Vorlesungen Uber Die Algebra Der Logik

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Aristotle's Syllogism and the Creation of Modern Logic

Author : Lukas M. Verburgt
Publisher : Bloomsbury Publishing
ISBN 13 : 1350228850
Total Pages : 321 pages
Book Rating : 4.3/5 (52 download)

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Book Synopsis Aristotle's Syllogism and the Creation of Modern Logic by : Lukas M. Verburgt

Download or read book Aristotle's Syllogism and the Creation of Modern Logic written by Lukas M. Verburgt and published by Bloomsbury Publishing. This book was released on 2023-01-26 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offering a bold new vision on the history of modern logic, Lukas M. Verburgt and Matteo Cosci focus on the lasting impact of Aristotle's syllogism between the 1820s and 1930s. For over two millennia, deductive logic was the syllogism and syllogism was the yardstick of sound human reasoning. During the 19th century, this hegemony fell apart and logicians, including Boole, Frege and Peirce, took deductive logic far beyond its Aristotelian borders. However, contrary to common wisdom, reflections on syllogism were also instrumental to the creation of new logical developments, such as first-order logic and early set theory. This volume presents the period under discussion as one of both tradition and innovation, both continuity and discontinuity. Modern logic broke away from the syllogistic tradition, but without Aristotle's syllogism, modern logic would not have been born. A vital follow up to The Aftermath of Syllogism, this book traces the longue durée history of syllogism from Richard Whately's revival of formal logic in the 1820s through the work of David Hilbert and the Göttingen school up to the 1930s. Bringing together a group of major international experts, it sheds crucial new light on the emergence of modern logic and the roots of analytic philosophy in the 19th and early 20th centuries.

Philosophie und Logik

Author : Werner Stelzner
Publisher : Walter de Gruyter
ISBN 13 : 9783110140699
Total Pages : 444 pages
Book Rating : 4.1/5 (46 download)

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Book Synopsis Philosophie und Logik by : Werner Stelzner

Download or read book Philosophie und Logik written by Werner Stelzner and published by Walter de Gruyter. This book was released on 1993 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Essays on Husserl's Logic and Philosophy of Mathematics

Author : Stefania Centrone
Publisher : Springer
ISBN 13 : 9402411321
Total Pages : 541 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Essays on Husserl's Logic and Philosophy of Mathematics by : Stefania Centrone

Download or read book Essays on Husserl's Logic and Philosophy of Mathematics written by Stefania Centrone and published by Springer. This book was released on 2017-09-07 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one.

Introduction to Symbolic Logic and Its Applications

Author : Rudolf Carnap
Publisher : Courier Corporation
ISBN 13 : 048614349X
Total Pages : 280 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to Symbolic Logic and Its Applications by : Rudolf Carnap

Download or read book Introduction to Symbolic Logic and Its Applications written by Rudolf Carnap and published by Courier Corporation. This book was released on 2012-07-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Clear, comprehensive, and rigorous treatment develops the subject from elementary concepts to the construction and analysis of relatively complex logical languages. Hundreds of problems, examples, and exercises. 1958 edition.

Modern Modalities

Author : Simo Knuuttila
Publisher : Springer Science & Business Media
ISBN 13 : 9400929153
Total Pages : 354 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Modern Modalities by : Simo Knuuttila

Download or read book Modern Modalities written by Simo Knuuttila and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The word "modem" in the title of this book refers primarily to post-medieval discussions, but it also hints at those medieval mo dal theories which were considered modem in contradistinction to ancient conceptions and which in different ways influenced philosophical discussions during the early modem period. The me dieval developments are investigated in the opening paper, 'The Foundations of Modality and Conceivability in Descartes and His Predecessors', by Lilli Alanen and Simo Knuuttila. Boethius's works from the early sixth century belonged to the sources from which early medieval thinkers obtained their knowledge of ancient thought. They offered extensive discus sions of traditional modal conceptions the basic forms of which were: (1) the paradigm of possibility as a potency striving to realize itself; (2) the "statistical" interpretation of modal no tions where necessity means actuality in all relevant cases or omnitemporal actuality, possibility means actuality in some rel evant cases or sometimes, and impossibility means omnitemporal non-actuality; and (3) the "logical" definition of possibility as something which, being assumed, results in nothing contradic tory. Boethius accepted the Aristotelian view according to which total possibilities in the first sense must prove their met tle through actualization and possibilities in the third sense are assumed to be realized in our actual history. On these presump tions, all of the above-mentioned ancient paradigms imply the Principle of Plenitude according to which no genuine possibility remains unrealized.

