Modeling cracks and cracking models: Structures, mechanisms, boundary conditions, constraints, inconsistencies and the proper domains of natural laws
The paper presents philosophical discussion how much of physics lies beyond the strict domain of laws, basing on examples from micro- and macroscopic physics, shock waves, crack propagation, symmetry breaking, etc. The author focuses on the role of laws in the characterization of models of real systems and phenomena in order to highlight the cognitive value of ''auxiliary'' elements in mathematical representation. He argues 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. While the actual domain of application of laws should be seen as much broader, in the broader domain of application their validity, centrality and consistency may be seriously compromised. It is shown that ``anomic'' representational elements, namely boundary conditions, state descriptions, configuration of parts, constraints, limits, structures and mechanisms, reveal themselves as central to the descriptive and explanatory power of theories and models. Based on some examples, it is shown that these elements are often interrelated. The author argues that laws cannot always specify completely and consistently what models should describe and, connectedly, that laws might not be true of the relevant kind of models either. An adequate account of successful science needs notions of models that can accommodate and take seriously the relevant characterization of phenomena or reality that anomic elements offer. Finally, it is shown how the results of the discussion could be applied to representation and explanation of unification, approximation and dispositional properties.
scientific article; zbMATH DE number 5005201
scientific article