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  1. Topology and Life Redux: Robert Rosen’s Relational Diagrams of Living Systems. [REVIEW]A. H. Louie & Stephen W. Kercel - 2007 - Axiomathes 17 (2):109-136.
    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 (...)
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  2.  8
    A Mathematical Science of Qualities: A Sequel.Liliana Albertazzi & A. H. Louie - 2016 - Biological Theory 11 (4):192-206.
    Following a previous article published in Biological Theory, in this study we present a mathematical theory for a science of qualities as directly perceived by living organisms, and based on morphological patterns. We address a range of qualitative phenomena as observables of a psychological system seen as an impredicative system. The starting point of our study is the notion that perceptual phenomena are projections of underlying invariants, objects that remain unchanged when transformations of a certain class under consideration are applied. (...)
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  3.  10
    A Relational Theory of the Visible.A. H. Louie - forthcoming - Axiomathes:1-24.
    On the basis of previous studies in relational biology and the phenomenological calculus, in my contribution I outline the mathematical foundations of biological perception generally, and visual perception specifically. In this approach, the premise is that objects in nature are not directly accessible, and that real manifestations are projections of these invariant objects. The morphology of observables is mathematically entailed by the duality of projections and projectors in a bilinear algebra that is the phenomenological calculus. The relationships between what is (...)
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  4.  76
    Essays on More Than Life Itself.A. H. Louie - 2011 - Axiomathes 21 (3):473-489.
    I comment on the preceding essays in this current thematic issue of Axiomathes , essays that discuss my 2009 book More Than Life Itself: A Synthetic Continuation in Relation Biology.
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  5.  75
    Functional Entailment and Immanent Causation in Relational Biology.A. H. Louie - 2008 - Axiomathes 18 (3):289-302.
    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.
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  6.  25
    Relational Biology of Symbiosis.A. H. Louie - 2010 - Axiomathes 20 (4):495-509.
    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.
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  7.  31
    Explications of Functional Entailment in Relational Pathophysiology.A. H. Louie - 2013 - Axiomathes 23 (1):81-107.
    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.
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