Books on Amazon
|Numbers||Thiel I 18
Numbers/Mathematics/Ontology/Mathematical Entities/Poincaré/Thiel: Definition Conventionalism (Poincaré:) Poincaré considers this concept to be a mistake for his contemporaries, who think that geometric statements, such as that the angular sum of the triangle can be proved via two right angles.
The empirical finding about spatial reality cannot clearly prescribe a geometry which characterizes this finding. The N.B. is not the measurement accuracy, but Poincaré says that the geometry remains freely selectable even with results within this measuring accuracy. We could also introduce additional physical laws for a measured triangle with less than 180°, e.g. the effect of "fields". The name "conventionalism" refers to this "free selectability" of the system of geometry.
Philosophie und Mathematik Darmstadt 1995