This paper explores the similarities between the conceptual structure of quantum theory and relational biology as developed within the Rashevsky-Rosen-Louie school of theoretical biology. With this aim, generalized quantum theory and the abstract formalism of (M,R)-systems are briefly presented. In particular, the notion of organizational invariance and relational identity are formalized mathematically and a particular example is given. Several quantum-like attributes of Rosen’s complex systems such as complementarity and nonseparability are discussed. Taken together, this work emphasizes the possible role of (...) self-referentiality and impredicativity in quantum theory. (shrink)

Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized (...) simulacra of them are uninformative of their key properties. This leads to the question of how we should reason about them. That question is answered in this paper by presenting an example of such reasoning, the demonstration of a topological strategy for understanding how the fundamental structure can form itself from within itself. (shrink)

I formulate in relational terms the ubiquitous biological interaction of symbiosis. I explicate the topology of the different modes of relational interactions of (M, R)-networks, the entailment diagrams that model the host and the symbiont. These modes all have biological realizations as various categories of symbiotic relationships, ranging from mutualism to parasitism to infection.

I explicate the crucial role played by efficient cause in Robert Rosen’s characterization of life, by elaborating on the topic of Aristotelian causality, and exploring the many alternate descriptions of causal and inferential entailments. In particular, I discuss the concepts of functional entailment and immanent causation, and examine how they fit into Robert Rosen’s relational-biology universe of living, anticipatory, and complex systems.

I explicate how various relational interactions between (M,R)-systems may have realizations in pathophysiology, and how the possible reversals of the effects of these interactions then become therapeutic models. Functional entailment receives a rigorous category-theoretic treatment, and plays a crucial role in this continuing saga of relational biology.