Redigee en 1666 a des fins universitaires (obtention d'un doctorat dans les deux Droits), la Disputatio De Casibus Perplexis in Jure de Leibniz aborde la question de l'ordonnancement juridique, a l'occasion d'une etude consacree aux enonces circulaires apparaissant dans le cadre des affranchissements, des legs et des suretes. Elle montre que leur suppression consiste a retablir un ordre de priorite chronologique ou normatif entre les termes en presence, par la maitrise des relations genre/espece et la formulation de regles justifiant (...) les exceptions. La hierarchie des normes et l'insertion des dispositions derogatoires dans un veritable jus commune, deviennent alors les pierres de touche d'une analyse encore actuelle, dont l'originalite tient au fait qu'elle applique les techniques d'interpretatio legis des Commentateurs du mos italicus, et parvient a les integrer dans une veritable organisation classificatrice du Droit conduisant directement a la codification. Le rationalisme juridique de cette Disputatio devient ainsi l'expression par excellence de trois siecles de doctrine consacres a l'argumentation topique et a la suppression des cas perplexes par l'introduction des circonstances dans l'evaluation des rapports sujet/predicat. (shrink)

This paper provides a semantic analysis of admissible rules and associated completeness conditions for arbitrary deductive systems, using the framework of abstract algebraic logic. Algebraizability is not assumed, so the meaning and significance of the principal notions vary with the level of the Leibniz hierarchy at which they are presented. As a case study of the resulting theory, the nonalgebraizable fragments of relevance logic are considered.

This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.

Mulla Sadra and Leibniz are two philosophers of the East and the West, and belong to two different worlds. Though they were unaware of ideas of each other, they share certain points that are comparable. Monads constitute the basis of Leibniz's thought and he refer to their features in his various works. Mulla Sadra's philosophy also is based on being and he tried to deal with its reality in his philosophy. Though Leibniz's monads are many and Mulla (...) Sadras being is one, they use certain terms for monads and being which are very close to each other and are comparable from different points of view. Leibniz monads while being many are one as well. Similarly Mulla Sadra's philosophy too enjoys multiplicity in unity. Leibniz's monads enjoy perception and Mulla Sadra's being too coexist withknowledge. In this paper apart from comparing Leibniz's monads and Mulla Sadra's concept of being, their philosophies also have been compared and their common and different points have been unraveled. (shrink)

A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be (...) determined by Leibniz conditions consisting of meet-prime logics only. (shrink)

There is a long line of thinkers in the philosophy of mathematics who have sought to base an account of proof on what might be called a 'metaphysical ordering' of the truths of mathematics. Use the term 'metaphysical' to describe these orderings is intended to call attention to the fact that they are regarded as objective and not subjective and that they are conceived primarily as orderings of truths and only secondarily as orderings of beliefs. -/- I describe and consider (...) two models for such orderings, (i) an implicational model and something I call (ii) a mosaic model. -/- Both models fail to do what such orderings should do. Moreover, in both cases, the trouble arises because the class of truths to be ordered is taken to be closed under various weakening implications. This is a result of their employing a global conception of logic. (shrink)

In abstract algebraic logic, the general study of propositional non-classical logics has been traditionally based on the abstraction of the Lindenbaum-Tarski process. In this process one considers the Leibniz relation of indiscernible formulae. Such approach has resulted in a classification of logics partly based on generalizations of equivalence connectives: the Leibniz hierarchy. This paper performs an analogous abstract study of non-classical logics based on the kind of generalized implication connectives they possess. It yields a new classification of (...) logics expanding Leibniz hierarchy: the hierarchy of implicational logics. In this framework the notion of implicational semilinear logic can be naturally introduced as a property of the implication, namely a logic L is an implicational semilinear logic iff it has an implication such that L is complete w.r.t. the matrices where the implication induces a linear order, a property which is typically satisfied by well-known systems of fuzzy logic. The hierarchy of implicational logics is then restricted to the semilinear case obtaining a classification of implicational semilinear logics that encompasses almost all the known examples of fuzzy logics and suggests new directions for research in the field. (shrink)

