the rules ["axioms"] of the F.E.D. "first dialectical ideography" rules-system ["axioms-system"], whose main rules were presented to this thread in a previous blog-entry, entry # 4 --
http://feddialectics-miguel.blogspot.com/2011/08/axioms-rules-of-fed-first-dialectical.html
"Thought it might be useful to reproduce here the core "axioms" -- the main rules -- of the "rules-system", or "axioms-system" ["axiomatic system"] of the F.E.D. "First Dialectical Arithmetic".
-- as well as the "Dyadic Seldon Function" itself, are aimed at inducing the above-rendered "m.o.", the above-rendered <<modus operandi>> -- the above-rendered "algorithmic" behavior: "the re-squaring of the previously squared", i.e., "the re-self-reflecting of each result of previous self-reflection", or, the "re-self-<<aufheben>>-ing" of each result of previous "self-<<aufheben>>s" -- in each generic "dialector" of the NQ_ dialectical ideography, when those generic "dialectors" are assigned to, or interpreted as standing for, i.e., as connoting, dialectical ontological categories, as named as such, generically, in the steps above, by the names "thesis", and "anti-thesis", and "syn-thesis", and "second anti-thesis", and so on.
Now, please note that the pattern of this method, or algorithm, is "evolute", not "convolute" --
evolute vs. convolute
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm
-- in that, for example, the content of step a. is still present in the content of step b., though also present "anded" with something new, or something newly-explicit/actual, formerly implicit/potential.
Likewise, the content of step b. [and therefore also the content of step a.] remains present in the content of step c., although, again, together with something(s) new. And so on, for each of the higher/later steps.
This "re-present-ation" of the past is part of the "conservation moment" of that universal process which is the very essence of all dialectic: the <<aufheben>> process of "conservation-elevation/transformation".
That is, step b. is not just --
"anti-thesis".
-- as it would be per a "convolute" product rule, but is, instead --
"thesis" & "anti-thesis"
-- because the "thesis", though surpassed in step b., is still, even if "faded", not forgotten; is still present in the "accumulator" of this "qualitative computation"; is still extant in the human memory of the user, and in the memories of the user's audience(s) -- even if somewhat "fadedly" present from "full present-ness" in both, relative to the "present-ness" to memory of the most recently "presented" ontological category, for both.
Likewise, step c. is not just --
"syn-thesis"
-- or even just --
"syn-thesis" & "second anti-thesis"
-- or even just --
"anti-thesis" & "syn-thesis" & "second anti-thesis"
-- but is, instead --
"thesis" & "anti-thesis" & "syn-thesis" &
"second anti-thesis"
-- since, as Hegel said, '''the [record of the] process of arriving at the result is [part of] the result'''.
F.E.D. holds this principle of "evoluteness" to be one of its several historically-<<gene>>-ric "universal principles", applying, albeit for different, "<<speci>>-al", reasons, to both the "physio-onto-dynamasis" <<species>> and the "ideo-onto-dynamasis" <<species>> of the universal pattern of ontology net-expansion.
ontology dynamics & onto-dynamasis
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/OntoDynamasis/OntoDynamasis.htm
ontology, physio-ontology, & ideo-ontology
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/PhysioOntology/PhysioOntology.htm
Some Examples.
A. Hegel's <<Logik>>.
Note: A "Triadic Seldon Function's" output develops from one category in step. a., to three categories in step b., to nine categories in step c., and so on, whereas the output of a "Dyadic Seldon Function", such as employed above, develops, as we have seen, from one category in step a., to two categories in step b., to four categories in step c.[, to eight categories in step d.], and so on, i.e., a category count, for the Triad-ic Seldon Function, of three to the power zero for step zero, of three to the power one for step one, of three to the power two for step two, and so on, versus a category-count, for the Dyad-ic Seldon Function, of two to the power zero for step zero, of two to the power one for step one, of two to the power two for step two, and so on.
step a. Abstract Being.
step b. Abstract Being "cubed" =
"Thought it might be useful to reproduce here the core "axioms" -- the main rules -- of the "rules-system", or "axioms-system" ["axiomatic system"] of the F.E.D. "First Dialectical Arithmetic".
-- as well as the "Dyadic Seldon Function" itself, are aimed at inducing the above-rendered "m.o.", the above-rendered <<modus operandi>> -- the above-rendered "algorithmic" behavior: "the re-squaring of the previously squared", i.e., "the re-self-reflecting of each result of previous self-reflection", or, the "re-self-<<aufheben>>-ing" of each result of previous "self-<<aufheben>>s" -- in each generic "dialector" of the NQ_ dialectical ideography, when those generic "dialectors" are assigned to, or interpreted as standing for, i.e., as connoting, dialectical ontological categories, as named as such, generically, in the steps above, by the names "thesis", and "anti-thesis", and "syn-thesis", and "second anti-thesis", and so on.
