Logic S Lost Genius

Author : Eckart Menzler-Trott
Publisher : American Mathematical Soc.
Page : 442 pages
File Size : 50,9 Mb
Release : 2016-05-05
Category : Electronic
ISBN : 9781470428129

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Logic's Lost Genius by Eckart Menzler-Trott Pdf

Gerhard Gentzen (1909–1945) is the founder of modern structural proof theory. His lasting methods, rules, and structures resulted not only in the technical mathematical discipline called “proof theory” but also in verification programs that are essential in computer science. The appearance, clarity, and elegance of Gentzen's work on natural deduction, the sequent calculus, and ordinal proof theory continue to be impressive even today. The present book gives the first comprehensive, detailed, accurate scientific biography expounding the life and work of Gerhard Gentzen, one of our greatest logicians, until his arrest and death in Prague in 1945. Particular emphasis in the book is put on the conditions of scientific research, in this case mathematical logic, in National Socialist Germany, the ideological fight for “German logic”, and their mutual protagonists. Numerous hitherto unpublished sources, family documents, archival material, interviews, and letters, as well as Gentzen's lectures for the mathematical public, make this book an indispensable source of information on this important mathematician, his work, and his time. The volume is completed by two deep substantial essays by Jan von Plato and Craig Smoryński on Gentzen's proof theory; its relation to the ideas of Hilbert, Brouwer, Weyl, and Gödel; and its development up to the present day. Smoryński explains the Hilbert program in more than the usual slogan form and shows why consistency is important. Von Plato shows in detail the benefits of Gentzen's program. This important book is a self-contained starting point for any work on Gentzen and his logic. The book is accessible to a wide audience with different backgrounds and is suitable for general readers, researchers, students, and teachers.

Author : Nikolaos Galatos,Kazushige Terui
Publisher : Springer Nature
Page : 382 pages
File Size : 46,8 Mb
Release : 2021-12-13
Category : Philosophy
ISBN : 9783030769208

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Hiroakira Ono on Substructural Logics by Nikolaos Galatos,Kazushige Terui Pdf

This volume is dedicated to Hiroakira Ono life’s work on substructural logics. Chapters, written by well-established academics, cover topics related to universal algebra, algebraic logic and the Full Lambek calculus; the book includes a short biography about Hiroakira Ono. The book starts with detailed surveys on universal algebra, abstract algebraic logic, topological dualities, and connections to computer science. It further contains specialised contributions on connections to formal languages (recognizability in residuated lattices and connections to the finite embedding property), covering systems for modal substructural logics, results on the existence and disjunction properties and finally a study of conservativity of expansions. This book will be primarily of interest to researchers working in algebraic and non-classical logic.

Author : Jan von Plato
Publisher : Princeton University Press
Page : 400 pages
File Size : 51,9 Mb
Release : 2017-08-02
Category : Science
ISBN : 9781400885039

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The Great Formal Machinery Works by Jan von Plato Pdf

The information age owes its existence to a little-known but crucial development, the theoretical study of logic and the foundations of mathematics. The Great Formal Machinery Works draws on original sources and rare archival materials to trace the history of the theories of deduction and computation that laid the logical foundations for the digital revolution. Jan von Plato examines the contributions of figures such as Aristotle; the nineteenth-century German polymath Hermann Grassmann; George Boole, whose Boolean logic would prove essential to programming languages and computing; Ernst Schröder, best known for his work on algebraic logic; and Giuseppe Peano, cofounder of mathematical logic. Von Plato shows how the idea of a formal proof in mathematics emerged gradually in the second half of the nineteenth century, hand in hand with the notion of a formal process of computation. A turning point was reached by 1930, when Kurt Gödel conceived his celebrated incompleteness theorems. They were an enormous boost to the study of formal languages and computability, which were brought to perfection by the end of the 1930s with precise theories of formal languages and formal deduction and parallel theories of algorithmic computability. Von Plato describes how the first theoretical ideas of a computer soon emerged in the work of Alan Turing in 1936 and John von Neumann some years later. Shedding new light on this crucial chapter in the history of science, The Great Formal Machinery Works is essential reading for students and researchers in logic, mathematics, and computer science.

