This project reports on the specialized exegesis of the conceptual and methodological foundations of Aristotle’s Poetics as a productive science of both ancient and modern telic significance. The metapragmatic productivity of the Poetics that aids poets arises out of Aristotle’s use of what I have named ‘Arithmoi of Phenomena’ as methods to determine essential understandings of our experience. The central focus in this report is on Aristotle’s method of causal “species” or genre differentiation in poetic science as grounded in the different poetic capacities for imitating – in media, of objects, by manners, and all together with purposiveness. Intrinsic to Aristotle’s methods of species differentiation and the definition of Tragedy is the fact that they explicitly include the teleological functions of the catharsis of pity and fear. His overt use of teleological reasoning about artistic imitation as a source of learning and delight that is common to all humans is what makes his Poetics useful to poets and aesthetically enlightening to audiences. This background of productive teleology allows a reconstruction of Ernst Mayr’s “teleological consummatory acts,” despite Mayr’s later abandonment of the concept in favor of a reduction of life-form activities to computed behaviors (Mayr 1974, 2004). Aristotle’s understanding of the Attic Greek political society and ethical character, as well as universally shared human poetic capacities, enabled him to find the functions of human excellence within the healing and completing purposes of catharsis in the city. The larger project has the underlying purpose of approaching our contemporary problems of and with teleology and the relations of those problems to various modes of numeracy involved in the daily activities of human beings. Those diversely varied “everyday” activities from citizen to scientist are constitutive of a recurring plurality of ‘common sense habitats’ that vary across culturally situated times and locations but share similar covarying numeric skill sets that can be abstractly stated in relation to each other. The wider project attempts this clarificatory goal through a foray into a sequence of combinatoric models with different underlying numeracies that builds an heuristic bridge to modern formal systems, starting with Aristotle’s differentiation of a small number of poetic “species” and ending with countably infinite symbol systems. The sequence of combinatoric models exhibits two very different concepts of “essence” that are both generative of human significances: phenomenal essence and mathematical essence. It exhibits these differences through an analysis of the problem of a decreasing teleological expressiveness and an increasing formal precision in symbolization in the movement from Natural Languages to Formal Symbolic Languages. The sequence tracks how expressions of numeracy (arithmoi) move from the greater telic expressiveness of higher-order phenomenal representations in natural languages to the greater mathematical precisions of higher-order formality in artificial languages.