Now, please note that the pattern of this method, or algorithm, is "evolute", not "convolute" --
evolute vs. convolute
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/Evolute/Evolute.htm
-- in that, for example, the content of step a. is still present in the content of step b., though also present "anded" with something new, or something newly-explicit/actual, formerly implicit/potential.
Likewise, the content of step b. [and therefore also the content of step a.] remains present in the content of step c., although, again, together with something(s) new. And so on, for each of the higher/later steps.
This "re-present-ation" of the past is part of the "conservation moment" of that universal process which is the very essence of all dialectic: the <<aufheben>> process of "conservation-elevation/transformation".
That is, step b. is not just --
"anti-thesis".
-- as it would be per a "convolute" product rule, but is, instead --
"thesis" & "anti-thesis"
-- because the "thesis", though surpassed in step b., is still, even if "faded", not forgotten; is still present in the "accumulator" of this "qualitative computation"; is still extant in the human memory of the user, and in the memories of the user's audience(s) -- even if somewhat "fadedly" present from "full present-ness" in both, relative to the "present-ness" to memory of the most recently "presented" ontological category, for both.
Likewise, step c. is not just --
"syn-thesis"
-- or even just --
"syn-thesis" & "second anti-thesis"
-- or even just --
"anti-thesis" & "syn-thesis" & "second anti-thesis"
-- but is, instead --
"thesis" & "anti-thesis" & "syn-thesis" &
"second anti-thesis"
-- since, as Hegel said, '''the [record of the] process of arriving at the result is [part of] the result'''.
F.E.D. holds this principle of "evoluteness" to be one of its several historically-<<gene>>-ric "universal principles", applying, albeit for different, "<<speci>>-al", reasons, to both the "physio-onto-dynamasis" <<species>> and the "ideo-onto-dynamasis" <<species>> of the universal pattern of ontology net-expansion.
ontology dynamics & onto-dynamasis
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/OntoDynamasis/OntoDynamasis.htm
ontology, physio-ontology, & ideo-ontology
http://point-of-departure.org/Point-Of-Departure/ClarificationsArchive/PhysioOntology/PhysioOntology.htm
Some Examples.
A. Hegel's <<Logik>>.
Note: A "Triadic Seldon Function's" output develops from one category in step. a., to three categories in step b., to nine categories in step c., and so on, whereas the output of a "Dyadic Seldon Function", such as employed above, develops, as we have seen, from one category in step a., to two categories in step b., to four categories in step c.[, to eight categories in step d.], and so on, i.e., a category count, for the Triad-ic Seldon Function, of three to the power zero for step zero, of three to the power one for step one, of three to the power two for step two, and so on, versus a category-count, for the Dyad-ic Seldon Function, of two to the power zero for step zero, of two to the power one for step one, of two to the power two for step two, and so on.
step a. Abstract Being.
step b. Abstract Being "cubed" =
Abstract Being & Abstract Nothing & Becoming
[per "Triad-ic" Seldon function], =
B + N + q/NB.
B. Marx's Capital. Marx designates, in his Preface to the first German edition of Capital, vol. I. [pages 7 to 8, International Publishers, New World paperback edition, fifth printing, 1973], two distinct <<arche'>>, or starting-points, for his four volume treatise on the societal-self-reproductive system of the "capital-relation", i.e., for the epoch of capital as predominant human-social-relation-of-production:
". . . in bourgeois society the commodity form of the product of labour -- or the value-form of the commodity -- is the economic cell-form."
The "shallower" <<arche'>> is, thus, the commodity[-capital] value-form in general, as, i.e., <<genos>>. The "deeper" <<arche'>> is, thus, the "elementary or accidental form of [commodity[-capital]-]value", as, i.e., first <<species>> thereof.
Both <<arche'>> are embedded, as such, in the "content-structure" of Marx's actual text of Capital, vol. I. We will exemplify both, below.
"Shallower"-<<arche'>> version.
step a. Commodities.
B. Marx's Capital. Marx designates, in his Preface to the first German edition of Capital, vol. I. [pages 7 to 8, International Publishers, New World paperback edition, fifth printing, 1973], two distinct <<arche'>>, or starting-points, for his four volume treatise on the societal-self-reproductive system of the "capital-relation", i.e., for the epoch of capital as predominant human-social-relation-of-production:
". . . in bourgeois society the commodity form of the product of labour -- or the value-form of the commodity -- is the economic cell-form."
