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  1. Before and Beyond Leibniz: Tschirnhaus and Wolff on Experience and Method.Corey W. Dyck - manuscript
    In this chapter, I consider the largely overlooked influence of E. W. von Tschirnhaus' treatise on method, the Medicina mentis, on Wolff's early philosophical project (in both its conception and execution). As I argue, part of Tschirnhaus' importance for Wolff lies in the use he makes of principles gained from experience as a foundation for the scientific enterprise in the context of his broader philosophical rationalism. I will show that this lesson from Tschirnhaus runs through Wolff's earliest philosophical discussions, and (...)
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  2. Leibniz's and Kant's Philosophical Ideas Vs. Hilbert's Program.Roman Murawski - unknown - Poznan Studies in the Philosophy of the Sciences and the Humanities 98:29-39.
  3. Are Infinite Explanations Self-Explanatory?Alexandre Billon - forthcoming - Erkenntnis:1-20.
    Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian “infinite book copies” (...)
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  4. Requisite Theory in Leibniz= Teoría de Los Requisitos En Leibniz.Julian Velarde Lombrana - forthcoming - Teorema: International Journal of Philosophy.
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  5. Leibniz’s Binary Algebra and its Role in the Expression and Classification of Numbers.Mattia Brancato - 2021 - Philosophia Scientiae 25:71-94.
    Leibniz’s binary numeral system is generally studied for its arithmetical relevance, but the analysis of several unpublished manuscripts shows that from the very beginning Leibniz also envisaged a new form of algebra in the context of dyadics based on the idea that its letters can only express numbers that are either 1 or 0. In this paper, I shall present the most notable results of this binary algebra: the determination of the algorithm for the expansion of squares and the development (...)
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  6. Leibniz’s Binary Algebra and its Role in the Expression and Classification of Numbers.Mattia Brancato - 2021 - Philosophia Scientae 25:71-94.
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  7. ¿Qué es una ficción en matemáticas? Leibniz y los infinitesimales como ficciones.Oscar Miguel Esquisabel - 2021 - Logos. Anales Del Seminario de Metafísica [Universidad Complutense de Madrid, España] 54 (2):279-295.
    El objetivo de este trabajo es examinar el concepto leibniziano de ficción matemática, con especial énfasis en la tesis de Leibniz acerca del carácter ficcional de las nociones infinitarias. Se propone en primer lugar, como marco general de la investigación, un conjunto de cinco condiciones que una ficción tiene que cumplir para ser matemáticamente admisible. Sobre la base de las concepciones de Leibniz acerca del conocimiento simbólico, se propone la ficción matemática como la clase de nociones confusas que carecen de (...)
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  8. Exposants et tangentes chez Leibniz à Paris, entre formes et géométrie.Arilès Remaki - 2021 - Philosophia Scientiae 25:95-132.
    L’œuvre mathématique de Leibniz a ceci d’intéressant qu’au travers des innombrables manuscrits de travail dont nous disposons dans ses archives à Hanovre, le philosophe nous a confié le matériel nécessaire pour rétablir ses divers cheminements de recherche ainsi que ses méthodes de découvertes à l’origine de ses créations mathématiques. L’exemple des exposants que nous allons traiter permet d’éclairer utilement la façon dont Leibniz apprend les mathématiques et change progressivement de posture et de démarche. Ainsi, dans sa première année parisienne, la (...)
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  9. Exposants Et Tangentes Chez Leibniz À Paris, Entre Formes Et géométrieExponents and Tangents in Leibniz’s Work in Paris.Arilès Remaki - 2021 - Philosophia Scientae 25:95-132.
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  10. Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology, Ed. Vincenzo De Risi.Laurynas Adomaitis - 2020 - The Leibniz Review 30:163-171.
  11. Leibniz: Dissertation on Combinatorial Art. Translated with Introduction and Commentary by Massimo Mugnai, Han van Ruler, and Martin Wilson.Richard T. W. Arthur - 2020 - The Leibniz Review 30:141-145.
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  12. Dissertation on Combinatorial Art.G. W. Leibniz - 2020 - Oxford: Oxford University Press.
