Linking Game Theoretical Approaches With Constructive Type Theory
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Linking Game Theoretical Approaches With Constructive Type Theory
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Author : Nicolas Clerbout
language : en
Publisher: Springer
Release Date : 2015-07-08
Linking Game Theoretical Approaches With Constructive Type Theory written by Nicolas Clerbout and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-08 with Philosophy categories.
This title links two of the most dominant research streams in philosophy of logic, namely game theory and proof theory. As the work’s subtitle expresses, the authors will build this link by means of the dialogical approach to logic. One important aspect of the present study is that the authors restrict themselves to the logically valid fragment of Constructive Type Theory (CTT). The reason is that, once that fragment is achieved the result can be extended to cover the whole CTT system. The first chapters in the brief offer overviews on the two frameworks discussed in the book with an emphasis on the dialogical framework. The third chapter demonstrates the left-to-right direction of the equivalence result. This is followed by a chapter that demonstrates the use of the algorithm in showing how to transform a specific winning strategy into a CCT-demonstration of the axiom of choice. The fifth chapter develops the algorithm from CTT-demonstrations to dialogical strategies. This brief concludes by introducing elements of discussion which are to be developed in subsequent work.
Immanent Reasoning Or Equality In Action
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Author : Shahid Rahman
language : en
Publisher: Springer
Release Date : 2018-08-16
Immanent Reasoning Or Equality In Action written by Shahid Rahman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-16 with Philosophy categories.
This monograph proposes a new way of implementing interaction in logic. It also provides an elementary introduction to Constructive Type Theory (CTT). The authors equally emphasize basic ideas and finer technical details. In addition, many worked out exercises and examples will help readers to better understand the concepts under discussion. One of the chief ideas animating this study is that the dialogical understanding of definitional equality and its execution provide both a simple and a direct way of implementing the CTT approach within a game-theoretical conception of meaning. In addition, the importance of the play level over the strategy level is stressed, binding together the matter of execution with that of equality and the finitary perspective on games constituting meaning. According to this perspective the emergence of concepts are not only games of giving and asking for reasons (games involving Why-questions), they are also games that include moves establishing how it is that the reasons brought forward accomplish their explicative task. Thus, immanent reasoning games are dialogical games of Why and How.
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.
Arsyad Al Banjari S Insights On Parallel Reasoning And Dialectic In Law
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Author : Muhammad Iqbal
language : en
Publisher: Springer Nature
Release Date : 2022-06-16
Arsyad Al Banjari S Insights On Parallel Reasoning And Dialectic In Law written by Muhammad Iqbal and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-16 with Philosophy categories.
This book provides an epistemological study of the great Islamic scholar of Banjarese origin, Syeikh Muhammad Arsyad al-Banjari (1710-1812) who contributed to the development of Islam in Indonesia and, in general, Southeast Asia. The work focuses on Arsyad al-Banjari’s dialectical use and understanding of qiyās or correlational inference as a model of parallel reasoning or analogy in Islamic jurisprudence. This constituted the most prominent instrument he applied in his effort of integrating Islamic law into the Banjarese society.This work studies how Arsyad al-Banjari integrates jadal theory or dialectic in Islamic jurisprudence, within his application of qiyās. The author develops a framework for qiyās which acts as the interface between jadal, dialogical logic, and Per Martin-Löf’s Constructive Type Theory (CTT). One of the epistemological results emerging from the present study is that the different forms of qiyās applied by Arsyad al-Banjari represent an innovative and sophisticated form of reasoning. The volume is divided into three parts that discuss the types of qiyās as well their dialectical and argumentative aspects, historical background and context of Banjar, and demonstrates how the theory of qiyās comes quite close to the contemporary model of parallel reasoning for sciences and mathematics developed by Paul Bartha (2010). This volume will be of interest to historians and philosophers in general, and logicians and historians of philosophy in particular.
Epistemology Knowledge And The Impact Of Interaction
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Author : Juan Redmond
language : en
Publisher: Springer
Release Date : 2016-04-28
Epistemology Knowledge And The Impact Of Interaction written by Juan Redmond and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-28 with Philosophy categories.
With this volume of the series Logic, Epistemology, and the Unity of Science edited by S. Rahman et al. a challenging dialogue is being continued. The series’ first volume argued that one way to recover the connections between logic, philosophy of sciences, and sciences is to acknowledge the host of alternative logics which are currently being developed. The present volume focuses on four key themes. First of all, several chapters unpack the connection between knowledge and epistemology with particular focus on the notion of knowledge as resulting from interaction. Secondly, new epistemological perspectives on linguistics, the foundations of mathematics and logic, physics, biology and law are a subject of analysis. Thirdly, several chapters are dedicated to a discussion of Constructive Type Theory and more generally of the proof-theoretical notion of meaning.Finally, the book brings together studies on the epistemic role of abduction and argumentation theory, both linked to non-monotonic approaches to the dynamics of knowledge.
Paul Lorenzen Mathematician And Logician
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Author : Gerhard Heinzmann
language : en
Publisher: Springer Nature
Release Date : 2021-08-17
Paul Lorenzen Mathematician And Logician written by Gerhard Heinzmann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-17 with Mathematics categories.
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.
Past And Present Interactions In Legal Reasoning And Logic
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Author : Matthias Armgardt
language : en
Publisher: Springer
Release Date : 2015-05-18
Past And Present Interactions In Legal Reasoning And Logic written by Matthias Armgardt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-18 with Philosophy categories.
