CALCULEMUS - THE PROBLEM OF THE APPLICATION OF LOGIC AND MATHEMATICS

Starting out from Descartes' and Leibniz' idea of a mathesis universal is the achievements of modern mathematics are divided into three major parts: The creation of algorithms, the invention of proofs, and the a pplication of mathematics to the description of nature. This applicabi lity has repeatedly been viewed as being just a miracle. One major ide a to diminsh the miraculous impression was to view mathematics as expl oring the vast area of all kinds of abstract structures, thus establis hing a huge store of humanly possible thinking from which the physicis t has only to choose the structure appropriate for the case before him . There remains, however, the problem of mathematical overdeterminatio n of physics: the structures suitable for application usually contain mathematical elements that remain without physical interpretation. The true miracle then seems to be that it is often very difficult, if not impossible, to eliminate those uninterpreted elements from physical t heory.