  13. Continuity, Containment, and Coincidence: Leibniz in the History of the Exact Sciences: Vincenzo De Risi (Ed.): Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, and Epistemology. Dordrecht: Springer, 2019, 298pp, 103.99€ HB.Christopher P. Noble - 2020 - Metascience 29 (3):523-526.
  14. Equivalence of Hypotheses and Galilean Censure in Leibniz: A Conspiracy or a Way to Moderate Censure?Laurynas Adomaitis - 2019 - Revue d'Histoire des Sciences 72 (1):63-85.
    Spending six months in Rome in 1689 Gottfried Wilhelm Leibniz (1646–1716) occupied himself with the question of Copernican and Galilean censure. An established reading of the Rome papers suggests that Leibniz’s attempt to have the Copernican censure lifted was derived solely from the equivalence of hypotheses stemming from the relativity of motion; and involved Leibniz’s compromising his belief in the truth of the Copernican hypothesis by arguing that it should only be interpreted instrumentally; and that Leibniz believed in the unrestricted (...)
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  15. The Idea of Continuity as Mathematical-Philosophical Invariant.Eldar Amirov - 2019 - “Metafizika” Journal 2 (8):p. 87-100.
    The concept of ‘ideas’ plays central role in philosophy. The genesis of the idea of continuity and its essential role in intellectual history have been analyzed in this research. The main question of this research is how the idea of continuity came to the human cognitive system. In this context, we analyzed the epistemological function of this idea. In intellectual history, the idea of continuity was first introduced by Leibniz. After him, this idea, as a paradigm, formed the base of (...)
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  16. Leibniz and the Structure of Sciences: Modern Perspectives on the History of Logic, Mathematics, Epistemology.Vincenzo De Risi (ed.) - 2019 - Springer.
    The book offers a collection of essays on various aspects of Leibniz’s scientific thought, written by historians of science and world-leading experts on Leibniz. The essays deal with a vast array of topics on the exact sciences: Leibniz’s logic, mereology, the notion of infinity and cardinality, the foundations of geometry, the theory of curves and differential geometry, and finally dynamics and general epistemology. Several chapters attempt a reading of Leibniz’s scientific works through modern mathematical tools, and compare Leibniz’s results in (...)
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  17. Principia Calculi Rationalis.Gottfried Wilhelm Leibniz & Wolfgang Lenzen - 2019 - The Leibniz Review 29:51-57.
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  18. Ex Nihilo Nihil Fit.Wolfgang Lenzen - 2019 - The Leibniz Review 29:59-81.
    In the essay “Principia Calculi rationalis” Leibniz attempts to prove the theory of the syllogism within his own logic of concepts. This task would be quite easy if one made unrestricted use of the fundamental laws discovered by Leibniz, e.g., in the “General Inquiries” of 1686. In the essays of August 1690, Leibniz had developed some similar proofs which, however, he considered as unsatisfactory because they presupposed the unproven law of contraposition: “If concept A contains concept B, then conversely Non-B (...)
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  19. Three Infinities in Early Modern Philosophy.Anat Schechtman - 2019 - Mind 128 (512):1117-1147.
    Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...)
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  20. Logic Through a Leibnizian Lens.Craig Warmke - 2019 - Philosophers' Imprint 19.
    Leibniz's conceptual containment theory says that singular propositions of the form a is F are true when the complete concept of being a contains the concept of being F. In this paper, I provide a new semantics for first-order logic built around this idea. The semantics resolves longstanding problems for Leibniz's theory and can represent, without possible worlds, both hyperintensional distinctions among properties and a certain kind of presumably impossible situation that standard approaches cannot represent. The semantics also captures the (...)
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  21. Leibniz’s Legacy and Impact.Julia Weckend & Lloyd Strickland (eds.) - 2019 - New York: Routledge.
    This volume tells the story of the legacy and impact of the great German polymath Gottfried Wilhelm Leibniz (1646-1716). Leibniz made significant contributions to many areas, including philosophy, mathematics, political and social theory, theology, and various sciences. The essays in this volume explores the effects of Leibniz’s profound insights on subsequent generations of thinkers by tracing the ways in which his ideas have been defended and developed in the three centuries since his death. Each of the 11 essays is concerned (...)