The "shallower" <<arche'>> is, thus, the commodity[-capital] value-form in general, as, i.e., <<genos>>. The "deeper" <<arche'>> is, thus, the "elementary or accidental form of [commodity[-capital]-]value", as, i.e., first <<species>> thereof.
Both <<arche'>> are embedded, as such, in the "content-structure" of Marx's actual text of Capital, vol. I. We will exemplify both, below.
"Shallower"-<<arche'>> version.
step a. Commodities.
step b.
Commodities "squared" =
Commodities "self-reflexed" =
Commodities + Monies.
step c.
(Commodities + Monies) "squared" =
Commodities +
Monies +
Monies Mediated Commodities Circulations +
Capitals.
"Deeper"-<<arche'>> version.
step a. Value-Form A.
step b.
Value-Form A "squared" =
Value-Form A "self-reflexed" =
Value-Form A + Value-Form B.
step c.
(Value-Form A + Value-Form B) "squared" =
Value-Form A + Value-Form B + Value-Form C +
The Money Form [of [Capital-]Value] .
Note that, indeed, Value-Form B, the "Total or Expanded Form of [Commodity[-Capital]-]Value" is, indeed, a "meta-<<monad>>-ization" of the <<monads>>, or units, of Value-Form A, the "Elementary or Accidental [, or Isolated] Form of [Commodity[-Capital]-]Value", and that --
Value-Form C, "The General Form of Value", is, indeed, a "hybrid", or "complex unity", of --
Value-Form B
-- with--
-- with--
Value-Form A.
C. F.E.D.'s Method of Presentation of the axioms-systems-progression of their systems of dialectical arithmetic -- "The Meta-Systematic Dialectic of the Dialectical Arithmetics Themselves".
step a. Unqualified Quantifiers System.
step b.
Unqualified Quantifiers System "squared" =
Unqualified Quantifiers System "self-reflexed" =
Unqualified Quantifiers System +
Unquantifiable Ontical Qualifiers System.
step c.
(Unqualified Quantifiers System, +
Unquantifiable Ontical Qualifiers System), "squared" =
Unqualified Quantifiers System +
Unquantifiable Ontical Qualifiers System +
Quantifiable Ontical Qualifiers System +
Unquantifiable Metrical Qualifiers System.
D. Historical Dialectic of Nature as Totality, per F.E.D. 's book A Dialectical "Theory of Everything" [excerpt, with "shallower"-<<arche'>>].
D. Historical Dialectic of Nature as Totality, per F.E.D. 's book A Dialectical "Theory of Everything" [excerpt, with "shallower"-<<arche'>>].
step a. atoms.
step b.
atoms "squared" =
atoms "self-refluxed" =
atoms + molecules.
step c.
(atoms + molecules) "squared" =
atoms +
molecules +
cosmological atoms to molecules conversion-processes +
prokaryotic "living" cells.
E. Historical Dialectic of Nature as Totality, excerpt for just the dialectic of "humanitys".
step a. "humanitys".
prokaryotic "living" cells.
E. Historical Dialectic of Nature as Totality, excerpt for just the dialectic of "humanitys".
step a. "humanitys".
step b.
"humanitys" "squared" =
"humanitys" "self-refluxed" =
"humanitys" + "meta-humanitys".
step c.
("humanitys" + "meta-humanitys") "squared" =
"humanitys" +
"meta-humanitys" +
cosmological "humanitys"-with-"meta-humanitys"-hybrids/alliances + . . ..
"Sub-dialectic" of practices, or "praxes", implicitly ensuing within / "inside" the "meta-humanitys" category.
cosmological "humanitys"-with-"meta-humanitys"-hybrids/alliances + . . ..
"Sub-dialectic" of practices, or "praxes", implicitly ensuing within / "inside" the "meta-humanitys" category.
sub-step a. human-genome biological self-re-engineering.
sub-step b.
human-genome biological self-re-engineering "squared" =
human-genome biological self-re-engineering "self-refluxed" =
human-genome biological self-re-engineering +
non-biological android robotics.
non-biological android robotics.
sub-step c.
(human-genome biological self-re-engineering +
non-biological android robotics) "squared" =
human-genome biological self-re-engineering +
non-biological android robotics +
cyborg prothetics / bionics + . . ..
