Abstract

All biological objects in living systems are composed of their components. They are also involved in biological mechanisms that produce regular phenomena. Mechanistic philosophy is a recent framework for understanding biological sciences. In this dissertation, I will suggest a categorical formalism of mechanism supported by algebraic constraints by virtue of a mathematical language, category theory. First, I formalize the essential groundwork for mechanistic explanations, component parts, and activities by assuming that mechanistic explanations do not allow for infinite decomposition of components, and that they essentially require explanatory baselines. Second, I formalize temporal organizations by introducing Petri nets and monoidal categories. Then, I argue that phenomenal models of mechanisms as explananda of mechanistic explanations are semantic interpretations of models of dynamical systems. By doing so, I show a mathematical alliance of dynamical systems with temporal organizations of biological mechanisms. Third, I formalize spatial organizations and argue that spatial organizations provide significant clues to make mechanistic explanations. Mechanistic explanations must include relevant components of a mechanism, particularly activities. Activities are responsible for producing explanandum phenomena. I will emphasize that spatially organized features of entities are prerequisite resources to determine relevant activities to produce explanandum phenomena. Further, we will notice that hierarchical relations are established between entities and their own sub-parts, not between a mechanism and components. Fourth, I will emphasize that constitutive relations are not associated with causation at all. Consequently, I conclude that categorical formalism is a promising approach to represent biological mechanisms and expect that the mechanistic philosophy will be positioned as an integrative framework of diverse scientific fields such as physics, chemistry, and biology.