Principles and Proofs

Principles and Proofs

Author: Richard D. McKirahan Jr.

Publisher: Princeton University Press

Published: 2017-03-14

Total Pages: 355

ISBN-13: 140088716X

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By a thorough study of the Posterior Analytics and related Aristotelian texts, Richard McKirahan reconstructs Aristotle's theory of episteme--science. The Posterior Analytics contains the first extensive treatment of the nature and structure of science in the history of philosophy, and McKirahan's aim is to interpret it sympathetically, following the lead of the text, rather than imposing contemporary frameworks on it. In addition to treating the theory as a whole, the author uses textual and philological as well as philosophical material to interpret many important but difficult individual passages. A number of issues left obscure by the Aristotelian material are settled by reference to Euclid's geometrical practice in the Elements. To justify this use of Euclid, McKirahan makes a comparative analysis of fundamental features of Euclidian geometry with the corresponding elements of Aristotle's theory. Emerging from that discussion is a more precise and more complex picture of the relation between Aristotle's theory and Greek mathematics--a picture of mutual, rather than one-way, dependence. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.


Book Synopsis Principles and Proofs by : Richard D. McKirahan Jr.

Download or read book Principles and Proofs written by Richard D. McKirahan Jr. and published by Princeton University Press. This book was released on 2017-03-14 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: By a thorough study of the Posterior Analytics and related Aristotelian texts, Richard McKirahan reconstructs Aristotle's theory of episteme--science. The Posterior Analytics contains the first extensive treatment of the nature and structure of science in the history of philosophy, and McKirahan's aim is to interpret it sympathetically, following the lead of the text, rather than imposing contemporary frameworks on it. In addition to treating the theory as a whole, the author uses textual and philological as well as philosophical material to interpret many important but difficult individual passages. A number of issues left obscure by the Aristotelian material are settled by reference to Euclid's geometrical practice in the Elements. To justify this use of Euclid, McKirahan makes a comparative analysis of fundamental features of Euclidian geometry with the corresponding elements of Aristotle's theory. Emerging from that discussion is a more precise and more complex picture of the relation between Aristotle's theory and Greek mathematics--a picture of mutual, rather than one-way, dependence. Originally published in 1992. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Aristotle's Modal Proofs

Aristotle's Modal Proofs

Author: Adriane Rini

Publisher: Springer Science & Business Media

Published: 2010-12-13

Total Pages: 246

ISBN-13: 9400700504

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Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general.


Book Synopsis Aristotle's Modal Proofs by : Adriane Rini

Download or read book Aristotle's Modal Proofs written by Adriane Rini and published by Springer Science & Business Media. This book was released on 2010-12-13 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aristotle’s modal syllogistic is his study of patterns of reasoning about necessity and possibility. Many scholars think the modal syllogistic is incoherent, a ‘realm of darkness’. Others think it is coherent, but devise complicated formal modellings to mimic Aristotle’s results. This volume provides a simple interpretation of Aristotle’s modal syllogistic using standard predicate logic. Rini distinguishes between red terms, such as ‘horse’, ‘plant’ or ‘man’, which name things in virtue of features those things must have, and green terms, such as ‘moving’, which name things in virtue of their non-necessary features. By applying this distinction to the Prior Analytics, Rini shows how traditional interpretive puzzles about the modal syllogistic melt away and the simple structure of Aristotle’s own proofs is revealed. The result is an applied logic which provides needed links between Aristotle’s views of science and logical demonstration. The volume is particularly valuable to researchers and students of the history of logic, Aristotle’s theory of modality, and the philosophy of logic in general.

An Interpretation of Aristotle's Theory of the Modes and Forms of Proof

An Interpretation of Aristotle's Theory of the Modes and Forms of Proof

Author: Lewis Roland Rutherford

Publisher:

Published: 1970

Total Pages: 229

ISBN-13:

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Book Synopsis An Interpretation of Aristotle's Theory of the Modes and Forms of Proof by : Lewis Roland Rutherford

Download or read book An Interpretation of Aristotle's Theory of the Modes and Forms of Proof written by Lewis Roland Rutherford and published by . This book was released on 1970 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Knowledge and Demonstration

Knowledge and Demonstration

Author: Orna Harari

Publisher: Springer Science & Business Media

Published: 2005-02-15

Total Pages: 180

ISBN-13: 1402027885

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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.


