Ohad Nachtomy

This paper explores the philosophical transitions in the relations between existence and possibility in Leibniz and Kant. It begins with Leibniz’s formulation of a strictly logical notion of possibility; proceeds with Kant’s pre-critical statement in 1763 that existence is not a predicate; and ends with the _Critique of Pure Reason_ in which the theory of possibility is constrained by the subjective conditions of experience (to supply the material for thinking possibilities) and is thus relativized to the human mind. I present Leibniz’s view of possibility against the traditional view of temporal modalities; and, in this light, his dual notion of existence. I then argue that, in Kant’s pre-critical essay of 1763, the view that existence is not a predicate is strongly related to the logical view of possibility advanced by Leibniz. I conclude with Kant’s transition to the critical period and its implications on the analysis of modality.

This chapter examines Leibniz’s comment on fragment 22 of Pascal’s _Pensées_ in the Port-Royal Edition (currently Lafuma 199). Leibniz responds to Pascal’s employment of the infinitely large and infinitely small and to the way he uses infinity to describe living beings through the example of a mite (_ciron_). In contrast, Leibniz employs the image of a living mirror (_miroir vivant_). The chapter argues that, despite superficial similarities, Leibniz’s use of infinity to define living beings stands in stark contrast to Pascal’s use of infinity, in that it stresses unity and harmony rather than divisibility and disparity. Leibniz’s use of infinity through the notion of a living mirror suggests that each individual forms an integral part of a well-connected and harmonious system. Whereas Pascal uses infinity to highlight our alienation and incomprehension of the world, for Leibniz infinity serves as a mark of unity, connectedness, and belonging.

Leibniz’s theory of organic _emboîtement i_s well known, but seldom analyzed in detail. The model of embodiment Leibniz deploys is not a material one, not the kind of physical _emboîtement_ that we find exemplified in Russian dolls, which are physically encapsulated one within the other, or the view of living things as subtle machines advanced by Descartes. This paper will examine several models of embodiment: physical, logical, expressive/representative, as well as a model of functional organization. I will conclude that the latter captures most adequately the Leibnizian view of a living being as a nested individual and the kind of embodiment it involves. What makes all these nested individuals components of a single individual is that they all follow one dominant program of action which may be seen as composed of many subprograms. But they all serve a single end (telos) that informs the developmental program of an individual.

In this article, I argue that Leibniz connects the notion of infinity and life so that, after the New System of Nature, infinity figures as a mark of living beings. I examine Leibniz’s sources for this view, arguing that it is best seen as a synthesis of mathematical, empirical, theological, and metaphysical sources. I then focus on the metaphysical source, examining the connection between infinity, perfection, and being in some detail. My conclusion is that Leibniz defines living beings as infinite in a qualified (graded) sense, so that they are infinite in kind, that is, infinite in some ways but limited in others, and that their infinity is distinct from the absolute infinity (and perfection) of God, on the one hand, and the mere infinity of mathematical things, on the other.

This paper examines Spinoza's complex treatment of wonder (admiratio) in relation to his broader philosophical project. While Descartes valorised wonder as a starting point for inquiry, Spinoza critiques it as a cognitive distraction that impedes adequate understanding. This paper shows that Spinoza's reconfiguration of wonder exemplifies his strategy of reinterpreting traditional concepts within a naturalistic framework. By positioning wonder as a byproduct of ignorance and a tool exploited by religious and political authorities, Spinoza critiques Cartesian dualism, theological dogma and the manipulation of human affectivity. Ultimately, this paper demonstrates that Spinoza's nuanced view of wonder is essential for understanding his alternative model of human flourishing, grounded in reason, self‐determination and the intellectual love of God. Spinoza's analysis remains relevant to contemporary debates about secularism, scientific understanding and the human need for meaning.

abstract: Throughout his career, Leibniz defines individual substances in different ways. In the 1680s, especially in the Discourse on Metaphysics, Leibniz develops an original definition of substance through the complete concept of an individual (CCI). Most commentators hold that the CCI fades out in Leibniz's later philosophy. Others argue that the "law of the series" (LoS) replaces the definition of an individual substance through the CCI. We argue that these definitions are complementary. Early versions of the LoS inform the development of the CCI in the 1680s and are clearly pronounced in Leibniz's later texts. We discuss several often-neglected texts that show that the CCI is still present in Leibniz's late writings. We support the complementarity thesis by suggesting that the CCI primarily characterizes possible individuals, whereas the LoS characterizes actual individuals. As such, the LoS is especially apt to highlight the dynamic traits that Leibniz ascribes to individual substances from the 1690s.

