In three venues apart from this blog, the content of my immediately previous blog-entry has evoked the following three dialogues.
The names have been changed to protect the innocent, or to protect the guilty, as the case may be.
Regards,
Miguel
Query 1: '''Miguel, can you explain the a^3 equation again? ....and what do you mean by self-negation?'''
Response 1: '''Sure!
The full Seldon formula for dialectic, that can go as far beyond just the first three terms of the triadic dialectic, if need be for a given, specific dialectical model, is --
a^(3^S)
-- where the S is a whole number that counts the Steps of the dialectical categories-progression.
This formula means that the exponent of category a -- 3 -- is itself raised to a further exponent, S.
So, starting from S = 0, for the 0th Step of the argument/progression, we obtain --
a^3^0 = a^1 = a
-- and you just get back category a, the starting point of the whole progression of categories.
When you move on to S = 1, for the 1st Step of the argument/progression, you get the formula that you asked about [note that, in Seldon's category-notation, x + x = x, not "2x", because having more than one "copy" of a given category-symbol is redundant and immaterial; e.g., one apple "plus" THE SAME one apple is still JUST THAT one apple. ] --
a^3^1 = a^3 = a x a x a = a of (a of a) = a(a(a)) = ~(~(a)) =
aaa = a x ( a + b) = aa + ab = a + b + ab = a + b + C(a, b)
-- you can see that the "negation operator" here -- the "negator", '~' -- for the category a, in the negation of the negation of category a --
~(~(a))
-- is the category a ITSELF: ~ = category a itself, FOR / RELATIVE TO category a.
When you move on to S = 2, the 2nd Step of the argument/progression, your get --
a^(3^2) = a^9
-- which generates a "sum" of 9 qualitatively distinct categories: a triad OF TRIADS.
And so on, to higher Steps in the argument/progression, if needed to model the reality at hand.
Thus --
~a = a x a = aa = a + b
-- stands for the dialectical, "SELF-Negation" of category a.
Dialectical self-negation is NOT the same as formal logical, propositional negation.
Dialectical self-negation is NOT just a "Not".
Dialectical self-negation is a SELF-<<Aufheben>> operation -- to use the German word, <<aufheben>>, the word that, for example, Hegel, Marx, and Engels used when writing about dialectic -- such that category a concurrently (1) transforms, (2) conserves, and (3) elevates category a itself, IN CATEGORY a's OWN WAY [also called "determinate negation", or "concrete negation", which transforms a "something" into a "something else", as opposed to formal, "abstract negation", which turns a "something" into a "nothing"].
For example, in the dialectic of pre-human Nature, when atoms expandedly reproduce their populations at various loci within the self-evolving cosmos -- within the galactic interstellar medium of each typical galaxy -- and also "self-concentrate" in terms of physical-space proximity, e.g., in the early "atomic clouds" from which new stars are self-born, atoms begin to form molecules, initially a new, unprecedented, never-before existing kind/category of physical being.
A molecule is a 'meta-atom', in that each molecule is made up out of a [typically] heterogeneous multiplicity of atoms -- H2O, CO2, CN, CH4, NH4, etc., etc.
Atoms themselves, growing quantitatively, i.e. growing in numbers, e.g., from ongoing stellar nucleosynthesis/novae/other stellar mass ejection, and concentrating -- self-densifying -- in local physical space volumes, themselves cause the qualitative change of the irruption of the first molecules.
Thus, this natural-historical process constitutes a dialectical SELF-negation of atoms, which produces more atoms but also the qualitatively different, new, more advanced kinds of things that are molecules --
atoms ---> atoms + molecules.
