In diesem Aufsatz wird das Problem der Inkompossibilität bei Leibniz diskutiert. Zwei mögliche Substanzen sind inkompossibel, wenn und nur wenn es nicht möglich ist, daß sie in einer gemeinsamen Welt existieren, d. h. es für Gott unmöglich ist, eine Welt zu erschaffen, in der beide Substanzen existieren. Der Begriff von Inkompossibilität ist nun jedoch aufgrund der völligen Unabhängigkeit der Substanzen voneinander in Gefahr, sich als gehaltlos zu erweisen. Unser Ausgangspunkt im Folgenden ist Hintikkas Analyse des Problems. Wir versuchen zu zeigen, (...) wie es für Leibniz möglich ist, in seiner Theorie der Individuation ohne Relationen auszukommen und sich auf sie dennoch zu stützen, um dem Begriff der Inkompossibilität Gehalt zu verleihen. Dazu bedienen wir uns auch der Ideen von Russell über die Quelle der Inkompossibilität bei Leibniz: Um ihre Herkunft aufzuspüren, müssen wir das Konzept von der Welt, welches Leibniz verwandt hat, noch beleuchten -unsere Lösung des Problems kann dann als eine Art Synthese der sogenannten analytischen und synthetischen Lösungen angesehen werden. (shrink)

In this paper I present a new approach to the so called ars obligatoria of the thirteenth and early fourteenth century. In standard medieval disputations an opponent attacks a thesis defended by the respondent. Some thirteenth-century authors distinguish two duties that the respondent has. First, he must grant whatever seems to be true. Second, he must grant whatever follows from what he has already granted. When the first duty is overridden by the specific duty to defend a false thesis (which (...) is the main requirement of ars obligatoria), the second duty becomes the logical duty of keeping the set of one's answers consistent. A natural result of this model is the development of a concept of possibility based on the syntactic concept of formally correct inference, and not on any semantic considerations. (shrink)

This paper discusses why speech regulations are logically necessary for any account of a moral right to free speech. My argument for limiting the right to free speech (and more widely any right to freedom) will be grounded in compossibility. Rights to freedom, formally speaking, are claims by an agent that other people not interfere with them; a compossible set of rights is one where the domains of permissible actions–permitted by each claim (and its correlative duty) within the set–do (...) not contradict one another across claims. I will argue that in order for claims to be coherent, they cannot generate contradictory domains, and that for a claim to non-interference to not generate contradictory domains across multiple people with the same claim, the claim must be restricted. This account as it currently stands can at least generate conclusions on the permissibility of incitement. (shrink)

We give a theory of epistemic modals in the framework of possibility semantics and axiomatize the corresponding logic, arguing that it aptly characterizes the ways in which reasoning with epistemic modals does, and does not, diverge from classical modal logic.

This thesis is a study of G.W. Leibniz’s views on compossibility. Leibniz calls substances that can be brought into existence together “compossible,” and he says that substances that cannot be brought into existence together are “incompossible.” Incompossibility and compossibility together divide substances into sets of individual substances that make up possible worlds. God then chooses from these possible worlds the best one to bring into existence. Thus without compossibility, the contingency of the world, and even God’s choice (...) could have no rational basis. It is on these grounds that Leibniz thought compossibility was the most powerful—and perhaps, only—defense against the position that the actual world is the only possible world. This is a position that was powerfully argued for by Benedict de Spinoza. For largely theological reasons Spinoza’s position was unacceptable to Leibniz. Since Leibniz’s own time thinkers have found it difficult to see why all the substances are not compossible with one another given certain other philosophical and theological claims Leibniz is committed to. This state of affairs has been exacerbated by the fact that Leibniz himself seems not to have been concerned with providing a clear answer to this conundrum. In an attempt to fill in this omission, and to justify Leibniz’s intuition philosophers have proposed varying accounts of compossibility. Unfortunately, all of these accounts fall short of upholding a comprehensive rational explanation of the world’s contingency based on the objective rational choice of God. My dissertation presents a picture that is multi-faceted in its sensitivity to Leibniz’s theological, physical and logical concerns while nevertheless harmonizing with other tenets of Leibniz’s overall philosophy. I seek to achieve this end by defending the view that compossibility is based on the logical properties of the complete concepts of substances understood as embedded within networks of mutual intelligibility. (shrink)

