Syllogistic Logic And Mathematical Proof

DOWNLOAD

Download Syllogistic Logic And Mathematical Proof PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Syllogistic Logic And Mathematical Proof 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

Syllogistic Logic And Mathematical Proof

DOWNLOAD
Author : PROF PAOLO. MUGNAI MANCOSU (PROF MASSIMO.)
language : en
Publisher: Oxford University Press
Release Date : 2023-05-18

Syllogistic Logic And Mathematical Proof written by PROF PAOLO. MUGNAI MANCOSU (PROF MASSIMO.) 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 2023-05-18 with categories.

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.

Syllogistic Logic And Mathematical Proof

DOWNLOAD
Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2023-04-21

Syllogistic Logic And Mathematical Proof written by Paolo Mancosu 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 2023-04-21 with Philosophy categories.

Does syllogistic logic have the resources to capture mathematical proof? This volume provides the first unified account of the history of attempts to answer this question, the reasoning behind the different positions taken, and their far-reaching implications. Aristotle had claimed that scientific knowledge, which includes mathematics, is provided by syllogisms of a special sort: 'scientific' ('demonstrative') syllogisms. In ancient Greece and in the Middle Ages, the claim that Euclid's theorems could be recast syllogistically was accepted without further scrutiny. Nevertheless, as early as Galen, the importance of relational reasoning for mathematics had already been recognized. Further critical voices emerged in the Renaissance and the question of whether mathematical proofs could be recast syllogistically attracted more sustained attention over the following three centuries. Supported by more detailed analyses of Euclidean theorems, this led to attempts to extend logical theory to include relational reasoning, and to arguments purporting to reduce relational reasoning to a syllogistic form. Philosophical proposals to the effect that mathematical reasoning is heterogenous with respect to logical proofs were famously defended by Kant, and the implications of the debate about the adequacy of syllogistic logic for mathematics are at the very core of Kant's account of synthetic a priori judgments. While it is now widely accepted that syllogistic logic is not sufficient to account for the logic of mathematical proof, the history and the analysis of this debate, running from Aristotle to de Morgan and beyond, is a fascinating and crucial insight into the relationship between philosophy and mathematics.

Ancient Logic And Its Modern Interpretations

DOWNLOAD
Author : J. Corcoran
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Ancient Logic And Its Modern Interpretations written by J. Corcoran 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 2012-12-06 with Philosophy categories.

During the last half century there has been revolutionary progress in logic and in logic-related areas such as linguistics. HistoricaI knowledge of the origins of these subjects has also increased significantly. Thus, it would seem that the problem of determining the extent to which ancient logical and linguistic theories admit of accurate interpretation in modern terms is now ripe for investigation. The purpose of the symposium was to gather logicians, philosophers, linguists, mathematicians and philologists to present research results bearing on the above problem with emphasis on logic. Presentations and discussions at the symposium focused themselves into five areas: ancient semantics, modern research in ancient logic, Aristotle's logic, Stoic logic, and directions for future research in ancient logic and logic-related areas. Seven of the papers which appear below were originally presented at the symposium. In every case, discussion at the symposium led to revisions, in some cases to extensive revisions. The editor suggested still further revisions, but in every case the author was the finaljudge of the work that appears under his name.

Knowledge And Demonstration

DOWNLOAD
Author : Orna Harari
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-02-15

Knowledge And Demonstration written by Orna Harari 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 2005-02-15 with Philosophy categories.

This study explores the theoretical relationship between Aristotle’s theory of syllogism and his conception of demonstrative knowledge. More specifically, I consider why Aristotle’s theory of demonstration presupposes his theory of syllogism. In reconsidering the relationship between Aristotle’s two Analytics, I modify this widely discussed question. The problem of the relationship between Aristotle’s logic and his theory of proof is commonly approached from the standpoint of whether the theory of demonstration presupposes the theory of syllogism. By contrast, I assume the theoretical relationship between these two theories from the start. This assumption is based on much explicit textual evidence indicating that Aristotle considers the theory of demonstration a branch of the theory of syllogism. I see no textual reasons for doubting the theoretical relationship between Aristotle’s two Analytics so I attempt to uncover here the common theoretical assumptions that relate the syllogistic form of reasoning to the cognitive state (i. e. , knowledge), which is attained through syllogistic inferences. This modification of the traditional approach reflects the wider objective of this essay. Unlike the traditional interpretation, which views the Posterior Analytics in light of scientific practice, this study aims to lay the foundation for a comprehensive interpretation of the Posterior Analytics, considering this work from a metaphysical perspective. One of my major assertions is that Aristotle’s conception of substance is essential for a grasp of his theory of demonstration in general, and of the role of syllogistic logic in particular.

