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Principles/Poincaré: asserts with regard to the principles of mechanics: never will a new experiment lead to abandon them. The operation which it is to compare with the facts has no meaning.
E.g. principle of inertia. You can only give it a meaning if you consider a certain relationship point to be chosen. Disregarding this definition would deprive the expression of its meaning. There are as many laws as different relationship points! If the principle of inertia were wrong in relation to a certain point, it would become true when another one was chosen. And it would always be free to choose this latter. It is impossible to close this backdoor.
E.g. Principle of equality of action and reaction: (also Poincaré): "The focus of an isolated system can only have a straight and uniform motion."
Can this be verified by an experiment? No, the only isolated system is the universe. So the question makes no sense. "We are always free to accept that our principle is correct."
E.g. Chemistry: The Law of multiple proportions: Whatever the results of the analysis may be, it is always certain to find three integers, by virtue of which the law is verifiable with more accuracy than the experiments have.
E.g. Law of the rational indices: crystallography. There are always certain errors during measurements. The crystalographer, who wants to correct the law experimentally, certainly did not understand the meaning of the words he uses. Here as in the case of the multiple proportions, these are purely mathematical expressions, which lack any physical sense.
Duhem: It would only lead to public places, if one were to say that the conditions were almost commensurable: for everything in the world is almost commensurable. Any kind of incommensurable relationship is always nearly commensurable.
It would be absurd to want to subject certain principles of mechanics to the direct control of the experiment. Does it follow that these hypotheses cannot be achieved by experimental contradictions? No!
Isolated, these hypotheses have no experimental significance. It cannot be a question of confirming or refuting the experiments. But these hypotheses are used as essential foundations in the construction of theories. These theories (crystallography, mechanics, chemistry) are representations designed to be compared with the facts. The experimental contradiction then always concerns a group as a whole. So it disappears what could have appeared paradoxical in the assertion that certain physical theories are based on hypotheses which cannot be interpreted physically.
Principles/Poincaré: "The experiment can build the principles of mechanics, but not destroy them".
HadamardVs: "Duhem has shown that it is not about isolated hypotheses, but the totality of the hypotheses of mechanics, whose experimental verification can be attempted.
It is up to the physicist's instinct to look for the fault from which the whole system suffers. No absolute principle leads this investigation. If there is a struggle between hypotheses, the healthy commen sense decides after some time.
E.g. According to Foucault's experiment, Biot abandoned the emission hypothesis. Pure logic would not have been enough for this waiver. It was not an experimentum crucis.
Ziel und Struktur der physikalischen Theorien Hamburg 1998