04.03 Actual and Formal Systems – Beyond Networks: The Evolution of Living Systems
Channel: Johannes Jaeger
Date: 30/04/2020

Module 4 of "Beyond Networks" asks what a system is and how we use models to study systems. This lecture forms the core of the module. While actual systems mainfest themselves as patterned processes, formalised systems consist of a set of relationships between mathematical objects (such as variables). Formal systems are models that are usually seen as representing actual systems. Using the simple example of a linear pendulum, I show how we can construct such a model. Models relate to the real world as maps do to the territory: both are objects, not statements, and can't be 'true' or 'false'. Rather models are applicable in a certain context or not. Maps and models select some salient features of the actual system they represent, while neglecting others. Their use is relative to the question that is being investigated. For this reason, we need to shift our attention from the abstract relationship between actual and formal systems, to the activity of modelling systems as a scientific practice.

If you are interested in the mathematical foundations of formal systems theory, there is no better place than Mesarovic & Takahara's classic book called "General Systems Theory: Mathematical Foundations," published in 1975. It is not an easy read. It took me two months to get through the first two chapters. You've been warned.

Most of the rest of the argument in here is based on Ron Giere's "Scientific Perspectivism" (2006). Have I already mentioned you should read this book? It's short. It's clear. It's hugely important, not only for philosophers, but also for every working scientist. When you're done with that, treat yourself to Giere's 1999 "Science Without Laws."