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Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the twenty-second publication in the Lecture Notes in Logic series, will launch a discussion about the concept of intensionality in philosophy, logic, linguistics and mathematics. These articles grew out of a workshop held at the University of Munich in October, 2000. Some articles address philosophical issues raised by the possible worlds approach to intensionality; others are devoted to technical aspects of modal logic. The volume highlights the particular interdisciplinary nature of intensionality with articles spanning philosophy, linguistics, mathematics and computer science.

Logic, Symbolic and mathematical --- Mathematics --- Philosophy

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This book on proof theory centers around the legacy of Kurt Schütte and its current impact on the subject. Schütte was the last doctoral student of David Hilbert who was the first to see that proofs can be viewed as structured mathematical objects amenable to investigation by mathematical methods (metamathematics). Schütte inaugurated the important paradigm shift from finite proofs to infinite proofs and developed the mathematical tools for their analysis. Infinitary proof theory flourished in his hands in the 1960s, culminating in the famous bound Γ0 for the limit of predicative mathematics (a fame shared with Feferman). Later his interests shifted to developing infinite proof calculi for impredicative theories. Schütte had a keen interest in advancing ordinal analysis to ever stronger theories and was still working on some of the strongest systems in his eighties. The articles in this volume from leading experts close to his research, show the enduring influence of his work in modern proof theory. They range from eye witness accounts of his scientific life to developments at the current research frontier, including papers by Schütte himself that have never been published before.

Mathematical logic. --- Logic. --- Mathematical Logic and Foundations. --- Mathematical Logic and Formal Languages. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Methodology --- Mathematicians

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Gerhard Gentzen has been described as logic’s lost genius, whom Gödel called a better logician than himself. This work comprises articles by leading proof theorists, attesting to Gentzen’s enduring legacy to mathematical logic and beyond. The contributions range from philosophical reflections and re-evaluations of Gentzen’s original consistency proofs to the most recent developments in proof theory. Gentzen founded modern proof theory. His sequent calculus and natural deduction system beautifully explain the deep symmetries of logic. They underlie modern developments in computer science such as automated theorem proving and type theory. .

Mathematical logic --- wiskunde --- logica

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Verantwortung: Dieser Begriff prägt derzeit viele aktuelle Debatten in Gesellschaft und Wissenschaft. Das Buch versucht eine Präzisierung des Begriffs, indem es die Ausgestaltung von Verantwortung im Werk und Wirken bedeutender Persönlichkeiten wie Hannah Arendt, Karl Barth, Ernst Bloch, Emmanuel Levinas, Max Weber und Carl Friedrich von Weizsäcker nachzeichnet und seine besondere Relevanz in Gesellschaft und Wissenschaft reflektiert. Angesichts einer sich rasant wandelnden Welt mit zentralen Herausforderungen wie Klimawandel und Migration, aber auch Digitalisierung und Forschung zu Künstlicher Intelligenz stellt sich die Frage nach der Verantwortung immer dringlicher.

Ethik --- Wissenschaft --- Künstliche Intelligenz --- Hannah Arendt --- Karl Barth --- Ernst Bloch --- Emmanuel Levinas --- Max Weber --- Carl Friedrich von Weizsäcker

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The aim of this volume is to collect original contributions by the best specialists from the area of proof theory, constructivity, and computation and discuss recent trends and results in these areas. Some emphasis will be put on ordinal analysis, reductive proof theory, explicit mathematics and type-theoretic formalisms, and abstract computations. The volume is dedicated to the 60th birthday of Professor Gerhard Jäger, who has been instrumental in shaping and promoting logic in Switzerland for the last 25 years. It comprises contributions from the symposium “Advances in Proof Theory”, which was held in Bern in December 2013. Proof theory came into being in the twenties of the last century, when it was inaugurated by David Hilbert in order to secure the foundations of mathematics. It was substantially influenced by Gödel's famous incompleteness theorems of 1930 and Gentzen's new consistency proof for the axiom system of first order number theory in 1936. Today, proof theory is a well-established branch of mathematical and philosophical logic and one of the pillars of the foundations of mathematics. Proof theory explores constructive and computational aspects of mathematical reasoning; it is particularly suitable for dealing with various questions in computer science. .

Logic. --- Proof theory --- Logic, Symbolic and mathematical --- Logic, Symbolic and mathematical. --- Mathematical Logic and Foundations. --- Argumentation --- Deduction (Logic) --- Deductive logic --- Dialectic (Logic) --- Logic, Deductive --- Intellect --- Philosophy --- Psychology --- Science --- Reasoning --- Thought and thinking --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Methodology --- Mathematical logic.