In this paper I defend the compossibility of presentism and time travel from two objections. One objection is that the presentist’s model of time leaves nowhere to travel to; the second objection attempts to equate presentist time travel with suicide. After targeting some misplaced scrutiny of the first objection, I show that presentists have the resources to account for the facts that make for time travel on the traditional Lewisian view. In light of this ability, I argue that both (...) of the objections fail. (shrink)

Leibniz's well-known thesis that the actual world is just one among many possible worlds relies on the claim that some possibles are incompossible , meaning that they cannot belong to the same world. Notwithstanding its central role in Leibniz's philosophy, commentators have disagreed about how to understand the compossibility relation. We examine several influential interpretations and demonstrate their shortcomings. We then sketch a new reading, the cosmological interpretation, and argue that it accommodates two key conditions that any successful interpretation (...) must satisfy. (shrink)

공가능성(compossibility) 개념은 라이프니츠 연구자들 사이에서 가장 활발하게 연구되고 있는 분야 중 하나이다. 이 논문에서 나는 우선 공가능성에 대한 영향력 있는 네 가지 해석들을 살펴보고 각 해석의 장단점을 지적한다. 더불어 나는 그동안 연구자들 사이에서 간과되었던 한 가지 문제를 지적한다. 공가능성에 대한 영향력 있는 해석들은 모두 명시적 혹은 암묵적으로 공가능성을 이행적(transitive)인 관계로 파악하고 있다. 그러나 나는 이 논문에서 라이프니츠가 공가능성을 비이행적인 관계로 이해하고 있음을 보임으로써, 공가능성에 대한 기존의 해석들에 대한 새로운 문제를 제기한다.

This collection brings together nine essays addressing the problem of compossibility in Leibniz's system of thought. The problem of compossibility is that of determining by what mechanism two independently possible substances are jointly possible, and thus do form part of the same possible world. The collection opens with an excellent introduction to the terrain, reviews established approaches to the problem, and will be extremely helpful to both those new to, and those familiar with, Leibniz.Adam Harmer's essay provides a (...) detailed analysis of the "world apart" doctrine, for which he considers three different interpretations: causal, ontological, and phenomenal, as well as weak and strong forms... (shrink)

Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem implies (...) that there can be no algorithm for producing optimal worlds, assuming an optimal world contains truth-discerning creatures, though this is not to say that such worlds cannot arise naturally. (shrink)

Leibniz entertained the idea that, as a set of “striving possibles” competes for existence, the largest and most perfect world comes into being. The paper proposes 8 criteria for a Leibniz-world. It argues that a) there is no algorithm e.g., one involving pairwise compossibility-testing that can produce even possible Leibniz-worlds; b) individual substances presuppose completed worlds; c) the uniqueness of the actual world is a matter of theological preference, not an outcome of the assembly-process; and d) Goedel’s theorem implies (...) that there can be no algorithm for producing optimal worlds, assuming an optimal world contains truth-discerning creatures, though this is not to say that such worlds cannot arise naturally. (shrink)

This volume brings together a number of original articles by leading Leibniz scholars to address the meaning and significance of Leibniz’s notions of compossibility and possible worlds. In order to avoid the conclusion that everything that exists is necessary, or that all possibles are actual, as Spinoza held, Leibniz argued that not all possible substances are compossible, that is, capable of coexisting. In Leibniz’s view, the compossibility relation divides all possible substances into disjoint sets, each of which constitutes (...) a possible world, or a way that God might have created things. For Leibniz, then, it is the compossibility relation that individuates possible worlds; and possible worlds form the objects of God’s choice, from among which he chooses the best for creation. Thus the notions of compossibility and possible worlds are of major significance for Leibniz’s metaphysics, his theodicy, and, ultimately, for his ethics. Given the fact, however, that none of the approaches to understanding Leibniz’s notions of compossibility and possible words suggested to date have gained universal acceptance, the goal of this book is to gather a body of new papers that explore ways of either refining previous interpretations in light of the objections that have been raised against them, or ways of framing new interpretations that will contribute to a fresh understanding of these key notions in Leibniz’s thought. (shrink)

