Pentcho Valev

2018-01-05 09:36:43 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 "small number of fundamental assumptions, the so-called axioms", clearly defined, are indispensable.

2. The results of the theory are DEDUCED from the "small number of fundamental assumptions, the so-called 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 question is:

What if the "small number of fundamental assumptions, the so-called axioms" don't exist, or, even if they exist, some results of the theory are not deduced from them?

My answer: In this case the theory is not even wrong.

Pentcho Valev

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 "small number of fundamental assumptions, the so-called axioms", clearly defined, are indispensable.

2. The results of the theory are DEDUCED from the "small number of fundamental assumptions, the so-called 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 question is:

What if the "small number of fundamental assumptions, the so-called axioms" don't exist, or, even if they exist, some results of the theory are not deduced from them?

My answer: In this case the theory is not even wrong.

Pentcho Valev