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One of the conceptual difficulties that Hegel and perhaps earlier philosophers had was terminological. How could they label what they experienced or envisaged when it was fractal in nature, construction and design, scale free in aspect?

Thanks to Benoit Mandelbrot we changed from being frightened or shushed into not discussing or peering into the infinite regression of our analysis. Unlike Kant we followed Cantor. We tried to name the infinities, and it drove him mad on several occasions. But it was Benoit who served as a collection point for many others who ventured into that domain. It was Benoit who spearheaded an offensive on the citadels of Mathrmatica and tore open a breach to let the monsters in! Zombie apocalypse! Only the Zombies were the Staid and defiant professoriate, the board of mathematicians who tried to stave off the inevitable. The breach gun of course was the rising computational tools of programmable calculators and computers.

Ultimately as my self awareness develops it will mean that my experiential continuum will become indistinguishable from the universal monad. It will be a scale free fractal alignment, not a mirroring only, as previous philosophers struggled to express this profound state of Nirvana with Shunya?
Yhe universal monad is a scale free fractal of every monad totality the " I" can conceive. Each unit or monad is essentially a universe at a different scale. It is the primitive manifestation we perceive at the sensory level on which we synthesise our dialectic constructions up to the universal monad, where we and the universal monad are no longer distinguishable, and all distinctions become meaningless.

As it is unlikely that an individual consciousness will apprehend this state sufficiently to fully communicate it. It is thus a matter of logical or analytical positivism or faith that it even exists! So ultimately the founding principle is acceptance.

Weise, werden, Erzeugen, entstehen.!  These are crucial concepts in this section.

First though it is important to realise that Herman has not yet defined a concept one might call " reality". This is perhaps why some cannot get to grips with his use of Hegelian dialectic. So far everything has been in terms of thought experience, that conscious quality one perforce has to accept because to reject it is akin to madness and permanent disorientation. Some call it awareness or consciousness it I call it an experiential continuum.

Thus thought experience in General is where Herman  situated himself.

Weise is thus that tested quality that is perceptible in another's behaviour, their style, manner, speech, practice etc. It is that quality that one most readily associates with learned behaviour, and thus from that concept it forms the basis for wit, wisdom, intelligence, intellect, a cognisance that associates to all the answers to the questions: how?, who? what?, where?, when?, and yes to a pinch, just a little portion of why?. .
In oneself one is aware of Weise as an intuitive competency , hard won by life's experience, on the edge of unconscious and conscious competency and inate know how. But it demonstrates itself not just internally and subjectively but more importantly objectively and evidently.

The idea that an entity can come into being onto Weisse is unfamiliar but sensible. Weise results in evidential behaviours, thus it is a vehicle for evidencing qualities that may be otherwise invisible or not known. Like a compact disc the grooves or embossed patterns carry information in addition to the disc itself. Thus this information reeified onto the disc just as these thought reified  entities reify "onto" Weise.

Commentary
Every reified thought can be " unfolded" onto a twofold cognisance.!

This point is crucial to his argument and dialectic. There is always at leastn2 ways of considering the same experience, to ways of expressing the same experince two ways of arriving at the same conclusions.

In point of fact there is always more than one way to come to a performance of any action so here Hermann is trying to establish the necessity and sufficiency of 2 !

He needs 2 for a dialectic process anyway so that must not be overlooked, but here he is already preparing the ground or a quantitative apprehension.

In point of fact he is tracing over the Pythagorean insights. The Pythagoreans understood pragmatically tha reality could be analogised in sketch fom. A drawn picture could capture aspects of the experiential continuum in a referential way. The difference between what we experienced and what we drew of our experience is the difference between a continual form and a discrete format!

Our senses may be thought to provide us with a continuous experience, but a picture drawn by hand or photographed provides us with a discrete experience. That discrete experince is dependent and characterised by setting and binding.

This is a rather general 2 fold process not yet defined by Hemann, but self evidently it refers to the piecemeal way we have to laboriously construct representations of our experiences which by contrast seem immediate.

For example, to build a house requires the builder to set out the bricks, and the cement and then to bind them together in a house pattern.  The idea of settings and bindings is thus a general conceptual mechanism by which he will drive his dialectic.

