Relational biology and Church's thesis

Abstract

Church's Thesis is a metamathematical hypothesis that says the concepts of effective calculability and computability are coextensive. It is reasonable to consider everything that happens in the material world to be 'effective'. If Church's Thesis were true in the natural world, then it would mean that all material processes could be expressed in purely syntactic terms. A corollary in relational biology is that a living system must have noncomputable models. Thus the existence of living systems implies that Church's Thesis is false as a physical proposition. The paper begins with a review of the tenets of relational biology, which is the standpoint from which this exposition on the Foundations of Mathematics and Theoretical Biology is composed.

Keywords: Church's thesis; Closure to efficient causation; Effectiveness; Modelling relation; Noncomputability; Relational biology.