Leibniz defends two apparently inconsistent doctrines. On the one hand, he holds that substances are independent entities and that God can, at least in principle, create any possible substance whatsoever no matter what else he creates. On the other hand, Leibniz insists that some possible substances are incompossible with one another and thus cannot coexist. I first discuss three attempts of dealing with this tension in Leibniz’s work that have recently been made in the literature: the logical approach, the lawful (...) approach, and McDonough’s tiling approach. I conclude that none of them solves the problem satisfactorily. I then argue that a modified version of the lawful approach, which also takes into account some of the insights of the two other options, is the most promising strategy. I believe that it is crucial to realize that it is, at least in principle, in God’s power to co-create incompossible substances. I do not take this to imply, however, that such substances can coexist. Since coexistence requires being in the same world, and because not all collections of possible substances are worlds in Leibniz’s sense, I argue that co-creation does not entail coexistence. Thus in order to get clear on Leibniz’s conception of compossibility, I suggest that we must better understand what a possible world is for Leibniz. What does it mean, then, for a collection of possible substances to form a world? I argue, first, that all complete concepts of the relevant possible substances need to have the same laws inscribed in them this is in line with some versions of the lawful approach). In addition, I argue that every complete concept in the relevant collection must also involve the concept of every other substance in the collection. Moreover, I maintain that these two requirements are not reducible to each other and that they are individually necessary and only jointly sufficient for a collection of substances to form a world. Only substances whose complete concepts fulfill both conditions can coexist and thus be compossible. (shrink)

Hillel Steiner argues that a necessary and sufficient condition for the compossibility of a set of rights is that those rights be extensionally differentiable. However, given that two or more actions can extensionally overlap without thereby being mutually unperformable, if such actions are specified in the relevant rights, then those rights will not be incompossible, notwithstanding their extensional overlap. The set of compossible sets of rights then is greater than the subset of extensionally differentiable rights, and extensional differentiability is (...) a sufficient but unnecessary condition of compossibility. (shrink)

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. (shrink)

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. (shrink)

Ohad Nachtomy restates the main points of “Plenitude and Compossibility” with admirable fidelity and economy. His proposed revisions, based on the distinction between incomplete and complete substances and on the mind-relativity of relations, are intriguing additions to his earlier paper in Studia Leibnitiana and deserve careful consideration. Some brief remarks on the context of the problem, will, I hope, help to set the stage for the assessment of our various views.

Leibniz maintains that even though God’s intellect contains all possibles, some of these possibles are not compossible. This incompossibility of some possibles is supposed to explain which collections of possibles are possible worlds and why God does not actualize the collection of all possibles. In order to fully understand how this works, we need to establish what precisely Leibniz takes to be the source of incompossibility, that is, which divine attribute or faculty gives rise to the incompossibility of certain possibles. (...) Different interpretations answer this question in different ways. This chapter explores the role that God’s faculties play on some of the standard interpretations of Leibniz’s notion of incompossibility and argues that we are faced with a dilemma: even though incompossibility must somehow arise from God’s faculties, none of the faculties usually distinguished seems up to the task. To escape this dilemma, we need to revise the traditional understanding of the divine faculties. More specifically, we need to recognize wisdom as an attribute that is distinct from intellect, power, and will and that is the source of incompossibility. (shrink)