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  22. Syllogistic Expansion in the Leibnizian Reduction Scheme.Arman Besler - 2018 - Kilikya Felsefe Dergisi / Cilicia Journal of Philosophy 5 (2):1-16.
    The standard inferential scheme of traditional assertoric syllogistic, based on the initial chapters of Aristotle’s Prior Analytics, employs single-premissed deductions, i.e., principles of immediate inference, in the reduction of imperfect valid moods to perfect moods. G. W. Leibniz has attempted to replace this scheme with his own version of syllogistic reduction, in which the principles of immediate inference themselves are modelled as valid syllogisms. This paper examines the place of this modelling, i.e. syllogistic expansion, of immediate inferences in Leibniz’s scheme (...)
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  23. Leibniz y las matemáticas: Problemas en torno al cálculo infinitesimal / Leibniz on Mathematics: Problems Concerning Infinitesimal calculus.Alberto Luis López - 2018 - In Luis Antonio Velasco Guzmán & Víctor Manuel Hernández Márquez (eds.), Gottfried Wilhelm Leibniz: Las bases de la modernidad. México: Universidad Nacional Autónoma de México. pp. 31-62.
    El cálculo infinitesimal elaborado por Leibniz en la segunda mitad del siglo XVII tuvo, como era de esperarse, muchos adeptos pero también importantes críticos. Uno pensaría que cuatro siglos después de haber sido presentado éste, en las revistas, academias y sociedades de la época, habría ya poco qué decir sobre el mismo; sin embargo, cuando uno se acerca al cálculo de Leibniz –tal y como me sucedió hace tiempo– fácilmente puede percatarse de que el debate en torno al cálculo leibniziano (...)
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  24. Interpreting the Infinitesimal Mathematics of Leibniz and Euler.Jacques Bair, Piotr Błaszczyk, Robert Ely, Valérie Henry, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Semen S. Kutateladze, Thomas McGaffey, Patrick Reeder, David M. Schaps, David Sherry & Steven Shnider - 2017 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 48 (2):195-238.
    We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...)
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  25. Is Leibnizian Calculus Embeddable in First Order Logic?Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, Taras Kudryk, Thomas Mormann & David Sherry - 2017 - Foundations of Science 22 (4):73 - 88.
    To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...)
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  26. Leibniz in Paris: A Discussion Concerning the Infinite Number of All Units.Oscar M. Esquisabel & Federico Raffo Quintana - 2017 - Revista Portuguesa de Filosofia 73 (3-4):1319-1342.
    In this paper, we analyze the arguments that Leibniz develops against the concept of infinite number in his first Parisian text on the mathematics of the infinite, the Accessio ad arithmeticam infinitorum. With this goal, we approach this problem from two angles. The first, rather philosophical or axiomatic, argues against the number of all numbers appealing to a reductio ad absurdum, showing that the acceptance of the infinite number goes against the principle of the whole and the part, which is (...)
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  27. Content Analysis of the Demonstration of the Existence of God Proposed by Leibniz in 1666.Krystyna Krauze-Błachowicz - 2017 - Roczniki Filozoficzne 65 (2):57-75.
    Leibniz’s juvenile work De arte combinatoria of 1666 included the “Proof for the Existence of God.” This proof bears a mathematical character and is constructed in line with Euclid’s pattern. I attempted to logically formalize it in 1982. In this text, on the basis of then analysis and the contents of the proof, I seek to show what concept of substance Leibniz used on behalf of the proof. Besides, Leibnizian conception of the whole and part as well as Leibniz’s definitional (...)
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  28. Leibniz’s Ontological Proof of the Existence of God and the Problem of »Impossible Objects«.Wolfgang Lenzen - 2017 - Logica Universalis 11 (1):85-104.
    The core idea of the ontological proof is to show that the concept of existence is somehow contained in the concept of God, and that therefore God’s existence can be logically derived—without any further assumptions about the external world—from the very idea, or definition, of God. Now, G.W. Leibniz has argued repeatedly that the traditional versions of the ontological proof are not fully conclusive, because they rest on the tacit assumption that the concept of God is possible, i.e. free from (...)
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  29. Leibniz’s Theory of Propositional Terms.Marko Malink - 2017 - The Leibniz Review 27:139-155.
