Dear Psycho-History Group Members,
Perhaps more than any other modern philosopher, it was Hegel who sought to fulfill the Platonian Programme of Charting the 'Conceptual Cosmos', i.e., the Realm of the fundamental "Idea-Monads", or "Idea"-UNITS, which, per the Idealist view, eternally undergirds all of Nature-al, including Human-Nature-al, Actuality -- the .... "Eide-Gene"- and "Eide-species"-....-structured realm of Plato's Dialectical "Arithmoi Eide-tikoi".
In the Great Circle of Hegel's System, from "Logik" to "Natur" to "Geist" back to "Logik" again, Hegel sought to implement the Platonian prescription, of "doing away with assumptions", by having the "Logik" serve double, dual duty, as both premise/assumption and ultimate conclusion again, in a circular self-justifying chain of systematic, dialectical derivations --
"There remain geometry and those other allied studies which, as we have said, do in some measure apprehend reality; but we observe that they cannot yield anything clearer than a dream-like vision of the real so long as they leave the assumptions they employ unquestioned and can give no account of them. If your premise is something you do not really know and your conclusion and the intermediate steps are a tissue of things you do not really know, your reasoning may be consistent with itself, but how can it ever amount to knowledge? ... So... the method of dialectic is the only one which takes this course, doing away with assumptions. ... Dialectic will stand as the coping-stone of the whole structure; there is no other study that deserves to be put above it."
[Nicholas Rescher; Dialectics: A Controversy-Oriented Approach to the Theory of Knowledge; SUNY Press (Albany, NY: 1977); pages 46-48].
The opening exposition of the first of the three "nodes" of this Great Circle of Hegel's "En Kyklo Paideia", Hegel's "Logik", was originally published by Hegel in 1812, has, in its first two Chapters, the following large-scale structure, in outline --
Volume I. The Objective "Logik"
Book I. The Doctrine of Being
Section I. Determinateness [Quality]
Chapter 1. [Abstract] Being
A. [Abstract] Being
B. [Abstract] Nothing
C. [Abstract] Becoming
Chapter 2. Determinate Being
.
.
.
While it is our ambition to reveal the intuitive justification of the
dialectical-logical "followership"-relations -- the exact sequence -- of the "ideo-ontological" categories of Hegel's entire categorial progression in the "Systematic-Dialectical" Order of Presentation in his "Logik", including for its Volume II., The Subjective "Logik", to the extent that it can be so justified, we will attempt to model only the concept-progression of the first two chapters, as outlined above, for the purposes of this present posting.
This intuitive, heuristic, intensional, and ideographical model of the above, opening, portion Hegel's "Logik" will be presented in the language of the [subscipt-N]Q-underscore, or N\Q [this Q should be underscored, but Yahoo typography does not avail] Dialectical Ideography, or "Dialectical "Characteristica Universalis" [ = Universal "Character-Language", or "Universal Philosophical Algebra"], employing the "axioms", including the "rules of calculation", posited to this forum in an earlier posting [which see, for the details on the "purely qualitative computations" employed here].
More information on this new, "contra-Boolean", "Dialectical Symbolic Logic" can be found via the following link --
www.dialectics.org . . .
The "arche'", the beginning "ideo-ontological" category, or "Concept", of Hegel's "idea-ontology", or "universe of fundamental ideas", is that which Hegel names ["Abstract"] Being, which we will denote by using the second phonogram of our alphabet AS a mnemonic, "abbreviative" ideogram, "standing for" Hegel's Concept of "Abstract Being", in the unity of all of its explicit and implicit connotations or "intensions" -- i.e., its TOTALITY OF MEANING(s) -- by, simply, B, or, equivalently, by q-subscript-B, or q|B.
We use the symbol/ideogram '=', to denote the relationship named "equal by definition" as well as the relationship named "equal by computation", since Yahoo typography does not support the traditional "three parallel segments" symbol for the former.
For our model, we will identify this beginning idea-object with the beginning or initial "ontological qualifier meta-number" of the N\Q arithmetic, such that --
N\Q = {q|N} = { q|1, q|2, q|3, q|4, . . . }
-- namely, q|1.
