Dynamic and stochastic systems as a framework for metaphysics and the philosophy of science

TL;DR

This paper introduces a general framework for analyzing dynamical and stochastic systems, providing tools to address philosophical questions about laws, necessity, and the nature of scientific regularities.

Contribution

It offers a novel, unified formal framework for describing dynamical and stochastic systems applicable to philosophical analysis.

Findings

Framework clarifies definitions of necessity and possibility.

Analyzes the role of symmetries and laws in scientific inference.

Addresses the metaphysical significance of space and time in systems.

Abstract

Scientists often think of the world (or some part of it) as a dynamical system, a stochastic process, or a generalization of such a system. Prominent examples of systems are (i) the system of planets orbiting the sun or any other classical mechanical system, (ii) a hydrogen atom or any other quantum-mechanical system, and (iii) the earth's atmosphere or any other statistical mechanical system. We introduce a simple and general framework for describing such systems and show how it can be used to examine some familiar philosophical questions, including the following: how can we define nomological possibility, necessity, determinism, and indeterminism; what are symmetries and laws; what regularities must a system display to make scientific inference possible; is there any metaphysical basis for invoking principles of parsimony such as Occam's Razor when we make such inferences; and what is the role of space and time in a system? Our framework is intended to serve as a toolbox for the formal analysis of systems that is applicable in several areas of philosophy.