  30. Remarks on the Lucky Proof Problem.Marco Messeri - 2017 - The Leibniz Review 27:1-19.
    Several scholars have argued that Leibniz’s infinite analysis theory of contingency faces the Problem of Lucky Proof. This problem will be discussed here and a solution offered, trying to show that Leibniz’s proof-theory does not generate the alleged paradox. It will be stressed that only the opportunity to be proved by God, and not by us, is relevant to the issue of modality. At the heart of our proposal lies the claim that, on the one hand, Leibniz’s individual concepts are (...)
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  31. The Logic of Leibniz’s Generales Inquisitiones de Analysi Notionum Et Veritatum. [REVIEW]Massimo Mugnai - 2017 - The Leibniz Review 27:117-137.
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  32. Automating Leibniz’s Theory of Concepts.Indrasen Poola - 2017 - Stanford Encyclopedia of Philosophy 1.
    Our computational metaphysics group describes its use of au- tomated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of (...)
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  33. Necessity, a Leibnizian Thesis, and a Dialogical Semantics.Mohammad Shafiei - 2017 - South American Journal of Logic 3 (1):1-23.
    In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed.
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  34. Tercentenary Essays on the Philosophy & Science of G.W. Leibniz.L. Strickland, E. Vynckier & J. Weckend - 2017 - Palgrave-Macmillan.
    This book presents new research into key areas of the work of German philosopher and mathematician Gottfried Wilhelm Leibniz (1646-1716). Reflecting various aspects of Leibniz's thought, this book offers a collection of original research arranged into four separate themes: Science, Metaphysics, Epistemology, and Religion and Theology. With in-depth articles by experts such as Maria Rosa Antognazza, Nicholas Jolley, Agustín Echavarría, Richard Arthur and Paul Lodge, this book is an invaluable resource not only for readers just beginning to discover Leibniz, but (...)
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  35. Leibniz Versus Ishiguro: Closing a Quarter Century of Syncategoremania.Tiziana Bascelli, Piotr Błaszczyk, Vladimir Kanovei, Karin U. Katz, Mikhail G. Katz, David M. Schaps & David Sherry - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (1):117-147.
    Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...)
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  36. Leibniz E o Paradigma da Perspectiva.João F. N. Cortese - 2016 - Cadernos Espinosanos 34:137-162.
    No século XVII, vemos a emergência de uma nova abordagem geométrica às seções cônicas. Desenvolvida inicialmente por Girard Desargues e por Blaise Pascal, tal geometria é herdeira do método de representação pela perspectiva linear a aponta na direção da geometria projetiva do século XIX. Estudos recentes de J. Echeverría e de V. Debuiche iniciaram a discussão da recepção de tais trabalhos por Leibniz, assim como a relação deles com os trabalhos do próprio Leibniz em perspectiva e com a Geometria situs. (...)
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  37. Leibniz on the Parallel Postulate and the Foundations of Geometry: The Unpublished Manuscripts.Vincenzo De Risi - 2016 - New York/London: Birkhäuser.
    This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz’s work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the 17th-century studies on (...)
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  38. Leibniz’s Logic and the “Cube of Opposition”.Wolfgang Lenzen - 2016 - Logica Universalis 10 (2-3):171-189.
    After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz. Within Leibniz’s algebra of concepts, the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as ‘S contains P’ and ‘S contains Not-P’, ‘S doesn’t contain P’ and ‘S doesn’t contain Not-P’, respectively. Next we consider Leibniz’s version of the so-called Quantification of (...)
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  39. - G.W. Leibniz, "Obras filosóficas y científicas", vol. 5: "Lengua Universal, Característica y Lógica".Cabañas Leticia & Velarde Julián - 2016 - Granada: Comares.
    La conexión interna entre lengua universal, característica y cálculo (lógico) viene establecida por la unidad de un método lógico–epistemológico que comprende los varios sistemas característicos construidos por Leibniz como progresivas aproximaciones a la lengua universal, concebida como la lengua perfecta, cuyos caracteres expresan los requisitos de las cosas y mediante el análisis de esos caracteres podemos acceder al conocimiento de las mismas. La lengua característica posibilita la expresabilidad y la comunicabilidad de los pensamientos, de las nociones y de su combinación; (...)
