Relational Biology III: Efficient Causation as Biological Constraints

Introduction

The first two parts of this trilogy explored the core tenets of relational biology, its departure from Newtonian mechanistic approaches, and its implications for understanding life. In Relational Biology I: Is it Possible to Simulate Life?, we examined Robert Rosen’s critique of algorithmic approaches to modeling life, emphasizing the distinction between modeling and simulation. We highlighted Rosen’s argument that living systems are closed to efficient causation, making them irreducible to Turing-computable models. However, this did not entail a categorical rejection of artificial life efforts, but rather a call for alternative, relational approaches.

In Relational Biology II: Towards a Faithful Model of Life, we explored Rosen’s (M,R)-systems in detail, illustrating how closure to efficient causation provides a formal basis for biological self-maintenance. Unlike traditional state-space representations, relational biology models systems in terms of morphisms and entailment structures, capturing the interdependencies that sustain life. We acknowledged the epistemological and biological gaps in Rosen’s formulations, particularly the abstraction from empirical biology. The key challenge that emerged was the historical dependency of life—something relational models, by being inherently time-invariant, fail to capture. Biological systems are not merely self-maintaining; they develop, grow, and evolve, which demands a richer account of temporality and constraints.

This final chapter seeks to push relational biology beyond its traditional static formulations. While Rosen’s models provided a foundational shift away from Newtonian reductionism, they remain time-invariant, failing to account for the historical dependence of life. Living systems are not merely networks of entailment—they evolve, adapt, and respond to their environments across multiple timescales. By integrating insights from self-organization, constraint-based modeling, and causation, we will explore how constraints mediate biological processes, allowing for both stability and change. This perspective offers a path forward, one that reconciles Rosen’s theoretical insights with the empirical reality of life’s dynamism.

Solving time-invariance

In a recent paper, Tomasz Korbak proposes a temporal parametrization for (M,R)-systems. Korbak’s analysis of Rosen’s (M,R)-systems highlights an often-overlooked tension: Rosen’s models, as many other relational models, assume time-invariance. Yet, life is fundamentally historical. By grounding relational biology in category theory, Rosen formulated a universal framework that, if sound, applies to all mathematical structures. However, this same generality comes at the cost of neglecting temporal processes.

Korbak proposes a reinterpretation of (M,R)-systems using self-organization as multi-level constraint propagation. Here, biological systems must exhibit at least two nested feedback loops: one ensuring adaptability and another ensuring robustness. This formulation aligns with enactivist and dynamical perspectives, emphasizing the co-dependence of structure and function over time. Korbak also critiques Rosen’s mechanistic reductionism, arguing that modern mechanistic explanations have converged toward relational modeling. This suggests that Rosen’s critique of mechanistic explanations might need revision in light of contemporary work on mechanisms in biology.

Perhaps the most striking claim in Korbak’s paper is that (M,R)-systems can, in principle, be computed iteratively. While Rosen argued that entailment structures preclude algorithmic simulation, Korbak suggests that self-referring structures can be handled computationally through bookkeeping methods that track state dependencies. This does not mean that (M,R)-systems reduce to Turing machines, but rather that their computational intractability is less absolute than Rosen claimed. A simple reformulation of (M,R)-systems, Korbak argues, can capture their essential properties while remaining implementable within an iterative computational framework.

What is a constraint?

To fully appreciate the role of constraints in biological organization, we must turn to biosemiotics, which studies the prelinguistic meaning-making, biological interpretation processes, production of signs and codes, and communication processes in the biological realm. On his side, Howard Pattee argued that constraints are essential for understanding how biological systems generate order. Unlike physical laws, which describe universal regularities, constraints define the conditions under which specific processes can occur. In biological systems, constraints are dynamically maintained and modified, allowing for adaptability and evolution.

On the other hand, Peter Cariani extends this perspective by linking constraints to symbolic processing. Symbols function as constraints on physical processes, allowing biological systems to interpret and respond to their environment. This aligns with Korbak’s argument that self-organization involves multi-level constraint propagation, where different timescales govern different modes of causation. Taken together, Pattee and Cariani’s insights suggest that constraints offer a richer, more dynamic understanding of efficient causation than Rosen’s original formulation allowed.

A constraint, under the prism of biosemiotics, can be understood as a conserved entity or relationship that reduces the degrees of freedom of a system’s dynamics, shaping its possible trajectories. Pattee emphasizes that constraints are not merely passive limitations but active structuring conditions that enable organized behavior. Cariani adds that constraints can take symbolic form, mediating the relationship between internal organization and external interactions. This dual nature—both structural and informational—positions constraints as fundamental to the regulation and evolution of biological systems.

Closure of constraints

Almost a decade ago, Montévil and Mossio refined the concept of closure by distinguishing between two causal regimes: processes and constraints. Processes encompass the thermodynamic flow of matter and energy, while constraints are entities that persist across these processes, shaping and regulating them. The authors argue that Rosen’s definition of closure to efficient causation is too abstract, failing to specify the concrete entities that function as efficient causes in biological systems.

Organizational closure, in their view, is best understood as the closure of constraints. Constraints act as contingent causes that reduce the degrees of freedom in a system, enabling functional organization. Importantly, constraints are not reducible to thermodynamic flow—they exist in a distinct causal regime. This distinction clarifies a major ambiguity in Rosen’s work: while he defined closure in terms of efficient causation, he did not explicitly identify which structures played this role. By framing closure in terms of constraints, Montévil and Mossio provide a more precise and operationalizable account of biological organization.

One crucial implication of this framework is that biological systems must remain open to material causation and informational perturbations while maintaining closure to organizational constraints. This aligns with the idea that biological systems evolve by modifying their constraints, allowing for adaptation over generational timescales. However, Montévil and Mossio’s approach raises questions about its compatibility with Pattee’s and Cariani’s conceptions of constraints. While all three accounts emphasize the role of constraints in biological organization, Montévil and Mossio focus more on structural persistence, whereas Pattee and Cariani emphasize symbolic control and interpretability. I feel these two visions of constraint could be unified via Hofmeyr’s (F,A)-systems, discussed in detail in the second chapter of this trilogy.

Conclusion

This final installment of the trilogy has sought to reconcile Rosen’s insights with contemporary perspectives on self-organization, constraints, and biological causation. While Rosen’s (M,R)-systems provide a powerful formalism for relational closure, the time-invariance of relational models limit their applicability to real biological systems. Korbak’s reformulation highlights the need for multi-level constraint dynamics, allowing for historical dependency and iterative computation. Pattee and Cariani deepen our understanding of constraints as both physical and symbolic regulators of biological organization. Montévil and Mossio refine the concept of closure by distinguishing between processes and constraints, providing a more precise causal framework.

Together, these perspectives point toward a unified theory of biological organization that integrates relational models with historical dynamics. Constraints emerge as the key mediators of efficient causation, shaping biological processes while remaining open to modification and evolution. By embracing this constraint-based view, relational biology can move beyond its static formulations and fully account for the temporality and adaptability of living systems. In doing so, it bridges the gap between formal abstraction and empirical reality, offering a more comprehensive framework for understanding the nature of life.