Modeling Cracks and Cracking Models: Structures, Mechanisms, Boundary Conditions, Constraints, Inconsistencies and The Proper Domains of Natural Laws

Abstract

The emphasis on models hasn't completely eliminated laws from scientific discourse and philosophical discussion. Instead, I want to argue that much of physics lies beyond the strict domain of laws. I shall argue that in important cases the physics, or physical understanding, does not lie either in laws or in their properties, such as universality, consistency and symmetry. I shall argue that the domain of application commonly attributed to laws is too narrow. That is, laws can still play an important, though peculiar, role outside their strict domain of validity. I shall argue also that, by way of a trade-off, while the actual domain of application of laws should be seen as much broader. At the same time, what I call 'anomic' representational elements reveal themselves as central to the descriptive and explanatory power of theories and models: boundary conditions, state descriptions, structures, constraints, limits and mechanisms. I conclude with a brief consideration of how my discussion has consequences for discussion of understanding, unification, approximation and dispositional properties. I focus on examples from physics, macroscopic and microscopic, phenomenological and fundametal: shock waves, propagation of cracks, symmetry breaking, and others. This law-eccentric kind of knowledge is central to both modeling the world and intervening in it.

Static-Dynamic Hybridity in Dynamical Models of Cognition

“…While here we focus on cognition, it is important to note that the features of dynamic models we identify are ubiquitous across the sciences. The philosophers Jordi Cat Cat (2005), Mark Wilson Wilson (2017), Sarah Green and Robert Batterman Green and Batterman (2017) have been particularly attentive to the way that dynamical models in areas as diverse as physics and biology use subtle representational devices to incorporate information about a system's steadystate and equilibrium behaviors. Accordingly, a virtue of the present discussion is that it creates a potential bridge between work on dynamical systems in cognitive science and the more general study of how dynamical models function across the sciences.…”