Book Synopsis Knowledge and Demonstration by : Orna Harari

Download or read book Knowledge and Demonstration written by Orna Harari and published by Springer Science & Business Media. This book was released on 2005-02-15 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Aristotle and Logical Theory

Aristotle and Logical Theory

Author: Jonathan Lear

Publisher: Cambridge University Press

Published: 1980-05-08

Total Pages: 140

ISBN-13: 9780521230315

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Aristotle was the first and one of the greatest logicians. He not only devised the first system of formal logic, but also raised many fundamental problems in the philosophy of logic. In this book, Dr Lear shows how Aristotle's discussion of logical consequence, validity and proof can contribute to contemporary debates in the philosophy of logic. No background knowledge of Aristotle is assumed.


Book Synopsis Aristotle and Logical Theory by : Jonathan Lear

Download or read book Aristotle and Logical Theory written by Jonathan Lear and published by Cambridge University Press. This book was released on 1980-05-08 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aristotle was the first and one of the greatest logicians. He not only devised the first system of formal logic, but also raised many fundamental problems in the philosophy of logic. In this book, Dr Lear shows how Aristotle's discussion of logical consequence, validity and proof can contribute to contemporary debates in the philosophy of logic. No background knowledge of Aristotle is assumed.

Aristotle’s Theory of the Syllogism

Aristotle’s Theory of the Syllogism

Author: G. Patzig

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 232

ISBN-13: 9401707871

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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.


Book Synopsis Aristotle’s Theory of the Syllogism by : G. Patzig

Download or read book Aristotle’s Theory of the Syllogism written by G. Patzig and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Syllogistic Underlying Logic. His Model with His Proofs of Soundness and Completeness

Aristotle's Syllogistic Underlying Logic. His Model with His Proofs of Soundness and Completeness

Author: George Boger

Publisher: College Publications

Published: 2022-05-05

Total Pages: 446

ISBN-13: 9781848904026

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Aristotle's Syllogistic Underlying Logic is a ground- breaking and thorough study of Aristotle's logic, including a new translation of select chapters of Prior Analytics that treat the logic's formal components. This study shows that Aristotle consciously modeled his Underlying Logic, that Prior Analytics is a metasystematic discourse with its own underlying logic. The author clearly demonstrates that Aristotle conceived his logic as natural by explicating his notion of human cognition, central to which is his epistemic concern with syllogistic mediation that restricts a syllogism to two premises. The study further represents Aristotle's philosophy of logic as having a fully developed ontology that underlies the epistemics of syllogistic argumentation. It identifies his distinctions between syntax and semantics and provides his definitions of logical consequence and deducibility to demonstrate his metasystematic sophistication. The study carefully sets out Aristotle's metasystematic analyses and his proof-theoretic demonstrations of the logic's soundness and completeness. Unlike previous scholarship, this study works with the entire corpus of the Organon - inclusive of On Expression, Predications, Topics, Sophistical Refutations and chapters of Metaphysics - to assemble Aristotle's underlying logic in Aristotle's own words with extensive citation of primary texts. The translations are accompanied by the original Greek texts that serve as a ready resource for comparative analyses. For the translation of Prior Analytics, the Greek text and the translation appear on facing pages. The author includes a set of principles used for making the translation. An especially innovative feature of the new translation is to block passages of the text and to insert subsection titles that help (1) to elucidate Aristotle's meaning, (2) to indicate the movement of his thinking, and (3) to reveal the careful and systematic character of his logical investigations. The reader will find, in one volume, a thorough and meticulous examination of the full compass of Aristotle's logical investigations that establish him as the founder of formal logic.


