Mathesis Universalis Computability And Proof
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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.
Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification
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Author : Klaus Mainzer
language : en
Publisher: World Scientific
Release Date : 2021-07-27
Proof And Computation Ii From Proof Theory And Univalent Mathematics To Program Extraction And Verification 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 2021-07-27 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 proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. 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.
Is Law Computable
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Author : Simon Deakin
language : en
Publisher: Bloomsbury Publishing
Release Date : 2020-11-26
Is Law Computable written by Simon Deakin and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-26 with Law categories.
What does computable law mean for the autonomy, authority, and legitimacy of the legal system? Are we witnessing a shift from Rule of Law to a new Rule of Technology? Should we even build these things in the first place? This unique volume collects original papers by a group of leading international scholars to address some of the fascinating questions raised by the encroachment of Artificial Intelligence (AI) into more aspects of legal process, administration, and culture. Weighing near-term benefits against the longer-term, and potentially path-dependent, implications of replacing human legal authority with computational systems, this volume pushes back against the more uncritical accounts of AI in law and the eagerness of scholars, governments, and LegalTech developers, to overlook the more fundamental - and perhaps 'bigger picture' - ramifications of computable law. With contributions by Simon Deakin, Christopher Markou, Mireille Hildebrandt, Roger Brownsword, Sylvie Delacroix, Lyria Bennet Moses, Ryan Abbott, Jennifer Cobbe, Lily Hands, John Morison, Alex Sarch, and Dilan Thampapillai, as well as a foreword from Frank Pasquale.
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.
Handbook Of Constructive Mathematics
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Author : Douglas Bridges
language : en
Publisher: Cambridge University Press
Release Date : 2023-05-11
Handbook Of Constructive Mathematics written by Douglas Bridges and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-11 with Mathematics categories.
Constructive mathematics – mathematics in which 'there exists' always means 'we can construct' – is enjoying a renaissance. fifty years on from Bishop's groundbreaking account of constructive analysis, constructive mathematics has spread out to touch almost all areas of mathematics and to have profound influence in theoretical computer science. This handbook gives the most complete overview of modern constructive mathematics, with contributions from leading specialists surveying the subject's myriad aspects. Major themes include: constructive algebra and geometry, constructive analysis, constructive topology, constructive logic and foundations of mathematics, and computational aspects of constructive mathematics. A series of introductory chapters provides graduate students and other newcomers to the subject with foundations for the surveys that follow. Edited by four of the most eminent experts in the field, this is an indispensable reference for constructive mathematicians and a fascinating vista of modern constructivism for the increasing number of researchers interested in constructive approaches.
Prawitz S Epistemic Grounding
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Author : Antonio Piccolomini d’Aragona
language : en
Publisher: Springer Nature
Release Date : 2023-01-01
Prawitz S Epistemic Grounding written by Antonio Piccolomini d’Aragona and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-01 with Philosophy categories.
This book presents an in-depth and critical reconstruction of Prawitz’s epistemic grounding, and discusses it within the broader field of proof-theoretic semantics. The theory of grounds is also provided with a formal framework, through which several relevant results are proved. Investigating Prawitz’s theory of grounds, this work answers one of the most fundamental questions in logic: why and how do some inferences have the epistemic power to compel us to accept their conclusion, if we have accepted their premises? Prawitz proposes an innovative description of inferential acts, as applications of constructive operations on grounds for the premises, yielding a ground for the conclusion. The book is divided into three parts. In the first, the author discusses the reasons that have led Prawitz to abandon his previous semantics of valid arguments and proofs. The second part presents Prawitz’s grounding as found in his ground-theoretic papers. Finally, in the third part, a formal apparatus is developed, consisting of a class of languages whose terms are equipped with denotation functions associating them to operations and grounds, as well as of a class of systems where important properties of the terms can be proved.
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.
Comprehending The Complexity Of Countries
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Author : Hans Kuijper
language : en
Publisher: Springer Nature
Release Date : 2022-01-18
Comprehending The Complexity Of Countries written by Hans Kuijper and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-18 with Social Science categories.
This book argues for computer-aided collaborative country research based on the science of complex and dynamic systems. It provides an in-depth discussion of systems and computer science, concluding that proper understanding of a country is only possible if a genuinely interdisciplinary and truly international approach is taken; one that is based on complexity science and supported by computer science. Country studies should be carefully designed and collaboratively carried out, and a new generation of country students should pay more attention to the fast growing potential of digitized and electronically connected libraries. In this frenzied age of globalization, foreign policy makers may – to the benefit of a better world – profit from the radically new country studies pleaded for in the book. Its author emphasizes that reductionism and holism are not antagonistic but complementary, arguing that parts are always parts of a whole and a whole has always parts.
The New Yearbook For Phenomenology And Phenomenological Philosophy
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Author : Burt Hopkins
language : en
Publisher: Routledge
Release Date : 2021-09-20
The New Yearbook For Phenomenology And Phenomenological Philosophy written by Burt Hopkins and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-20 with Philosophy categories.
Volume XVIII Special Issue: Gian-Carlo Rota and The End of Objectivity, 2019 Aim and Scope: The New Yearbook for Phenomenology and Phenomenological Philosophy provides an annual international forum for phenomenological research in the spirit of Husserl's groundbreaking work and the extension of this work by such figures as Scheler, Heidegger, Sartre, Levinas, Merleau-Ponty and Gadamer. Contributors: Gabriele Baratelli, Stefania Centrone, Giovanna C. Cifoletti, Jean-Marie Coquard, Steven Crowell, Deborah De Rosa, Daniele De Santis, Nicolas de Warren, Agnese Di Riccio, Aurélien Djian, Yuval Dolev, Mirja Hartimo, Burt C. Hopkins, Talia Leven, Ah Hyun Moon, Luis Niel, Fabrizio Palombi, Mario Ariel González Porta, Gian-Carlo Rota, Michael Roubach, Franco Trabattoni and Michele Vagnetti. Submissions: Manuscripts, prepared for blind review, should be submitted to the Editors ([email protected] and [email protected]) electronically via e-mail attachments.
Reflections On The Foundations Of Mathematics
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Author : Stefania Centrone
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Reflections On The Foundations Of Mathematics 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 2019-11-11 with Mathematics categories.
This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.