This constitutes a "self-<<aufheben>> self-negation" of atoms, because molecules are --
(1) a [self-]TRANSFORMATION of atoms, that are qualitatively different from atoms;
(2) a [self-]CONSERVATION of atoms, because the atoms are still there, INSIDE each molecule, and;
(3) a [self-]ELEVATION of atoms, because molecules represent a new, higher [more inclusive] PLANE OF EXISTENCE, relative to the [lower, less-inclusive] PLANE OF EXISTENCE occupied / constituted by atoms / primordial interstellar atomic clouds:
atoms^3 = atoms x atoms x atoms = ~(~(atoms)) =
atoms + molecules + Combinations/Hybrids of atoms with molecules
-- e.g., C(atoms, molecules) = "galactic, interstellar MOLECULAR[/atomic] CLOUDS".'''
Query 2. '''Thank you for your contribution.'''
'''There is much of interest in what you write, though I doubt whether a beginner coming to subject for the first time would be able to understand much of what you have written.'''
'''I prefer to keep explanations as simple as possible.'''
'''Just one comment on the content of your contribution: You locate dialectics in thought – i.e. in concepts.'''
'''Just one comment on the content of your contribution: You locate dialectics in thought – i.e. in concepts.'''
'''That is undoubtedly correct, but I would say that
the external world – or what one can call things-in-themselves – also have a
dialectical character.'''
'''And it is simpler to start with explaining the
characteristics of “what is” before considering how we know that which is.'''
Response 2. "'Thank you for your substantive feedback!!'''
'''I think that you are right -- my "simple
explanation" of dialectics would only work for beginners who have
familiarity with abstract algebras, or, at least, who are not intimidated by
formulas, as so many are today.'''
'''I also agree with you that the dialectic pattern applies not
only to movements of human thought, but to movements in the objective world of
pre-human/extra-human nature as well.'''
'''I erred in not writing this viewpoint, which I share with
you, into my explanation more clearly.'''
'''My seventh sentence should have read something more like:
"The reality that we represent by a kind-of-thing
category, call it "a", interacts with itself, or 'intra-acts',
because of its internal strife -- in the internal mind, or in the external
world, or in both concurrently, and the same, generic category-notation can
capture the dynamics for both idea-objects-only categories, and for categories
of physical things." '''
'''In any case, the Seldonians, avoiding this mistake, have applied
this category-notation to formulate dialectical models -- e.g., of the
historical evolution of the social forces of production, of the historical
evolution of the social relations of production, and of the historical
evolution of human-social formations -- models that consist of MANY more than
three categories in series.'''
'''Given that you are clearly NOT a beginner in the subject of
dialectics, you might enjoy all seven of the Seldonians' "psychohistorical
dialectical equations", including the three that I just mentioned --
Query 3. '''Okay...I'm confused -- the colours make it a pain to read.'''
Response 3. '''That's funny, other people tell me that they like the text color -- makes for a more colorful, "illuminated manuscript" kind of feel, they say.'''
'''In any case, the syntactic purpose of the text color-coding is to help readers keep track of the -- crucial -- ordinality of the categories in the dialectical category-progressions, for up to the first seven categories.'''
'''That is, the order of the color-spectrum, from lower to higher frequencies of EMR, namely --
RED ORANGE YELLOW GREEN BLUE INDIGO VIOLET
-- is paired with the ordinal qualities of --
{ first-ness, second-ness, third-ness, fourth-ness, fifth-ness, sixth-ness, and seventh-ness }
-- under the theory that abstract ordinality, i.e. '''pure time''' [cf. famous essay by William Rowan Hamilton], is the most abstract, most fundamental determination of dialectic.
The color coding of, e.g., the symbol for category a, in a different color from that of, e.g., the symbol for category b, also helps to highlight that these categories represent qualitatively different content, not just quantitatively-different content, viz. --
a is not greater than b
AND
a is not equal to b
AND
a is not less than b
THEREFORE
a is not quantitatively equal to b nor is it quantitatively unequal to b
ERGO
a is qualitatively unequal to b
-- i.e, that underscored algebraic symbols such as a and b function, not as ordinary numbers, but, on the contrary, as 'contra-Boolean meta-numbers'.'''
'''Any more substantive confusions that I can help clear up?'''.
FINI, so far!
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