Bücher von Giovanni Sommaruga

In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Gottingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

It is commonly assumed that computers process information. But what is inf- mation? In a technical, important, but nevertheless rather narrow sense, Sh- non'sinformationtheorygivesa?rstanswertothisquestion.Thistheoryfocuses on measuring the information content of a message. Essentially this measure is the reduction of the uncertainty obtained by receiving a message. The unc- tainty of a situation of ignorance in turn is measured by entropy. This theory hashad an immense impact on the technologyof information storage,data c- pression, information transmission and coding and still is a very active domain of research. Shannon's theory has also attractedmuch interest in a more philosophic look at information, although it was readily remarked that it is only a "e;syntactic"e; theory of information and neglects "e;semantic"e; issues. Several attempts have been made in philosophy to give information theory a semantic ?avor, but still mostly based on or at least linked to Shannon's theory. Approaches to semantic informationtheoryalsoveryoftenmakeuseofformallogic.Thereby,information is linked to reasoning, deduction and inference, as well as to decision making. Further, entropy and related measure were soon found to have important connotations with regard to statistical inference. Surely, statistical data and observation represent information, information about unknown, hidden para- ters. Thus a whole branch of statistics developed around concepts of Shannon's information theory or derived from them. Also some proper measurements - propriate for statistics, like Fisher's information, were proposed.

A comprehensive survey of Martin-Loef's constructive type theory, considerable parts of which have only been presented by Martin-Loef in lecture form or as part of conference talks. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material.

A comprehensive survey of Martin-Loef's constructive type theory, considerable parts of which have only been presented by Martin-Loef in lecture form or as part of conference talks. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material.