Like a coiled spring Grassmann launches into a dialectical partition of all the sciences and natural philosophies, thus it is hard to appreciate without some background to the topic he is addressing.
Das Sein that is captured by formal "sciences", and das Sein that is captured by Real or Physical or Empirical "sciences", form the poles of his dialectic. They are not mutually exclusive, as sciences that do not belong to the classification of "real", are perforce, if decideable in the class of "not real", but not necessarily in the class of "formal" sciences. Similarly "formal" sciences may lie entirely within the collection of "real" sciences or not.
Grassmann gives some idea of the characteristics that define the "truth" value of each collection compared or valued against Das Sein. Emphasising that this evaluation is almost entirely subjective, relying on "Denken"- subjective thought, or thinking, Grassmann proceeds to draw out the dialectic consequences.
That which we call "lawful", and incontrovertible is in fact the result of subjective evaluation or subjective interrogation. Thus how we paint, draw and construct our sciences are subject to dialectical processes. Dialectics can therefore fundamentally establish or transform or overturn a conventional view of all science, and all knowledge, and all dependent and resultant behaviours, attiudes, approaches and field boundaries, and thus all categorisation and ontological taxonomies and schemes. In short the knowledge and information array as we currently have it organised.
Of course this happens within the individual, subjectively, and depending on the individuals predilection to change. Thus, as revolutionary as Grassmann's approach is, in the real world it has to win over hearts and minds one at a time. It does not help this goal, if it is his goal, by being obscure.
Somehow i do not think Grassmann realised how out of communication range he was with his peers, and this i believe is due to the radical nature of his education , as evinced by his fathers principles, but also due to his autistic tendencies.
The years of rejection imposed on him by Prussian society, actually preserved his original ideas without too much modification, and thus provide a valuable resource for revolutionary thinkers today.