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81. The Leibniz Review: Volume > 21
Richard T. W. Arthur Presupposition, Aggregation, and Leibniz’s Argument for a Plurality of Substances
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This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this depends on a generalized notion of aggregation, according to which a thing may be an aggregate of its constituents if every one of its actual parts presupposes such constituents, but is not composed from them. One of the premises of this argument is the reality of bodies. If this premise is denied, Leibniz’s argument for the infinitude of substances, and even of their plurality, cannot go through.
82. The Leibniz Review: Volume > 22
Adrian Nita Time as a Condition of Possibility: Reply to Michael Futch
83. The Leibniz Review: Volume > 22
Irena Backus The Mature Leibniz on Predestination
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This essay investigates how Leibniz and Daniel Ernst Jablonski handled the ironing out of intra-protestant religious differences, notably on predestination in the years ca. 1697-1702. I shall be focusing on the recently published union document between the Lutherans of Hanover and the Calvinists of Brandenburg, entitled the Unvorgreiffliches Bedencken (hereafter UB) and on the equally recently published and hitherto practically unknown Meditationes pacatae de praedestinatione et gratia, fato et libero arbitrio of 1701-ca. 1706 2. This is a series of Leibniz’s annotations on Jablonski’s Latin translation of article 17 (predestination) of the bishop of Salisbury, Gilbert Burnet’s Exposition of the 39 Articles of the Church of England. I shall try to show how the issue of predestination is handled in the UB by Leibniz and how his notes on the Meditationes complement and modify Jablonski’s Latin edition of the 17th article of Burnet’s Exposition the Thirty-Nine Articles of the Church of England. This will enable us to isolate the set of theological problems faced by the Lutheran and Calvinist participants in the negotium irenicum of 1697 -1702 and to point to the specific nature of the solutions proposed by Leibniz which were philosophical rather than theological. The underlying issue here is that of coexistence of philosophy and theology in Leibniz’s system. Indeed, one of the persistent questions about this philosopher concerns the exact relationship between his metaphysics (including physics and mathematics) and his theological views: which determined which? I hope to take the debate further here by analysing Leibniz’s contribution to the specifically theological issue of predestination, which, it will emerge, has direct bearing on Leibniz’s Essais de théodicée of 1710.
84. The Leibniz Review: Volume > 22
Giovanni Merlo Complexity, Existence and Infinite Analysis
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According to Leibniz’s infinite-analysis account of contingency, any derivative truth is contingent if and only if it does not admit of a finite proof. Following a tradition that goes back at least as far as Bertrand Russell, several interpreters have been tempted to explain this biconditional in terms of two other principles: first, that a derivative truth is contingent if and only if it contains infinitely complex concepts and, second, that a derivative truth contains infinitely complex concepts if and only if it does not admit of a finite proof. A consequence of this interpretation is that Leibniz’s infinite-analysis account of contingency falls prey to Robert Adams’s Problem of Lucky Proof. I will argue that this interpretation is mistaken and that, once it is properly understood how the idea of an infinite proof fits into Leibniz’s circle of modal notions, the problem of lucky proof simply disappears.
85. The Leibniz Review: Volume > 22
Gonzalo Rodriguez-Pereyra Leibniz’s Argument for the Identity of Indiscernibles in his Letter to Casati (with Transcription and Translation)
86. The Leibniz Review: Volume > 22
Samuel Levey On Unity, Borrowed Reality and Multitude in Leibniz
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In this paper I argue that what has been called Leibniz’s “aggregate argument” for unities in things in fact comprises three quite distinct lines of argument, with different concepts being advanced under the name ‘unity’ and meriting quite different conceptual treatment. Two of those arguments, what I call the Borrowed Reality Argument and the Multitude Argument, also appear in later writings to be further elaborated into arguments not just for unities but for simples. I consider the arguments in detail. I suggest that one of the two, the Borrowed Reality Argument, is philosophically more promising and has the stronger evidence for being central in Leibniz’s thought as he argues for the existence of simple substances.
87. The Leibniz Review: Volume > 22
Anne-Lise Rey Reply to Ohad Nachtomy
88. The Leibniz Review: Volume > 22
Daniel Garber Robert Merrihew Adams and Leibniz
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This essay reviews Robert Merrihew Adams’ approaches to the philosophy of Leibniz, both his general methodological approaches, and some of the main themes of his work. It attempts to assess his contribution both to the study of Leibniz and to the history of philosophy more generally.
89. The Leibniz Review: Volume > 22
Alison Peterman Spinoza on the “Principles of Natural Things”
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This essay considers Spinoza’s responses to two questions: what is responsible for the variety in the physical world and by what mechanism do finite bodies causally interact? I begin by elucidating Spinoza’s solution to the problem of variety by considering his comments on Cartesian physics in an epistolary exchange with Tschirnhaus late in Spinoza’s life. I go on to reconstruct Spinoza’s unique account of causation among finite bodies by considering Leibniz’s attack on the Spinozist explanation of variety. It turns out that Spinoza’s explanations of the variety of bodies, on the one hand, and of causation among finite bodies, on the other, generate a tension in his system that can only be resolved by taking Spinoza to employ two notions of “existence.” I conclude by offering evidence that this is in fact what Spinoza does.
