Hilbert's program. An essay on mathematical instrumentalism
The main philosophical idea of Hilbert's program, viz. to prove the security, i.e. consistency of non-trivial ``ideal'' mathematical methods using only very elementary and thence obviously secure ones, i.e. ``finitary'' methods, often is claimed to be refuted by Gödel's incompleteness theorems, especially by the second one. In the present essay the author carefully analyzes the (pre-)suppositions which are - or have to be - used to prove such claims. His goal is to show that at present all those claims which have been made in the relevant literature (seem to) use some dubitable principles and hence cannot be taken as really disproving the Hilbertian aims. Of course, it is impossible to establish in such a way what Hilbert originally intended. But the author successfully localizes essential points in anti-Hilbertian argumentations which should be discussed in more detail. The book is well written and recommended reading for everyone interested in the philosophical dimensions of technical results from foundations of mathematics and pure logic.
scientific article; zbMATH DE number 4043803