Deduction, Computation, Experiment
Deduction, Computation, Experiment

Author: Rossella Lupacchini

Publisher: Springer Science & Business Media

Published: 2008-09-25

Total Pages: 285

ISBN-13: 8847007844

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This volume is located in a cross-disciplinary ?eld bringing together mat- matics, logic, natural science and philosophy. Re?ection on the e?ectiveness of proof brings out a number of questions that have always been latent in the informal understanding of the subject. What makes a symbolic constr- tion signi?cant? What makes an assumption reasonable? What makes a proof reliable? G ̈ odel, Church and Turing, in di?erent ways, achieve a deep und- standing of the notion of e?ective calculability involved in the nature of proof. Turing’s work in particular provides a “precise and unquestionably adequate” de?nition of the general notion of a formal system in terms of a machine with a ?nite number of parts. On the other hand, Eugene Wigner refers to the - reasonable e?ectiveness of mathematics in the natural sciences as a miracle. Where should the boundary be traced between mathematical procedures and physical processes? What is the characteristic use of a proof as a com- tation, as opposed to its use as an experiment? What does natural science tell us about the e?ectiveness of proof? What is the role of mathematical proofs in the discovery and validation of empirical theories? The papers collected in this book are intended to search for some answers, to discuss conceptual and logical issues underlying such questions and, perhaps, to call attention to other relevant questions.

Paraconsistency: Logic and Applications
Paraconsistency: Logic and Applications

Author: Koji Tanaka

Publisher: Springer Science & Business Media

Published: 2012-07-26

Total Pages: 380

ISBN-13: 9400744382

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A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change this situation. The book includes almost every major author currently working in the field. The papers are on the cutting edge of the literature some of which discuss current debates and others present important new ideas. The editors have avoided papers about technical details of paraconsistent logic, but instead concentrated upon works that discuss more "big picture" ideas. Different treatments of paradoxes takes centre stage in many of the papers, but also there are several papers on how to interpret paraconistent logic and some on how it can be applied to philosophy of mathematics, the philosophy of language, and metaphysics.

Dag Prawitz on Proofs and Meaning
Dag Prawitz on Proofs and Meaning

Author: Heinrich Wansing

Publisher: Springer

Published: 2014-11-27

Total Pages: 469

ISBN-13: 3319110411

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This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of p roofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence.

From a Heuristic Point of View
From a Heuristic Point of View

Author: Cesare Cozzo

Publisher: Cambridge Scholars Publishing

Published: 2014-07-03

Total Pages: 295

ISBN-13: 1443863351

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How do we get new knowledge? Following the maverick tradition in the philosophy of science, Carlo Cellucci gradually came to the conclusion that logic can only fulfill its role in mathematics, science and philosophy if it helps us to answer this question. He argues that mathematical logic is inadequate and that we need a new logic, framed in a naturalistic conception of knowledge and philosophy – the heuristic conception. This path from logic to a naturalistic conception of knowledge and philosophy explains the title, From a Heuristic Point of View, which recalls the celebrated collection of essays, From a Logical Point of View, by Willard Van Orman Quine, the father of modern naturalized epistemology. The word ‘heuristic’ points to Cellucci’s favorite theme and the main difference between him and Quine: the emphasis on discovery and building a ‘logic’ for generating new knowledge. This book is a collection of essays from leading figures in this field who discuss, criticize, or expand on the main topics in Cellucci’s work, dealing with some of the most challenging questions in logic, science and philosophy.

Computational & Experimental Methods in Multiphase & Complex Flow X
Computational & Experimental Methods in Multiphase & Complex Flow X

Author: S. Hernández

Publisher: WIT Press

Published: 2019-07-23

Total Pages: 251

ISBN-13: 1784663298

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Composed of papers presented at the 10th conference on Multiphase flow this book presents the latest research on the subject. The research included in this volume focuses on using synergies between experimental and computational techniques to gain a better understanding of all classes of multiphase and complex flow.

Reason and Rationality
Reason and Rationality

Author: Maria Cristina Amoretti

Publisher: Walter de Gruyter

Published: 2013-05-02

Total Pages: 254

ISBN-13: 3110325861

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Reason and rationality represent crucial elements of the self-image of human beings and have unquestionably been among the most debated issues in Western philosophy, dating from ancient Greece, through the Middle Ages, and to the present day. Many words and thoughts have already been spent trying to define the nature and standards of reason and rationality, what they could or ought to be, and under what conditions something can be said to be rational. This volume focuses instead on the relationships of reason and rationality to some relevant specific topics, i.e., science, knowledge, gender, politics, ethics, religion, aesthetics, language, logic, and metaphysics, trying to uncover and clarify both the connections and differences in their various characterisations and uses.