An Elementary Treatise On Logic

DOWNLOAD
Author : Hezekiah G. Ufford
language : en
Publisher:
Release Date : 1823

An Elementary Treatise On Logic written by Hezekiah G. Ufford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1823 with Logic categories.

The Place Of Syllogistic In Logical Theory

DOWNLOAD
Author : Michael Clark (M.A.)
language : en
Publisher:
Release Date : 1980

The Place Of Syllogistic In Logical Theory written by Michael Clark (M.A.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.

Logic Sets And The Techniques Of Mathematical Proofs

DOWNLOAD
Author : Brahima Mbodje Ph. D.
language : en
Publisher: AuthorHouse
Release Date : 2011-06

Logic Sets And The Techniques Of Mathematical Proofs written by Brahima Mbodje Ph. D. and has been published by AuthorHouse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06 with Education categories.

As its title indicates, this book is about logic, sets and mathematical proofs. It is a careful, patient and rigorous introduction for readers with very limited mathematical maturity. It teaches the reader not only how to read a mathematical proof, but also how to write one. To achieve this, we carefully lay out all the various proof methods encountered in mathematical discourse, give their logical justifications, and apply them to the study of topics [such as real numbers, relations, functions, sequences, fine sets, infinite sets, countable sets, uncountable sets and transfinite numbers] whose mastery is important for anyone contemplating advanced studies in mathematics. The book is completely self-contained; since the prerequisites for reading it are only a sound background in high school algebra. Though this book is meant to be a companion specifically for senior high school pupils and college undergraduate students, it will also be of immense value to anyone interested in acquiring the tools and way of thinking of the mathematician.

Introduction To Logic Second Edition

DOWNLOAD
Author : Genesereth Michael
language : en
Publisher: Springer Nature
Release Date : 2013-08-16

Introduction To Logic Second Edition written by Genesereth Michael and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-08-16 with Mathematics categories.

This book is a gentle but rigorous introduction to Formal Logic. It is intended primarily for use at the college level. However, it can also be used for advanced secondary school students, and it can be used at the start of graduate school for those who have not yet seen the material. The approach to teaching logic used here emerged from more than 20 years of teaching logic to students at Stanford University and from teaching logic to tens of thousands of others via online courses on the World Wide Web. The approach differs from that taken by other books in logic in two essential ways, one having to do with content, the other with form. Like many other books on logic, this one covers logical syntax and semantics and proof theory plus induction. However, unlike other books, this book begins with Herbrand semantics rather than the more traditional Tarskian semantics. This approach makes the material considerably easier for students to understand and leaves them with a deeper understanding of what logic is all about. In addition to this text, there are online exercises (with automated grading), online logic tools and applications, online videos of lectures, and an online forum for discussion. They are available at logic.stanford.edu/intrologic/

Aristotle S Theory Of The Syllogism

DOWNLOAD
Author : G. Patzig
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Aristotle S Theory Of The Syllogism written by G. Patzig 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 Philosophy categories.

The present book is the English version of a monograph 'Die aristotelische Syllogistik', which first appeared ten years ago in the series of Abhand 1 lungen edited by the Academy of Sciences in Gottingen. In the preface to the English edition, I would first like to express my indebtedness to Mr. J. Barnes, now fellow of Oriel College, Oxford. He not only translated what must have been a difficult text with exemplary precision and ingenuity, but followed critically every argument and check ed every reference. While translating it, he has improved the book. Of those changes which I have made on Mr. Barnes' suggestion I note only the more important ones on pages 4, 12, 24sq, 32, 39, 6lsq, and 158. Since the second edition of the German text appeared in 1963 some further reviews have been published, or come to my notice, which I have 2 been able to make use of in improving the text of this new edition. I must mention here especially the detailed critical discussions of my results and arguments published by Professor W. Wieland in the Philosophische Rundschau 14 (1966), 1-27 and by Professor E. Scheibe in Gnomon 39 (1967), 454-64. Both scholars, while agreeing with the main drift and method of my interpretation, criticise some of my results and disagree with some of my arguments. It would not be possible to discuss these technical matters here with the necessary thoroughness.

Aristotle S Syllogism And The Creation Of Modern Logic

DOWNLOAD
Author : Lukas M. Verburgt
language : en
Publisher: Bloomsbury Publishing
Release Date : 2023-01-26

Aristotle S Syllogism And The Creation Of Modern Logic written by Lukas M. Verburgt and has been published by Bloomsbury Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-26 with Philosophy categories.

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.