A short seventeenth-century text, sometimes cited as one of the first essays in mathematical logic, is introduced, translated and evaluated. Although by no means sharing the depth and magnitude of the investigations by Leibniz being undertaken at the same time, and although in particular not yet applying algebraic symbolism to logical structures, the treatise is of historical interest as an early published attempt to trace out analogies between logical and mathematical form, and may be viewed as a preliminary step toward (...) the formalization of logic. (shrink)

HISTORICAL INTRODUCTION Although many of the details of the development of logic in the Middle Ages remain to be filled in, it is well known that between ...

This book traces the development of formal logic from its origins in ancient Greece to the present day. The authors first discuss the work of logicians from Aristotle to Frege, showing how they were influenced by the philosophical or mathematical ideas of their time. They then examine developments in the present century.

In the New Essays on Human Understanding, Leibniz argues chapter by chapter with John Locke's Essay Concerning Human Understanding, challenging his views about knowledge, personal identity, God, morality, mind and matter, nature versus nurture, logic and language, and a host of other topics. The work is a series of sharp, deep discussions by one great philosopher of the work of another. Leibniz's references to his contemporaries and his discussions of the ideas and institutions of the age make this a fascinating (...) and valuable document in the history of ideas. The work was originally written in French, and the version by Peter Remnant and Jonathan Bennett, based on the only reliable French edition (published in 1962), first appeared in 1981 and has become the standard English translation. It has been thoroughly revised for this series and provided with a new and longer introduction, a chronology on Leibniz's life and career and a guide to further reading. (shrink)

v. 1. Compendium logicae. Apologeticus de ratione poeticae artis. Trattato contra li astrologi -- v. 2. Compendium philosophiae naturalis, Compendium philosophiae moralis.

In der vorliegenden Arbeit wird Leibniz' wahrscheinlich detailliertestes und ausgefeiltestes System untersucht: ein Kalkül der Einfügung und eine der Konjunktion ähnliche Operation, die er realis abjectio nennt. Das System soll hinreichend detailliert und mit hinreichender Präzision vorgestellt werden, um zu zeigen, daβ es ausgefeilt formal logisch ist und eine Anzahl originärer und wichtiger Züge aufweist. Neben seinem eigenständigen Interesse ist dieses System wichtig wegen seiner Auswirkungen auf andere Aspekte von Leibniz' Logik und Philosophie, und ein weiteres Ziel dieser Arbeit ist, (...) einige dieser Verbindungen aufzuspüren. (shrink)

This book is a collection of essays published by the author in the long run of about 20 years and is centered on the reconstruction of Leibniz’s logical calculi. All the essays have been revised for the present edition and some of them constituted the background for Lenzen’s first monograph on Leibniz’s logic. A feature common to all these essays is the vindication of the relevance and originality of Leibniz’s logical achievements. Lenzen manifests strong dissatisfaction with the evaluations of Leibniz’s (...) logic previously offered by interpreters like Louis Couturat, Clarence I. Lewis, Karl Dürr, William and Martha Kneale, and states that till now Leibniz’s results in the field of logic have been widely underestimated. The book contains a careful and detailed examination of almost all Leibniz’s papers on the logical calculus and it is based on the knowledge of a wide range of texts unknown to previous interpreters. Lenzen’s acquaintance with the entire corpus of Leibniz’s logical texts is impressive. Some chapters of the book in particular contain very solid and useful logical analyses. Chapter 7, for instance, includes the most profound account of Leibniz’s theory of negation I ever read. Chapter 8 presents in a very clear way Leibniz’s attempt to reduce traditional syllogistic to a calculus based on logical inclusion between terms. Chapter 14 is devoted to Leibniz’s a priori proof of the existence of God and presents the first edition of an important manuscript on the proof. On chapters 3 and 5 a series of convincing reasons are given to argue that Leibniz’s concept of ens does not have to be considered a constant in the logical calculus. In brief: this work discusses a wide range of topics in such a clear and learned way that it will surely become a reference book for scholars interested in the study of Leibniz’s logical papers in the forthcoming years. (shrink)

