Objectivity Realism And Proof
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Objectivity Realism And Proof
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Author : Francesca Boccuni
language : en
Publisher: Springer
Release Date : 2016-07-05
Objectivity Realism And Proof written by Francesca Boccuni and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-05 with Science categories.
This volume covers a wide range of topics in the most recent debates in the philosophy of mathematics, and is dedicated to how semantic, epistemological, ontological and logical issues interact in the attempt to give a satisfactory picture of mathematical knowledge. The essays collected here explore the semantic and epistemic problems raised by different kinds of mathematical objects, by their characterization in terms of axiomatic theories, and by the objectivity of both pure and applied mathematics. They investigate controversial aspects of contemporary theories such as neo-logicist abstractionism, structuralism, or multiversism about sets, by discussing different conceptions of mathematical realism and rival relativistic views on the mathematical universe. They consider fundamental philosophical notions such as set, cardinal number, truth, ground, finiteness and infinity, examining how their informal conceptions can best be captured in formal theories. The philosophy of mathematics is an extremely lively field of inquiry, with extensive reaches in disciplines such as logic and philosophy of logic, semantics, ontology, epistemology, cognitive sciences, as well as history and philosophy of mathematics and science. By bringing together well-known scholars and younger researchers, the essays in this collection – prompted by the meetings of the Italian Network for the Philosophy of Mathematics (FilMat) – show how much valuable research is currently being pursued in this area, and how many roads ahead are still open for promising solutions to long-standing philosophical concerns. Promoted by the Italian Network for the Philosophy of Mathematics – FilMat
Philosophy After Objectivity
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Author : Paul K. Moser
language : en
Publisher: Oxford University Press
Release Date : 1999-10-07
Philosophy After Objectivity written by Paul K. Moser and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-10-07 with Philosophy categories.
Since the beginning of philosophy, philosophers have sought objective knowledge: knowledge of things whose existence does not depend on one's conceiving of them. This book uses lessons from debates over objective knowledge to characterize the kinds of reasons pertinent to philosophical and other theoretical views. It argues that we cannot meet skeptics' typical demands for nonquestion-begging support for claims to objective truth, and that therefore we should not regard our supporting reasons as resistant to skeptical challenges. One key lesson is that a constructive, explanatory approach to philosophy must change the subject from skeptic-resistant reasons to perspectival reasons arising from variable semantic commitments and instrumental, purpose-relative considerations. The book lays foundations for such a reorientation of philosophy, treating fundamental methodological issues in ontology, epistemology, the theory of meaning, the philosophy of mind, and the theory of practical rationality. It explains how certain perennial debates in philosophy rest not on genuine disagreement, but on conceptual diversity: talk about different matters. The book shows how acknowledgment of conceptual diversity can resolve a range of traditional disputes in philosophy. It also explains why philosophers need not anchor their discipline in the physicalism of the natural sciences.
Intuitionistic Proof Versus Classical Truth
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Author : Enrico Martino
language : en
Publisher: Springer
Release Date : 2018-02-23
Intuitionistic Proof Versus Classical Truth written by Enrico Martino and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-23 with Mathematics categories.
This book examines the role of acts of choice in classical and intuitionistic mathematics. Featuring fifteen papers – both new and previously published – it offers a fresh analysis of concepts developed by the mathematician and philosopher L.E.J. Brouwer, the founder of intuitionism. The author explores Brouwer’s idealization of the creative subject as the basis for intuitionistic truth, and in the process he also discusses an important, related question: to what extent does the intuitionistic perspective succeed in avoiding the classical realistic notion of truth? The papers detail realistic aspects in the idealization of the creative subject and investigate the hidden role of choice even in classical logic and mathematics, covering such topics as bar theorem, type theory, inductive evidence, Beth models, fallible models, and more. In addition, the author offers a critical analysis of the response of key mathematicians and philosophers to Brouwer’s work. These figures include Michael Dummett, Saul Kripke, Per Martin-Löf, and Arend Heyting. This book appeals to researchers and graduate students with an interest in philosophy of mathematics, linguistics, and mathematics.
Kant S Transcendental Proof Of Realism
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Author : Kenneth R. Westphal
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-02
Kant S Transcendental Proof Of Realism written by Kenneth R. Westphal 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 2004-12-02 with History categories.
Kenneth Westphal offers a detailed study of Kant's method of 'transcendental reflection' and its use in the Critique of Pure Reason. His book will be of interest to all who are interested in Kant's theoretical philosophy or in contemporary epistemology.
Foundations Of Objective Knowledge
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Author : Sergio L. de C. Fernandes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Foundations Of Objective Knowledge written by Sergio L. de C. Fernandes 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 Science categories.