L'une des applications de la de Leibniz aboutit à la thèse que toutes les substances créées forment une hiérarchie continue selon leur degré de perfection. Des critiques ont soutenu que cette thèse est contradictoire à l'affirmation de Leibniz que les êtres rationnels, étant des images de la divinité et constituant ainsi une classe distincte d'êtres créés, sont plus près de la perfection que tous les autres. L'objection est que cette affirmation crée une lacune entre les êtres rationnels et (...) les êtres nonrationnels qu'aucune ordonnance continue en fonction de degré de perfection ne saurait combler. Dans la présente étude, je pose que la métaphysique de Leibniz satisfait les deux exigences: d'une part, l'exigence que tous les êtres peuvent être rangés en ligne continue selon leur degré de perfection, et d'autre part, l'exigence que les êtres rationnels constituent une classe à part parmi les êtres créés. (shrink)

Nach Leibniz ist der Schliissel zu metaphysischer Wahrheit Gottes ontologische und moralische Perfektion. In Übereinstimmung mit seiner unendlichen Güte erschafft Gott eine maximal perfekte Welt. Diese maximale Perfektion beinhaltet, daß alle Aspekte der Erschaffungen Gottes einem Gesetz der Kontinuität gehorchen – "die Natur macht keine Sprünge", und daher beinhaltet jeder Übergang Kontinuität. Die unendliche Güte Gottes beinhaltet auch unendliche Gerechtigkeit. Für Leibniz verlangt die Gerechtigkeit Gottes aber, daß die Kreaturen, die für ihre Handlungen verantwortlich sind, besonderer Art sein (...) müssen: sie wurden im Bilde Gottes erschaffen; das heißt, daß sie selbst rationale Schöpfer sind. Dies scheint einen grundsätzlichen Unterschied von alien anderen Kreaturen vorauszusetzen, was aber augenscheinlich einen Verstoß gegen das Gesetz der Kontinuität wäre. Die Autoren behandeln die Frage, ob Leibniz tatsächlich beide Prinzipien benutzt und ob – und wenn ja wie – er das folgegerecht tun kann. (shrink)

In this paper, I aim to offer a clear explanation of what monadic domination, understood as a relation obtaining exclusively among monads, amounts to in the philosophy of Leibniz (and this insofar as monadic domination is conceived by Leibniz not to account for the substantial unity of composite substances). Central to my account is the Aristotelian notion of a hierarchy of activities, as well as a particular understanding of the relations that obtain among the perceptions of monads (...) that stand in relations of monadic domination and subordination. (shrink)

In General Inquiries on the Analysis of Notions and Truths, Leibniz articulates for the first time his favourite solution to the problem of contingency and displays the main features of his logical calculus. Leibniz composed the work in 1686, the same year in which he began to correspond with Arnauld and wrote the Discourse on Metaphysics. General Inquiries supplements these contemporary entries in Leibniz's philosophical oeuvre and demonstrates the intimate connection that links Leibniz's philosophy with the (...) attempt to create a new kind of logic. This edition presents the text and translation of the General Inquiries along with an introduction and commentary. Given the composite structure of the text, where logic and metaphysics strongly intertwine, Mugnai's introduction falls into two sections, respectively dedicated to logic and metaphysics. The first section ('Logic') begins with a preliminary account of Leibniz's project for a universal characteristic and focuses on the relationships between rational grammar and logic, and discusses the general structure and the main ingredients of Leibniz's logical calculus. The second section ('Metaphysics') is centred on the problem of contingency, which occupied Leibniz until the end of his life. Mugnai provides an account of the problem, and details Leibniz's proposed solution, based on the concept of infinite analysis. (shrink)

Bringing together Leibniz's writings on God and religion for the very first time, Leibniz on God and Religion: A Reader reflects the growing importance now placed on Leibniz's philosophical theology. This reader features a wealth of material, from journal articles and book reviews published in Leibniz's lifetime to private notes and essays, as well as items from his correspondence. Organised thematically into the following sections, this reader captures the changes in Leibniz's thinking over the course (...) of his career: The Catholic Demonstrations The existence and nature of God Reason and faith Ethics and the love of God The Bible Miracles and mysteries The churches and their doctrines Grace and predestination Sin, evil, and theodicy The afterlife Non-Christian religions In preparing this reader, Strickland has returned to Leibniz's original manuscripts to ensure accurate translations of key texts, the majority of which have not been available in English before. The reader also contains a number of texts previously unpublished in any form. Alongside the translations, this reader contains an introductory essay, explanatory notes on all of the texts, and suggestions for further reading. This valuable sourcebook enables students of all levels to achieve a well-rounded understanding of Leibniz's philosophical theology. (shrink)

