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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 (...) |
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In last year’s Review Gregory Brown took issue with Laurence Carlin’s interpretation of Leibniz’s argument as to why there could be no world soul. Carlin’s contention, in Brown’s words, is that Leibniz denies a soul to the world but not to bodies on the grounds that “while both the world and [an] aggregate of limited spatial extent are infinite in multitude, the former, but not the latter, is infinite in respect of magnitude and hence cannot be considered a whole”. Brown (...) |
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In this sequel to "The logic and meaning of plurals. Part I", I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the (...) |
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This is the second edition of an important introduction to Leibniz's philosophy of logic and language first published in 1972. It takes issue with several traditional interpretations of Leibniz (by Russell amongst others) while revealing how Leibniz's thought is related to issues of great interest in current logical theory. For this new edition, the author has added new chapters on infinitesimals and conditionals as well as taking account of reviews of the first edition. |
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By what process of development he came to this opinion, though in itself an important and interesting question, is logically irrelevant to the inquiry how far the opinion itself is correct ; and among his opinions, when these have been ascertained, it becomes desirable to prune away such as seem inconsistent with his main doctrines, before those doctrines themselves are subjected to a critical scrutiny. Philosophic truth and falsehood, in short, rather than historical fact, are what primarily demand our attention (...) |
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In notes from 1675-76 Leibniz is using the notion of an infinite number as an illustration of an impossible notion. In the same notes, he is also using this notion in contrast to the possibility of the ‘Ens perfectissumum’ (A.6.3 572; Pk 91; A.6.3 325). I suggest that Leibniz’s concern about the possibility of the notion of ‘the greatest or the most perfect being’ is partly motivated by his observation that similar notions, such as ‘the greatest number’, are impossible. This (...) |
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Mathematician and philosopher Hermann Weyl had our subject dead to rights. |
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This is a book review of Cantorian set theory and limitations of size by Michael Hallett. |
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Throughout his early writings, Leibniz was concerned with developing an acceptable account of God's relationship to the created world. In some of these early writings, he endorsed the idea that this relationship was similar to the human soul's relationship to the body. Though he eventually came to reject this idea, theanima mundi thesis remained the topic of several essays and correspondences during his career, culminating in the correspondence with Clarke. At first glance,Leibniz's discussions of this thesis may seem less important (...) |
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One argument that Leibniz employed to rule out the possibility of a world soul appears to turn on the assumption that the very notion of an infinite number or of an infinite whole is inconsistent. This argument was considered in a series of three papers published in The Leibniz Review: in the first, by Laurence Carlin, the argument was delineated and analyzed; in the second, by myself, the argument was criticized and rejected; in the third, by Richard Arthur, an attempt (...) |
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