The Best Writing on Mathematics 2010
The Best Writing on Mathematics 2010

Author: Mircea Pitici

Publisher: Princeton University Press

Published: 2021-09-14

Total Pages: 435

ISBN-13: 1400836123

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The year’s most memorable writing on mathematics This anthology brings together the year's finest writing on mathematics from around the world. Featuring promising new voices alongside some of the foremost names in mathematics, The Best Writing on Mathematics makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here readers will discover why Freeman Dyson thinks some mathematicians are birds while others are frogs; why Keith Devlin believes there's more to mathematics than proof; what Nick Paumgarten has to say about the timing patterns of New York City's traffic lights (and why jaywalking is the most mathematically efficient way to cross Sixty-sixth Street); what Samuel Arbesman can tell us about the epidemiology of the undead in zombie flicks; and much, much more. In addition to presenting the year's most memorable writing on mathematics, this must-have anthology also includes a foreword by esteemed mathematician William Thurston and an informative introduction by Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it's headed.

A Critical Reflection on Automated Science
A Critical Reflection on Automated Science

Author: Marta Bertolaso

Publisher: Springer Nature

Published: 2020-02-05

Total Pages: 302

ISBN-13: 3030250016

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This book provides a critical reflection on automated science and addresses the question whether the computational tools we developed in last decades are changing the way we humans do science. More concretely: Can machines replace scientists in crucial aspects of scientific practice? The contributors to this book re-think and refine some of the main concepts by which science is understood, drawing a fascinating picture of the developments we expect over the next decades of human-machine co-evolution. The volume covers examples from various fields and areas, such as molecular biology, climate modeling, clinical medicine, and artificial intelligence. The explosion of technological tools and drivers for scientific research calls for a renewed understanding of the human character of science. This book aims precisely to contribute to such a renewed understanding of science.

Computational Multiscale Modeling of Fluids and Solids
Computational Multiscale Modeling of Fluids and Solids

Author: Martin Oliver Steinhauser

Publisher: Springer Nature

Published: 2022-07-28

Total Pages: 450

ISBN-13: 3030989542

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The expanded 3rd edition of this established textbook offers an updated overview and review of the computational physics techniques used in materials modelling over different length and time scales. It describes in detail the theory and application of some of the most important methods used to simulate materials across the various levels of spatial and temporal resolution. Quantum mechanical methods such as the Hartree-Fock approximation for solving the Schrödinger equation at the smallest spatial resolution are discussed as well as the Molecular Dynamics and Monte-Carlo methods on the micro- and meso-scale up to macroscopic methods used predominantly in the Engineering world such as Finite Elements (FE) or Smoothed Particle Hydrodynamics (SPH). Extensively updated throughout, this new edition includes additional sections on polymer theory, statistical physics and continuum theory, the latter being the basis of FE methods and SPH. Each chapter now first provides an overview of the key topics covered, with a new “key points” section at the end. The book is aimed at beginning or advanced graduate students who want to enter the field of computational science on multi-scales. It provides an in-depth overview of the basic physical, mathematical and numerical principles for modelling solids and fluids on the micro-, meso-, and macro-scale. With a set of exercises, selected solutions and several case studies, it is a suitable book for students in physics, engineering, and materials science, and a practical reference resource for those already using materials modelling and computational methods in their research.

Advanced Computational Methods and Experiments in Heat Transfer X
Advanced Computational Methods and Experiments in Heat Transfer X

Author: Bengt Sundén

Publisher: WIT Press

Published: 2008-06-19

Total Pages: 241

ISBN-13: 1845641221

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In engineering design and development, reliable and accurate computational methods are requested to replace or complement expensive and time consuming experimental trial and error work. Tremendous advancements have been achieved during recent years due to improved numerical solutions of non-linear partial differential equations and computer developments to achieve efficient and rapid calculations. Nevertheless, to further progress in computational methods will require developments in theoretical and predictive procedures – both basic and innovative – and in applied research. Accurate experimental investigations are needed to validate the numerical calculations. This book contains the edited versions of the papers presented at the Tenth International Conference on Advanced Computational Methods and Experimental Measurements in Heat Transfer and Mass Transfer held in Maribor, Slovenia in July 2008. The objective of this conference series is to provide a forum for presentation and discussion of advanced topics, new approaches and application of advanced computational methods and experimental measurements to heat and mass transfer problems. The contributed papers are grouped in the following appropriate sections to provide better access for readers: Natural and forced convection; Heat exchangers; Advances in computational methods; Heat recovery; Heat transfer; Modelling and experiments.