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- Richard Arthur, The Enigma of Leibniz's Atomism.Reminiscing about his early views on the continuum problem in a dialogue penned in 1689,2 Leibniz recalled the period in his youth when he had enthusiastically subscribed to the "New Philosophy", embracing the composition of the continuum out of points and the doctrine that “a slower motion is one interrupted by small intervals of rest.”3 Speaking of himself through the character Lubinianus, he continues: And I indulged other dogmas of this kind, to which people are prone when they are willing to entertain every imagination, and do not notice the infinity lurking everywhere in things. But although when I became a geometer I relinquished these opinions, atoms and the vacuum held out for a long time, like certain relics in my mind rebelling against the idea of infinity; for even though I conceded that every continuum could be divided to infinity in thought, I still did not grasp that in reality there were parts in things exceeding every number, as a consequence of motion in a plenum. That “atoms and the vacuum held out for a long time” among Leibniz’s cherished views is readily confirmed by an examination of his manuscripts. One may find papers containing some measure of commitment to atomism intermittently throughout the period from 1666 to 1676; moreover, if his later memory is to be trusted, he first “gave himself over to” atomism as early as 1661.4 As for his reasons for rejecting atoms, Leibniz’s mature..
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Between 1701 and 1705 Leibniz focused on the task of securing theological reunion between Lutherans and Calvinists, the two major Protestant sects at the time. Doing so, he believed, required reconciliation on two key topics, namely, the doctrine of the Eucharist, and the doctrine of election. To bring unity on the second issue, Leibniz composed a lengthy treatise based on a commentary on the Thirty-nine articles of the Church of England. This treatise stakes out a position springing from Leibniz’s own views. In this essay, I examine the views Leibniz defends in this treatise. I show that Leibniz’s views are much friendlier to the Arminian perspective than to the Calvinist one. I also show that this result is surprising since Arminian views seem incompatible with views on freedom and the problem of evil standardly attributed to Leibniz. This lack of fit should compel a re-examination of these standard attributions.
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| | Scholar | At my library | More options ... Toward the end of 1676 Leibniz met Spinoza a number of times. In one of those meetings Leibniz presented a proof of the possibility of God's existence. In his proof Leibniz presupposed that a proposition is necessarily true only if its truth is either demonstrable or self-evident and that the divine perfections are simple and affirmative qualities. I contend that Leibniz's presuppositions undermine, rather than establish, the necessary existence of 'a God of the kind in whom the pious believe'. My assessment is based upon a consideration of Leibniz's argument in the context of other early papers, works written before the "Discourse on Metaphysics" in 1686.
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| | Scholar | At my library | More options ... Although scholars have often settled upon 1686 as the year in which the central elements of Leibniz’s philosophy first appear in systematic form, certain of his positions appear to have been firmly in place at least ten years earlier. Papers written in 1676 reveal that Leibniz had already by that time established the fundamental feature of his single-substance metaphysics: the insubstantiality of matter. As he defines it, matter is a mode, but a mode of peculiar status, a sort of “top mode,” which, together with change, is requisite to the existence of any other modes, or “things.” Things for Leibniz include all bodies and their qualities, and in some places also appear to include minds, although Leibniz for religious reasons equivocates here, and wants to resist. Nevertheless, Leibniz’s desire to move toward a version of the Aristotelian notion of matter as the principle of individuation is clearly in evidence as he works to set out a view which can accommodate mechanistic physics while avoiding the perceived atheistic threat inherent in both Cartesian dualism and Spinozistic monism.
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| | Scholar | At my library | More options ... In this paper we argue for the robustness of Leibniz's commitment to the reality (but not substantiality) of body. We claim that a number of his most important metaphysical doctrines — among them, psychophysical parallelism, the harmony between efficient and final causes, the connection of all things, and the argument for the plurality of substances stemming from his solution to the continuum problem— make no sense if he is interpreted as giving an eliminative reduction of bodies to perceptions.
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| | Scholar | More options ... I elaborate and defend an interpretation of Leibniz on which he is committed to a stronger space-time structure than so-called Leibnizian space-time, with absolute speeds grounded in his concept of force rather than in substantival space and time. I argue that this interpretation is well-motivated by Leibniz's mature writings, that it renders his views on space, time, motion, and force consistent with his metaphysics, and that it makes better sense of his replies to Clarke than does the standard interpretation. Further, it illuminates the way in which Leibniz took his physics to be grounded in his metaphysics.
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| | Other links: journals.uchicago.edu dx.doi.org | Scholar | At my library | More options ... In the texts of the middle years (roughly, the 1680s and 90s), Leibniz appears to endorse two incompatible approaches to motion, one a realist approach, the other a phenomenalist approach. I argue that once we attend to certain nuances in his account we can see that in fact he has only one, coherent approach to motion during this period. I conclude by considering whether the view of motion I want to impute to Leibniz during his middle years ranks as a kind of realism or rather as some kind of phenomenalism or idealism.
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| | Scholar | At my library | More options ... The article presents Leibniz's preoccupation (in 1675?6) with the difference between the notion of infinite number, which he regards as impossible, and that of the infinite being, which he regards as possible. I call this issue ?Leibniz's Problem? and examine Spinoza's solution to a similar problem that arises in the context of his philosophy. ?Spinoza's solution? is expounded in his letter on the infinite (Ep.12), which Leibniz read and annotated in April 1676. The gist of Spinoza's solution is to distinguish between three kinds of infinity and, in particular, between one that applies to substance, and one that applies to numbers, seen as auxiliaries of the imagination. The rest of the paper examines the extent to which Spinoza's solution solves Leibniz's problem. The main thesis I advance is that, when Spinoza and Leibniz say that the divine substance is infinite, in most contexts it is to be understood in non-numerical and non-quantitative terms. Instead, for Spinoza and Leibniz, a substance is said to be infinite in a qualitative sense stressing that it is complete, perfect and indivisible. I argue that this approach solves one strand of Leibniz's problem and leaves another unsolved.
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| | Other links: dx.doi.org | Scholar | At my library | More options ... Llull and Leibniz both subscribed to conceptual atomism, the belief that the majority of concepts are compounds constructed from a relatively small number of primitive concepts. Llull worked out techniques for finding the logically possible combinations of his primitives, but Leibniz criticized Llull’s execution of these techniques. This article argues that Leibniz was right about things being more complicated than Llull thought but that he was wrong about the details. The paper attempts to correct these details.
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| | Scholar | At my library | More options ... Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings.
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| | Scholar | More options ... In this paper I attempt to trace the development of Gottfried Leibniz’s early thought on the status of the actually infinitely small in relation to the continuum. I argue that before he arrived at his mature interpretation of infinitesimals as fictions, he had advocated their existence as actually existing entities in the continuum. From among his early attempts on the continuum problem I distinguish four distinct phases in his interpretation of infinitesimals: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no gaps between them; (iii) (1672-75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus); (iv) (1676 onward) infinitesimals are fictitious entities, which may be used as compendia loquendi to abbreviate mathematical reasonings; they are justifiable in terms of finite quantities taken as arbitrarily small, in such a way that the resulting error is smaller than any pre-assigned margin. Thus according to this analysis Leibniz arrived at his interpretation of infinitesimals as fictions already in 1676, and not in the 1700's in response to the controversy between Nieuwentijt and Varignon, as is often believed.
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| | Scholar | More options ... Discussion of Richard Arthur, The enigma of Leibniz's atomism
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