Anti-Aristotelianisms

I'm sorry to stir up so much trouble, but I'm seeing a basic philosophical problem in the foundation of this line of thinking: when we study history, when we objectify it, and we thereby necessarily affirm a kind of Platonism. We implicitly affirm our own position at some ideal point; a place from which our gaze originates, and at which our soul resides. The present. This location must always lies beyond, outside of the surrounding pattern of worldly events. This point allows us to frame what we observe; to measure 'outer' ('other') events from a fixed perspective, and thus identify definite patterns of interrelationship between and among them. These are the patterns that Plato identifies as the Forms. They are the definite, mathematical functions describing patterns of interrelationship we see manifested in the goings-on of the world around us. These patterns are the only true object of knowledge; at least any knowledge conceived as transcendental familiarity.
The simplest Form as such is the dialectic: binary code! It can compile iteratively and collapse back upon itself to produce all manner of forms. In fact, due to the ordered infinity recognized by Cantor as the Form of the set of all integers, we can literally model any mathematical pattern in binary code. This magical mathematical reducibility underlies the early development and conception of the computer -i.e. by Turing- as a universal instrument; a metamachine. The computer, because its hardware instantiates a dialectical language, can simulate -or model, we could say; mimic- the functional apparatus of any other machine. Including other computer programs, which are really just more limited, more functionally heterogeneous instantiations of mathematical thought, thought of as the continuity of functional syntax...
So does privileging the mathematical necessarily mean that we should devalue more naive kinds of experience? This is an important point to clarify, and Whitehead is one of the best when it comes to this point. In his later work, particularly Modes of Thought, he insisted that Form should not be exclusively identified with thought. Rather, he insists on the relative superficiality of conceptual thought to the totality of our conscious experience:

“The pitfall of philosophy is exclusive concentration on these manageable relationships, to the neglect of the underlying necessities of nature. Thus thinkers repudiate our intimate vague experiences in favor of a mere play of distinct sensations, coupled with a fable about underlying reality.”

And I'm not trying to start a quarrel with Whitehead. On the contrary, I think he raises precisely the point that we need to realize: outmoded linguistic forms can't be dispatched with weapons that they themselves have supplied. The clear conceptual divisions of Aristotelian logic have fascinated our epoch as surely as the songs of the Homeric poets fascinated the public of Plato's and Socrates' time. This is emphatically not to say that it should be abolished, or replaced by a superior form. Just as the transition from oral to literate forms of thought and social organization are and were much more subtle and complex than mere replacement, so does the transition heralded by digital and electronic media today need to learn to include and incorporate the advances made by its predecessor.
When we attempt to negate Aristotelian logic, or to categorize definitively Platonic Idealism, we are actually engaging in nonsensical linguistic operations, we are building programs with recursive loops in them, that will not be able to ever stop, to ever arrive at a solution, but will instead spin around in circles forever. Not that this is necessarily always a bad thing! A trans-Aristotelian-and-Platonic logic would have to learn to perform its data-processing operations without relying on negation, and to think the Forms of things without relying on outmoded categories.
Perhaps to sum this up: in our critique of idealism we are forced to rely on idealism, i.e. in our assumption of categorical formations -idealist/pragmatic, visual/acoustic, spatial/temporal, etc. Derrida, working a little after Havelock, and in a much different milieu, identified a set of similar formations as essential metaphysical binaries of Western Philosophy. Perhaps it is, after all, only through something like the Derridean method of Deconstruction that we could truly achieve the return of a Protagorean, or even a Socratic Pragmatism...?