Book Synopsis Aristotle's Syllogistic Underlying Logic. His Model with His Proofs of Soundness and Completeness by : George Boger

Download or read book Aristotle's Syllogistic Underlying Logic. His Model with His Proofs of Soundness and Completeness written by George Boger and published by College Publications. This book was released on 2022-05-05 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aristotle's Syllogistic Underlying Logic is a ground- breaking and thorough study of Aristotle's logic, including a new translation of select chapters of Prior Analytics that treat the logic's formal components. This study shows that Aristotle consciously modeled his Underlying Logic, that Prior Analytics is a metasystematic discourse with its own underlying logic. The author clearly demonstrates that Aristotle conceived his logic as natural by explicating his notion of human cognition, central to which is his epistemic concern with syllogistic mediation that restricts a syllogism to two premises. The study further represents Aristotle's philosophy of logic as having a fully developed ontology that underlies the epistemics of syllogistic argumentation. It identifies his distinctions between syntax and semantics and provides his definitions of logical consequence and deducibility to demonstrate his metasystematic sophistication. The study carefully sets out Aristotle's metasystematic analyses and his proof-theoretic demonstrations of the logic's soundness and completeness. Unlike previous scholarship, this study works with the entire corpus of the Organon - inclusive of On Expression, Predications, Topics, Sophistical Refutations and chapters of Metaphysics - to assemble Aristotle's underlying logic in Aristotle's own words with extensive citation of primary texts. The translations are accompanied by the original Greek texts that serve as a ready resource for comparative analyses. For the translation of Prior Analytics, the Greek text and the translation appear on facing pages. The author includes a set of principles used for making the translation. An especially innovative feature of the new translation is to block passages of the text and to insert subsection titles that help (1) to elucidate Aristotle's meaning, (2) to indicate the movement of his thinking, and (3) to reveal the careful and systematic character of his logical investigations. The reader will find, in one volume, a thorough and meticulous examination of the full compass of Aristotle's logical investigations that establish him as the founder of formal logic.

Aristotle's Theory of Bodies

Aristotle's Theory of Bodies

Author: Christian Pfeiffer

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 240

ISBN-13: 0191085308

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Christian Pfeiffer explores an important, but neglected topic in Aristotle's theoretical philosophy: the theory of bodies. A body is a three-dimensionally extended and continuous magnitude bounded by surfaces. This notion is distinct from the notion of a perceptible or physical substance. Substances have bodies, that is to say, they are extended, their parts are continuous with each other and they have boundaries, which demarcate them from their surroundings. Pfeiffer argues that body, thus understood, has a pivotal role in Aristotle's natural philosophy. A theory of body is a presupposed in, e.g., Aristotle's account of the infinite, place, or action and passion, because their being bodies explains why things have a location or how they can act upon each other. The notion of body can be ranked among the central concepts for natural science which are discussed in Physics III-IV. The book is the first comprehensive and rigorous account of the features substances have in virtue of being bodies. It provides an analysis of the concept of three-dimensional magnitude and related notions like boundary, extension, contact, continuity, often comparing it to modern conceptions of it. Both the structural features and the ontological status of body is discussed. This makes it significant for scholars working on contemporary metaphysics and mereology because the concept of a material object is intimately tied to its spatial or topological properties.


Book Synopsis Aristotle's Theory of Bodies by : Christian Pfeiffer

Download or read book Aristotle's Theory of Bodies written by Christian Pfeiffer and published by Oxford University Press. This book was released on 2018-07-12 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Christian Pfeiffer explores an important, but neglected topic in Aristotle's theoretical philosophy: the theory of bodies. A body is a three-dimensionally extended and continuous magnitude bounded by surfaces. This notion is distinct from the notion of a perceptible or physical substance. Substances have bodies, that is to say, they are extended, their parts are continuous with each other and they have boundaries, which demarcate them from their surroundings. Pfeiffer argues that body, thus understood, has a pivotal role in Aristotle's natural philosophy. A theory of body is a presupposed in, e.g., Aristotle's account of the infinite, place, or action and passion, because their being bodies explains why things have a location or how they can act upon each other. The notion of body can be ranked among the central concepts for natural science which are discussed in Physics III-IV. The book is the first comprehensive and rigorous account of the features substances have in virtue of being bodies. It provides an analysis of the concept of three-dimensional magnitude and related notions like boundary, extension, contact, continuity, often comparing it to modern conceptions of it. Both the structural features and the ontological status of body is discussed. This makes it significant for scholars working on contemporary metaphysics and mereology because the concept of a material object is intimately tied to its spatial or topological properties.

