I 250
Method/Duhem: The method of ad absurdum guiding can become an evidence. In order to prove that a theorem is correct, it is sufficient to drive the exactly opposite theorem into an absurd consequence. The Greek mathematicians had made extended use of this method.
Those who equate the experimental contradiction with the ad absurdum guiding mean that one makes equal use in physics as in geometry. That's not right.
The name experimentum Crucis refers to a crossroad of the decision.
E.g. there are two hypotheses about the nature of the light.
I 251
For Newton, Laplace, and Biot light consists of projectiles. For Huygens, Fresnel et al. it consists of vibrations. According to the first, light moves faster in water than in the air. Foucault's experiment with rotating mirrors proves that the greenish strip ... appears at a certain point. The dispute is decided, light is not a body, but a vibration propagating in the ether.
DuhemVs: The experiment of Foucault does not decide between two hypotheses of emission and undulation, but between two theoretical groups, which must be taken as a whole, between two complete systems of Newton's optics and Huygens' optics. >
Hypotheses, >
Theories.
I 252
But let us assume that both are correct. In addition to two theorems of geometry that contradict each other, there is no place for a third. This is different in physics.
I 253
Experiment/Method/Duhem: One cannot reconstruct the form of ad absurdum guiding with the experimental method. The geometry, however, also has the direct proof, but it cannot be comprehended in the experiment either. >
Experiments, >
Observation.
I 260
E.g. the theoretician cannot only use the Kepler laws for justification, since these are determined solely by the concrete individual objects. He must show that the observed disturbances coincide with the previously calculated ones.
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I 278
Method/Duhem: Interlocutor: The discussion that leads to a theory is a link, it is not justified to seek in it a physical sense.
The demand that every mathematical operation used in the course is given a physical sense would inhibit the progress. One has also tried to ban the differential calculus for physics. >
Calculus.