Author : Paolo Mancosu
Publisher : OUP Oxford
Page : 632 pages
File Size : 44,7 Mb
Release : 2014-01-09
Category : Philosophy
ISBN : 9780191021992

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The Adventure of Reason by Paolo Mancosu Pdf

Paolo Mancosu presents a series of innovative studies in the history and the philosophy of logic and mathematics in the first half of the twentieth century. The Adventure of Reason is divided into five main sections: history of logic (from Russell to Tarski); foundational issues (Hilbert's program, constructivity, Wittgenstein, Gödel); mathematics and phenomenology (Weyl, Becker, Mahnke); nominalism (Quine, Tarski); semantics (Tarski, Carnap, Neurath). Mancosu exploits extensive untapped archival sources to make available a wealth of new material that deepens in significant ways our understanding of these fascinating areas of modern intellectual history. At the same time, the book is a contribution to recent philosophical debates, in particular on the prospects for a successful nominalist reconstruction of mathematics, the nature of finitist intuition, the viability of alternative definitions of logical consequence, and the extent to which phenomenology can hope to account for the exact sciences.

Author : Barry S. Cooper,Anuj Dawar,Benedikt Löwe
Publisher : Springer
Page : 756 pages
File Size : 53,8 Mb
Release : 2012-05-28
Category : Computers
ISBN : 9783642308703

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How the World Computes by Barry S. Cooper,Anuj Dawar,Benedikt Löwe Pdf

This book constitutes the refereed proceedings of the Turing Centenary Conference and the 8th Conference on Computability in Europe, CiE 2012, held in Cambridge, UK, in June 2012. The 53 revised papers presented together with 6 invited lectures were carefully reviewed and selected with an acceptance rate of under 29,8%. The CiE 2012 Turing Centenary Conference will be remembered as a historic event in the continuing development of the powerful explanatory role of computability across a wide spectrum of research areas. The papers presented at CiE 2012 represent the best of current research in the area, and forms a fitting tribute to the short but brilliant trajectory of Alan Mathison Turing. Both the conference series and the association promote the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences such as physics and biology, and also including the promotion of related non-scientific fields such as philosophy and history of computing.

Author : Reinhard Kahle,Michael Rathjen
Publisher : Springer
Page : 561 pages
File Size : 54,6 Mb
Release : 2015-11-02
Category : Mathematics
ISBN : 9783319101033

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Gentzen's Centenary by Reinhard Kahle,Michael Rathjen Pdf

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.

Author : Gerhard Heinzmann,Gereon Wolters
Publisher : Springer Nature
Page : 268 pages
File Size : 49,6 Mb
Release : 2021-08-17
Category : Mathematics
ISBN : 9783030658243

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Paul Lorenzen -- Mathematician and Logician by Gerhard Heinzmann,Gereon Wolters Pdf

This open access book examines the many contributions of Paul Lorenzen, an outstanding philosopher from the latter half of the 20th century. It features papers focused on integrating Lorenzen's original approach into the history of logic and mathematics. The papers also explore how practitioners can implement Lorenzen’s systematical ideas in today’s debates on proof-theoretic semantics, databank management, and stochastics. Coverage details key contributions of Lorenzen to constructive mathematics, Lorenzen’s work on lattice-groups and divisibility theory, and modern set theory and Lorenzen’s critique of actual infinity. The contributors also look at the main problem of Grundlagenforschung and Lorenzen’s consistency proof and Hilbert’s larger program. In addition, the papers offer a constructive examination of a Russell-style Ramified Type Theory and a way out of the circularity puzzle within the operative justification of logic and mathematics. Paul Lorenzen's name is associated with the Erlangen School of Methodical Constructivism, of which the approach in linguistic philosophy and philosophy of science determined philosophical discussions especially in Germany in the 1960s and 1970s. This volume features 10 papers from a meeting that took place at the University of Konstanz.