We signify this mental act of identification, "assignment", or "interpretation", via the ideogram ''.
Thus, we write --
q|1 B, or, symmetrically, B q|1
-- meaning that, in the "homeomorphic defect" of this model, we attribute all of the algorithmic properties of q|1 to the "intension-symbol", "connotation-symbol", "category-symbol", and "Concept-symbol", B.
We use, e.g., "x^2" to denote "x-squared" -- x with the "exponent" or "raised" to the "power" of 2, and, e.g., x^(2^3) to denote x "raised" to the power of 2^3, or 8.
We seek to generate the following progression of category-series, or
category-sums, by letting the two-levels-of-exponentiation formula for the generic dialectic, [q|1]^(2^(s)), where s counts the steps in the presentation / argument, guide the repeated, self-iterated self-reflexion of the Concept, denoted B, in its specific dialectic, modeled as B^(2^(s)), to see if the thus algorithmically-guided progression of connotational, intensional symbols, makes intuitive, heuristic, connotative sense.
We use symbol formations like "X ---> [Y + Z]", to "ideogramize" the expression "X BECOMES [Y + Z]", or " "Over Time", or "Upon Further Reflection", X TRANSFORMS ITSELF INTO [Y + Z]".
The progression of Hegel's "Logik", Chapters 1 & 2, that we wish our model to reproduce, and to distill the "sense" of, is --
[Abstract] Being --->
[Abstract] Being + [Abstract] Nothing --->
[Abstract] Being + [Abstract] Nothing + [Abstract] Becoming --->
[Abstract][Being + Nothing + Becoming] +
Determinate [= No-Longer-Abstract] Being.
0. Step 0., with s = 0, simply [re-]posits the B x B = BB = B(B) = B^(2) =
B + delta_B =
B + q|BB =
B + N
Being ---> Being(Being) = Being "of" Being =
Being "squared" = Being^(2) =
Being + delta_Being =
Being + Nothing.
Note that, generically, this result has the form:
Thesis + Contra-Thesis.
Thus -- if this progression is intuitively plausible to you -- you now have a dialectical model of Parts A. and B. of Hegel's dialectical "Logik", per the outline above, via step s = 1 of the two-exponential-level "self-iteration" formula B^(2^(s)).
But what of Hegel's Part C.?
Our model, to encompass Hegel's Part C., must INTUITIVELY yield, in its second step, for s = 2, something like --
( Being + Nothing ) --->
( Being + Nothing )( ( Being + Nothing ) ) =
( Being + Nothing ) "of" ( Being + Nothing ) =
( Being + Nothing ) reflecting upon ( Being + Nothing) =
( Being + Nothing ) x ( Being + Nothing )
( Being + Nothing )^(2) =
( Being + Nothing + Becoming . . . ).
So, let's look at the "Connotative Logic" of step s = 2.
2. Step 2., with s = 2, applies the conceptual activity / functioning
/"ideo-eventity" / "mental-process-object" connoted by ( B + N ) to itself:
B^(2^(2)) = B^(4) = ( B^(2) )^(2) =
B^(2 x 2) = ( B + N )^(2) =
( B + N ) "of" ( B + N ) = ( B + N )( ( B + N ) ) =
( ( B + N ) + delta_( B + N ) ) =
( B + N + q|NB + q|NN ) =
( q|B + q|BB + q|NB + q|NN ).
So, what do the two new, emergent, "Idea-symbols" / "Category-symbols" / "Concept-symbols", namely q|NB and q|NN, connote for us?
q|NB:
This ideographic symbol connotes, per the standard F.E.D. interpretation, the "subsumption" of B by N, the "subsumption" of "Being" by "Nothing" / "[self-]conversion" of "Being" into "Nothing", a "moment" which Hegel describes as the passage, or [self-]movement, from "Being" to "Nothing", or as the process of "Ceasing-to-be".
This symbol also has the reverse, "commutative", shadow-connotation of q|BN, the subsumption of N by B, the subsumption of "Nothing" by "Being", the [self-]conversion of "Nothing" into "Being", the other "moment", which Hegel describes as the passage, or self-movement, from "Nothing" to "Being", or as the process of "Coming-to-be".