He shows how this 2 fold pattern can be used to account for something that on the face of it is adequately accounted for by one magical act.

This process of simplifying to one cognisance permeates physics, and has lead to procedural errors in understanding. As an example the electric fluid was described in Volta's time as consisting of 2 fluids. It was well accepted as a convincing explanation of empirical results. However Franklin decided to reduce it to one fluid of consequence..

The difficulty in explaining physics in one particular cognisance is its blinding to empirical data that shows there are dual behaviours! By accepting dual cognisances as the foundation of apprehension one comprehends more naturally the supposed contradictions that must exist in a single cognisance.

A dual cognisance arising from a unity or rather a unit arising from a dual cognisance is precisely where Hegel began his synthesis and analysis of the phenomenology of Geist( spirit/ mind).

The deepest open " secret" of the Pythagoreans is the Monad/ Metron. This concept arises out of a dualist( iso meaning dual) process of judgements and judgement calls. The monad represents the foundational unit into which the ultimate unit or Monas is deconstructed by the human thought process. The Monas is by their philosophy deconstructed into Henads and each Henads further deconstructed and so on. In contrast their Monas  is constructed or synthesised by gathering together in thought foundational monads that build into the wholes that appear as the synthesis continues to its ultimate goal, the Monas!

The open analogy of this philosophy is the Mosaic. One cannot understand the Pythagoreans without appreciating the Mosaic as a foundational cognisance, not just an art form, which it also is.

Using the mosaic analogy it is clearer to restate Hermanns thinking here in terms of a "continuous picture "and the same image as a "synthesised mosaic". This is the dual cognisance or 2 fold cognisance of any reeified thought form, at least the one that concerns Hermann at this time.

Commentary
"Reeified entities can be reeified in 2 ways, either as a continuous whole or as a combined set of discrete pieces! The first is easy to label you just pull it out of a hat whole
The second you label by setting out the discrete pieces and combining them together into a whole
But you can see the continuos whole as a discrete act, and the combining of the discrete pieces as a continuous action!
So the 2 ways are kind of mixed up in there together. They are a dual fluid kind of perception!"

Ok,this is a gross simplification of Hermanns meditative homiletic! It lacks the detailed twists and turns of the subtle realisation that things are not what they seem. You do not come away feeling that there is a fundmental shift in your perception caused by wrestling with the text!

It is therefore crucial to realise that what Hermann is writing is not an explanatory article, but a persuasive and thus hypnogogic meditative manifesto! The Hegelian dialectic is not meant to be a set of facts. It is a written dialogue of one persons process of perception conveyed to another questing fellow traveller. It isnot written as an exclusive monologue that keeps the reader outside the process. It is written as a dialogue, like Galileos Dialogo that includes Every man and his wife , kids and pets in the ongoing discussion!

This is the Socratic Platonic method, which rather than answering questions raises more questions in the minds of the participants. Each person resolves these on his own advices!

However, homiletics is a sham method that uses these techniques to convince you of a dogmatic view. It's a fine balance. Hermann holds a dogmatic view, it is his Förderung. But his view is clearly new and not dominant. Thus his dogmatism is acceptable as defending his point of view, rather than imposing a dominant societal view onto an open mind incapable of critically reviewing it.

One might also view his dogmatism as arrogance. Thus Hermann is constrained to persuade by apprehensible examples and logic by these possible reactions to his presentations. He has to walk the line between being a doormat and and a stout guardian of the prize( we call them bouncers in today's clubland scene!)

There are many versions of Hermnns ideas promulgated today, so I guess he managed to pull it off. Others however like Gibbs and Hamilon seemed to go for world domination ! They clashed and Gibbs came out the winner over Hamilton using the concepts and tools Hetmann had so generously laid out for all mankind. However Gibbs did not understnd Grassmanns Algebras, a fact he admitted in writing. Hamiltons Quaternions ontthe other hand he grasped but objected to the use of imaginary quantities! He was backed by Lord Krlvin and many other reactionaries including Lewis Carrol whose Alice in Wonderland stories contain a sustained attack on the mathesis of the imaginaries!

