This collection of papers, celebrating the contributions of Swedish logician Dag Prawitz to Proof Theory, has been assembled from those presented at the Natural Deduction conference organized in Rio de Janeiro to honour his seminal research. Dag Prawitz’s work forms the basis of intuitionistic type theory and his inversion principle constitutes the foundation of most modern accounts of proof-theoretic semantics in Logic, Linguistics and Theoretical Computer Science. The range of contributions includes material on the extension of natural deduction with higher-order (...) rules, as opposed to higher-order connectives, and a paper discussing the application of natural deduction rules to dealing with equality in predicate calculus. The volume continues with a key chapter summarizing work on the extension of the Curry-Howard isomorphism, via methods of category theory that have been successfully applied to linear logic, as well as many other contributions from highly regarded authorities. With an illustrious group of contributors addressing a wealth of topics and applications, this volume is a valuable addition to the libraries of academics in the multiple disciplines whose development has been given added scope by the methodologies supplied by natural deduction. The volume is representative of the rich and varied directions that Prawitz work has inspired in the area of natural deduction. (shrink)

‘The Principles of the Pure Type Theory’ is a translation of Leon Chwistek's 1922 paper ‘Zasady czystej teorii typów’. It summarizes Chwistek's results from a series of studies of the logic of Whitehead and Russell's Principia Mathematica which were published between 1912 and 1924. Chwistek's main argument involves a criticism of the axiom of reducibility. Moreover, ‘The Principles of the Pure Type Theory’ is a source for Chwistek's views on an issue in Whitehead and Russell's ‘no-class theory of classes’ involving (...) the notion of ‘scope’. (shrink)

The paper begins by delimiting the scope of ‘logic’ and ‘philosophy of science’ and goes on to present the biographies and select bibliographies of 36 émigré scholars from Germany and Austria working in these fields. An evaluation of this material, and of data on societies, congresses, lecture series, books and periodicals on logic and philosophy of science, is then undertaken. Against the rich background of activity in the 20s and 30s of our century, there is manifest a rapid decline of (...) high-ranking research in the philosophy of science and in logic in Germany and Austria. Since, with one exception, émigré logicians and philosophers of science did not return after the breakdown of the Third Reich, recovery in these fields has been extremely slow. Pertinent knowledge had to be re-imported, and a satisfactory level has been reached only with the coming of a new generation. (shrink)

In 1928 Ivan Orlov published a remarkable paper which contains the first formulation of a relevant logic. The paper remained largely unknown to English-speakers until this discovery of relevant log...

This is a review, with historical and critical comments, of a paper by I. E. Orlov from 1928, which gives the oldest known axiomatization of the implication-negation fragment of the relevant logic R. Orlov's paper also foreshadows the modal translation of systems with an intuitionistic negation into S4-type extensions of systems with a classical, involutive, negation. Orlov introduces the modal postulates of S4 before Becker, Lewis and Gödel. Orlov's work, which seems to be nearly completely ignored, is related to the (...) contemporaneous work on the axiomatization of intuitionistic logic. (shrink)

Van Heijenoort’s account of the historical development of modern logic was composed in 1974 and first published in 1992 with an introduction by his former student. What follows is a new edition with a revised and expanded introduction and additional notes.

This volume portrays the Polish or Lvov-Warsaw School, one of the most influential schools in analytic philosophy, which, as discussed in the thorough introduction, presented an alternative working picture of the unity of science.