Jonathan Edwards est considéré comme le premier philosophe original de l’Amérique. Sa pensée est à comprendre dans le contexte de la théologie calviniste dont elle interprète en métaphysique les thèmes principaux. A travers la notion de l’idée spirituelle, elle énonce une épistémologie où la relecture de la connaissance intellectuelle à partir des catégories esthétiques et éthiques conduit vers l’ébauche d’une noétique de la compossibilité. Quant à sa théorie de la volonté, à travers le refus de considérer toute détermination extérieure ou (...) antérieure, elle présente une homogénéité du volontaire, anticipant l’enseignement de Kant.Edwards is the first original philosopher of America. His thought is to be understood in the context of Protestant theology : he endeavours to give a metaphysical interpretation of the major principles of Calvinistic theology. Through the notion of the « spiritual idea », he is working out an epistemology where the reformulation of intellectual knowledge thanks to ethical and esthetical considerations, leads towards a theory of the compossibility. As far as his doctrine of the will is concerned, he is bracketing the very question of all external determination. He is thus led to expound the homogeneity of the voluntary sphere in anticipation of Kantean teaching. (shrink)

The article deals with the issue of public items (objects, processes, events) in the philosophy of Leibniz. Starting from the famous passage of the Monadology which illustrates his conception of the substance by the image of a city perceived from different perspectives, the author shows how Leibniz conceives the public character of certain items, i.e. the reality of the phenomena that express them, not only in disagreement with the causal model, according to which public items would be the causal source (...) of shared perceptions, but in disagreement even with the correspondence model, according to which shared perceptions would correspond to external objects. The key to understand the position of Leibniz is rather to look at his concept of the compossible, which makes it possible to explain the congruence between shared perceptions without having to resort to the concept of correspondence. (shrink)

Leibniz argues that God doesn't create everything possible because not all possible things are compossible, that is, compatible with each other. Much recent debate has focused on Leibniz's conception of compossibility. One important aspect of this debate, which has not been examined directly, is the distinction between possible worlds and possible creations: the notion of possible world is more robust than simply whatever God can create. Many commentators have relied on this distinction without a clear formulation of it. I (...) develop the distinction between possible worlds and possible creations by looking at how Leibniz characterizes what God is capable of creating. I argue that possible creations must be both logically consistent and determinate. Possible creations differ from possible worlds insofar as possible creations fail to be either maximal or harmonious. I conclude, therefore, that focusing on the notion of determinateness offers a new approach to answering the question why doesn't God create everything possible? (shrink)

Almost everyone agrees, under some interpretation, that a world is nomologically accessible if and only if it obeys the laws of the base world. This surface agreement, however, has led many to attach little importance to different interpretations, thereby conflating two distinct concepts of nomological accessibility. According to the Shared Law Account (hereafter SL), a target world is nomologically accessible from the base world if, and only if, all and only the laws of the base world are laws at the (...) target world. The Compossible Events Account (hereafiter CE) holds that a target world is nomologically accessible from the base world if, and only if, all events of the target world are compossible with the laws of the base world. After demonstrating that these accounts are distinct, I shall show that the distinction matters. Not only is the correct modal system for nomic necessity determined by which characterizes accessibility, but some arguments against Humean supenfenience depend upon SL. In the final section I show that CE is the correct interpretation. (shrink)

As is well known, Leibniz criticises Descartes for not having shown that God (considered as ens perfectissimum ) is possible, and tries to fill this gap by proving God’s possibility on the basis of absolutely positive and simple perfections. For many readers, however, these perfections have appeared problematic or unintelligible. In my paper, I primarily want to show, that they can be made comprehensible by working out their foundations in Plato’s theory of ideas. On this basis, I want to explain, (...) how this allows to understand the compossibility of perfections, essences or ideas (in the Leibnizian regio idearum ) and how such an understanding fits into his version of the ontological proof. For this purpose, the first part of my paper follows two closely related lines of investigation. On the one hand, I focus on Leibniz’s theory of ideas and try to explain in which way he combines his criticism of Descartes’s proof with a criticism of the Cartesian understanding of clear and distinct ideas. On the other hand, I discuss his transformation of Platonic ideas into essences leading from actually existing entities to real possibilities. In order to provide a foundation for this, I start with a glance at Descartes’s ontological proof and at his replies to Caterus and Mersenne concentrating on the problem of God’s possibility. The second part of my paper will work out Leibniz’s own version of the ontological proof and its Platonic background. (shrink)