Gibbs " vectors" in fact contain bits and pieces from everywhere, and we're a crib sheet of useful notations and formulae . This is why he did not include Hetmanns use of the imaginary quantities of Eulet! Later developers of Gibbs crib sheet introduced imaginary quantities at a later stage, in particular Pauli justified their inclusion in describing electon behaviour data using Heidelbergs matrix Algrbra Approach( Weise!)

The point I am making is both Hamilton and Hetmann inspired by LaGrange attempted to set out a spaciometric Algebra, but from different dogmatisms. Hermanns was based on the perceptions of space inhere in our neurology, which he got at through the Hegelian dialectic method and approach. Hamilton was based on his academic status as an innovator in mathmatical Astronomy and physics and his defense of the doctrine of imaginary quantities. This was related to his religious and theosophical beliefs that imaginary quantities were somehow divine revelatory quantities, at last revealed by god to man so man might truly apprehend and comprehend nature as it really is!

Both Hermann and Hamilton believed they were doing gods work in the new scientific and poetic age, one for the Holy Roman Empire of Prussia, fast breaking up and in need of deep revisionary thought and reform; the other or the new burgeoning industrial powers of the west, brimming with new scientific and technological discovery and advancing bravely forward into a new visionary and poetic future. In fact Hamilton wanted to give up his mathematical and astronomical work to become a poet of this new breath taking vision, like Blake, Yeats and Wordsworth!

The contrast could not be more spectacular! The comparison though was their common conception of an algebra for space based on geometrivl concepts . But not the old geometry of Lesbegue ! Both extracted the Pythagorean geometry from that deadly maul! Hermann by reseating it on 3d space not Axioms, Hamilton by attempting to derive quantity from Pure Time!

Hamiltons imagination blinds him to the fact that he has to use spatial metaphors to describe his conception of time. But Hermann is trenchant , undeviating from what it is one is actually experiencing when quantising and quantifying. One cannot avoid space! Fortunately Hermann had direct access to Hegelian dialectical thought, which gave him a vehicle to express his perceptions like no other. Hamilton was trained in and constrained in Aristotelian logic. And not only constrained but devoted to his jailor! No wonder he felt trapped by his seeming success.

The more I study Hetmanns writing in these short passages the more I see the radically different perspectives that led to an overlapping terminology, not at all describing the same things!

I have adopted the word label for consistency so that Begriff which I intuitively prefer as a gripper or a handle, might reveal the concept I believe Hermann perceived. Words as labels, soon and easily reduces to symbols as labels. And in this section the labels being derived so far are the words describing the ontological aspects of things hitherto only thought of asThoughts.

<a href="http://www.youtube.com/v/nsZsd5qtbo4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/nsZsd5qtbo4&rel=1&fs=1&hd=1</a>

Video one on undecideabikity on computer phill channel

<a href="http://www.youtube.com/v/nsZsd5qtbo4&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/nsZsd5qtbo4&rel=1&fs=1&hd=1</a>

 Ausdehnungslehre 1844 induction


5. Every special / specific entity( no.3) becomes one such  through the label of the Differing Elements group wherethrough there will be coordinated into one group various specific  entities, and through which entities, entities of the likes group will be coordinated into one; wherethrough  there  will be subordinated to the same general entities  an "Other Special Entities"  group  

The thing reified out of the likes group  we can name the algebraic form, the thing reified out of the differing elements group we can name the combinatorial form

The contradictory statement of the like things list and the differing things list is equally a case of a fleeting fluid thing. The like thing is perceived as different, already as much as one and the other like thing to it are separated in some way (and without this separation it was a single thing, thus not a like situation); the differing thing is perceived as like already as much  as an entity of both is linked, through  the practice which itself is related to both, thus "both" is one combined thing.

But now , both limbs in no way are there abouts immersed in one another so that a measure stick one was having  to apply through which to appoint how much likes  to be set between  the presenting items and how much differences , but even if also  the likes always some random value already on the differences  are adhered and vice versa still every time in the moment a unit is built by the tracking during which the latter appears to be the presuppositional foundation of the former.

Under the algebraic form is not just simply the tally numbers, but also that with which in the field of the continuous things the tally numbers are inter communicant; and under the combinatorial form is  not only the combinations but also that which is understood to be with continuous things inter communicant .

