Cartography of the multiple formal systems of molecular autopoiesis: from the biology of cognition and enaction to anticipation and active inference.

A rich literature has grown up over the years that bears with autopoiesis, which tends to assume that it is a model, a theory, a principle, a definition of life, a property, refers to self-organization or even to hastily conclude that it is hylomorphic, hylozoist, in need of reformulation or to be overcome, making its status even more unclear. Maturana insists that autopoiesis is none of these and rather it is the causal organization of living systems as natural systems (NS) such that when it stops, they die. He calls this molecular autopoiesis (MA), which comprises two domains of existence: that of the self-producing organization (self-fabrication) and that of the structural coupling/enaction (cognition). Like all-NS in the universe, MA is amenable to be defined in theoretical terms, i.e. encoded in mathematical models and/or formal systems (FS). Framing the multiple formal systems of autopoiesis (FSA) into the Rosen's modeling relation (a process of bringing into equivalence the causality of NS and the inferential rules of FS), allows a classification of FSA into analytical categories, most importantly Turing machine (algorithmic) vs non-Turing machine (non-algorithmic) based, and FSA with a purely reactive mathematical image as cybernetic systems, i.e. feedbacks based, or conversely, as anticipatory systems making active inferences. It is thus the intent of the present work to advance the precision with which different FS may be observed to comply (preserve correspondence) with MA in its worldly state as a NS. The modeling relation between MA and the range of FS proposed as potentially illuminating their processes forecloses the applicability of Turing-based algorithmic computational models. This outcome indicates that MA, as modelled through Varela's calculus of self-reference or more especially through Rosen's (M,R)-system, is essentially anticipatory without violating structural determinism nor causality whatsoever, hence enaction may involve it. This quality may capture a fundamentally different mode of being in living systems as opposed to mechanical-computational systems. Implications in different fields of biology from the origin of life to planetary biology as well as in cognitive science and artificial intelligence are of interest.