Every field of enquiry or praxis adopts a position vis-à-vis the manner in which it treats issues of universality and singularity. Speculative mathematics, for instance, could be defined by its operation in the realm of the deduction and exposition of universals (it is not necessary for its objects to correlate to ‘actually existing’, observable material instances, although of course it may be the case that such instances either exist or are subsequently discovered). Accordingly, its objects are ontologically ideal and epistemologically rational. Alpha taxonomy, on the other hand, proceeds in precisely the opposite direction, being a field definable by its operation in a realm of observable singularities (it is not necessary that the objects under investigation correlate to any pre-established universal categories, although it may of course be the case that such categories do already exist or are later created). Its objects are accordingly ontologically material and epistemologically empirical.

As we have just seen however, such neat apportioning is illusory inasmuch as the stability of any domain of enquiry qua materialism or idealism – and by extension therefore, qua rationalism or empiricism – is being continually dialectically subverted, the one constantly collapsing and passing over into the other, annulling the possibility of a self-sustaining totality or a unity as self-coincidence. Every domain of research is, therefore, subject to a vanishing point: the very instant a domain of research coincides with itself, it disappears into its other, unveiling a blank, a blind spot, a nothingness, a lack, at its core. This nothingness, this blind-spot, is simultaneously its singularity and that on the basis of which it is universalisable; the nothingness of the subject which is the subject, moreover, is what takes the subject spilling out beyond itself. The mode of being proper to any domain of research is, in which case, universally-singular or singularly-universal.

What this invites us to entertain—even, if not especially, in those areas of enquiry that appear to be most complete-unto-themselves—is the necessity of a split, the necessity of split subjects: every subject is always already riven and any chance of holistic, epistemic unity, is ruled out priori. Of crucial importance, then, is the manner in which research is organised around the vanishing point that is this gap guaranteeing non-coincidence with self. Indeed, it is in precisely those research subjects where such blind-spots appears least evident, in which the certainty of self-coincidence is most vociferously proclaimed, that we ought most vigorously to counter with an insistence upon what psychoanalysis calls a disavowal….Since we have strayed into the drawing of analogies with psychoanalysis, let us risk venturing further in order to pose a question: might there be a relationship between this necessarily split subject of research and Freud’s foremost discovery – i.e., that every human subject is split and therefore fails to coincide with themselves, a state similarly abandoning the human subject like the research it undertakes, to estrangement, to alienation from self? Might it be the case that the psychoanalytic split (human) subject corresponds to the necessity of the split (research) subject – that the latter conditions the former and the former the latter?