Objectivity, Realism, and Proof

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Publisher : Springer
ISBN 13 : 3319316443
Total Pages : 344 pages
Book Rating : 4.3/5 (193 download)

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Book Synopsis Objectivity, Realism, and Proof by : Francesca Boccuni

Download or read book Objectivity, Realism, and Proof written by Francesca Boccuni and published by Springer. This book was released on 2016-07-05 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Objectivity

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Author :
Publisher : John Wiley & Sons
ISBN 13 : 1509502092
Total Pages : 216 pages
Book Rating : 4.5/5 (95 download)

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Book Synopsis Objectivity by : Guy Axtell

Download or read book Objectivity written by Guy Axtell and published by John Wiley & Sons. This book was released on 2016-09-12 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: What do you find more trustworthy, experts or numbers, personal 'know-how' or 'objective facts'? Can science claim special authority based on the objectivity of its methods? Are our ethical decisions always better when we strive to be impartial and unbiased? Why should we value objectivity, and is it achievable anyway? These are a few of the thought-provoking questions Guy Axtell asks in this comprehensive new text book, employing examples from the natural and social sciences as well as philosophy. This unique introduction surveys the key issues in a clear and concise way, assessing the nature of objectivity and value of the demand to be impartial decision-makers. Moving beyond the fundamentals, Axtell explores contemporary feminist and social epistemological attempts to 'reconstruct' the concept of objectivity, explains the implications of the so-called science wars for philosophy and the analytical method, and the ethical consequences of these debates. Objectivity is an excellent introduction to one of the most exciting areas of study in philosophy and science today. Students and scholars alike will value this balanced guide to a hotly contested, and vitally important, topic.

Philosophy after Objectivity

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Publisher : Oxford University Press
ISBN 13 : 0195351355
Total Pages : 282 pages
Book Rating : 4.1/5 (953 download)

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Book Synopsis Philosophy after Objectivity by : Paul K. Moser

Download or read book Philosophy after Objectivity written by Paul K. Moser and published by Oxford University Press. This book was released on 1999-10-07 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Truth and Objectivity

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Publisher : Harvard University Press
ISBN 13 : 0674045386
Total Pages : 263 pages
Book Rating : 4.6/5 (74 download)

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Book Synopsis Truth and Objectivity by : Crispin Wright

Download or read book Truth and Objectivity written by Crispin Wright and published by Harvard University Press. This book was released on 2009-07-01 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crispin Wright offers an original perspective on the place of “realism” in philosophical inquiry. He proposes a radically new framework for discussing the claims of the realists and the anti-realists. This framework rejects the classical “deflationary” conception of truth yet allows both disputants to respect the intuition that judgments, whose status they contest, are at least semantically fitted for truth and may often justifiably be regarded as true. In the course of his argument, Wright offers original critical discussions of many central concerns of philosophers interested in realism, including the “deflationary” conception of truth, internal realist truth, scientific realism and the theoreticity of observation, and the role of moral states of affairs in explanations of moral beliefs.

Foundations of Objective Knowledge

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Publisher : Springer Science & Business Media
ISBN 13 : 9789027718099
Total Pages : 302 pages
Book Rating : 4.7/5 (18 download)

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Book Synopsis Foundations of Objective Knowledge by : Sergio L. de C. Fernandes

Download or read book Foundations of Objective Knowledge written by Sergio L. de C. Fernandes and published by Springer Science & Business Media. This book was released on 1985-03-31 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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Publisher : Springer Nature
ISBN 13 : 3031202945
Total Pages : 284 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Prawitz's Epistemic Grounding by : Antonio Piccolomini d’Aragona

Download or read book Prawitz's Epistemic Grounding written by Antonio Piccolomini d’Aragona and published by Springer Nature. This book was released on 2023-01-01 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Hyperuniverse Project and Maximality

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Publisher : Birkhäuser
ISBN 13 : 3319629352
Total Pages : 265 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis The Hyperuniverse Project and Maximality by : Carolin Antos

Download or read book The Hyperuniverse Project and Maximality written by Carolin Antos and published by Birkhäuser. This book was released on 2018-01-30 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Bolzano's Philosophy of Grounding

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Publisher : Oxford University Press
ISBN 13 : 019284797X
Total Pages : 473 pages
Book Rating : 4.1/5 (928 download)

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Book Synopsis Bolzano's Philosophy of Grounding by : Stefan Roski

Download or read book Bolzano's Philosophy of Grounding written by Stefan Roski and published by Oxford University Press. This book was released on 2022 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides translations of Bolzano's most important work on grounding, including previously untranslated material"--

Philosophy and Model Theory

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Publisher : Oxford University Press
ISBN 13 : 0198790392
Total Pages : 534 pages
Book Rating : 4.1/5 (987 download)

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Book Synopsis Philosophy and Model Theory by : Tim Button

Download or read book Philosophy and Model Theory written by Tim Button and published by Oxford University Press. This book was released on 2018 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model theory is an important area of mathematical logic which has deep philosophical roots, many philosophical applications, and great philosophical interest in itself. The aim of this book is to introduce, organise, survey, and develop these connections between philosophy and model theory, for the benefit of philosophers and logicians alike.