Galileo’s Logic of Discovery and Proof

Galileo’s Logic of Discovery and Proof

Author: W. A. Wallace

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 413

ISBN-13: 9401580405

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This volume is presented as a companion study to my translation of Galileo's MS 27, Galileo's Logical Treatises, which contains Galileo's appropriated questions on Aristotle's Posterior Analytics - a work only recently transcribed from the Latin autograph. Its purpose is to acquaint an English-reading audience with the teaching in those treatises. This is basically a sixteenth-century logic of discovery and of proof about which little is known in the present day, yet one that arguably guided the most significant research program of the seventeenth century. Despite its historical and systematic importance, the teaching is difficult to explain to the modern reader. Part of the problem stems from the fragmentary nature of the manuscript in which it is preserved, part from the contents of the teaching itself, which requires a considerable propadeutic for its comprehension. A word of explanation is thus required to set out the structure of the volume and to detail the editorial decisions that underlie its organization. Two major manuscript studies have advanced the cause of scholarship on Galileo within the past two decades. The first relates to Galileo's experimental activity at Padua prior to his discoveries with the telescope that led to the publication of his Sidereus nuncius in 1610. Much of this activity has been uncovered by Stillman Drake in analyses of manuscript fragments associated with the composition of Galileo's Two New Sciences, fragments now bound in a codex identified as MS 72 in the collection of Galileiana at the Biblioteca Nazionale Centrale in Florence.


Book Synopsis Galileo’s Logic of Discovery and Proof by : W. A. Wallace

Download or read book Galileo’s Logic of Discovery and Proof written by W. A. Wallace and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is presented as a companion study to my translation of Galileo's MS 27, Galileo's Logical Treatises, which contains Galileo's appropriated questions on Aristotle's Posterior Analytics - a work only recently transcribed from the Latin autograph. Its purpose is to acquaint an English-reading audience with the teaching in those treatises. This is basically a sixteenth-century logic of discovery and of proof about which little is known in the present day, yet one that arguably guided the most significant research program of the seventeenth century. Despite its historical and systematic importance, the teaching is difficult to explain to the modern reader. Part of the problem stems from the fragmentary nature of the manuscript in which it is preserved, part from the contents of the teaching itself, which requires a considerable propadeutic for its comprehension. A word of explanation is thus required to set out the structure of the volume and to detail the editorial decisions that underlie its organization. Two major manuscript studies have advanced the cause of scholarship on Galileo within the past two decades. The first relates to Galileo's experimental activity at Padua prior to his discoveries with the telescope that led to the publication of his Sidereus nuncius in 1610. Much of this activity has been uncovered by Stillman Drake in analyses of manuscript fragments associated with the composition of Galileo's Two New Sciences, fragments now bound in a codex identified as MS 72 in the collection of Galileiana at the Biblioteca Nazionale Centrale in Florence.

The Philosophy of Argument and Audience Reception

The Philosophy of Argument and Audience Reception

Author: Christopher W. Tindale

Publisher: Cambridge University Press

Published: 2015-04-30

Total Pages: 257

ISBN-13: 1107101115

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This book approaches the topic of argumentation from the perspective of audiences, rather than the perspective of arguers or arguments.


Book Synopsis The Philosophy of Argument and Audience Reception by : Christopher W. Tindale

Download or read book The Philosophy of Argument and Audience Reception written by Christopher W. Tindale and published by Cambridge University Press. This book was released on 2015-04-30 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book approaches the topic of argumentation from the perspective of audiences, rather than the perspective of arguers or arguments.