Leibniz tries to prove God’s possibility on the basis of absolutely positive and simple perfections. I primarily want to show, how these controversial perfections can be made comprehensible by working out their foundations in Plato’s theory of ideas. After having concentrated on the Cartesian proof and Leibniz’s criticism in the first part of my paper, I now focus on his own version of the proof and its Platonic background. First, I discuss the structure, the advantages and disadvantages of the famous (...) argument in “Quod ens perfectissimum existit” [1676]. Then I investigate his reasons for assuming absolutely positive and simple perfections by tracing them back to Platonic ideas, including the paradigmatic role of the kosmos noȇtos for the compossibility of essences in the regio idearum. I also consider in which sense Plato’s theory of ideas already preforms the structure of ontological proofs, and how it tells against the assumption of a strictly univocal meaning of existence. (shrink)

It follows from Humean principles of plenitude, I argue, that island universes are possible: physical reality might have 'absolutely isolated' parts. This makes trouble for Lewis's modal realism; but the realist has a way out. First, accept absolute actuality, which is defensible, I argue, on independent grounds. Second, revise the standard analysis of modality: modal operators are 'plural', not 'individual', quantifiers over possible worlds. This solves the problem of island universes and confers three additional benefits: an 'unqualified' principle of (...) class='Hi'>compossibility can be accepted; the possibility of nothing can be accommodated; and the identity of indiscernible worlds can be decisively refuted. (shrink)

WINNER BEST SOCIAL PHILOSOPHY BOOK IN 2021 / NASSP BOOK AWARD 2022 -/- Together we can often achieve things that are impossible to do on our own. We can prevent something bad from happening or we can produce something good, even if none of us could do it by herself. But when are we morally required to do something of moral importance together with others? This book develops an original theory of collective moral obligations. These are obligations that individual moral (...) agents hold jointly, but not as unified collective agents. To think of some of our obligations as joint or collective is the best way of making sense of our intuitions regarding collective moral action problems. Where we have reason to believe that our efforts are most efficient as part of a collective endeavor we may incur collective obligations together with others who are similarly placed as long as we are able to establish compossible individual contributory strategies towards that goal. The book concludes with a discussion of “massively shared obligations” to large-scale moral problems such as global poverty. (shrink)

This chapter analyses the problem of free will and moral responsibility, to which the history of philosophy records three standard reactions. Compatibilists maintain that it is possible for us to have the free will required for moral responsibility if determinism is true. Others contend that determinism is not compossible with our having the free will required for moral responsibility – they are incompatibilists – but they resist the reasons for determinism and claim that we do possess free will of this (...) kind. They advocate the libertarian position. Hard determinists are also incompatibilists, but they accept that determinism is true and that we lack the sort of free will required for moral responsibility. Source and leeway theories, and the notions of incompatibilism and libertarianism, are discussed. (shrink)

Evidential decision theory (EDT) says that the choiceworthiness of an option depends on its evidential connections to possible outcomes. Causal decision theory (CDT) holds that it depends on your beliefs about its causal connections. While Newcomb cases support CDT, Arif Ahmed has described examples that support EDT. A new account is needed to get all cases right. I argue that an option A's choiceworthiness is determined by the probability that a good outcome ensues at possible A‐worlds that match actuality in (...) the facts causally unaffected by your decision (the “unaffected facts”). Moreover, you should evaluate A on the assumption that A is compossible with the unaffected facts. This view entails that you should use EDT when evaluating A on the assumption that the unaffected facts determine your action, but use CDT when assessing A on the opposite assumption. A's choiceworthiness equals a weighted average of these conditional assessments. The weights are determined by your beliefs about whether the unaffected fact determine your action. This account gets both Newcomb and Ahmed cases right. According to an influential view, whether you take the unaffected facts to determine your action can make a difference to whether you can regard yourself as free and the action as being under your control. While my account is neutral on this issue, it entails that whether you take the unaffected facts to determine your action is important in a different way: it matters to whether you should follow EDT or CDT. (shrink)

