I'm reading The Principles of Non-Philosophy and re-reading Philosophy and Non-Philosophy by François Laruelle and I keep coming across this description of the philosophical decision described as a "fractional matrix in 2/3rd terms." For example he states in the first work:
The most universal invariant trait of philosophy is a fractional matrix in 2/3 terms: it gives itself an interiority and an exteriority, an immanence and a transcendence simultaneously, in a synthetic or hierarchal structure, the one overcoming the other in turn. This matrix of “Philosophical Decision” can be read as the identity of a double relation of philosophy to itself. First, an identity of 2/3 (insofar as the third term, synthesis, is immanent to the dyad, philosophy being in need of itself). Second, a 3/2 identity (insofar as the term of synthesis is transcendent to the dyad, philosophy being in excess of itself). Through this structure, philosophy claims to determine itself beyond all its empirical determinations which it only calculates in order to prescribe it in an auto-position in which it is titular, an auto-comprehension or auto-legislation, auto-naming, etc. In this formal trait the circularity of philosophical argumentation takes root along with its procedures of auto-validation.
Ross Wolf (see http://thecharnelhouse.org/2008/07/03/thoughts-on-francois-laruelle%E2%80%99s-preface-and-introduction-to-principles-of-non-philosophy-as-translated-by-fractal-ontology%E2%80%99s-taylor-adkins/) states that it is a reference to Hegel's "henology" and describes it in the Fichtean terms of thesis-antithesis-synthesis: "The “3” side invariably refers to the transcendentally exterior “synthesis,” while the “2” refers to the immanently interior dualism of “thesis” and “antithesis” (to use crude Fichtean terms)." However, I still want to know that the significance of Laruelle's use of a fractional matrix is. Can anyone conceptualize this or define a "fractional matrix" in either layman's terms or "philo-speak"?