Constructivity And Computability In Historical And Philosophical Perspective
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Constructivity And Computability In Historical And Philosophical Perspective
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Author : Jacques Dubucs
language : en
Publisher: Springer
Release Date : 2014-08-27
Constructivity And Computability In Historical And Philosophical Perspective written by Jacques Dubucs and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Philosophy categories.
Ranging from Alan Turing’s seminal 1936 paper to the latest work on Kolmogorov complexity and linear logic, this comprehensive new work clarifies the relationship between computability on the one hand and constructivity on the other. The authors argue that even though constructivists have largely shed Brouwer’s solipsistic attitude to logic, there remain points of disagreement to this day. Focusing on the growing pains computability experienced as it was forced to address the demands of rapidly expanding applications, the content maps the developments following Turing’s ground-breaking linkage of computation and the machine, the resulting birth of complexity theory, the innovations of Kolmogorov complexity and resolving the dissonances between proof theoretical semantics and canonical proof feasibility. Finally, it explores one of the most fundamental questions concerning the interface between constructivity and computability: whether the theory of recursive functions is needed for a rigorous development of constructive mathematics. This volume contributes to the unity of science by overcoming disunities rather than offering an overarching framework. It posits that computability’s adoption of a classical, ontological point of view kept these imperatives separated. In studying the relationship between the two, it is a vital step forward in overcoming the disagreements and misunderstandings which stand in the way of a unifying view of logic.
Connecting With Computability
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Author : Liesbeth De Mol
language : en
Publisher: Springer Nature
Release Date : 2021-07-01
Connecting With Computability written by Liesbeth De Mol and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-01 with Computers categories.
This book constitutes the proceedings of the 17th Conference on Computability in Europe, CiE 2021, organized by the University of Ghent in July 2021. Due to COVID-19 pandemic the conference was held virtually. The 48 full papers presented in this volume were carefully reviewed and selected from 50 submissions. CiE promotes the development of computability-related science, ranging over mathematics, computer science and applications in various natural and engineering sciences, such as physics and biology, as well as related fields, such as philosophy and history of computing. CiE 2021 had as its motto Connecting with Computability, a clear acknowledgement of the connecting and interdisciplinary nature of the conference series which is all the more important in a time where people are more than ever disconnected from one another due to the COVID-19 pandemic.
Proof And Computation Digitization In Mathematics Computer Science And Philosophy
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2018-05-30
Proof And Computation Digitization In Mathematics Computer Science And Philosophy written by Klaus Mainzer and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-30 with Mathematics categories.
This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Essays On G Del S Reception Of Leibniz Husserl And Brouwer
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Author : Mark van Atten
language : en
Publisher: Springer
Release Date : 2014-11-21
Essays On G Del S Reception Of Leibniz Husserl And Brouwer written by Mark van Atten and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-21 with Philosophy categories.
This volume tackles Gödel's two-stage project of first using Husserl's transcendental phenomenology to reconstruct and develop Leibniz' monadology, and then founding classical mathematics on the metaphysics thus obtained. The author analyses the historical and systematic aspects of that project, and then evaluates it, with an emphasis on the second stage. The book is organised around Gödel's use of Leibniz, Husserl and Brouwer. Far from considering past philosophers irrelevant to actual systematic concerns, Gödel embraced the use of historical authors to frame his own philosophical perspective. The philosophies of Leibniz and Husserl define his project, while Brouwer's intuitionism is its principal foil: the close affinities between phenomenology and intuitionism set the bar for Gödel's attempt to go far beyond intuitionism. The four central essays are `Monads and sets', `On the philosophical development of Kurt Gödel', `Gödel and intuitionism', and `Construction and constitution in mathematics'. The first analyses and criticises Gödel's attempt to justify, by an argument from analogy with the monadology, the reflection principle in set theory. It also provides further support for Gödel's idea that the monadology needs to be reconstructed phenomenologically, by showing that the unsupplemented monadology is not able to found mathematics directly. The second studies Gödel's reading of Husserl, its relation to Leibniz' monadology, and its influence on his publishe d writings. The third discusses how on various occasions Brouwer's intuitionism actually inspired Gödel's work, in particular the Dialectica Interpretation. The fourth addresses the question whether classical mathematics admits of the phenomenological foundation that Gödel envisaged, and concludes that it does not. The remaining essays provide further context. The essays collected here were written and published over the last decade. Notes have been added to record further thoughts, changes of mind, connections between the essays, and updates of references.
Dialog Systems
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Author : Teresa Lopez-Soto
language : en
Publisher: Springer Nature
Release Date : 2021-03-10
Dialog Systems written by Teresa Lopez-Soto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Philosophy categories.
This book focuses on dialog from a varied combination of fields: Linguistics, Philosophy of Language and Computation. It builds on the hypothesis that meaning in human communication arises at the discourse level rather than at the word level. The book offers a complex analytical framework and integration of the central areas of research around human communication. The content revolves around meaning but it also gives evidence of the connection among different points of view. Besides discussing issues of general interest to the field, the book triggers theoretical argumentation that is currently under scientific discussion. It examines such topics as immanent reasoning joined with Recanati's lekta and free enrichment, challenges of internet conversation, inner dialogs, cognition and language, and the relation between assertion and denial. It proposes a dialogical framework for intra-negotiation and gives a geolinguistic perspective on spoken discourse. Finally, it examines dialog and abduction and sheds light on a generation of dialog contexts by means of multimodal logic applied to speech acts.
