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Author: William W. Tait
Publisher: Oxford University Press, USA
ISBN: 9780195141924
Category : Mathematics
Languages : en
Pages : 354
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Book Description
Publisher description
Author: William W. Tait
Publisher: Oxford University Press, USA
ISBN: 9780195141924
Category : Mathematics
Languages : en
Pages : 354
Get Book Here
Book Description
Publisher description
Author: Charles Parsons
Publisher: Harvard University Press
ISBN: 0674065425
Category : Philosophy
Languages : en
Pages : 257
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Book Description
In From Kant to Husserl, Charles Parsons examines a wide range of historical opinion on philosophical questions from mathematics to phenomenology. Amplifying his early ideas on Kant’s philosophy of arithmetic, the author then turns to reflections on Frege, Brentano, and Husserl.
Author: T. M. Scanlon
Publisher: Oxford University Press, USA
ISBN: 0199678480
Category : Philosophy
Languages : en
Pages : 143
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Book Description
Is what we have reason to do a matter of fact? If so, what kind of truth is involved, how can we know it, and how do reasons motivate and explain action? In this concise and lucid book T.M. Scanlon offers answers, with a qualified defence of normative cognitivism - the view that there are normative truths about reasons for action.
Author: Charles Parsons
Publisher: Cambridge University Press
ISBN: 1139467271
Category : Science
Languages : en
Pages : 400
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Book Description
Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.
Author: Ruth Chang
Publisher: Routledge
ISBN: 100033712X
Category : Philosophy
Languages : en
Pages : 716
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Book Description
Over the last several decades, questions about practical reason have come to occupy the center stage in ethics and metaethics. The Routledge Handbook of Practical Reason is an outstanding reference source to this exciting and distinctive subject area and is the first volume of its kind. Comprising thirty-six chapters by an international team of contributors, the Handbook provides a comprehensive overview of the field and is divided into five parts: Foundational Matters Practical Reason in the History of Philosophy Philosophy of Practical Reason as Action Theory and Moral Psychology Philosophy of Practical Reason as Theory of Practical Normativity The Philosophy of Practical Reason as the Theory of Practical Rationality The Handbook also includes two chapters by the late Derek Parfit, ‘Objectivism about Reasons’ and ‘Normative Non-Naturalism.’ The Routledge Handbook of Practical Reason is essential reading for philosophy students and researchers in metaethics, philosophy of action, action theory, ethics, and the history of philosophy.
Author: Erich H. Reck
Publisher: Oxford University Press
ISBN: 0190641223
Category : Mathematics
Languages : en
Pages : 469
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Book Description
This edited volume explores the previously underacknowledged 'pre-history' of mathematical structuralism, showing that structuralism has deep roots in the history of modern mathematics. The contributors explore this history along two distinct but interconnected dimensions. First, they reconsider the methodological contributions of major figures in the history of mathematics. Second, they re-examine a range of philosophical reflections from mathematically-inclinded philosophers like Russell, Carnap, and Quine, whose work led to profound conclusions about logical, epistemological, and metaphysic.
Author: Sean Morris
Publisher: Cambridge University Press
ISBN: 1108604536
Category : Philosophy
Languages : en
Pages : 221
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Book Description
Quine's set theory, New Foundations, has often been treated as an anomaly in the history and philosophy of set theory. In this book, Sean Morris shows that it is in fact well-motivated, emerging in a natural way from the early development of set theory. Morris introduces and explores the notion of set theory as explication: the view that there is no single correct axiomatization of set theory, but rather that the various axiomatizations all serve to explicate the notion of set and are judged largely according to pragmatic criteria. Morris also brings out the important interplay between New Foundations, Quine's philosophy of set theory, and his philosophy more generally. We see that his early technical work in logic foreshadows his later famed naturalism, with his philosophy of set theory playing a crucial role in his primary philosophical project of clarifying our conceptual scheme and specifically its logical and mathematical components.
Author: Gerhard Jäger
Publisher: Springer
ISBN: 3319633341
Category : Mathematics
Languages : en
Pages : 617
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Book Description
This volume honours the life and work of Solomon Feferman, one of the most prominent mathematical logicians of the latter half of the 20th century. In the collection of essays presented here, researchers examine Feferman’s work on mathematical as well as specific methodological and philosophical issues that tie into mathematics. Feferman’s work was largely based in mathematical logic (namely model theory, set theory, proof theory and computability theory), but also branched out into methodological and philosophical issues, making it well known beyond the borders of the mathematics community. With regard to methodological issues, Feferman supported concrete projects. On the one hand, these projects calibrate the proof theoretic strength of subsystems of analysis and set theory and provide ways of overcoming the limitations imposed by Gödel’s incompleteness theorems through appropriate conceptual expansions. On the other, they seek to identify novel axiomatic foundations for mathematical practice, truth theories, and category theory. In his philosophical research, Feferman explored questions such as “What is logic?” and proposed particular positions regarding the foundations of mathematics including, for example, his “conceptual structuralism.” The contributing authors of the volume examine all of the above issues. Their papers are accompanied by an autobiography presented by Feferman that reflects on the evolution and intellectual contexts of his work. The contributing authors critically examine Feferman’s work and, in part, actively expand on his concrete mathematical projects. The volume illuminates Feferman’s distinctive work and, in the process, provides an enlightening perspective on the foundations of mathematics and logic.
Author: Gabriele M. Mras
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110654547
Category : Philosophy
Languages : en
Pages : 581
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Book Description
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.
Author: Penelope Maddy
Publisher: OUP Oxford
ISBN: 0191616532
Category : Philosophy
Languages : en
Pages : 160
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Book Description
Mathematics depends on proofs, and proofs must begin somewhere, from some fundamental assumptions. For nearly a century, the axioms of set theory have played this role, so the question of how these axioms are properly judged takes on a central importance. Approaching the question from a broadly naturalistic or second-philosophical point of view, Defending the Axioms isolates the appropriate methods for such evaluations and investigates the ontological and epistemological backdrop that makes them appropriate. In the end, a new account of the objectivity of mathematics emerges, one refreshingly free of metaphysical commitments.
