Arbitrary Reference In Logic And Mathematics
DOWNLOAD
Download Arbitrary Reference In Logic And Mathematics PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Arbitrary Reference In Logic And Mathematics book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Arbitrary Reference In Logic And Mathematics
DOWNLOAD
Author : Massimiliano Carrara
language : en
Publisher: Springer Nature
Release Date : 2024-08-16
Arbitrary Reference In Logic And Mathematics written by Massimiliano Carrara and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-08-16 with Philosophy categories.
This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded. In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular.
Arbitrary Reference In Logic And Mathematics
DOWNLOAD
Author : Massimiliano Carrara
language : en
Publisher: Springer
Release Date : 2024-09-16
Arbitrary Reference In Logic And Mathematics written by Massimiliano Carrara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-16 with Philosophy categories.
This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded. In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms. This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular.
From Logic To Practice
DOWNLOAD
Author : Gabriele Lolli
language : en
Publisher: Springer
Release Date : 2014-11-28
From Logic To Practice written by Gabriele Lolli and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-28 with Philosophy categories.
This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
Intuitionistic Proof Versus Classical Truth
DOWNLOAD
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.
Philosophy Of Logic And Mathematics
DOWNLOAD
Author : Gabriele M. Mras
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2019-11-18
Philosophy Of Logic And Mathematics written by Gabriele M. Mras and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-18 with Philosophy categories.
This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Günther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Mühlhölzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Woleński and Richard Zach.
Principia Mathematica
DOWNLOAD
Author : Alfred North Whitehead
language : en
Publisher: Cambridge University Press
Release Date : 1927
Principia Mathematica written by Alfred North Whitehead 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 1927 with Mathematics categories.
The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.
Unity And Plurality
DOWNLOAD
Author : Massimiliano Carrara
language : en
Publisher: Oxford University Press
Release Date : 2016
Unity And Plurality written by Massimiliano Carrara 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 2016 with Language Arts & Disciplines categories.
Unity and Plurality presents novel ways of thinking about plurality while casting new light on the interconnections among the logical, philosophical, and linguistic aspects of plurals. The volume brings together new work on the logic and ontology of plurality and on the semantics of plurals in natural language. Plural reference, the view that definite plurals such as 'the students' refer to several entities at once (the individual students), is an approach favoured by logicians and philosophers, who take sentences with plurals ('the students gathered') not to be committed to entities beyond individuals, entities such as classes, sums, or sets. By contrast, linguistic semantics has been dominated by a singularist approach to plurals, taking the semantic value of a definite plural such as 'the students' to be a mereological sum or set. Moreover, semantics has been dominated by a particular ontological view of plurality, that of extensional mereology. This volume aims to build a bridge between the two traditions and to show the fruitfulness of nonstandard mereological approaches. A team of leading experts investigates new perspectives that arise from plural logic and non-standard mereology and explore novel applications to natural language phenomena.
Logical Studies Of Paraconsistent Reasoning In Science And Mathematics
DOWNLOAD
Author : Holger Andreas
language : en
Publisher: Springer
Release Date : 2016-12-02
Logical Studies Of Paraconsistent Reasoning In Science And Mathematics written by Holger Andreas and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-02 with Philosophy categories.
This book covers work written by leading scholars from different schools within the research area of paraconsistency. The authors critically investigate how contemporary paraconsistent logics can be used to better understand human reasoning in science and mathematics. Offering a variety of perspectives, they shed a new light on the question of whether paraconsistent logics can function as the underlying logics of inconsistent but useful scientific and mathematical theories. The great variety of paraconsistent logics gives rise to various, interrelated questions, such as what are the desiderata a paraconsistent logic should satisfy, is there prospect of a universal approach to paraconsistent reasoning with axiomatic theories, and to what extent is reasoning about sets structurally analogous to reasoning about truth. Furthermore, the authors consider paraconsistent logic’s status as either a normative or descriptive discipline (or one which falls in between) and which inconsistent but non-trivial axiomatic theories are well understood by which types of paraconsistent approaches. This volume addresses such questions from different perspectives in order to (i) obtain a representative overview of the state of the art in the philosophical debate on paraconsistency, (ii) come up with fresh ideas for the future of paraconsistency, and most importantly (iii) provide paraconsistent logic with a stronger philosophical foundation, taking into account the developments within the different schools of paraconsistency.
Objects Structures And Logics
DOWNLOAD
Author : Gianluigi Oliveri
language : en
Publisher: Springer Nature
Release Date : 2022-03-08
Objects Structures And Logics written by Gianluigi Oliveri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Science categories.
This edited collection casts light on central issues within contemporary philosophy of mathematics such as the realism/anti-realism dispute; the relationship between logic and metaphysics; and the question of whether mathematics is a science of objects or structures. The discussions offered in the papers involve an in-depth investigation of, among other things, the notions of mathematical truth, proof, and grounding; and, often, a special emphasis is placed on considerations relating to mathematical practice. A distinguishing feature of the book is the multicultural nature of the community that has produced it. Philosophers, logicians, and mathematicians have all contributed high-quality articles which will prove valuable to researchers and students alike.
Language Truth And Logic In Mathematics
DOWNLOAD
Author : Jaakko Hintikka
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Language Truth And Logic In Mathematics written by Jaakko Hintikka 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 Mathematics categories.
One can distinguish, roughly speaking, two different approaches to the philosophy of mathematics. On the one hand, some philosophers (and some mathematicians) take the nature and the results of mathematicians' activities as given, and go on to ask what philosophical morals one might perhaps find in their story. On the other hand, some philosophers, logicians and mathematicians have tried or are trying to subject the very concepts which mathematicians are using in their work to critical scrutiny. In practice this usually means scrutinizing the logical and linguistic tools mathematicians wield. Such scrutiny can scarcely help relying on philosophical ideas and principles. In other words it can scarcely help being literally a study of language, truth and logic in mathematics, albeit not necessarily in the spirit of AJ. Ayer. As its title indicates, the essays included in the present volume represent the latter approach. In most of them one of the fundamental concepts in the foundations of mathematics and logic is subjected to a scrutiny from a largely novel point of view. Typically, it turns out that the concept in question is in need of a revision or reconsideration or at least can be given a new twist. The results of such a re-examination are not primarily critical, however, but typically open up new constructive possibilities. The consequences of such deconstructions and reconstructions are often quite sweeping, and are explored in the same paper or in others.