The Importance of Meta-Conceptual Frameworks
Meta-conceptual frameworks like category theory, constructor theory, Peircian speculative grammar are emerging all ways to formalize complex adaptive systems at the boundaries.
They are like most formal models, at best a descriptive model of reality. However they sufficiently abstract to appeal to human capable reasoning and thus aid in setting the boundary conditions on where computational systems can take over.
A useful analogy to make here is in constraint solvers where the ‘programmer’ sets up the constraints for an algorithm to crunch away to find a solution. A meta-conceptual framework aids one in defining the useful constraints that a complex system should conform to.
Computational irreducibility bounds what a reasoning system can predict about a complex system. This reality is the key motivation for the development of meta-conceptual formal models.
The flaw in many theories about complex systems like the brain (i.e. IIT, FEP, Bayesian brain) is that they are antiquated and impoverished. They are all based on mathematics invented many centuries ago.
It’s a ludicrous leap of faith to believe that mathematics employed to describe inanimate systems (i.e. billiard balls and ideal gasses) would be the core framework to describe minds. Many of these researchers in these areas delude themselves of the power of their math.
Formal models serve an important need but let’s not delude ourselves about employing only the mathematics that we are familiar with. There are limits to the continuous mathematics we have learned in school to describe systems that are rate-independent.
Complex systems with dynamics that are based on ‘virtual motion’ are systems entirely different from those that are governed by the laws of physics. Reality is built on layers of constraints and each new layer imposes its only peculiar dynamics.
The differences in dynamics of each layer can perhaps be described using a common meta-conceptual formal language. Category Theory is a reminder of how many mathematical fields can also be described at the boundary with a common language.
The issue that many have with meta-conceptual languages is that they don’t afford any predictability. They are too abstract to be able to lead to equations of motion that one could shove into a computer to calculate if given the right initial conditions.
This bias however ignores the nature of complex systems. We cannot perform the calculations based on initial conditions because we cannot specify the initial conditions.
Furthermore, the intrinsic feedback that exists in any complex system implies that at best we can specify only the boundaries at a conceptual level different from the instance level.
But here we are today with too many academics who continue to have a sad devotion to that ancient religion has not helped you conjure up new insights on complex systems. One cannot think out of the box if one does not have the language of what describes what is out of the box.
Meta-conceptual formal languages are an out-of-the-box languages of thought.