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

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 Platonian Dialectic --

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

Dear Reader,

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, “individuals” level.

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 the “individual”  «species» of that, second, level.

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

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-units’ is, 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.

Regards,

Miguel