Rosen's no-go theorem for regular categories

TL;DR

This paper examines Rosen's no-go theorem within category theory, arguing that the intrinsic differences between biological and artificial systems stem from fundamental categorical properties related to variability and description.

Contribution

It provides a category-theoretic argument supporting Rosen's claim that living systems cannot be fully mechanistic due to their synthetic and variable nature.

Findings

Rosen's theorem is rooted in categorical properties of systems.

Synthetic systems cannot be fully captured by static analytical categories.

Biological systems exhibit properties that defy mechanistic modeling.

Abstract

The famous biologist Robert Rosen argued for an intrinsic difference between biological and artificial life, supporting the claim that `living systems are not mechanisms'. This result, understood as the claim that life-like mechanisms are non-computable, can be phrased as the non-existence of an equivalence between a category of `static'/analytic elements and a category of `variable'/synthetic elements. The property of a system of being synthetic, understood as being the gluing of `variable families' of analytica, must imply that the latter class of objects does not retain sufficient information in order to describe said variability; we contribute to this thesis with an argument rooted in elementary category theory. Seen as such, Rosen's `proof' that no living system can be a mechanism arises from a tension between two contrapuntal needs: on one side, the necessity to consider (synthetically) variable families of systems; on the other, the necessity to describe a syntheticum via an universally chosen analyticum.