Sunday, December 22, 2013

Platonian Dialectic -- ‘Ideo-Taxonomic Content-Structure’ of a Generic / Minimal «Arithmos Eidetikos».

Full[er] Title:  

 Platonian Dialectic --

Ideo-Taxonomic Content-Structure of a Generic / Minimal «Arithmos Eidetikos».

Dear Readers,

The ‘‘‘minimal’’’ ‘content-structure’ of the original, Platonian, «Arithmos Eidetikos» dialectic is that of a ‘class-ification’ of «Eide», or of «Ideas», that is, of an 'Eide-Systematic Eide-Taxonomy', or an Ideo-Taxonomy, for which ‘‘‘minimality’’’ means that it consists of a single category-unit at its most general,  «genos», third level, a multiplicity of «species» category-units at its more specific, «species», second level, and an even larger multiplicity of individual «Eide»-units ‘“under”’ each of its «species» category-units at its first, most detailed, “individualslevel.

The individual units «aufheben» -- that is, they simultaneously, as a single movement, annul at their own level / elevate-in-abstractness-or-in-generality / conserve-in-implicitude within the next higher level -- i.e., into the «species»-level, by means of meta-individual-ization’, meta-unit-ization’, or meta-«monad»-ization’.

The multiplicity of «species» categorial-units «aufheben» into the single «genos» category-unit by meta-unit-ization’ of the individual «species» as category-units , that is, by the meta-«monad»-ization’ of the «species»-level «monads», i.e., of theindividual  «species» of that, second, level.

This ‘content-structure’ is depicted in the diagram below.

This diagram describes a ‘content-structure’ that is not simply “synchronic”, in the sense of modern variants of Hegelian and Marxian ‘‘‘systematic dialectic’’’, or synchronic dialectic.

That is, it does not present the systematic order of the categories comprehending a given sub-totality for just a single, synchronic “slice”, or “cross-section”, "cut", selected, and sampled from just one moment of the diachronic extention’, i.e., of the history, of the system or sub-totality to be thereby presented in ‘de-chaoticized’, ‘theorized’, systematic order.

Given Plato’s Parmenidean proclivities, when it comes to Plato’s «Arithmoi Eidetikoi», this picture depicts a potentially infinite assemblages of absolutely identical such “slices”, whether sampled from past eternity, from the present historical moment, or from future eternity -- every moment, every slice containing the same, immutable content.

Referencing this depiction, we can define the layers / levels / ‘qualo-fractal scales’ of the structure of its content as follows --

Definition.  «Idea-Genos».  An «Eide-Genos» category-unit is a meta-«Eide-Species»’ category-unit, made up out of the heterogeneous multiplicity of its «Eide-Species» [sub-]category-units, each of which «Eide-Species» category-unitsis, in its totality, qualitatively unequal to every other «Eide-Species» category-unit, due to its «differentia specifica» -- although each «Eide-Species» category-unit may not, in every case, be a qualitative opposite of every other «Eide-Species» category-unit in its «Eide-Genos».  However, each of these «Eide-Species» category-units do share a definite ‘«gene»-ric’ quality, “property”, predicate, feature, attribute, or characteristic in common, that determines their «Eide-Genos», their “belonging” to that «Eide-Genos», and which constitutes the quality which defines that, their «Eide-Genos».  That is, the «Eide-Genos» category-unit is the product of the 'meta-unit-ization' of its «Eide-Species» category-units.

Definition.  «Idea-Species».  An «Eide-Species» category-unit is a meta-individual categorial unit, a meta-«Idea-Monad»’ category-unit, made up out of a heterogeneous multiplicity of mutually similar but not mutually-identical base units, elementary individuals which are NOT categories implicitly “containing” a multiplicity of such individual «Ideas».  All of these ‘‘‘ultimate individuals’’’ [‘‘‘ultimate’’’ not absolutely, but rather relative to the given universe of discourse] share a ‘«speci»-fic’ quality, “property”, predicate, feature, attribute, or characteristic, that determines their «Species», their “belonging” to that «Species», and the quality which defines that «Eide-Species».  That is, an «Eide-Species» category-unit is the product of the 'meta-unit-ization' of its «Eide-Monad», NON-category-units.

Definition.  «Idea-Monad».  An «Eide-Monad» is an ultimate individual, NON-category-unit [‘‘‘ultimate’’’ not absolutely, but rather relative to the given universe of discourse], a unit of the most concrete -- de-abstracted or pre-abstracted -- vertical «arché»-level of this 3-scale / 3-layer / 3-level, qualo-fractal ‘content-structure’:  a ‘‘‘multi-chromatic’’’, ‘‘‘multi-foliate’’’, ‘multi-predicate’ logical unit, or ‘‘‘logical individual’’’, analogous to the ultimate ‘‘‘ur-elements’’’ of a set, i.e., to the elements which are not, themselves, also sets.



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