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Mathesis Universalis, Computability and Proof, Stefania Centrone; Sara Negri; Deniz Sarikaya; Pet


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Автор: Stefania Centrone; Sara Negri; Deniz Sarikaya; Pet
Название:  Mathesis Universalis, Computability and Proof
ISBN: 9783030204464
Издательство: Springer
Классификация:



ISBN-10: 3030204464
Обложка/Формат: Hardcover
Страницы: 374
Вес: 0.74 кг.
Дата издания: 2019
Серия: Synthese Library
Язык: English
Издание: 1st ed. 2019
Иллюстрации: 38 illustrations, black and white; xiv, 374 p. 38 illus.
Размер: 234 x 156 x 22
Читательская аудитория: Professional & vocational
Основная тема: Philosophy
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: In a fragment entitled Elementa Nova Matheseos Universalis (1683?) Leibniz writes “the mathesis […] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects” (“objets quelconques”). It is an abstract theory of combinations and relations among objects whatsoever.In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” (“Gr?nde”) of others, and the latter are “consequences” (“Folgen”) of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory.The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification.
Дополнительное описание:
1. Introduction: Mathesis Universalis, Proof and Computation (Stefania Centrone).- 2. Diplomacy of Trust in the European Crisis (Enno Aufderheide).- 3. Mathesis Universalis and Homotopy Type Theory (Steve Awodey).- 4. Note on the Benefit of Proof Rep



Proofs and Algorithms: Introduction to Logic and Computability Theory

Автор: Gilles Dowek
Название: Proofs and Algorithms: Introduction to Logic and Computability Theory
ISBN: 0857291203 ISBN-13(EAN): 9780857291202
Издательство: Springer
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Цена: 4884.00 р.
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Описание: Logic is a branch of philosophy, mathematics and computer science. It studies the required methods to determine whether a statement is true, such as reasoning and computation.Proofs and Algorithms: Introduction to Logic and Computability is an introduction to the fundamental concepts of contemporary logic - those of a proof, a computable function, a model and a set. It presents a series of results, both positive and negative, - Church's undecidability theorem, G?del’s incompleteness theorem, the theorem asserting the semi-decidability of provability - that have profoundly changed our vision of reasoning, computation, and finally truth itself.Designed for undergraduate students, this book presents all that philosophers, mathematicians and computer scientists should know about logic.

Ordinal Computability: An Introduction to Infinitary Machines

Автор: Merlin Carl
Название: Ordinal Computability: An Introduction to Infinitary Machines
ISBN: 3110495627 ISBN-13(EAN): 9783110495621
Издательство: Walter de Gruyter
Цена: 18586.00 р.
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Описание: Ordinal Computability discusses models of computation obtained by generalizing classical models, such as Turing machines or register machines, to transfinite working time and space. In particular, recognizability, randomness, and applications to other areas of mathematics are covered.

Martin Davis on Computability, Computational Logic, and Mathematical Foundations

Автор: Eugenio G. Omodeo; Alberto Policriti
Название: Martin Davis on Computability, Computational Logic, and Mathematical Foundations
ISBN: 3319418416 ISBN-13(EAN): 9783319418414
Издательство: Springer
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Цена: 16769.00 р.
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Описание: This book presents a set of historical recollections on the work of Martin Davis and his role in advancing our understanding of the connections between logic, computing, and unsolvability.

Computability and logic

Автор: George S. Boolos
Название: Computability and logic
ISBN: 0521701465 ISBN-13(EAN): 9780521701464
Издательство: Cambridge Academ
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Цена: 5069.00 р.
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Описание: Computability and Logic has become a classic because of its accessibility to students without a mathematical background and because it covers not simply the staple topics of an intermediate logic course, but also a large number of optional topics, from Turing`s theory of computability to Ramsey`s theorem. This fifth edition was first published in 2007.

Computability and Complexity

Автор: Adam Day; Michael Fellows; Noam Greenberg; Bakhady
Название: Computability and Complexity
ISBN: 3319500619 ISBN-13(EAN): 9783319500614
Издательство: Springer
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Цена: 13974.00 р.
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Описание: The volume contains 42 papers presenting original unpublished research, or expository and survey results in Turing degrees, computably enumerable sets, computable algebra, computable model theory, algorithmic randomness, reverse mathematics, and parameterized complexity, all areas in which Rod Downey has had significant interests and influence.

Computability in Analysis and Physics

Автор: Pour-El
Название: Computability in Analysis and Physics
ISBN: 1107168449 ISBN-13(EAN): 9781107168442
Издательство: Cambridge Academ
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Цена: 18216.00 р.
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Описание: This is the first graduate-level treatment of computable analysis within the tradition of classical mathematical reasoning. The authors are concerned with the computability or noncomputability of standard processes in analysis and physics. The book is self-contained and serves well as an introduction to research in this area.

Higher-Order Computability

Автор: John Longley; Dag Normann
Название: Higher-Order Computability
ISBN: 3662479915 ISBN-13(EAN): 9783662479919
Издательство: Springer
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Цена: 18167.00 р.
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Описание: This book offers a self-contained exposition of the theory of computability in a higher-order context, where `computable operations` may themselves be passed as arguments to other computable operations.

Higher-Order Computability

Автор: John Longley; Dag Normann
Название: Higher-Order Computability
ISBN: 3662517116 ISBN-13(EAN): 9783662517116
Издательство: Springer
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Цена: 15372.00 р.
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Описание: This book offers a self-contained exposition of the theory of computability in a higher-order context, where `computable operations` may themselves be passed as arguments to other computable operations.

Definability and computability /

Автор: Ershov, I?U?rii? Leonidovich.
Название: Definability and computability /
ISBN: 0306110393 ISBN-13(EAN): 9780306110399
Издательство: Springer
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Цена: 32004.00 р.
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Описание: In this book, Yurii L. Ershov posits the view that computability-in the broadest sense-can be regarded as the Sigma-definability in the suitable sets. He presents a new approach to providing the G del incompleteness theorem based on systematic use of the formulas with the restricted quantifiers. The volume also includes a novel exposition on the foundations of the theory of admissible sets with urelements, using the Gandy theorem throughout the theory's development. Other topics discussed are forcing, Sigma-definability, dynamic logic, and Sigma-predicates of finite types.


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