This volume explores the relation between legal reasoning and logic from both a historical and a systematic perspective. The topics addressed include, among others, conditional legal acts, disjunctions in legal acts, presumptions and conjectures, conflicts of values, Jørgensen ́s Dilemma, the Rhetor ́s Dilemma, the theory of legal fictions and the categorization of contracts. The unifying problematic of these contributions concerns the conditional structures and, more particularly, the relationship between legal theory and legal reasoning in the context of conditions. The contributions in this work constitute the first results of the ANR-DFG joint research project “JuriLog” (Jurisprudence and Logic), which aims at fostering the cooperation between legal scholars and philosophers. On the one hand, lawyers and legal scholars have an interest in emphasizing the logical character of legal reasoning. In this respect, the present enquiry examines the question of how logic, especially newer forms of dialogical logic, can be made fruitful as a significant area of philosophy for jurisprudence and legal practice. On the other hand, logicians find in legal reasoning a striving towards clear definitions and inference-procedures that is relevant to their discipline. In order to fully understand such reciprocal relationships, it is necessary to bridge the gap between law, logic and philosophy in contemporary academic research. The essays collected in this volume all work towards this common goal. The book is divided in three sections. In the first part, the strong relation between Roman Law and logic is explored with respect to the analysis of disjunctive statements in legal acts. The second part focuses on Leibniz ́s legal theory. The third part, finally, is dedicated to current interactions between law and logic.
Inferences By Parallel Reasoning In Islamic Jurisprudence
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Author : Shahid Rahman
language : en
Publisher: Springer Nature
Release Date : 2020-01-13
Inferences By Parallel Reasoning In Islamic Jurisprudence written by Shahid Rahman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-13 with Philosophy categories.
This monograph proposes a new (dialogical) way of studying the different forms of correlational inference, known in the Islamic jurisprudence as qiyās. According to the authors’ view, qiyās represents an innovative and sophisticated form of dialectical reasoning that not only provides new epistemological insights into legal argumentation in general (including legal reasoning in Common and Civil Law) but also furnishes a fine-grained pattern for parallel reasoning which can be deployed in a wide range of problem-solving contexts and does not seem to reduce to the standard forms of analogical reasoning studied in contemporary philosophy of science and argumentation theory. After an overview of the emergence of qiyās and of the work of al-Shīrāzī penned by Soufi Youcef, the authors discuss al-Shīrāzī’s classification of correlational inferences of the occasioning factor (qiyās al-'illa). The second part of the volume deliberates on the system of correlational inferences by indication and resemblance (qiyās al-dalāla, qiyās al-shabah). The third part develops the main theoretical background of the authors’ work, namely, the dialogical approach to Martin-Löf's Constructive Type Theory. The authors present this in a general form and independently of adaptations deployed in parts I and II. Part III also includes an appendix on the relevant notions of Constructive Type Theory, which has been extracted from an overview written by Ansten Klev. The book concludes with some brief remarks on contemporary approaches to analogy in Common and Civil Law and also to parallel reasoning in general.
The Philosophers And Mathematics
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Author : Hassan Tahiri
language : en
Publisher: Springer
Release Date : 2018-08-14
The Philosophers And Mathematics written by Hassan Tahiri and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-14 with Mathematics categories.
This book explores the unique relationship between two different approaches to understand the nature of knowledge, reality, and existence. It collects essays that examine the distinctive historical relationship between mathematics and philosophy. Readers learn what key philosophers throughout the ages thought about mathematics. This includes both thinkers who recognized the relevance of mathematics to their own work as well as those who chose to completely ignore its many achievements. The essays offer insight into the role that mathematics played in the formation of each included philosopher’s doctrine as well as the impact its remarkable expansion had on the philosophical systems each erected. Conversely, the authors also highlight the ways that philosophy contributed to the growth and transformation of mathematics. Throughout, significant historical examples help to illustrate these points in a vivid way. Mathematics has often been a favored interlocutor of philosophers and a major source of inspiration. This book is the outcome of an international conference held in honor of Roshdi Rashed, a renowned historian of mathematics. It provides researchers, students, and interested readers with remarkable insights into the history of an important relationship throughout the ages.
Attracted To Conflict Dynamic Foundations Of Destructive Social Relations
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Author : Robin R. Vallacher
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-07-08
Attracted To Conflict Dynamic Foundations Of Destructive Social Relations written by Robin R. Vallacher 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 2014-07-08 with Social Science categories.
Conflict is inherent in virtually every aspect of human relations, from sport to parliamentary democracy, from fashion in the arts to paradigmatic challenges in the sciences, and from economic activity to intimate relationships. Yet, it can become among the most serious social problems humans face when it loses its constructive features and becomes protracted over time with no obvious means of resolution. This book addresses the subject of intractable social conflict from a new vantage point. Here, these types of conflict represent self-organizing phenomena, emerging quite naturally from the ongoing dynamics in human interaction at any scale—from the interpersonal to the international. Using the universal language and computational framework of nonlinear dynamical systems theory in combination with recent insights from social psychology, intractable conflict is understood as a system locked in special attractor states that constrain the thoughts and actions of the parties to the conflict. The emergence and maintenance of attractors for conflict can be described by means of formal models that incorporate the results of computer simulations, experiments, field research, and archival analyses. Multi-disciplinary research reflecting these approaches provides encouraging support for the dynamical systems perspective. Importantly, this text presents new views on conflict resolution. In contrast to traditional approaches that tend to focus on basic, short-lived cause-effect relations, the dynamical perspective emphasizes the temporal patterns and potential for emergence in destructive relations. Attractor deconstruction entails restoring complexity to a conflict scenario by isolating elements or changing the feedback loops among them. The creation of a latent attractor trades on the tendency toward multi-stability in dynamical systems and entails the consolidation of incongruent (positive) elements into a coherent structure. In the bifurcation scenario, factors are identified that can change the number and types of attractors in a conflict scenario. The implementation of these strategies may hold the key to unlocking intractable conflict, creating the potential for constructive social relations.