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Definition of Theory in Physics (Why Theories Are Not Even Wrong)
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Pentcho Valev
2018-01-05 09:39:02 UTC
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"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
Pentcho Valev
2018-01-06 10:06:12 UTC
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Einstein's definitions again:

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."x https://www.marxists.org/reference/archive/einstein/works/1910s/relative/ap03.htm

So a physics theory is either a (not even wrong) empirical concoction or an axiomatic (deductive) construction. There is no third alternative. Empirical theorizing means "invincible models that can forever be amended":

Sabine Hossenfelder (Bee): "The criticism you raise that there are lots of speculative models that have no known relevance for the description of nature has very little to do with string theory but is a general disease of the research area. Lots of theorists produce lots of models that have no chance of ever being tested or ruled out because that's how they earn a living. The smaller the probability of the model being ruled out in their lifetime, the better. It's basic economics. Survival of the 'fittest' resulting in the natural selection of invincible models that can forever be amended." http://www.math.columbia.edu/~woit/wordpress/?p=9375

Pentcho Valev

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