My preference is for an ordinal approach to phenomenology - one that attempts to move past the sort of Kantian finitude Husserl maintained by relegating the real to first-person conscious appearances of the real. The ordinal phenomenological approach, by contrast, involves the twin notions of ordinality and ontological parity. I've already discussed how Peirce, Buchler, Hartshorne, and Whitehead offer radically different phenomenologies than the sort of (Kantian) transcendental phenomenology that one finds in Husserl and how each of them employs the twin pillars of the ordinal phenomenological approach.
The most pressing question is this, however: Is the reduction made by human consciousness (as an act intended for human consciousness) essential to the phenomenological method itself? It seems that in Husserl's tireless attempt to define the phenomenological method throughout the course of his career such a question could never have been asked. This seems true if only because as a method phenomenology's very identity as a "description-of-appearances-to-consciousness" - the science of the experience of consciousness - begs the epoche's necessity. The epoche seems necessary for the sake of scientific objectivity in terms of what is described by consciousness, but not for the sake of what itself is being described. That is to say, Husserl is speaking of an objective appearance to consciousness, not objective reality as it is apart from conscious appearances.
In terms of the content behind the approach, one may further press the question. For phenomenology, does the range of its method and "objective" correlate (the "what," so to speak, of its analysis) match "all of the way down"? Or, is it possible that whatever content to be described exceeds the consciousness attempting to describe it? If phenomenology is properly made speculative (mathematized if we follow C.S. Peirce, or Alain Badiou, or turned logically modal or categorical, as in Peirce, Buchler, Whitehead, or Hartshorne), then current day speculative realism's ontological demonstrations are capable of becoming epistemological descriptions should speculative realism decide to follow the methodological tenets of the ordinal phenomenological approach.
Moreover, if the qualitative aspect of modal-categorical revelation present in the ordinal approach is provided an adequate level of objective demonstration, we then need only ask how does such an approach regard the conditions for consciousness which enacts method. In other words, how are the categories of cosmos isomorphic to the consciousness that happens to be rendering them and employing them. Note that this does not work the way around (moving from the categories of conscious experience to cosmos, which was the Kantian-Husserlian transcendental mistake). In the ordinal approach one moves to transcend beyond conscious experience through the categories where any qualitative dimension presented is a dimension excised of consciousness and described purely in categorical-modal (e.g. "mathematical") terms.
Given that a speculative, realist phenomenology is possible if we follow the above lines of thinking (speculative realism and phenomenology means ordinal phenomenology) but is only possible by following strictly the ordinal method - ontological parity and ordinality in modal-categorial terms - then the "experiential" component of phenomenological analysis, its "qualitative" dimension - is able to rely upon self-disclosure of cosmos rather than description by observing consciousness. That is, cosmos preserved in its extrahuman (inhuman) qualitative elements despite the elimination of its first-person "present to consciousness" viewpoint. This in other words is to say that the objective reality of sensation, quality, experiential feeling, need not be felt or experienced or "presented to" in order to be real as it is already a part of a reality that is itself independent of the human experiencing or perceiving it. Phenomenology, methodologically, wouldn't be the knowing-what of experience but the exhibition of the becoming-how of the real in all of its various dimensions (categorical, modal, qualitative, etc. etc.), a demonstration and then description of reality's possible becoming independent of that becoming's appearance to a conscious being describing it.
In any case, those are just a few thoughts on how phenomenology might in the future be able to be of some use for those interested in speculative realist philosophy.