Kant and Popper. The affmity between the philosophy of Kant and the philosophy of Karl Popper has often been noted, and most decisively in Popper's own reflections on his thought. But in this work before us, Sergio Fernandes has given a cogent, comprehensive, and challenging investigation of Kant which differs from what we may call Popper's Kant while nevertheless showing Kant as very much a precursor of Popper. The investigation is directly conceptual, although Fernandes has also contributed to a novel historical understanding of Kant in his reinterpretation; the novelty is the genuine result of meticulous study of texts and commentators, characterized by the author's thorough command of the epistemological issues in the philosophy of science in the 20th century as much as by his mastery of the Kantian themes of the 18th. Naturally, we may wish to understand whether Kant is relevant to Popper's philosophy of knowledge, how Popper has understood Kant, and to what extent the Popperian Kant has systematically or historically been of influence on later philosophy of science, as seen by Popper or not.
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.
Truth Existence And Explanation
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Author : Mario Piazza
language : en
Publisher: Springer
Release Date : 2018-10-24
Truth Existence And Explanation written by Mario Piazza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-24 with Mathematics categories.
This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016.
The Hyperuniverse Project And Maximality
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Author : Carolin Antos
language : en
Publisher: Birkhäuser
Release Date : 2018-01-30
The Hyperuniverse Project And Maximality written by Carolin Antos and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-30 with Mathematics categories.
This collection documents the work of the Hyperuniverse Project which is a new approach to set-theoretic truth based on justifiable principles and which leads to the resolution of many questions independent from ZFC. The contributions give an overview of the program, illustrate its mathematical content and implications, and also discuss its philosophical assumptions. It will thus be of wide appeal among mathematicians and philosophers with an interest in the foundations of set theory. The Hyperuniverse Project was supported by the John Templeton Foundation from January 2013 until September 2015
Systemics Of Incompleteness And Quasi Systems
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Author : Gianfranco Minati
language : en
Publisher: Springer
Release Date : 2019-06-20
Systemics Of Incompleteness And Quasi Systems written by Gianfranco Minati and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-20 with Mathematics categories.
This book contains the proceedings of the Seventh National Conference of the Italian Systems Society. The title, Systemics of Incompleteness and Quasi-Systems, aims to underline the need for Systemics and Systems Science to deal with the concepts of incompleteness and quasiness. Classical models of Systemics are intended to represent comprehensive aspects of phenomena and processes. They consider the phenomena in their temporal and spatial completeness. In these cases, possible incompleteness in the modelling is assumed to have a provisional or practical nature, which is still under study, and because there is no theoretical reason why the modelling cannot be complete. In principle, this is a matter of non-complex phenomena, to be considered using the concepts of the First Systemics. When dealing with emergence, there are phenomena which must be modelled by systems having multiple models, depending on the aspects being taken into consideration. Here, incompleteness in the modelling is intrinsic, theoretically relating changes in properties, structures, and status of system. Rather than consider the same system parametrically changing over time, we consider sequences of systems coherently. We consider contexts and processes for which modelling is incomplete, being related to only some properties, as well as those for which such modelling is theoretically incomplete—as in the case of processes of emergence and for approaches considered by the Second Systemics. In this regard, we consider here the generic concept of quasi explicating such incompleteness. The concept of quasi is used in various disciplines including quasi-crystals, quasi-particles, quasi-electric fields, and quasi-periodicity. In general, the concept of quasiness for systems concerns their continuous structural changes which are always meta-stable, waiting for events to collapse over other configurations and possible forms of stability; whose equivalence depends on the type of phenomenon under study. Interest in the concept of quasiness is not related to its meaning of rough approximation, but because it indicates an incompleteness which is structurally sufficient to accommodate processes of emergence and sustain coherence or generate new, equivalent or non-equivalent, levels. The conference was devoted to identifying, discussing and understanding possible interrelationships of theoretical disciplinary improvements, recognised as having prospective fundamental roles for a new Quasi-Systemics. The latter should be able to deal with problems related to complexity in more general and realistic ways, when a system is not always a system and not always the same system. In this context, the inter-disciplinarity should consist, for instance, of a constructionist, incomplete, non-ideological, multiple, contradiction-tolerant, Systemics, always in progress, and in its turn, emergent.
Philosophy And Model Theory
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Author : Tim Button
language : en
Publisher: Oxford University Press
Release Date : 2018-03-09
Philosophy And Model Theory written by Tim Button and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-09 with Philosophy categories.
Model theory is used in every theoretical branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging uses of model theory have created a highly fragmented literature. On the one hand, many philosophically significant results are found only in mathematics textbooks: these are aimed squarely at mathematicians; they typically presuppose that the reader has a serious background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are scattered across disconnected pockets of papers. The first aim of this book, then, is to explore the philosophical uses of model theory, focusing on the central topics of reference, realism, and doxology. Its second aim is to address important questions in the philosophy of model theory, such as: sameness of theories and structure, the boundaries of logic, and the classification of mathematical structures. Philosophy and Model Theory will be accessible to anyone who has completed an introductory logic course. It does not assume that readers have encountered model theory before, but starts right at the beginning, discussing philosophical issues that arise even with conceptually basic model theory. Moreover, the book is largely self-contained: model-theoretic notions are defined as and when they are needed for the philosophical discussion, and many of the most philosophically significant results are given accessible proofs.