Truth, Existence and Explanation

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Publisher : Springer
ISBN 13 : 3319933426
Total Pages : 272 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Truth, Existence and Explanation by : Mario Piazza

Download or read book Truth, Existence and Explanation written by Mario Piazza and published by Springer. This book was released on 2018-10-24 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Morality and Mathematics

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Publisher : Oxford University Press, USA
ISBN 13 : 0198823665
Total Pages : 219 pages
Book Rating : 4.1/5 (988 download)

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Book Synopsis Morality and Mathematics by : Justin Clarke-Doane

Download or read book Morality and Mathematics written by Justin Clarke-Doane and published by Oxford University Press, USA. This book was released on 2020-03-12 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: To what extent are the subjects of our thoughts and talk real? This is the question of realism. In this book, Justin Clarke-Doane explores arguments for and against moral realism and mathematical realism, how they interact, and what they can tell us about areas of philosophical interest more generally. He argues that, contrary to widespread belief, our mathematical beliefs have no better claim to being self-evident or provable than our moral beliefs. Nor do our mathematical beliefs have better claim to being empirically justified than our moral beliefs. It is also incorrect that reflection on the "genealogy" of our moral beliefs establishes a lack of parity between the cases. In general, if one is a moral antirealist on the basis of epistemological considerations, then one ought to be a mathematical antirealist as well. And, yet, Clarke-Doane shows that moral realism and mathematical realism do not stand or fall together -- and for a surprising reason. Moral questions, insofar as they are practical, are objective in a sense that mathematical questions are not, and the sense in which they are objective can only be explained by assuming practical anti-realism. One upshot of the discussion is that the concepts of realism and objectivity, which are widely identified, are actually in tension. Another is that the objective questions in the neighborhood of factual areas like logic, modality, grounding, and nature are practical questions too. Practical philosophy should, therefore, take center stage.

Reflections on the Foundations of Mathematics

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Publisher : Springer Nature
ISBN 13 : 3030156559
Total Pages : 511 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Reflections on the Foundations of Mathematics by : Stefania Centrone

Download or read book Reflections on the Foundations of Mathematics written by Stefania Centrone and published by Springer Nature. This book was released on 2019-11-11 with total page 511 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Systemics of Incompleteness and Quasi-Systems

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Publisher : Springer
ISBN 13 : 3030152774
Total Pages : 351 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Systemics of Incompleteness and Quasi-Systems by : Gianfranco Minati

Download or read book Systemics of Incompleteness and Quasi-Systems written by Gianfranco Minati and published by Springer. This book was released on 2019-06-20 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Cognition and the Epistemology of Arithmetic

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Publisher : Cambridge University Press
ISBN 13 : 100946888X
Total Pages : 265 pages
Book Rating : 4.0/5 (94 download)

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Book Synopsis Numerical Cognition and the Epistemology of Arithmetic by : Markus Pantsar

Download or read book Numerical Cognition and the Epistemology of Arithmetic written by Markus Pantsar and published by Cambridge University Press. This book was released on 2024-03-31 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first book-length philosophical account of arithmetical knowledge that is based on the state-of-the-art empirical studies of numerical cognition.

Value and Justification

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Publisher : Cambridge University Press
ISBN 13 : 9780521397339
Total Pages : 564 pages
Book Rating : 4.3/5 (973 download)

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Book Synopsis Value and Justification by : Gerald F. Gaus

Download or read book Value and Justification written by Gerald F. Gaus and published by Cambridge University Press. This book was released on 1990-07-27 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rational moral action can neither be seen as a way of maximising personal values, nor derived from reason independent of them is this study's assertion. It contends that commitment to the moral point of view is presupposed by value systems.Rational moral action can neither be seen as a way of maximising personal values, nor derived from reason independent of them is this study's assertion. It contends that commitment to the moral point of view is presupposed by value systems.

Origins and Varieties of Logicism

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Publisher : Taylor & Francis
ISBN 13 : 1000508110
Total Pages : 419 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Origins and Varieties of Logicism by : Francesca Boccuni

Download or read book Origins and Varieties of Logicism written by Francesca Boccuni and published by Taylor & Francis. This book was released on 2021-11-29 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a plurality of perspectives on the historical origins of logicism and on contemporary developments of logicist insights in philosophy of mathematics. It uniquely provides up-to-date research and novel interpretations on a variety of intertwined themes and historical figures related to different versions of logicism. The essays, written by prominent scholars, are divided into three thematic sections. Part I focuses on major authors like Frege, Dedekind, and Russell, providing a historical and theoretical exploration of such figures in the philosophical and mathematical milieu in which logicist views were first expounded. Part II sheds new light on the interconnections between these founding figures and a number of influential other traditions, represented by authors like Hilbert, Husserl, and Peano, as well as on the reconsideration of logicism by Carnap and the logical empiricists. Finally, Part III assesses the legacy of such authors and of logicist themes for contemporary philosophy of mathematics, offering new perspectives on highly debated topics—neo-logicism and its extension to accounts of ordinal numbers and set-theory, the comparison between neo-Fregean and neo-Dedekindian varieties of logicism, and the relation between logicist foundational issues and empirical research on numerical cognition—which define the prospects of logicism in the years to come. This book offers a comprehensive account of the development of logicism and its contemporary relevance for the logico-philosophical foundations of mathematics. It will be of interest to graduate students and researchers working in philosophy of mathematics, philosophy of logic, and the history of analytic philosophy.

Epistemology or the Theory of Knowledge, 2 Volumes

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Author :
Publisher : Wipf and Stock Publishers
ISBN 13 : 1556352107
Total Pages : 776 pages
Book Rating : 4.5/5 (563 download)

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Book Synopsis Epistemology or the Theory of Knowledge, 2 Volumes by : P. Coffey

Download or read book Epistemology or the Theory of Knowledge, 2 Volumes written by P. Coffey and published by Wipf and Stock Publishers. This book was released on 2009-01-01 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: P. Coffey was Professor of Logic and Metaphysics at Maynooth College Ireland. His works include Ontology or the Theory of Being.