‘Dialectical, Ontological-Categorial Complexity’, or ‘«Aufheben»-Complexity’.

 

 

‘Dialectical,

 

 Ontological-Categorial

 

Complexity’,

 

or

 

‘«Aufheben»-Complexity’.

 

 

 

GLOBAL STRATEGIC HYPOTHESES.

 

 

 

 

 

 

 

 

 

 

 

Dear Reader,

 

 

The term “complexity” is often bandied about in contemporary discourse, all too often as a nebulous concept, with very little specificity or clarity as to the exact meaning of this term, and as to any means for its measurement.

 

 

However, in the Domain of Seldonian, ontological, categorial-progression dialectics, ‘‘‘complexity’’’ is a very simple, very clear, and easily-measurable feature of dialectical ontological categories. 

 

A given category is more ‘«aufheben»-complex’ than another category of its Domain, if each typical unit of that given category’s “kind” contains multiple [former] units of the latter category’s ‘units-kind’. 

 

Moreover, the “deeper down” the units of the latter category inside the units of the given category, the more units, or steps, by which the ‘«aufheben»-complexity’ of the given category exceeds the ‘«aufheben»-complexity’ of the latter category. 

 

For example, the galaxy units of the category “galaxies” are one complexity-unit, or one step more ‘«aufheben»-complex’, than are the star units of the category “stars” 

[see the graphical ‘‘‘compositional’’’ depiction, posted above].

 

This is because each single typical galaxy unit contains a vast and heterogeneous multiplicity of star units.

 

The “galaxies” category is also, by the same token, more “determinate” – more ‘determinations-rich’ – than the “stars” category.

 

This is because each typical galaxy unit subsumes the determinations or characteristics of star units, while also exhibiting determinations or characteristics which each typical star unit lacks, when it is grasped individually, relatively-abstractly; in abstraction from its surroundings. 

 

 

Similarly – ‘qualo-fractally’ – but even more so, the “galactic clusters” category, each of whose units are typically made up out of a large and heterogeneous multiplicity of galaxy units, is two units, or two steps, more ‘«aufheben»-complex’ than the “stars” category. 

 

This is because each of the typical units of the “galactic clusters” category contains multiple units of its immediate predecessor category – the “galaxies” category – each typical galaxy unit in turn containing a vast multiplicity of star units.  

 

Likewise, the next up, ‘self-hybrid’, next ‘antithesis-category’ or ‘contra-category’, the “galactic super-clusters” category, has, for its immediate ‘units-kind’, a heterogeneous multiplicity of, ‘multi-galaxy-cluster’, super-cluster units, each one, in turn, typically containing a heterogeneous multiplicity of galactic cluster units, each one, in turn, typically containing a heterogeneous multiplicity of galaxy units, each one, in turn, typically containing a vast multiplicity of star units. 

 

The “galactic super-clusters” category is thus three units, or three steps of ‘«aufheben»-complexity’ above and beyond the ‘«aufheben»-complexity’ of the “stars” category. 

 

And so on, up further in the ‘qualo-fractal compositional tower’ of dialectical, ontological categories, depicted in the image above. 

 

 

The above narrative description applies especially to the chain of, ‘self-hybrid-unit-ed’, ‘antithesis categories’, or ‘contra-categories’ – the only kind of categories depicted in the image above – whose ordinal ‘place-numbers’ are of the form 2^w, w in the [ordinal] whole numbers, W = {0, 1, 2, 3, 4,…}, or W = {zeroth, first, second, third, fourth,…}.

 

But the above description is also apt, in more involved ways, for the “hybrid” categories – ways which we will not pursue for this occasion. 

 

Suppose that the units of the ‘contra-category’ with ordinal number 2^w2, in comparison to the units of the ‘contra-category’ with ordinal number 2^w1 – such that W contains w2, which is > w1, also in W – are units which exhibit characteristics, or determinations, which units of ordinal number category 2^w1 lack.

 

We then also say that, while both categories subsume and share all of the characteristics or determinations of the units of the ordinal number 2^w1th category, the units of the ordinal number 2^w2th category exhibit additional characteristics or determinations, which are NOT those-of/shared-with the units of the ordinal number 

2^w1th category. 

 

We therefore term the ordinal number 2^w2th category a [perhaps multi-determinations’] ‘‘‘determinate negation’’’ category relative to the ordinal number 2^w1th category.

 

That is the relationship of ‘NOT-ness’, or “negativity”, and of mutual, partial, supplementary opposition, that obtains between those two dialectical, ontological categories, and between successive pairs of such ‘contra-categories’ in general.  

 

 

 

 

 

 

 

 

 

 

 

For more information regarding these Seldonian insights, and to read and/or download, free of charge, PDFs and/or JPGs of Foundation books, other texts, and images, please see:

 

www.dialectics.info

 

 

and

 

 

https://independent.academia.edu/KarlSeldon

 

 

 

 

 

 

 

 

 

 

 

For partially pictographical, ‘poster-ized’ visualizations of many of these Seldonian insights -- specimens of ‘dialectical art’ – as well as dialectically-illustrated books published by the F.E.D. Press, see –

 

https://www.etsy.com/shop/DialecticsMATH

 

 

 

 

 

 

 

 

 

 

 

¡ENJOY!

 

 

 

 

 

 

 

 

 

 

 

Regards,

 

Miguel Detonacciones,

 

Voting Member, Foundation Encyclopedia Dialectica [F.E.D.];

Elected Member, F.E.D. General Council;

Participant, F.E.D. Special Council for Public Liaison;

Officer, F.E.D. Office of Public Liaison.

 

 

 

 

 

 

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