90. The Leibniz Review: Volume > 24
Stephen Steward Solving the Lucky and Guaranteed Proof Problems
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Leibniz’s infinite-analysis theory of contingency says a truth is contingent if and only if it cannot be proved via analysis in finitely many steps. Some have argued that this theory faces the Problem of Lucky Proof—we might, by luck, complete our proof early in the analysis, and thus have a finite proof of a contingent truth—and the related Problem of Guaranteed Proof—even if we do not complete our proof early in the analysis, we are guaranteed to complete it in finitely many steps. I aim to solve both problems. For Leibniz, analysis is constrained by three rules: an analysis begins with the conclusion; subsequent steps replace a term by (part of) its real definition; and the analysis is finished only when an identity is reached. Furthermore, real definitions of complete concepts are infinitely complex, and Leibniz thinks infinities lack parts. From these observations, a solution to our problems follows: an analysis of a truth containing a complete concept cannot be completed in a finite number of steps—indeed, the first step of the analysis cannot be completed. I conclude by defusing some alleged counterexamples to my account.
91. The Leibniz Review: Volume > 24
Patrick Riley Leibniz’ “Monadologie” 1714-2014
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It is well-known that Leibniz ends and crowns the 1714 “Monadologie” with a version of his notion of jurisprudence universelle or “justice as the charity [love] of the wise:” for sections 83-90 of the Vienna manuscript claim that “the totality of all spirits must compose the City of God . . . this perfect government . . . the most perfect state that is possible . . . this truly universal monarchy [which is] a moral world in the natural world”—a moral world of iustitia in which “no good action would be unrewarded” for those “citizens” who “find pleasure . . . in the contemplation of [God’s] perfections, as is the way of genuine ‘pure love.’” But the opening four-fifths of the work offer Leibniz’ theory of “substance” (or monad) viewed as the necessary pre-condition of justice: for “on the knowledge of substance, and in the consequence of the soul, depends the knowledge of virtue and of justice” (to Pierre Coste, 1712). Thus without a complete and correct notion of substance/monad, no complete and correct notion commune de la justice would be conceivable. Hence the entire “Monadologie” can be understood as a theory of justice underpinned by a Grundlegung of moral “monads” or justice-loving rational “substances.” In this connection it is revelatory that Leibniz cites the relevant sections of the 1710 Théodicée in most of the 90 articles of the “Monadologie” (beginning indeed with article #1): for Théodicée (theos-dike) is (Leibniz says) “the justice of God,” and Leibniz makes that justice “appear” in the opening lines of the “Monadologie” (in effect) by referring the reader immediately to Théodicée #10 (“Preliminary Dissertation”) —which relates “im­mortal spirits” to a just God who is cherished through “genuine pure love.” This means that “the justice of God” as “higher love” colors the “Monadologie” instantly. Thus one need not “wait” for sections 83-90 to arrive in order for the “Monadologie” to be(come) a “theory of justice:” it is such ab initio.
92. The Leibniz Review: Volume > 24
Marine Picon Actualism and Analyticity: Leibniz's early thoughts towards a synthesis between Lutheran metaphysics and the foundation of knowledge
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Recent scholarship has established that, until the mid-1670s, Leibniz did not hold the possibilist ontology which, in his mature philosophy, provides the foundation for both his account of human freedom and of eternal truth. Concentrating on the Mainz period (1667-1672), this paper examines the conciliation, in those early writings, of an actualist ontology and a conception of necessary truth as analytical. The first section questions the view that Leibniz was educated in a “Platonist” tradition; the second section presents the actualist metaphysics that he adopted in the wake of his teachers; the third section shows how Leibniz could, contrary to those same teachers, hold an analytical view of eternal truth, even without the support of his later possibilist ontology and doctrine of real definitions.
93. The Leibniz Review: Volume > 24
Ohad Nachtomy, Tamar Levanon On Oneness and Substance in Leibniz’s Middle Years
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We argue in this paper that Leibniz’s characterization of a substance as “un être” in his correspondence with Arnauld stresses the per se unity of substance rather than oneness in number. We employ two central lines of reasoning. The first is a response to Mogens Lærke’s claim that one can mark the difference between Spinoza and Leibniz by observing that, while Spinoza’s notion of substance is essentially non-numerical, Leibniz’s view of substance is numerical. We argue that Leibniz, like Spinoza, qualifies the substance as “one” primarily in a non-numerical sense, where non-numerical means per se unity or qualitative uniqueness. The second line of reasoning suggests that the term “one” should be understood as a-unity-presupposed-by-multiplicity in two senses: a) externally, in the sense of being presupposed by higher complex structures, such as aggregates, and, b) internally, in the sense of having itself a complex structure. We develop an analogy along these lines between the role the notion of a fundamental unity plays in Leibniz’s view of numbers and his view of substance. In other words, we suggest that looking at the role units play in Leibniz’s view of mathematics can shed some light on the role they play in his metaphysics.
94. The Leibniz Review: Volume > 24
Richard T. W. Arthur Reply to Ohad Nachtomy
95. The Leibniz Review: Volume > 24
Philip Beeley Patrick Riley (1941–2015): Some reminiscences and reflections on his life
96. The Leibniz Review: Volume > 24
Patrick Riley In Honorem Irena Backus
97. The Leibniz Review: Volume > 3
Michael Latzer Leibniz’s Conception of Metaphysical Evil
98. The Leibniz Review: Volume > 4
Michael J. Murray Intellect, Will, and Freedom in Leibniz
99. The Leibniz Review: Volume > 4
Catherine Wilson Reply to Cover’s 1993 Review of Leibniz’s Metaphysics
100. The Leibniz Review: Volume > 4
Donald L.M. Baxter Corporeal Substances and True Unities