_The first unabridged English translation of the correspondence between Gottfried Wilhelm Leibniz and Georg Ernst Stahl detailing their opposing philosophies_ The correspondence between the eighteenth-century mathematician and philosopher G. W. Leibniz and G. E. Stahl, a chemist and physician at the court of King Friedrich Wilhelm I of Prussia, known as the Leibniz-Stahl Controversy, is one of the most important intellectual contributions on theoretical issues concerning pre-biological thinking. Editors François Duchesneau and Justin E. H. Smith offer readers (...) the first fully annotated English translation of this fascinating exchange of philosophical views on divine action, the order of nature, causality and teleology, and the soul-body relationship. (shrink)

In [14] we used the term finitely algebraizable for algebraizable logics in the sense of Blok and Pigozzi [2] and we introduced possibly infinitely algebraizable, for short, p.i.-algebraizable logics. In the present paper, we characterize the hierarchy of protoalgebraic, equivalential, finitely equivalential, p.i.-algebraizable, and finitely algebraizable logics by properties of the Leibniz operator. A Beth-style definability result yields that finitely equivalential and finitely algebraizable as well as equivalential and p.i.-algebraizable logics can be distinguished by injectivity of the (...) class='Hi'>Leibniz operator. Thus, from a characterization of equivalential logics we obtain a new short proof of the main result of [2] that a finitary logic is finitely algebraizable iff the Leibniz operator is injective and preserves unions of directed systems. It is generalized to nonfinitary logics. We characterize equivalential and, by adding injectivity, p.i.-algebraizable logics. (shrink)

The Discourse on Metaphysics is one of Leibniz's fundamental works. Written around January 1686, it is the most accomplished systematic expression of Leibniz's philosophy in the 1680s, the period in which Leibniz's philosophy reached maturity. Leibniz's goal in the Discourse is to give a metaphysics for Christianity; that is, to provide the answers that he believes Christians should give to the basic metaphysical questions. Why does the world exist? What is the world like? What kinds of (...) things exist? And what is the place of human beings in the world? To this purpose Leibniz discusses some of the most traditional topics of metaphysics, such as the nature of God, the purpose of God in creating the world, the nature of substance, the possibility of miracles, the nature of our knowledge, free will, and the justice behind salvation and damnation. This volume provides a new translation of the Discourse, complete with a critical introduction and a comprehensive philosophical commentary. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be (...) preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

About the text and translation -- The Monadology -- The structure of the Monadology -- The Monadology : text with running commentary -- Appendix: Theodicy -- The principles of nature and grace, founded on reason -- Leibniz to Nicole Remond : appendix on monads.

In den 90 Paragraphen der sogenannten Monadologie gibt Leibniz eine begriffliche Fassung und perspektivische Auslegung der Grundbegriffe seiner Metaphysik, die durch ihre Stringenz und deduktive Geschlossenheit die Position des Autors in der Philosophiegeschichte wesentlich bestimmt haben. Hier findet sich nicht nur eine ausführliche Diskussion seines 'Monade'-Begriffs, sondern auch die Verbindung zur 'prästabilierten Harmonie', in der die Gesetze des Körpers und der Seele zur Übereinstimmung kommen. Die neue, zweisprachige Ausgabe ist ausführlich kommentiert.

Leibniz's widely influential account of time provides a significant puzzle for those seeking to locate this account within his hierarchical ontology. Leibniz follows his scholastic predecessors in supposing that there are different grades of being, with substances being the most real and all other things possessing their reality via their relationships to substance. Following this picture, Leibniz suggests that phenomenal bodies only possess the being that they derive from the substances (i.e., monads) that ground them. Some would (...) argue that time likewise only possesses its being based on the bodies that it relates. Contrary to this suggestion (i.e., that time is twice removed from substances), I will argue that time is derived directly from rational souls. Thus, I will argue that time is on an ontological par with the phenomenal world of bodies. (shrink)

1. Reihe. Allgemeiner politischer und historischer Briefwechsel. v. <1-11, 13 >--2. Reihe. Philosophischer Briefwechsel. v. <1, 3 >--3. Reihe. Mathematischer naturwissenschaftlicher und technischer Briefwechsel --4. Reihe. Politische Schriften. v. <1-3 > --6. Reihe. Philosophische Schriften. v. <1-3, 6 >.

Betrachtungen über die Erkenntnis,die Wahrheit und die Ideen.--Übber die Verbesserung der ersten Philosophie und den Begriff der Substanz.--Neues System der Natur und der Verbindung der Substanzen sowie dier Vereinigung zwischen Seel und Körper.--Über den ersten Ursprung der Dinge.--Betrachtungen über die Lehre von einem einzigen allumfassenden Geiste.