On Oneness and Substance in Leibniz’s Middle Years

In some remarks from his later years, Leibniz connects Averroes's views on a unique active intellect with Spinoza's substance monism. The present article discusses the question of whether Averroes's notion of a unique active intellect could be understood as one of the sources of Leibniz's early substance monism. It will be argued that the early Leibniz was familiar with a variety of diverging interpretations of Averroes. Some of these ascribe individuation to a plurality of substantial forms and analyze the dependence of human intellectual activities on the active intellect in terms of 'assisting' causation. Other interpretations do imply versions of substance monism, either with respect to human minds or generally with respect to natural particulars. However, these versions of substance monism are compatible with versions of substance pluralism, either because a plurality of animal minds with activities of their own is acknowledged or because the notion of substance is regarded as an equivocal concept, corresponding to the different degrees in which created beings participate in the divine being. Considering the possible impact of these diverging interpretations on the early Leibniz will point towards the relevance of distinguishing the notions of substance as active being and of substance as independent being.

2010

British Journal for the History of Philosophy 22.2 (2014): 236-259

Leibniz claims that nature is actually infinite but rejects infinite number. Are his mathematical commitments out of step with his metaphysical ones? It is widely accepted that Leibniz has a viable response to this problem: there can be infinitely many created substances, but no infinite number of them. But there is a second problem that has not been satisfactorily resolved. It has been suggested that Leibniz’s argument against the world soul relies on his rejection of infinite number, and, as such, Leibniz cannot assert that any body has a soul without also accepting infinite number, since any body has infinitely many parts. Previous attempts to address this concern have misunderstood the character of Leibniz’s rejection of infinite number. I argue that Leibniz draws an important distinction between ‘wholes’ – collections of parts that can be thought of as a single thing – and ‘fictional wholes’ – collections of parts that cannot be thought of as a single thing, which allows us to make sense of his rejection of infinite number in a way that does not conflict either with his view that the world is actually infinite or that the bodies of substances have infinitely many parts.

The Review of Symbolic Logic, 2021

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the part-whole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals-as well as imaginary roots and other well-founded fictions-may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality.

PhD Thesis, 2015

3 This might not have been made explicit in the classical or early modern atomistic accounts, but it seems to be a consequence of the structure of atoms. As Bayle points out, "for every extension, no matter how small it may be, has a right and a left side, an upper and a lower side" (Pierre Bayle, Historical and Critical Dictionary. Selections, transl., with an introduction and notes by Richard H. Popkin (Indianapolis: Bobbs-Merrill, 1965), 360, i.e. 'Zeno', Note G). This seems even clearer in the case of Gassendi's atoms, which are not perfectly round, but have also hooks that allow them to interlock. But not only in classical theories of atomism does the reverse relation from indivisibles to simplicity not hold, it does neither for the young Leibniz, whose early attempts to account for the continuum at some point entail the claim that infinitesimals "and are characterized as lacking extension, but nonetheless containing parts having no distance from one another, what he calls "indistant" parts." (Richard T. W. Arthur, "Actual Infinitesimals in Leibniz's Early Thought," in The Philosophy of the Young Leibniz, ed. Mark Kulstad et al. (Suttgart: Franz Steiner Verlag, 2009), 12 [= Studia Leibnitiana Sonderhefte, Band 35.]) 8 The most extensive treatments of Leibniz's views concerning the continuum up to the 1680s can be found in the writings of Richard T. W. Arthur, especially his 'Introduction' to RA, and Philip Beeley's

Studia Leibnitiana, 2023

There are two axes of Leibniz's philosophy about bodies that are deeply intertwined, as this paper shows: the scientific investigation of bodies due to the application of mathematics to nature-Leibniz's mixed mathematics-and the issue of matter/bodies idealism. This intertwinement raises an issue: How did Leibniz frame the relationship between mathematics, natural sciences, and metaphysics? Due to the increasing application of mathematics to natural sciences, especially physics, philosophers of the early modern period used the reliability of mathematics to predict phenomena as the basis to infer the metaphysical outlook of nature. I argue that although Leibniz thought metaphysics must be scientifically informed and that mathematics is a valuable instrument to understand nature, metaphysics is more fundamental than mathematics and natural sciences. By highlighting the foundational relation between metaphysics and the sciences, this paper showcases an argument for the reality of bodies: the ideality of bodies, necessary for epistemic purposes, is not proof that they are not real.