At the present state of industrialized agriculture and specialized economy, achieving nutritional self-sufficiency on a personal level is widely considered a naïve goal, unsuited to the present technological era. Furthermore, nutritional self-sufficiency is considered overly demanding in terms of training, land, labor intensity, and time requirements. This study contests these common notions. Drawing on a study of a small (approximately 0.075 ha) low-input self-sufficient farm in an industrialized country, we show that achieving nutritional self-sufficiency on this farm required modest initial agricultural training, a small parcel of land, and, perhaps most surprisingly, a single day of labor per month, on average. We offer these results as proof of concept that, when properly planned, nutritional self-sufficiency may be sustained over an extended period (more than a decade) and that doing so may be compatible with working full-time outside the farm, as well as engaging in regular leisure activities. We also propose that some upscaling is viable at the industrial, small-scale, and household levels.

La communication qui suit porte sur le concept de relation tel que le définit Leibniz dans sa correspondance avec Arnauld. La première partie présente trois des présupposés impliqués dans ce concept, à savoir 1) qu'il y a des relations entre des individus possibles, 2) que ces relations sont nécessaires à la notion de mondes possibles et 3) qu'elles sont également nécessaires pour compléter l'individuation des individus possibles. Dans la deuxième partie, on verra que le premier présupposé semble entrer en conflit avec le nominalisme de Leibniz et son refus d'attribuer une réalité aux relations. Un problème de circularité entrave la résolution de ce conflit: d'une part, Leibniz considère en effet que les relations interindividuelles présupposent des individus, mais d'autre part, le troisième présupposé indique que de telles relations sont nécessaires à l'individuation même des individus possibles. Dans la troisième partie, on proposera une solution à ce problème de circularité au moyen du concept d'espace logique de possibilités. Dans cet espace logique, la place qu'occupe un individu est à la fois 1) constitutive de son concept et 2) une notion relationnelle. Grâce au concept de relation que propose Leibniz, les concepts d'individus et l'espace logique en viennent ainsi à se constituer mutuellement, ce qui ouvre une avenue hors de la circularité

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through Kant. Readers will learn about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic.

In her stimulating article, Catherine Wilson considers the moment of worlds-making in Leibniz’s philosophy. She raises the following question: “How do possible substances give rise to possible worlds?“ and observes that the moment of world-making is as puzzling as it is interesting. In section 2 of her article, Wilson considers two approaches to the question. According to the first, possible individuals logically precede possible worlds and possible worlds are constituted either by combinations of possible individuals or by mechanically checking the compossibility relations among them. This approach assumes that possible individuals are given and complete and that worlds result from their various conjunctions. On this approach, a world is a set of compossible individuals, i.e., a set of complete individuals whose co-existence is possible.

This work develops a Leibnizian approach to possibility by explicating the notions of possibility in general, in chapter 1; possible individuals in chapter 2; possible worlds in chapter 3; and actualization in chapter 4. ;A Leibnizian notion of possibility is characterized against the traditional view of an intelligible realm of thoughts in God's mind. It is understood in terms of self-consistent thoughts and is developed by explicating the notions of thought and of possibility in terms of the combinatorial structure common to both, that is, the construction of complex structures by progressive combinations of simple elements. According to this view, God mentally combines his simple forms, and complex concepts arise in his mind. Such complex and self-consistent concepts are deemed possible. ;Against this general view of possibility, a possible individual is identified with the combinatorial rule that produces a unique and maximally consistent structure of predicates. Such a rule is termed the "production rule" of the individual. The "production rule" unifies a series of predicates and constitutes the individual's logical subject and its principle of individuation. ;Given this view of a possible individual, the notion of a possible world is defined as a set of compossible individuals. It is argued that the compossiblity relation result from the consideration of two individuals in the same logical space. It is suggested that the inner structure of each individual entails its possible connections with other individuals, and that God's consideration of the individuals splits them into compossible sets or possible worlds. ;Finally, it is suggested that actualization involves endowing the "production rule" in God's mind with power of action. The union of a divine prescription of action with power of action yields an active and self-sufficient agent. Upon creation, the agent's activity generates the sequence of predicates prescribed to it by its production rule. ;The explication of the above notions accounts for the conceptual dependence of possible individuals and for the causal independence of created individuals--both of which are indispensable for Leibniz's notion of preestablished harmony.

