The desire to understand the mathematics of living systems is increasing. The widely held presupposition that the mathematics developed for modeling of physical systems as continuous functions can be extended to the discrete chemical reactions of genetic systems is viewed with skepticism. The skepticism is grounded in the issue of scientific invariance and the role of the International System of Units in representing the realities of the apodictic sciences. Various formal logics contribute to the theories of biochemistry and molecular biology (...) and genetics. Various paths of extension are invoked in these formal logics in order to express the information of biological apodicticism. Symbolizing the appropriate notations for invariant relations and for biological extensions of relations is fundamental to the exact generating functions of discrete algebraic biology. Aspects of philosophical perspectives of the relation scientific number systems are contrasted. The deep distinction between physical motion and biological motion is expressed in terms the roles of Aristotelian causes. The interior motion within perplex numbers is contrasted with the exterior motion of physical systems. The need for a new mathematics for biology is suggested. (shrink)

Ernst Mayr’s concept of dual causality in biology with the two forms of causes continues to provide an essential foundation for the philosophy of biology. They are equivalent to functional and evolutionary causes with both required for full biological explanations. The natural sciences can be classified into nomological, historical nomological and historical dual causality, the last including only biology. Because evolutionary causality is unique to biology and must be included for all complete biological explanations, biology is autonomous from the physical (...) sciences. (shrink)