The Leibniz Review

This paper won the 2022 Leibniz Society of North America Essay Competition. This paper deals with the metaphysics of the notion of quantity in the philosophy of Leibniz, and its aim is to defend the following bi-conditional: for any object x, x has a certain quantity if and only if x has a (metaphysical) limit or a bound. The direction from left to right is justified in §3, while in §4 I develop an argument to justify the direction from right to left. Since the bi-conditional links the metaphysical notion of limit to the mathematical notion of quantity (and I this way it links Leibniz’s metaphysics with his conception of Mathesis Universalis), it allows the use of metaphysics to clarify the features of his mathematical notion of quantity. This task is accomplished in §5 and §6. Finally, §7 discusses a possible objection.

International Philosophical Quarterly, 2006

A historically persistent way of reading Leibniz regards him as some kind of conceptualist. According to this interpretation, Leibniz was either an ontological con-ceptualist or an epistemological conceptualist. As an ontological conceptualist, Leibniz is taken to hold the view that there exist only concepts. As an epistemological conceptualist, he is seen as believing that we think only with concepts. I argue against both conceptual-ist renditions. I confront the ontological conceptualist view with Leibniz's metaphysics of creation. If the ontological conceptualist interpretation were right, then Leibniz could not invoke compossibility as a criterion of creation. But since he does invoke compossibility as a criterion of creation, the ontological conceptualist approach cannot be right. I confront the epistemological conceptualist interpretation with Leibniz's assertion of non-conceptual content. Since Leibniz acknowledges non-conceptual content at least when it comes to metaphysical knowledge, Leibniz could not have been an epistemological conceptualist either. So, Leibniz could not have been a conceptualist at all.

2020

Spinoza was not under the influence of Parmenides, but the Eleatic difficulties concerning the plurality of the mutable individual things must concern Spinoza deeply. For he, too, attempted to construct a monistic system.

Robert M. Adams claims that Leibniz's rehahilitation of the doctrine of incomplete entities is the most sustained etlort to integrate a theory of corporeal substances into the theory of simple substances. I discuss alternative interpretations of the theory of incomplete entities suggested by Marleen Rozemond and Pauline Phemister. Against Rozemond, I argue that the scholastic doctrine of incomplete entities is not dependent on a hylnmorphic analysis of corporeal suhstances, and therefore can be adapted by Leibniz. Against Phemister, I claim that Leibniz did not reduce the passivity of corporeal substances to modifications of passive aspects of simple substances. Against Adams, I argue that Leibniz's theory of the incompleteness of the mind cannot be understood adequately without understanding the reasons for his assertion that matter is incomplete without minds. Composite substances are seen as requisites for the reality of the material world, and therefore cannot be eliminated from Leibniz's metaphysics. P or Leibniz, a simple substance such as a soul or a mind is a "complete being" in the sense that it is the origin of its own actions, and that it represents in a confused way all its previous states.] Indeed, what could be more complete than a simple substance with its causal independence and autonomy in the production of its own states'! Nevel1heless, in the Addition a l' Explication du systeme nouveau (1698), written as a response to an extended review of the first edition of Fran~ois Lamy's De la C0l10iSSallce de soi-mcme," Leibniz embraces the Scholastic view that soul and body, in some sense, are incomplete entities. 3 Although the passages in which Leibniz takes up this thought in subsequent years are not very numerous, Robet1 M. Adams has suggested that it most fully expresses Leibniz's attempt to integrate a Scholastic theory of corporeal substance into his philosophy.4 Marleen Rozemond and Pauline Phemister have proposed interpretations that diverge markedly from Adams'. Rozemond objtcts that Leibniz cannot reproduce basic features of the Scholastic view within the framework of his own metaphysics. According to her interpretation, it is essential for the Scholastic theory that mind and body are related to each other as matter and form, which supplement each other as act and potency -a structure that the relations of mutual representation

P Lodge and T Stoneham eds. Locke and Leibniz on Substance (Routledge), 2015