The colonization of categories, or: how can we conceive of that which is being named by polynomials resolved through adjoining complex roots to their coefficients?
“Le fondement c’est donc ce qui nous donnera ou ne nous ne donnera pas le droit.” (Gilles Deleuze, Qu’est-ce que fonder?)
“I really do not know that anything has ever been more exciting than diagramming sentences. [When one is diagramming sentences] one is completely possessing something and incidentally one’s self.” (Gertrude Stein, Poetry and Grammar)
Polynomial terms, unlike nominal terms, are capable of settling their clauses in amphibolic multiplicitous structures. They subject what abounds from the vastness beyond that which is termed within a liminitude whose constitution is provided symbologistically, not syllogistically.
Every polynomial term involves variable values and constant values, of which the latter can be ‘spelt’ by attaching them to designate-able and balance-able constellations of coefficients. We can take the meaning of Coefficients quite literally, from efficient for capable of producing a desired effect, marked with the prefix com which indicates that the capability depends upon a the actuality of a distribution of roots. That which counts can be equipped with a logistic setup. Polynomials name terms whose literalness needs to be characterized. Polynomial terms are quantitative, yet they comprehend ever so much – tantum – as the term is rendered capable of bounding within the constellation of amphibolic multiplicities that makes up their systematic formula in which they feature. The determinability of this ever so much is adjoined to the terms properly. The symbolicity precedes and conditions the quantities expressed by algebraic terms.
A clause settles a sentence. To name a thing is to subject it to a an order, to address (kategorein) it’s unique place and value for public reference. A predicate constitutes the varieties of terminations and conclusions possible within arguments.
If the space of such address is amphibolic, if several subjects settle co-existentially within this space, we can say that the predicate of such subjects named is being colonized in the grammatical sense of the word: a colon is a grammatically complete, yet logically incomplete clause. If colonized predication is taken literally – and not symbologistically – it cannot but evoke a condition of unresolvable accusation, a condition where the casus accusativus, which expresses destination or goal of motion, reigns over anything that could be the case in any ordinary sense. In such a confined condition of conflict, considering the colonization of categorization holds the promise to offer room for resolution, out of the locus of negativity, via imagination. While limits have always been considered the form of magnitudes, such colonized categorization now organizes a limitudinality of what can be subjected to a quantitability which ranges over various infinities symbolically.