Minimal principles

Minimal principles

In the treatment of physical phenomena, it can sometimes be shown that, of all the processes or conditions which might occur, the ones actually occurring are those for which some characteristic physical quantity assumes a minimum value. These processes or conditions are known as minimal principles. The application of minimal principles provides a powerful method of attacking certain problems that would otherwise prove formidable if approached directly from first principles.

One simple minimal principle asserts that the state of stable equilibrium of any mechanical system is the state for which the potential energy is a minimum. Other general theorems of classical dynamics that are related to minimal principles are Hamilton's principle and the principle of least action. See Hamilton's principle, Least-action principle

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In endeavoring to describe the minimal principles required to justify scientific inferences, he deals with preliminaries concerning the nature of science and language; shows the necessity of inference to the scientific endeavor; analyzes such fundamental concepts of the inferred scientific world as physical space, historical time, and causal laws; explores the implications of scientific inference in terms of probability; and only then lays out his principle justification for scientific inference, which is based on the assumption that "when an event having a complex space-time structure occurs, it frequently happens that it is one of a train of events having the same or a very similar structure.

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