Logic in Physics or How to prove physical theory

[Guest Leah W. Ratner]

Contemporary physics from its beginning in the 17th century has been progressing in two parallel directions:empirical and mathematical. It brings one of unresolved problems of epistemology for these two branches are not well combined in the scientific theories. Mathematics is an instrument for describing the hypothetical propositions and making mathematical inferences from those hypotheses. But mathematics has no means for judging the truth of physical hypotheses. Empirical methods can provide us with the facts relating to the phenomenon. But, the facts can be selected, described and interpreted differently. Empirical methods have no means of selecting the concepts of a theory and testing the truth of proposed relationships among them. Thus, mathematical inference from the propositional function contains a purely mathematical relative value (dy/dx) as its result. There is no empirical means to test truth of such result. That brings the basic argument of classical logic to the fore:"If P, Then Q", and unresolved uncertainty in the methodology of science.

The only way to support a physical theory is to have a consistent logic structure as a framework of a theory that allows to select concepts that satisfy this strict logic structure and make conclusions that can be objectively explained and justified.

The author of "Non-linear theory of elasticity and optimal design", Elsevier/Science, 2003 (ISBN 0444514279) demonstrated - how to build and prove physical theory on the example of constructing the new nonlinear theory of elasticity. At least half of the book is devoted to the discussion of the principles of logic in a physical theory. The contents of the book can be found on the Internet sites of the publisher and some booksellers.

The book, also, can be found in some engineering libraries in sections TA653R38 2003.

leah ratner, author

[Jenab]

Mathematics is the servant of empiricism. In itself, mathematics contains no epistemology: no reference to actual things in the physical world. Empiricism bring mathematics its input. Mathematics exists to prevent confusion, to balance accounts, to simplify, to make attempts at describing observables, to find evidence for relationships between observables, and to predict the future behavior of observables. But without empiricism, mathematics has no bearing whatever on the real world.

[Guest Leah W. Ratner]

Mathematical descriptions often imply physical ideas. For examle, description of particular physical relations with a linear function suggests that the function does not have a limit that depends on the variables in the function. If it is not supported empirically, we have to select nonlinear description of the proposed physical relations. Then the limit of such function is a culmination of relations between the variable concepts in this function. In this example the physical idea that lead to the successful description and , probably, successful physical theory is the knowledge of outcome of certain mathematical description. Likewise, the empirical methods have no more potency than mathematical methods for constructing the successful predictive physical theory.

l.ratner