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In attempting to answer a query I googled back to some of my earlier posts in the fractal foundations thread

http://www.fractalforums.com/mathematics/foundations-of-mathematics-axioms-notions-and-the-universal-set-fs-as-a-model/330/

It shows that the concepts I am translating from Hermanns work are ones I expressed in my own way and words in 2010.

This of course only means that these concepts are accessible to a person willing to think deeply and logically about foundations of the things we take for granted or as givens in mathematics.

Do not be fooled, therefore , into thinking mathematics is not just a product of exercising careful dialectic thought patterns!  It is intuitive only because we have synthesised it to be intuitive. Like any craftsman, we are able to construct a product that resonates intuitively with how we prefer to carry out the thought act/ process.

The debate about infinity between Norman and Jim

<a href="http://www.youtube.com/v/WabHm1QWVCA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/WabHm1QWVCA&rel=1&fs=1&hd=1</a>

<a href="http://www.youtube.com/v/WabHm1QWVCA&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/WabHm1QWVCA&rel=1&fs=1&hd=1</a>

The case for infinite sets is not very coherent! But basically he is using some version of the distinctions that Hermann is proposing in the Einleitung. Thus the case is barely comprehensible without the Hegelian dialectic that underpins it. Jim is advancing an Aritotelian philosophical view, but heavily eited and critical of Aristotle! Norman is claiming to be a former Platonist looking for a philosophicl basis , and evidently interested in Aspects of Jims Aristotelian approach. Like me before reading the Vorrede I had never heard of Hegel, nor yet how influential his philosophy has been on shaping the modern geopolitical dynamics!

The Hegelian Grassmann philosophical basis for mathmatics is what I am translating now, and hermanns theory of Labels or Handles or Types, by which he avoids much of the procedural difficulties of infinite processes, infinite sets, and through which he is able to ply the Hegelian dialectical method of Alysis and synthesis.

Norman claims that infinite sets are defended by the mathematicians who wanted to found Mathematicl Analysis, especially the continuum. However algebraists do not require a continuum they need discrete labels. Thus we can see a Hegelian dialectical thesis and antithesis in this debate. the synthesis is precisely what Grassmann is dealing with in the Einleitung.

One can see from Hermnns viewpoint that Norman nd Jim are not even at the deepest split of the basis of mathematics! The deepest split in Hetmanns label types is between Algebric form and Combintorial form. In this analysis Zahl, Anzahl take on a specialignificance. They are first of ll not numbers! They are Tally marks. And these tally marks are applied not just to the continuous entities or in general the continuum, but also to the discrete entities in general the different spatially separated like things or differing things. These are perceivable as a unit by a momentary thought act in which the underlying process under consideration, at the time, requires them to be seen as Givens to e tied into a new combined thing or entity.

Thus the distinctions which so divide mathematicians in particular are fleeting and fluid.

The synthesis of the Hegelian method allows unlike things to be combined. This is a fundamental structural rule in algebra. Like things are gathered together, thus forming lists of like things which lists themselves are different " things". Thus at the level of the lists the list of the lists is a list of different subsists. This data structure in which the list idea can contain sublists is crucial to the synthetic resolution of many of the problems with the taxonomic linguistic Aritotelin analysis and approach.

Hermanns Hegelian approach sees the resolution of any distinction in a " higher" level which has the same structural format or layout( for example a list) but may have different characterising definitions. Thus whether we call a structure a list, a type, a set, a collection, a class etc, is fleeting in importance as a distinction because fluidly we can now apply the same structure at a higher or lower level in a Taxonomic structure.

The simple procedural marker is the concept of type and subtype, but also type and super type!

Continuous and discrete entities thus become fluidly combined into super type entires, and also may be constructed from subtype entities. Thus some thing that at one level may be said to be continuous at a sub level ay be made from discrete givens, and vice versa. For this to be the case we have to recognise our perception of the momentary nature of becoming! This is a deep psychological and neurological fundamental to all our systems of knowledge and expertise.hermann points this out by the use of analogical comparisons . What we think we know can be characterised by the dual cognisances of how things come to be in our consciousnesses.