Die oberste Theilung aller Wissenschaften ist die in reale und formale,
von denen die ersteren das Sein, als das dem Denken selbständig gegenübertretende,
im Denken abbilden, und ihre Wahrheit haben in der Uebereinstimmung des
Denkens mit jenem Sein; die letzteren hingegen das durch das Denken selbst gesetzte
zum Gegenstande haben, und ihre Wahrheit haben in der Uebereinstimmung
der Denkprocesse unter sich
The ultimate Partition of the Knowledges is that into "Real" and "Formal", from amongst these 2 parts the Knowledges of the first kind develop a concept of "experiential continuum" in the "subjective processing" centre, as that which by the subjective processing centre are typed "independently resilient to being trodden underfoot", and their Truth Value lies in their correspondence with that concept of "experiential continuum"; The Knowledges of the last type on the other hand to that concept, through the subjective processing centre are typed as "Self Set" as far as the content they contain, and their Truth Value lies in the underlying subjective thought process.
The subjective processing centre is able to input and output reality and it is able to input and output formality, and any combination of the 2. Formality has as a subset symbolic forms. The right choice of symbolic forms enables one to process reality symbolically through the subjective processing centre.
The subjective processing system inputs and outputs intensities. It is therefore difficult to realise that the visual processing part of the system is handling these intensities in the experience of surfaces, as the varieties and experiences of surfaces are so numerous.However the screen this note is being read on is adequate demonstration of the point being addressed.
Denken ist nur in Bezug auf Sein, was ihm gegenübertritt und durch Denken abgebildet wird;
aber dies Sein ist bei den realen Wissenschaften ein selbständiges , ausserhalb des Denkens
für sich bestehendes
The subjective processing centre exists only in relation to the "experiential continuum", those things which, to it, resist being trodden underfoot and, through the subjective processing centre, would be developed as a concept; But this experiential continuum is evidenced by the real Knowledges as an independent continuum, that is outside of the subjective processing centre, a by itself existing continuum.
bei den formalen hingegen ein durch das Denken selbst gesetztes,
was nun wieder einem zweiten Denkakte als Sein sich gegenüberstellt.
On the other hand the formal Knowledges support a type of experiential continuum, a "through the subjective processing centre", "self set" experiential continuum, that kind which this time also, resists itself being covered by a second subjective process action,, like an experiential continuum .
Grassmann here is struggling to explain the different experiences of reality without falling into the trap of asserting these explanations are distinct realities. I have described this before as the subjectively objective reality versus the internal subjective reality. However Grassmann is concerned with the distinction between reality and symbols, the real and the formal, and the empirical methods we use to distinguish and reeify the two, the conventions or proof and truth we utilise, the processing procedures which we use in the subjective processing centre..
Grassmann attempts to place reality above the subjective processing centre by his first comment on the relationship, but there is no sound way or rather this is a tautological situation in which no component has any preeminence. Thus the authors bias is displayed at this point.
The parts of language called prepositions , and indeed language in its entirety , represents a description of spatial relationships as well as spatial interactions. Thus in engaging with the text i get the authors spaciometry, rather than the indistinct and imprecise grammarian spaciometry. "Hingegen" for example represent spatially "down" and "against". I the literary context it is used to denote a following exposition which is contra to the preceding exposition. In other contexts it will be used appropriately but with a meaning relevant to the context.
Grassmann relies on the notions within spatial prepositions to exposit the fundamentals of reality, "gegenueber-" "against" "over" is important, "Ueber_" the basis of english over is about more than height, its about relative position to a referent. Uebertreten is to step over, ueberstellen is to place over. Setzen is to set by placing into a relative position, a position against which other things may be measured or defined.
Reality needs consciousness to be an existent phenomenon, and consciousness needs reality to exist, to have a space for existence. This tautology is what Grassmann develops. But alongside this he develops also a symbolic or formal representation of reality ALSO as a reality. The two he develops in comparison and contrast to each other.
Reality is chosen as more fundamental than consciousness by Grassmann, so consciousness acts on reality. All those experiences that resist being trodden over by this conscious action on reality are developed as a concept called reality (Sein) by a second process Grassmann denotes by "abbilden".
In contradistinction symbols have to be established or set as independent notions by a conscious act . Once set they too are defined as a type of reality by a second conscious action on them. Those symbols that resist being covered over by this action are defined as a reality. But this reality arises from definitions not from fundamental laws. A fundamental foundation of "laid down" definitions underpins the formal Knowledges and a fundamental collection of natural laws underpin the real Knowledges.
2 Subjective processes are identified in each of the 2 types of reality: gegenuebertrit and abbilden for the real Knowledges: gesetzten and gegenueberstellen for the formal Sciences.
Grassman goes on to lead the dialectic down the road of the Logic and Mathematics subject boundaries. This is an understandable mistake, and one which i have made frequently in the past. However, these subjects are not bounded, and in fact are hard to categorise, thus any development using them is going to be insubstantial and at best analogous.
The collection of notions in these subject areas is familiar but defies bounding. If a bound is set, then the whole meaning of the terms is set for the analysis and the development of the subjects is stopped by definition. Thus to avoid this , Grassmann's dialectic has to be performed over and over with each new definition of the subjects. As a consequence we can only arrive at inductive, probable conclusions from Grassmann's analysis and indeed by extension by any formal scientific treatment of a set of propositions.
The second type, "formal" reality, will only ever be inductive and probable, never deductive and actual. However, Grassmann argues that we need the interaction between the two if we want to advance a truth value to and through "Uebereinstimmung", the 2 types of it. This truth value then is itself based on an analogy between the 2 types.
I started off this long quest to found mathematiks on fractal geometry many years ao with a sever criticism of Russel, and now i apologise. I see and understand the roots of Russell's urgent Quest, and they are Grassmann's dialectic as perceived by AN Whitehead. That Grassmann was misunderstood is historical fact, but whether AN Whitehead got it right i have yet to find out. Certainly Whitehead did not succeed in his programme, nor did Russel, but was that Grassmann's programme? I doubt it at this moment because Grassmann always modified his aims based on results. What was paramount to him were the tools of analysis not the resultant "facts".