Hegel describes the combination, or unity, of these two "moments" -- of "Coming-to-be[" and "Ceasing-to-be" -- which is also the result of the combination, or '" complex/unity/unification/'unit-ification' "', of the Concept that Hegel names "Being" with the Concept that Hegel names "Nothing" -- as the Concept / Category / Idea-Function, or Idea-[Process-]Object that he names "Becoming".
Thus, we hold, q|NB = q|BN connotes a new idea-increment, that appropriately nameable as "Becoming".
The human mind, thinking the Concept of "Being", soon finds itself also thinking the Concept of "Nothing", and, shifting the emphasis of its thoughts to the Concept of "Nothing", soon finds itself remembering again that, if this "universal set" looks like it stands for "Nothing"-in-particular, "Nothing"-specific, if viewed EXTERNALLY, from its "OUT-SIDE", i.e., viewing its unitary outer skin only, as enclosing a single "set"; in effect, viewing its "[em-]braces" only, just '{' and '}', as it were, that this set, viewed INTERNALLY, from its "IN-SIDE", is seen in an exactly opposite light, as a vision of the plenitude of all particular being; as an exhaustive listing of the maximal qualitative diversity of every single "logical individual" in the universe, and, so, that human thought-process returns itself to the Concept of "Being" once again.
The human mind, observing itself in this continual OSCILLATION, moving from "Being" to "Nothing" ["Ceasing-[to]-be[ing]"; "Passing-Away[-from "Being"]], then, once again, as a result of that just-previous movement, moving itself again, back from "Nothing" to "Being" ["Coming-to-be[ing]]"; "Arising[-from-"Nothing"-to-"Being"]], should name its behavior in this thought-process by the word "Becoming", in that double sense, per Hegel.
q|NN:
All three of the Categories evoked so far have been "Abstract", or free of specific, particular, concrete attributes, or "determinations".
They have been "NOT-Determinate" categories; "NON-Determinate" categories; "IN-Determinate" Categories.
"Being" in this context means "Abstract Being", "Being" lacking any substantive, distinguishing features or facets. That is precisely why these "Being" immediately collapses, into / to "Become", "Nothing".
"Abstract Nothing", the "Contra-Thesis" Concept to this "Abstract Being" Concept, in this context, is even more "Abstract" than the "Abstract Being" Concept, which collapses into it, because this "Abstract Nothing" Concept intends absolutely no determinations whatsoever, whereas "Being" at first seems to be about -- pretends to be about -- something more, some "Quality" or other; "Quality" in general, until, upon further reflection, that ruse collapses, into "Nothing".
This, the "self-reflexion" of this nadir of determinateness, of this zenith of INdeterminateness, or "Abstract-ness", the Concept of "Abstract Nothing", calls forth, calls to mind, its own opposite, which is also the opposite of the entire --
"Abstract Being + Abstract Nothing + Abstract Becoming"
-- triad; the opposite of "Abstract-Ness" itself, namely "Determinate-Ness" -- "DETERMINATE Being".
Thus, q|NN connotes the Category / Concept of "Determinate Being", connoted here by D.
If this connotation-logic works -- "goes through" -- convincingly, for you, then you now have an dialectical-ideographic, shorthand mathematical model of the first two Chapters of Hegel's dialectical "Logik", in three steps, s = 0 to s = 1 to s = 2:
s = 0, B^(2^(0)) = B;
s = 1, B^(2^(1)) = B^(2) = B + N;
s = 2, B^(2^(2)) = [ B + N ]^(2) =
[ [ B + N ] + [ q|NB = q|BN ] + D ] =
B + N + q|NB + D.
Note that this third step in the "Systematic-Dialectical" presentation of
Hegel's "Dialectical Logic" has the generic form --
First Thesis + First Contra-Thesis + First Synthesis +
Second Contra-Thesis,
or
Thesis 1 + Contra-Thesis 1 + Uni-Thesis 1 +
Contra-Thesis 2.
Regards,
Psi_Sci
