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Fact/Duhem: The concept of facts has lost its independence because facts are always impregnated in theory.
Duhem seeks to control between Skylla of inductivism and the Charybdis of apriorism. The concept of the experimental law serves as a steering wheel.
Symbols cannot be called true or false, at best appropriate. This also applies to theories as purely symbolic representations. Duhem, however, assigns empirical content to empirical laws, which purely theoretical laws cannot claim.
An experimentum crucis (whose failure would disprove the whole theory) is rejected. (> Holism).
By increasing the accuracy of measurement, we have reduced the set of theoretical facts.
E.g. Geodetic lines on an infinite surface (I 182). There are those who return in themselves, and those who do not, although they do not move away infinitely (surface: infinitely extended ~ bullhorn)
Nevertheless, theoretically, the initial conditions can be determined accurately without obtaining ambiguities, for example when a sphere is to move on a geodetic line.
However, it is quite different when, instead of the theoretical, practical initial conditions are given. Unlimited set of different initial conditions.
If the initial conditions are not mathematically known, but determined by physical methods, and even if they are exact, the question posed will remain unanswerable.
Facts/Duhem: Concrete, very different facts can be confounded when interpreted by the theory that they are only form a single experiment and are represented by a single symbolic expression. One and the same theoretical fact can correspond to an infinite number of practical facts.
But also the same practical fact can correspond to an infinite number of theoretical facts, which are logically incompatible with each other. (> Quine,> Quine-Duhem thesis)
An experimenter might say: E.g. An increase of the pressure by 100 atmospheres increases the electromotive force by 0.085 volts. He could have said with the same authority: by 0.0844 or 0.0846 volts. For the mathematician the statements are contradictory. For the physicist, whose possibility of differentiation is limited because of the measurement accuracy, they have the same meaning.
Difference between mathematics and physics: deviating measurement results are no formal contradiction. > Quine, distinction analytic/synthetic.
Ziel und Struktur der physikalischen Theorien Hamburg 1998