Author: Antis Loizides
Publisher: Routledge
ISBN: 113502054X
Category : Philosophy
Languages : en
Pages : 282
Book Description
John Stuart Mill considered his A System of Logic, first published in 1843, the methodological foundation and intellectual groundwork of his later works in ethical, social, and political theory. Yet no book has attempted in the past to engage with the most important aspects of Mill's Logic. This volume brings together leading scholars to elucidate the key themes of this influential work, looking at such topics as his philosophy of language and mathematics, his view on logic, induction and deduction, free will, argumentation, ethology and psychology, as well as his account of normativity, kinds of pleasure, philosophical and political method and the "Art of Life."
Mill's A System of Logic
Alan Turing's Systems of Logic
Author: Andrew W. Appel
Publisher: Princeton University Press
ISBN: 0691164738
Category : Computers
Languages : en
Pages : 160
Book Description
A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.
Publisher: Princeton University Press
ISBN: 0691164738
Category : Computers
Languages : en
Pages : 160
Book Description
A facsimile edition of Alan Turing's influential Princeton thesis Between inventing the concept of a universal computer in 1936 and breaking the German Enigma code during World War II, Alan Turing (1912–1954), the British founder of computer science and artificial intelligence, came to Princeton University to study mathematical logic. Some of the greatest logicians in the world—including Alonzo Church, Kurt Gödel, John von Neumann, and Stephen Kleene—were at Princeton in the 1930s, and they were working on ideas that would lay the groundwork for what would become known as computer science. This book presents a facsimile of the original typescript of Turing's fascinating and influential 1938 Princeton PhD thesis, one of the key documents in the history of mathematics and computer science. The book also features essays by Andrew Appel and Solomon Feferman that explain the still-unfolding significance of the ideas Turing developed at Princeton. A work of philosophy as well as mathematics, Turing's thesis envisions a practical goal—a logical system to formalize mathematical proofs so they can be checked mechanically. If every step of a theorem could be verified mechanically, the burden on intuition would be limited to the axioms. Turing's point, as Appel writes, is that "mathematical reasoning can be done, and should be done, in mechanizable formal logic." Turing's vision of "constructive systems of logic for practical use" has become reality: in the twenty-first century, automated "formal methods" are now routine. Presented here in its original form, this fascinating thesis is one of the key documents in the history of mathematics and computer science.
Logic of Moral Science
Author: John Stuart Mill
Publisher: Courier Corporation
ISBN: 0486841979
Category : Philosophy
Languages : en
Pages : 130
Book Description
John Stuart Mill (1806–73) was the most influential English philosopher of the nineteenth century. His vast intellectual output covered a range of subjects — traditional philosophy and logic, economics, political science — and included this work, a founding document in the area now known as social science. In The Logic of the Moral Sciences, Mill applied his considerable talents to examining how the study of human behavior, society, and history could be established on a rational, philosophical basis. The philosopher maintains that casual empiricism and direct experiment are not applicable to the study of complex social phenomena. Instead, "empirical laws," drawn from historical generalizations, must be derivable from a deductive science of human nature. Mills' insights and approaches have remained relevant in the century and a half since this treatise's publication. This volume will prove of vital interest to historians of philosophy and the social sciences as well as to undergraduate social science majors.
Publisher: Courier Corporation
ISBN: 0486841979
Category : Philosophy
Languages : en
Pages : 130
Book Description
John Stuart Mill (1806–73) was the most influential English philosopher of the nineteenth century. His vast intellectual output covered a range of subjects — traditional philosophy and logic, economics, political science — and included this work, a founding document in the area now known as social science. In The Logic of the Moral Sciences, Mill applied his considerable talents to examining how the study of human behavior, society, and history could be established on a rational, philosophical basis. The philosopher maintains that casual empiricism and direct experiment are not applicable to the study of complex social phenomena. Instead, "empirical laws," drawn from historical generalizations, must be derivable from a deductive science of human nature. Mills' insights and approaches have remained relevant in the century and a half since this treatise's publication. This volume will prove of vital interest to historians of philosophy and the social sciences as well as to undergraduate social science majors.
Systems of Formal Logic
Author: L.H. Hackstaff
Publisher: Springer Science & Business Media
ISBN: 9789027700773
Category : Philosophy
Languages : en
Pages : 378
Book Description
The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.
Publisher: Springer Science & Business Media
ISBN: 9789027700773
Category : Philosophy
Languages : en
Pages : 378
Book Description
The present work constitutes an effort to approach the subject of symbol ic logic at the elementary to intermediate level in a novel way. The book is a study of a number of systems, their methods, their rela tions, their differences. In pursuit of this goal, a chapter explaining basic concepts of modern logic together with the truth-table techniques of definition and proof is first set out. In Chapter 2 a kind of ur-Iogic is built up and deductions are made on the basis of its axioms and rules. This axiom system, resembling a propositional system of Hilbert and Ber nays, is called P +, since it is a positive logic, i. e. , a logic devoid of nega tion. This system serves as a basis upon which a variety of further sys tems are constructed, including, among others, a full classical proposi tional calculus, an intuitionistic system, a minimum propositional calcu lus, a system equivalent to that of F. B. Fitch (Chapters 3 and 6). These are developed as axiomatic systems. By means of adding independent axioms to the basic system P +, the notions of independence both for primitive functors and for axiom sets are discussed, the axiom sets for a number of such systems, e. g. , Frege's propositional calculus, being shown to be non-independent. Equivalence and non-equivalence of systems are discussed in the same context. The deduction theorem is proved in Chapter 3 for all the axiomatic propositional calculi in the book.