Perspectives on the History of Mathematical Logic

Author : Thomas Drucker
Publisher : Springer Science & Business Media
ISBN 13 : 0817647694
Total Pages : 218 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Perspectives on the History of Mathematical Logic by : Thomas Drucker

Download or read book Perspectives on the History of Mathematical Logic written by Thomas Drucker and published by Springer Science & Business Media. This book was released on 2009-05-21 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

Handbook of Philosophical Logic

Author : Dov M. Gabbay
Publisher : Springer Science & Business Media
ISBN 13 : 9401598339
Total Pages : 404 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Handbook of Philosophical Logic by : Dov M. Gabbay

Download or read book Handbook of Philosophical Logic written by Dov M. Gabbay and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is with great pleasure that we are presenting to the community the second edition of this extraordinary handbook. It has been over 15 years since the publication of the first edition and there have been great changes in the landscape of philosophical logic since then. The first edition has proved invaluable to generations of students and researchers in formal philosophy and language, as well as to consumers of logic in many applied areas. The main logic article in the Encyclopaedia Britannica 1999 has described the first edition as 'the best starting point for exploring any of the topics in logic'. We are confident that the second edition will prove to be just as good. ! The first edition was the second handbook published for the logic commu nity. It followed the North Holland one volume Handbook of Mathematical Logic, published in 1977, edited by the late Jon Barwise, The four volume Handbook of Philosophical Logic, published 1983-1989 came at a fortunate temporal junction at the evolution of logic. This was the time when logic was gaining ground in computer science and artificial intelligence circles. These areas were under increasing commercial pressure to provide devices which help and/or replace the human in his daily activity. This pressure required the use of logic in the modelling of human activity and organisa tion on the one hand and to provide the theoretical basis for the computer program constructs on the other.

The Origin of the Logic of Symbolic Mathematics

Author : Burt C. Hopkins
Publisher : Indiana University Press
ISBN 13 : 0253005272
Total Pages : 593 pages
Book Rating : 4.2/5 (53 download)

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Book Synopsis The Origin of the Logic of Symbolic Mathematics by : Burt C. Hopkins

Download or read book The Origin of the Logic of Symbolic Mathematics written by Burt C. Hopkins and published by Indiana University Press. This book was released on 2011-09-07 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: Burt C. Hopkins presents the first in-depth study of the work of Edmund Husserl and Jacob Klein on the philosophical foundations of the logic of modern symbolic mathematics. Accounts of the philosophical origins of formalized concepts—especially mathematical concepts and the process of mathematical abstraction that generates them—have been paramount to the development of phenomenology. Both Husserl and Klein independently concluded that it is impossible to separate the historical origin of the thought that generates the basic concepts of mathematics from their philosophical meanings. Hopkins explores how Husserl and Klein arrived at their conclusion and its philosophical implications for the modern project of formalizing all knowledge.

A Formalization of Set Theory without Variables

Author : Alfred Tarski
Publisher : American Mathematical Soc.
ISBN 13 : 0821810413
Total Pages : 342 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis A Formalization of Set Theory without Variables by : Alfred Tarski

Download or read book A Formalization of Set Theory without Variables written by Alfred Tarski and published by American Mathematical Soc.. This book was released on 1987 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Culminates nearly half a century of the late Alfred Tarski's foundational studies in logic, mathematics, and the philosophy of science. This work shows that set theory and number theory can be developed within the framework of a new, different and simple equational formalism, closely related to the formalism of the theory of relation algebras.

Mathematical Logic

Author : Stephen Cole Kleene
Publisher : Courier Corporation
ISBN 13 : 0486317072
Total Pages : 436 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Mathematical Logic by : Stephen Cole Kleene

Download or read book Mathematical Logic written by Stephen Cole Kleene and published by Courier Corporation. This book was released on 2013-04-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents include an elementary but thorough overview of mathematical logic of 1st order; formal number theory; surveys of the work by Church, Turing, and others, including Gödel's completeness theorem, Gentzen's theorem, more.

Necessity Lost

Author : Sanford Shieh
Publisher : Oxford University Press
ISBN 13 : 0192568817
Total Pages : 641 pages
Book Rating : 4.1/5 (925 download)

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Book Synopsis Necessity Lost by : Sanford Shieh

Download or read book Necessity Lost written by Sanford Shieh and published by Oxford University Press. This book was released on 2019-03-21 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: A long tradition, going back to Aristotle, conceives of logic in terms of necessity and possibility: a deductive argument is correct if it is not possible for the conclusion to be false when the premises are true. A relatively unknown feature of the analytic tradition in philosophy is that, at its very inception, this venerable conception of the relation between logic and necessity and possibility - the concepts of modality - was put into question. The founders of analytic philosophy, Gottlob Frege and Bertrand Russell, held that these concepts are empty: there are no genuine distinctions among the necessary, the possible, and the actual. In this book, the first of two volumes, Sanford Shieh investigates the grounds of this position and its consequences for Frege's and Russell's conceptions of logic. The grounds lie in doctrines on truth, thought, and knowledge, as well as on the relation between mind and reality, that are central to the philosophies of Frege and Russell, and are of enduring philosophical interest. The upshot of this opposition to modality is that logic is fundamental, and, to be coherent, modal concepts would have to be reconstructed in logical terms. This rejection of modality in early analytic philosophy remains of contemporary significance, though the coherence of modal concepts is rarely questioned nowadays because it is generally assumed that suspicion of modality derives from logical positivism, which has not survived philosophical scrutiny. The anti-modal arguments of Frege and Russell, however, have nothing to do with positivism and remain a challenge to the contemporary acceptance of modal notions.