This paper develops some important observations from a recent article by Maria Rosa Antognazza published in The Leibniz Review 2015 under the title “The Hypercategorematic Infinite”, from which I take up the characterization of God, the most perfect Being, as infinite in a hypercategorematic sense, i.e., as a being beyond any determination. By contrast, creatures are determinate beings, and are thus limited and particular expressions of the divine essence. But since Leibniz takes both God and creatures to be infinite, creatures are simultaneously infinite and limited. This leads to seeing creatures as infinite in kind, in distinction from the absolute and hypercategorematic infinity of God. I present three lines of argument to substantiate this point: (1) seeing creatures as entailing a particular sequence of perfections and imperfections; (2) seeing creatures under the rubric of an intermediate degree of infinity and perfection that Leibniz, in 1676, calls “maximum in kind”; and (3) observing that primitive force, a defining feature of created substance, may be seen as infinite in a metaphysical sense. This leads to viewing Leibniz’s use of infinity within a Neoplatonic framework of descending degrees of Being: from the hypercategorematic infinite, identified with the most perfect Being; to the intermediate degree of maximum in kind, identified with creatures; to the lowest degree of entia rationis (or beings of reason), identified with mathematical and abstract entities.

Während Leibniz' Vorstellung eines vollständigen Begriffs viel Beachtung fand, blieb die Frage seiner Begründung im Verstand Gottes eher unbeachtet. In diesem Aufsatz versuche ich auf diese Frage einzugehen, indem ich den Zeitraum (ungefähr 1672-1679), in dem Leibniz die Vorstellung eines vollständigen Begriffs als eine explizite Definition eines Individuums entwickelte, näher untersuche. Meine Darstellung über die Begründung des individuellen Begriffs im Verstand Gottes beinhaltet drei Thesen: (1) Leibniz sieht einen inneren Zusammenhang zwischen der Bildung einfacher Begriffe zu zusammengesetzten Begriffen und der Individuation von Begriffen, so daß die Zusammengesetztheit der Begriffe zu ihrer Individualität und Einzigartigkeit beiträgt. (2) Ein individueller Begriff sollte nicht als eine Menge von Prädikaten betrachtet werden, sondern vielmehr als eine einzigartige Struktur von Prädikaten, in der die Reihenfolge der Prädikate eine essentielle Rolle spielt. (3) Ein individueller Begriff sollte nicht nur mit einer einzigartigen Struktur in Verbindung gebracht werden, sondern auch mit einer kombinatorischen Regel, die eine solche einzigartige Struktur von Prädikaten im Verstand Gottes erzeugt

This paper examines the Leibnizian background to Kant's critique of the ontological argument. I present Kant's claim that existence is not a real predicate, already formulated in his pre-critical essay of 1673, as a generalization of Leibniz's reasoning regarding the existence of created things. The first section studies Leibniz's equivocations on the notion of existence and shows that he employs two distinct notions of existence ? one for God and another for created substances. The second section examines Kant's position in his early paper of 1763. My claim is that Kant's view of existence in 1763, namely that it is not a predicate, is strongly related to the logical notion of possibility, formulated by Leibniz and accepted by Kant

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

In this article we examine the “phenotype” concept in light of recent technological advances in Genome-Wide Association Studies . By observing the technology and its presuppositions, we put forward the thesis that at least in this case genotype and phenotype are effectively coidentifled one by means of the other. We suggest that the coidentiflcation of genotype-phenotype couples in expression-based GWAS also indicates a conceptual dependence, which we call “co-deñnition.” We note that viewing these terms as codeflned runs against possible expectations, viz., that genotypes and phenotypes could ultimately be expressed independently from one another. In addition, the co-definition of genotypes and phenotypes in this context emphasizes the correlative character of both genotypes and phenotypes in GWAS

In her stimulating article, Catherine Wilson considers the moment of worlds-making in Leibniz’s philosophy. She raises the following question: “How do possible substances give rise to possible worlds?“ and observes that the moment of world-making is as puzzling as it is interesting. In section 2 of her article, Wilson considers two approaches to the question. According to the first, possible individuals logically precede possible worlds and possible worlds are constituted either by combinations of possible individuals or by mechanically checking the compossibility relations among them. This approach assumes that possible individuals are given and complete and that worlds result from their various conjunctions. On this approach, a world is a set of compossible individuals, i.e., a set of complete individuals whose co-existence is possible.