F. Historical Dialectic of the Dialectic Itself, per F.E.D. --
step a. Systematic Dialectic.
cyborg prothetics / bionics + . . ..
F. Historical Dialectic of the Dialectic Itself, per F.E.D. --
step a. Systematic Dialectic.
step b.
Systematic Dialectic "squared" =
Systematic Dialectic "self-refluxed" =
Systematic Dialectic + Historical Dialectic.
step c.
(Systematic Dialectic + Historical Dialectic) "squared" =
Systematic Dialectic +
Historical Dialectic +
Meta-Systematic Dialectic +
Meta-Systematic Dialectic +
Psychohistorical Dialectic.
G. F.E.D.'s Meta-Systematic Dialectic "meta-model" for their method-of-presentation of the "ideo-ontology" of the contemporary "meta-system" of the axiomatic systems of the "Standard" arithmetics.
step a. Natural Numbers System.
[the "second-order logic", +, axiomatic system of the N = {1, 2, 3, ...} "Natural" Numbers' Arithmetic].
step b.
Natural Numbers System "squared" =
Natural Numbers System "self-reflexed" =
Natural Numbers System +
Natural Numbers System +
The System of the "Aught" Numbers,
(---)
N + A.
[the "second-order logic", +, axiomatic system of the "Aughts",
(---)
N + A.
[the "second-order logic", +, axiomatic system of the "Aughts",
A = { 0s } = {1-1, 2-2, 3-3, ...}].
step c.
(Natural Numbers System +
The System of the "Aught" Numbers) "squared" =
Natural Numbers System +
The System of the "Aught" Numbers +
The System for Converting/Reconciling Natural Numbers Arithmetic to/with "Aught" Arithmetic +
The System of the "Minus" Numbers,
(---)
N + A + q/AN + M =
W + M
-- wherein --
q/AN = {0...01, 0...02, 0...03, ...}
-- and --
M = { ..., -3, -2, -1 }
-- and --
W = {0...0, 0...01, 0...02, 0...03, ...}
The System for Converting/Reconciling Natural Numbers Arithmetic to/with "Aught" Arithmetic +
The System of the "Minus" Numbers,
(---)
N + A + q/AN + M =
W + M
-- wherein --
q/AN = {0...01, 0...02, 0...03, ...}
-- and --
M = { ..., -3, -2, -1 }
-- and --
W = {0...0, 0...01, 0...02, 0...03, ...}
-- the "Whole" Numbers.
step d.
(N + A + q/AN + M) "squared" =
N + A + q/AN + M +
System for Converting/Reconciling Natural Numbers Arithmetic to/with Minus Arithmetic +
System for Converting/Reconciling Aught Number(s) Arithmetic to/with Minus Arithmetic +
System for Converting/Reconciling the...q/AN...System of Arithmetic to/with Minus Arithmetic +
System of Fractional Arithmetic
(---)
N + A + q/AN + M + q/MN + q/MA + q/MAN + F =
N + A + q/AN + M +
System for Converting/Reconciling Natural Numbers Arithmetic to/with Minus Arithmetic +
System for Converting/Reconciling Aught Number(s) Arithmetic to/with Minus Arithmetic +
System for Converting/Reconciling the...q/AN...System of Arithmetic to/with Minus Arithmetic +
System of Fractional Arithmetic
(---)
N + A + q/AN + M + q/MN + q/MA + q/MAN + F =
Z + F
-- wherein --
q/MN = {+0...01, +0...02, +0...03, ...}
-- and --
q/MA = { ±0s }...=...{ ±(1-1), ±(2-2), ±(3-3), ...}
-- and --
q/MAN = { ±0...0, +0...01, +0...02, +0...03, ...}
-- and --
F =
-- wherein --
q/MN = {+0...01, +0...02, +0...03, ...}
-- and --
q/MA = { ±0s }...=...{ ±(1-1), ±(2-2), ±(3-3), ...}
-- and --
q/MAN = { ±0...0, +0...01, +0...02, +0...03, ...}
-- and --
F =
{.....-0...03/1....-0...02/1....-0...01/1....±0...0/1....+ 0...01/1....+0...02/1....+0...03/1.....}
-- [more aptly, for every n and m in N, F = { m/n } = { ./. }, but leads to the "dense" number-set notated above by step e., in which the arithmetic of "ratio-nal" numbers, or comprehensive Quotient numbers -- the Q arithmetic -- emerges]
-- and --
Z =
{..., -0...03, -0...02, -0...01, ±0...0, +0...01, +0...02, +0...03, ...}.
Regards,
Miguel