Logic for Philosophy
Author: Theodore Sider
Publisher: Oxford University Press
ISBN: 0192658816
Category : Philosophy
Languages : en
Pages : 305
Book Description
Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.
Publisher: Oxford University Press
ISBN: 0192658816
Category : Philosophy
Languages : en
Pages : 305
Book Description
Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.
An Introduction to Symbolic Logic
Author: Langer
Publisher: Courier Corporation
ISBN: 9780486601649
Category : Mathematics
Languages : en
Pages : 388
Book Description
Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
Publisher: Courier Corporation
ISBN: 9780486601649
Category : Mathematics
Languages : en
Pages : 388
Book Description
Famous classic has introduced countless readers to symbolic logic with its thorough and precise exposition. Starts with simple symbols and conventions and concludes with the Boole-Schroeder and Russell-Whitehead systems. No special knowledge of mathematics necessary. "One of the clearest and simplest introductions to a subject which is very much alive." — Mathematics Gazette.
Leśniewski's Systems of Logic and Foundations of Mathematics
Author: Rafal Urbaniak
Publisher: Springer Science & Business Media
ISBN: 3319004824
Category : Science
Languages : en
Pages : 240
Book Description
This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.
Publisher: Springer Science & Business Media
ISBN: 3319004824
Category : Science
Languages : en
Pages : 240
Book Description
This meticulous critical assessment of the ground-breaking work of philosopher Stanislaw Leśniewski focuses exclusively on primary texts and explores the full range of output by one of the master logicians of the Lvov-Warsaw school. The author’s nuanced survey eschews secondary commentary, analyzing Leśniewski's core philosophical views and evaluating the formulations that were to have such a profound influence on the evolution of mathematical logic. One of the undisputed leaders of the cohort of brilliant logicians that congregated in Poland in the early twentieth century, Leśniewski was a guide and mentor to a generation of celebrated analytical philosophers (Alfred Tarski was his PhD student). His primary achievement was a system of foundational mathematical logic intended as an alternative to the Principia Mathematica of Alfred North Whitehead and Bertrand Russell. Its three strands—‘protothetic’, ‘ontology’, and ‘mereology’, are detailed in discrete sections of this volume, alongside a wealth other chapters grouped to provide the fullest possible coverage of Leśniewski’s academic output. With material on his early philosophical views, his contributions to set theory and his work on nominalism and higher-order quantification, this book offers a uniquely expansive critical commentary on one of analytical philosophy’s great pioneers.
A System of Indian Logic
Author: John Vattanky
Publisher: Routledge
ISBN: 1136846085
Category : Philosophy
Languages : en
Pages : 512
Book Description
Nyana is the most rational and logical of all the classical Indian philosophical systems. In the study of Nyana philosophy, Karikavali with its commentary Muktavali, both by Visvanatha Nyayapancanana, with the commentaries Dinakari and Ramarudri, have been of decisive significance for the last few centuries as advanced introductions to this subject. The present work concentrates on inference (anumana) in Karikavali, Muktavali and Dinakari, carefully divided into significant units according to the subject, and translates and interprets them. Its commentary makes use of the primary interpretation in Sanskrit contained especially in the Ramarudri and Subodhini. The book begins with the Sanskrit texts of Karikavali and Muktavali; followed by English translation of these texts. Next is given the Sanskrit text of Dinakari which comments on the first two texts, followed by its English translation. Lastly, the book contains a commentary on all the texts included.
Publisher: Routledge
ISBN: 1136846085
Category : Philosophy
Languages : en
Pages : 512
Book Description
Nyana is the most rational and logical of all the classical Indian philosophical systems. In the study of Nyana philosophy, Karikavali with its commentary Muktavali, both by Visvanatha Nyayapancanana, with the commentaries Dinakari and Ramarudri, have been of decisive significance for the last few centuries as advanced introductions to this subject. The present work concentrates on inference (anumana) in Karikavali, Muktavali and Dinakari, carefully divided into significant units according to the subject, and translates and interprets them. Its commentary makes use of the primary interpretation in Sanskrit contained especially in the Ramarudri and Subodhini. The book begins with the Sanskrit texts of Karikavali and Muktavali; followed by English translation of these texts. Next is given the Sanskrit text of Dinakari which comments on the first two texts, followed by its English translation. Lastly, the book contains a commentary on all the texts included.
An Introduction to Formal Logic
Author: Peter Smith
Publisher: Cambridge University Press
ISBN: 9780521008044
Category : Mathematics
Languages : en
Pages : 370
Book Description
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Publisher: Cambridge University Press
ISBN: 9780521008044
Category : Mathematics
Languages : en
Pages : 370
Book Description
Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
Design of Logic Systems
Author: DAVID PROTHEROE DOUGLAS LEWIN
Publisher: Springer
ISBN: 1489968563
Category : Computers
Languages : en
Pages : 713
Book Description
Publisher: Springer
ISBN: 1489968563
Category : Computers
Languages : en
Pages : 713
Book Description