Author : Charles LaPorte
Publisher : Cambridge University Press
Page : 227 pages
File Size : 52,6 Mb
Release : 2020-11-05
Category : Drama
ISBN : 9781108496155

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The Victorian Cult of Shakespeare by Charles LaPorte Pdf

How and why did Victorian culture make Shakespeare into a literary deity and his work into a secular Bible?

Author : Sandra Peart
Publisher : Taylor & Francis
Page : 424 pages
File Size : 41,6 Mb
Release : 2003
Category : Biography & Autobiography
ISBN : 0415143365

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W.S. Jevons by Sandra Peart Pdf

Author : Yusuke Kubota,Robert D. Levine
Publisher : MIT Press
Page : 420 pages
File Size : 48,7 Mb
Release : 2020-09-15
Category : Language Arts & Disciplines
ISBN : 9780262360791

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Type-Logical Syntax by Yusuke Kubota,Robert D. Levine Pdf

A novel logic-based framework for representing the syntax-semantics interface of natural language, applicable to a range of phenomena. In this book, Yusuke Kubota and Robert Levine propose a type-logical version of categorial grammar as a viable alternative model of natural language syntax and semantics. They show that this novel logic-based framework is applicable to a range of phenomena--especially in the domains of coordination and ellipsis--that have proven problematic for traditional approaches.

Author : Henry Sweet
Publisher : Unknown
Page : 540 pages
File Size : 44,6 Mb
Release : 1892
Category : English language
ISBN : BSB:BSB11642779

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A New English Grammar, Logical and Historical by Henry Sweet Pdf

Author : Henry Sweet
Publisher : Unknown
Page : 552 pages
File Size : 40,5 Mb
Release : 1891
Category : English language
ISBN : OXFORD:601887672

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A New English Grammar, Logical and Historical: Introduction, phonology, and accidence by Henry Sweet Pdf

Author : Richard Whately
Publisher : Unknown
Page : 304 pages
File Size : 45,6 Mb
Release : 1866
Category : Electronic
ISBN : NLI:3208915-10

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Elements of Logics by Richard Whately Pdf

Author : Stephanie Adair
Publisher : Walter de Gruyter GmbH & Co KG
Page : 312 pages
File Size : 50,7 Mb
Release : 2018-06-25
Category : Philosophy
ISBN : 9783110576078

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The Aesthetic Use of the Logical Functions in Kant's Third Critique by Stephanie Adair Pdf

In the third Critique Kant details an aesthetic operation of judgment that is surprising considering how judgment functioned in the first Critique. In this book, I defend an understanding of Kant’s theory of Geschmacksurteil as detailing an operation of the faculties that does not violate the cognitive structure laid out in the first Critique. My orientation is primarily epistemological, elaborating the determinations that govern the activity of pure aesthetic judging that specify it as a "bestimmte" type of judgment without transforming it into "ein bestimmendes Urteil". I focus on identifying how the logical functions from the table of judgments operate in the pure aesthetic judgment of taste to reveal "the moments to which this power of judgment attends in its reflection" (CPJ, 5:203). In the course of doing so, a picture emerges of how the world is not just cognizable in a Kantian framework but also charged with human feeling, acquiring the inexhaustible, inchoate meaningfulness that incites "much thinking" (CPJ, 5:315). The universal communicability of aesthetic pleasure serves as the foundation that grounds robust intersubjective relations, enabling genuine connection to others through a shared a priori feeling.

Author : Florentin Smarandache
Publisher : Infinite Study
Page : 157 pages
File Size : 41,5 Mb
Release : 2005
Category : Mathematics
ISBN : 9781599730806

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A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability (fourth edition) by Florentin Smarandache Pdf

N-Norm and N-conorm are extended in Neutrosophic Logic/Set.