2019-04-23 10:37:12 UTC
"By a theory I shall mean the deductive closure of a set of theoretical postulates together with an appropriate set of auxiliary hypotheses; that is, everything that can be deduced from this set." W. H. Newton-Smith, THE RATIONALITY OF SCIENCE, p. 199 http://cdn.preterhuman.net/texts/thought_and_writing/philosophy/rationality%20of%20science.pdf
Einstein offers essentially the same definition here:
Albert Einstein: "From a systematic theoretical point of view, we may imagine the process of evolution of an empirical science to be a continuous process of induction. Theories are evolved and are expressed in short compass as statements of a large number of individual observations in the form of empirical laws, from which the general laws can be ascertained by comparison. Regarded in this way, the development of a science bears some resemblance to the compilation of a classified catalogue. It is, as it were, a purely empirical enterprise. But this point of view by no means embraces the whole of the actual process ; for it slurs over the important part played by intuition and deductive thought in the development of an exact science. As soon as a science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms." https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ap03.htm
Two points should be noted:
1. The axioms (postulates), clearly defined, are indispensable.
2. The results of the theory are DEDUCED FROM AXIOMS, not guessed as Feynman used to teach:
Richard Feynman: "Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws." http://dillydust.com/The%20Character%20of%20Physical%20Law~tqw~_darksiderg.pdf
The crucial questions are:
What if the theory has no axioms? What if results of the theory are just "guessed", not deduced from axioms?
Answer: Then the theory, e.g. Einstein's general relativity, is a not-even-wrong empirical concoction, essentially equivalent to the EMPIRICAL curve fitting models defined here:
"The objective of curve fitting is to theoretically describe experimental data with a model (function or equation) and to find the parameters associated with this model. Models of primary importance to us are mechanistic models. Mechanistic models are specifically formulated to provide insight into a chemical, biological, or physical process that is thought to govern the phenomenon under study. Parameters derived from mechanistic models are quantitative estimates of real system properties (rate constants, dissociation constants, catalytic velocities etc.). It is important to distinguish mechanistic models from empirical models that are mathematical functions formulated to fit a particular curve but whose parameters do not necessarily correspond to a biological, chemical or physical property." http://collum.chem.cornell.edu/documents/Intro_Curve_Fitting.pdf