Motivated to bypass the twin basins of absolute relativism and dogmatic absolutism, an antinomic polarity into which thought tendentially falls, this paper offers various conceptual frameworks for overcoming antinomies in philosophical thought, and ultimately asserts that this overcoming occurs at a philosophical system’s purported source: its active site of real genesis. The author traces a constellation of thinkers who all invoke this suspended thirdness in their own disciplinary and conceptual registers, from Jean Cavaillès to Gilles Châtelet, C.S. Peirce to Cécile Malaspina, ultimately and speculatively suggesting that this third space, the (abductive) hinge of real genesis, might precede and activate a priori the consequent diremptions into the polarities of the transcendental and the historical, the mathematical and the physical, the global and the local, the continuous and the discrete, the rational and the empirical, and so on. Such a genetic realism, then, places a radical exigency on philosophical thinking: to grasp its real genetic conditions, that is, without a previously given criterion or method. Ultimately, the paper is most interested in suggesting ways to reconfigure the conceptual landscape around this genetic tension or originating hinge, to encourage thought towards the genetic real and away from disciplinary stagnation, towards generative models for systematic thought itself.