Perspectives On Interrogative Models Of Inquiry
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Author : Can Başkent
language : en
Publisher: Springer
Release Date : 2015-10-07
Perspectives On Interrogative Models Of Inquiry written by Can Başkent and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-07 with Philosophy categories.
This book explores the two major elements of Hintikka’s model of inquiry: underlying game theoretical motivations and the central role of questioning. The chapters build on the Hintikkan tradition extending Hintikka’s model and present a wide variety of approaches to the philosophy of inquiry from different directions, ranging from erotetic logic to Lakatosian philosophy, from socio-epistemologic approaches to strategic reasoning and mathematical practice. Hintikka's theory of inquiry is a well-known example of a dynamic epistemic procedure. In an interrogative inquiry, the inquirer is given a theory and a question. He then tries to answer the question based on the theory by posing questions to nature or an oracle. The initial formulation of this procedure by Hintikka is rather broad and informal. This volume introduces a carefully selected responses to the issues discussed by Hintikka. The articles in the volume were contributed by various authors associated with a research project on Hintikka's interrogative theory of inquiry conducted in the Institut d’Histoire et de Philosophie des Sciences et des Techniques (IHPST) of Paris, including those who visited to share their insight.
Constructive Semantics
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Author : Christina Weiss
language : en
Publisher: Springer Nature
Release Date : 2019-10-15
Constructive Semantics written by Christina Weiss and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-15 with Philosophy categories.
This edited book brings together research work in the field of constructive semantics with scholarship on the phenomenological foundations of logic and mathematics. It addresses one of the central issues in the epistemology and philosophy of mathematics, namely the relationship between phenomenological meaning constitution and constructive semantics. Contributing authors explore deep structural connections and fundamental differences between phenomenology and constructivism. Papers are drawn from contributions to a prestigious workshop held at the University of Friedrichshafen. Readers will discover insight into structural connections between the phenomenological concept of meaning constitution and constructivist concepts of meaning. Discussion ranges from more specific conceptualizations in the philosophy of logic and mathematics to more general considerations in epistemology, inferential semantics and phenomenology. Questions such as a possible phenomenological understanding of the relationship between structural rules and particle rules in dialogical logic are explored. Significant aspects of both phenomenology and dialectics, and dialectics and constructivism emerge. Graduates and researchers of philosophy, especially logic, as well as scholars of mathematics will all find something of interest in the expert insights presented in this volume.
The Architecture And Archaeology Of Modern Logic
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Author : Ansten Klev
language : en
Publisher: Springer Nature
Release Date : 2024-10-02
The Architecture And Archaeology Of Modern Logic written by Ansten Klev and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-02 with Philosophy categories.
This book honors the original and influential work by Göran Sundholm in the fields of the philosophy and history of logic and mathematics. Borne from two conferences held in Paris and Leiden on the occasion of Göran Sundholm’s retirement in 2019, the contributions collected in this volume represent work from leading logicians and philosophers. Reflecting Sundholm’s contributions to the history and philosophy of logic, this book is divided into two parts: the architecture and archaeology of logic. The essays collected in the ‘architecture’ section cover primarily the systematic approach to basic logical concepts taken by Sundholm, including type theory, epistemic assumptions, and notions of consequence. The ‘archaeology’ section includes contributions focused on Sundholm’s contributions to the history of philosophy and logic. Enclosing these two sections are, on the one end, autobiographical remarks of Sundholm's and, on the other, a paper on cooking and philosophy, reflectinganother of Sundholm's passions in life. This book is of interest to logicians, philosophers, mathematicians, and computer scientists.
Mathesis Universalis Computability And Proof
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-10-25
Mathesis Universalis Computability And Proof written by Stefania Centrone and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-25 with Philosophy categories.
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” (“Gründe”) 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.
History And Philosophy Of Constructive Type Theory
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Author : Giovanni Sommaruga
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
History And Philosophy Of Constructive Type Theory written by Giovanni Sommaruga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Philosophy categories.
A comprehensive survey of Martin-Löf's constructive type theory, considerable parts of which have only been presented by Martin-Löf in lecture form or as part of conference talks. Sommaruga surveys the prehistory of type theory and its highly complex development through eight different stages from 1970 to 1995. He also provides a systematic presentation of the latest version of the theory, as offered by Martin-Löf at Leiden University in Fall 1993. This presentation gives a fuller and updated account of the system. Earlier, brief presentations took no account of the issues related to the type-theoretical approach to logic and the foundations of mathematics, while here they are accorded an entire part of the book. Readership: Comprehensive accounts of the history and philosophy of constructive type theory and a considerable amount of related material. Readers need a solid background in standard logic and a first, basic acquaintance with type theory.