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Law Along the Frontier: Differential Equations and Their Boundary Conditions

Published online by Cambridge University Press:  31 January 2023

Mark Wilson
Mark Wilson*
Affiliation:
The Ohio State University
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Extract

This essay will survey various considerations that arise when a branch of physics requires formulation in terms of partial differential equations (or some facsimile thereof). My examples will derive almost exclusively from classical continuum (=smeared out matter) mechanics. Although the relevant formal facts are well known, it is difficult to find coherent discussions of how the underlying phenomena ought to be viewed. In this paper, I will give an introduction to some of the issues, although I will confess at the outset that I am not certain how these matters should be finally adjudicated. Certainly it would be helpful if philosophy paid more attention to the underlying issues.

Some of the points I will discuss bear upon some of Professor Sklar’s observations. Although my attention will be largely directed towards the status of boundary conditions (and related forms of singular surface), many of my examples can be adapted, mutatis mutandis, to initial conditions as well.

Type
Part XIV. Laws, Conditions and Determinism
Information
PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association , Volume 1990 , Issue 2: Volume Two: Symposia and Invited Papers 1990 , 1990 , pp. 565 - 575
Copyright
Copyright © Philosophy of Science Association 1991

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References

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