Proceedings

Author : Leon Henkin
Publisher : American Mathematical Soc.
ISBN 13 : 0821814257
Total Pages : 522 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Proceedings by : Leon Henkin

Download or read book Proceedings written by Leon Henkin and published by American Mathematical Soc.. This book was released on 1974 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Gottlob Frege: Frege's philosophy in context

Author : Michael Beaney
Publisher : Taylor & Francis
ISBN 13 : 9780415306027
Total Pages : 458 pages
Book Rating : 4.3/5 (6 download)

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Book Synopsis Gottlob Frege: Frege's philosophy in context by : Michael Beaney

Download or read book Gottlob Frege: Frege's philosophy in context written by Michael Beaney and published by Taylor & Francis. This book was released on 2005 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection brings together recent scholarship on Frege, including new translations of German material which is made available to Anglophone scholars for the first time.

Duality in 19th and 20th Century Mathematical Thinking

Author : Ralf Krömer
Publisher : Springer Nature
ISBN 13 : 3031597974
Total Pages : 962 pages
Book Rating : 4.0/5 (315 download)

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Book Synopsis Duality in 19th and 20th Century Mathematical Thinking by : Ralf Krömer

Download or read book Duality in 19th and 20th Century Mathematical Thinking written by Ralf Krömer and published by Springer Nature. This book was released on 2024 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume brings together scholars across various domains of the history and philosophy of mathematics, investigating duality as a multi-faceted phenomenon. Encompassing both systematic analysis and historical examination, the book endeavors to elucidate the status, roles, and dynamics of duality within the realms of 19th and 20th-century mathematics. Eschewing a priori notions, the contributors embrace the diverse interpretations and manifestations of duality, thus presenting a nuanced and comprehensive perspective on this intricate subject. Spanning a broad spectrum of mathematical topics and historical periods, the book uses detailed case studies to investigate the different forms in which duality appeared and still appears in mathematics, to study their respective histories, and to analyze interactions between the different forms of duality. The chapters inquire into questions such as the contextual occurrences of duality in mathematics, the influence of chosen forms of representation, the impact of investigations of duality on mathematical practices, and the historical interconnections among various instances of duality. Together, they aim to answer a core question: Is there such a thing as duality in mathematics, or are there just several things called by the same name and similar in some respect? What emerges is that duality can be considered as a basic structure of mathematical thinking, thereby opening new horizons for the research on the history and the philosophy of mathematics and the reflection on mathematics in general. The volume will appeal not only to experts in the discipline but also to advanced students of mathematics, history, and philosophy intrigued by the complexities of this captivating subject matter.

Husserl's Constitutive Phenomenology

Author : Bob Sandmeyer
Publisher : Routledge
ISBN 13 : 1135852898
Total Pages : 466 pages
Book Rating : 4.1/5 (358 download)

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Book Synopsis Husserl's Constitutive Phenomenology by : Bob Sandmeyer

Download or read book Husserl's Constitutive Phenomenology written by Bob Sandmeyer and published by Routledge. This book was released on 2009-01-11 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: If Edmund Husserl's true philosophy lay in his unpublished research manuscripts, as he argues, then it is in these – rather than the "introductions" and fragmentary studies he published during his lifetime – that we may possibly find a systematic of his philosophy. This work constitutes a study of the full range of Husserl's writings with the special task of uncovering there the systematic presentation or presentations of the transcendental phenomenological problematic. Sandmeyer's study contains an overview of Husserl's total set of writings, a translation of Husserl correspondence with Georg Misch, a translation of a draft outline of the "system of phenomenological philosophy" produced by Husserl in collaboration with his assistant, Eugen Fink, and it also closely traces the influence of Wilhelm Dilthey on Husserl's philosophy.

Gottlob Frege: Foundations of Arithmetic

Author : Gottlob Frege
Publisher : Routledge
ISBN 13 : 1000154424
Total Pages : 129 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Gottlob Frege: Foundations of Arithmetic by : Gottlob Frege

Download or read book Gottlob Frege: Foundations of Arithmetic written by Gottlob Frege and published by Routledge. This book was released on 2020-07-24 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of theLongman Library of Primary Sources in Philosophy, this edition of Frege's Foundations of Arithmetic is framed by a pedagogical structure designed to make this important work of philosophy more accessible and meaningful for undergraduates.

Philosophy of Logic and Mathematics

Author : Gabriele M. Mras
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110657880
Total Pages : 559 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Philosophy of Logic and Mathematics by : Gabriele M. Mras

Download or read book Philosophy of Logic and Mathematics written by Gabriele M. Mras and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-11-18 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.