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  40. Actual and Ideal Infinitesimals in Leibniz’s Specimen Dynamicum.Tzuchien Tho - 2016 - Journal of Early Modern Studies 5 (1):115-142.
    This article aims to treat the question of the reality of Leibniz’s infinitesimals from the perspective of their application in his account of corporeal motion. Rather than beginning with logical foundations or mathematical methodology, I analyze Leibniz’s use of an allegedly “instantiated” infinitesimal magnitude in his treatment of dead force in the Specimen Dynamicum. In this analysis I critique the interpretive strategy that uses the Leibnizian distinction, drawn from the often cited 1706 letter to De Volder, between actual and ideal (...)
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  41. Leibniz’s Actual Infinite in Relation to His Analysis of Matter.Richard T. W. Arthur - 2015 - In David Rabouin, Philip Beeley & Norma B. Goethe (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
  42. G.W. Leibniz, Interrelations Between Mathematics and Philosophy.Richard T. W. Arthur (ed.) - 2015 - Springer Verlag.
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  43. Leibniz, Philosopher Mathematician and Mathematical Philosopher.Philip Beeley - 2015 - In Norma B. Goethe, Philip Beeley & David Rabouin (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
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  44. The Interrelations Between Mathematics and Philosophy in Leibniz’s Thought.Norma B. Goethe, Philip Beeley & David Rabouin - 2015 - In Norma B. Goethe, Philip Beeley & David Rabouin (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
  45. Leibniz’s Mathematical and Philosophical Analysis of Time.Emily R. Grosholz - 2015 - In Norma B. Goethe, Philip Beeley & David Rabouin (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
  46. The Rhetor’s Dilemma: Leibniz’s Approach to an Ancient Case.Bettine Jankowski - 2015 - In Sandrine Chassagnard-Pinet, Patrice Canivez & Matthias Armgardt (eds.), Past and Present Interactions in Legal Reasoning and Logic. Springer Verlag.
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  47. Suspensive Condition and Dynamic Epistemic Logic: A Leibnizian Survey.Sébastien Magnier - 2015 - In Sandrine Chassagnard-Pinet, Patrice Canivez & Matthias Armgardt (eds.), Past and Present Interactions in Legal Reasoning and Logic. Springer Verlag.
  48. Automating Leibniz’s Theory of Concepts.Paul Edward Oppenheimer, Jesse Alama & Edward N. Zalta - 2015 - In Amy P. Felty & Aart Middeldorp (eds.), Automated Deduction – CADE 25: Proceedings of the 25th International Conference on Automated Deduction (Lecture Notes in Artificial Intelligence: Volume 9195), Berlin: Springer. Dordrecht: Springer. pp. 73-97.
    Our computational metaphysics group describes its use of automated reasoning tools to study Leibniz’s theory of concepts. We start with a reconstruction of Leibniz’s theory within the theory of abstract objects (henceforth ‘object theory’). Leibniz’s theory of concepts, under this reconstruction, has a non-modal algebra of concepts, a concept-containment theory of truth, and a modal metaphysics of complete individual concepts. We show how the object-theoretic reconstruction of these components of Leibniz’s theory can be represented for investigation by means of automated (...)
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  49. The Difficulty of Being Simple: On Some Interactions Between Mathematics and Philosophy in Leibniz’s Analysis of Notions.David Rabouin - 2015 - In Norma B. Goethe, Philip Beeley & David Rabouin (eds.), G.W. Leibniz, Interrelations Between Mathematics and Philosophy. Springer Verlag.
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  50. Leibniz’s Relational Conception of Number.Kyle Sereda - 2015 - The Leibniz Review 25:31-54.
    In this paper, I address a topic that has been mostly neglected in Leibniz scholarship: Leibniz’s conception of number. I argue that Leibniz thinks of numbers as a certain kind of relation, and that as such, numbers have a privileged place in his metaphysical system as entities that express a certain kind of possibility. Establishing the relational view requires reconciling two seemingly inconsistent definitions of number in Leibniz’s corpus; establishing where numbers fit in Leibniz’s ontology requires confronting a challenge from (...)
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