I examine the question why in Proclus' view genetic processes provide demonstrative explanations, in light of the interpretation of Aristotle's theory of demonstration in late antiquity. I show that in this interpretation mathematics is not an explanatory science in the strict sense because its objects, being immaterial, do not admit causal explanation. Placing Proclus' account of demonstrative explanation in this context, I argue that this account is aimed at answering the question whether mathematical proofs provide causal explanation as opposed to (...) grounds. I show further that Proclus can answer this question in the affirmative due to his realist view of mathematical objects and the priority he ascribes to causal relations over logical relations. (shrink)

SYMBOLIC LOGIC. CHAPTER I. ON THE FORMS OF LOGICAL PROPOSITION. IT has been mentioned in the Introduction that the System of Logic which this work is ...

This book is a collection of essays published by the author in the long run of about 20 years and is centered on the reconstruction of Leibniz’s logical calculi. All the essays have been revised for the present edition and some of them constituted the background for Lenzen’s first monograph on Leibniz’s logic. A feature common to all these essays is the vindication of the relevance and originality of Leibniz’s logical achievements. Lenzen manifests strong dissatisfaction with the evaluations of Leibniz’s (...) logic previously offered by interpreters like Louis Couturat, Clarence I. Lewis, Karl Dürr, William and Martha Kneale, and states that till now Leibniz’s results in the field of logic have been widely underestimated. The book contains a careful and detailed examination of almost all Leibniz’s papers on the logical calculus and it is based on the knowledge of a wide range of texts unknown to previous interpreters. Lenzen’s acquaintance with the entire corpus of Leibniz’s logical texts is impressive. Some chapters of the book in particular contain very solid and useful logical analyses. Chapter 7, for instance, includes the most profound account of Leibniz’s theory of negation I ever read. Chapter 8 presents in a very clear way Leibniz’s attempt to reduce traditional syllogistic to a calculus based on logical inclusion between terms. Chapter 14 is devoted to Leibniz’s a priori proof of the existence of God and presents the first edition of an important manuscript on the proof. On chapters 3 and 5 a series of convincing reasons are given to argue that Leibniz’s concept of ens does not have to be considered a constant in the logical calculus. In brief: this work discusses a wide range of topics in such a clear and learned way that it will surely become a reference book for scholars interested in the study of Leibniz’s logical papers in the forthcoming years. (shrink)

Truth, etc. is a wide-ranging study of ancient logic based upon the John Locke lectures given by the eminent philosopher Jonathan Barnes in Oxford. The book presupposes no knowledge of logic and no skill in ancient languages: all ancient texts are cited in English translation; and logical symbols and logical jargon are avoided so far as possible. Anyone interested in ancient philosophy, or in logic and its history, will find much to learn and enjoy here.

This scarce antiquarian book is a facsimile reprint of the original. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions that are true to the original work.

The work of joachim jungius on the logic of relations was not as original as some authors have thought, But he did make it clear that relational inferences should be distinguished from categorical inferences; and he was the first to recognize the argument 'a rectis ad obliqua', An example of which is 'all circles are figures, Therefore whoever draws a circle draws a figure'.

This paper offers a reconstruction of Alessandro Piccolomini's philosophy of mathematics, and reconstructs the role of Themistius and Averroes in the Renaissance debate on Aristotle's theory of proof. It also describes the interpretative context within which Piccolomini was working in order to show that he was not an isolated figure, but rather that he was fully involved in the debate on mathematics and physics of Italian Aristotelians of his time. The ideas of Lodovico Boccadiferro and Sperone Speroni will be analysed. (...) This paper demonstrates that Piccolomini's attack on the certitude of mathematics was a product of discussions between Aristotelians. (shrink)