Modal Plenitude—the view that, for every empirically adequate modal profile, there is an object whose modal profile it is—is held to be consistent with each of endurantist and perdurantist (three- and four-dimensionalist) views of persistence. Here I show that, because “endurer” and “perdurer” are two substantially different kinds of entity, compossible with each other and consistent with empirical data, Modal Plenitude actually entails a third view about persistence that I call “Persistence Egalitarianism.” In every non-empty spacetime region there are two (...) persisting objects: one that endures through the temporal dimension of that region, and another that perdures through the region. Additionally, if the argument from anthropocentrism makes a strong case for Modal Plenitude, then an equally strong and parallel case supports Persistence Egalitarianism. I close with the meta-semantic consequences of persistence egalitarianism for ordinary object talk. (shrink)

Leibniz claims that God acts in the best possible way, and that this includes creating exactly one world. But worlds are aggregates, and aggregates have a low degree of reality or metaphysical perfection, perhaps none at all. This is Leibniz’s tendency toward acosmism, or the view that there this no such thing as creation-as-a-whole. Many interpreters reconcile Leibniz’s acosmist tendency with the high value of worlds by proposing that God sums the value of each substance created, so that the best (...) world is just the world with the most substances. I call this way of determining the value of a world the Additive Theory of Value (ATV), and argue that it leads to the current and insoluble form of the problem of incompossibility. To avoid the problem, I read “possible worlds” in “God chooses the best of all possible worlds” as referring to God’s ideas of worlds. These ideas, though built up from essences, are themselves unities and so well suited to be the value bearers that Leibniz’s theodicy requires. They have their own value, thanks to their unity, and that unity is not preserved when more essences are added. (shrink)

James Sterba has recently argued that the free will defense fails to explain the compossibility of a perfect God and the amount and degree of moral evil that we see. I think he is mistaken about this. I thus find myself in the awkward and unexpected position, as a non-theist myself, of defending the free will defense. In this paper, I will try to show that once we take care to focus on what the free will defense is trying (...) to accomplish, and by what means it tries to do so, we will see that Sterba’s criticism of it misses the mark. (shrink)

Confronting the threat of a Spinozistic necessitarianism, Leibniz insists that not all possible substances are compossible—that they can't all be instantiated together—and thus that not all possible worlds are compossible—that they can't all be instantiated together. While it is easy to appreciate Leibniz's reasons for embracing this view, it has proven difficult to see how his doctrine of incompossibility might be reconciled with the broader commitments of his larger philosophical system. This essay develops, in four sections, a novel solution to (...) the "puzzle of incompossibility." The first section frames the difficulty more carefully and briefly argues that the two dominant strategies developed by Leibniz's commentators fail to solve it fully insofar as they require simply abandoning one or another of its motivating commitments. The second and third sections show how Leibniz's guiding analogy of a geometrical packing or tiling problem may be applied to solve the puzzle of incompossibility in the context of finite and infinite worlds composed of extended corporeal substances. Finally, the fourth section shows how the strategy of Leibniz's packing analogy might be applied even in the context of a thoroughly idealist metaphysics in which the only true substances are nonextended, mindlike "monads." The essay concludes by drawing some connections between Leibniz's thinking about the puzzle of incompossibility and the development of his views concerning the status of corporeal substances and extended bodies. CiteULike Connotea Del.icio.us Digg Reddit Technorati What's this? (shrink)

We argue that S is in a position to know that p iff S can know that p. Thus, what makes position-to-know-ascriptions true is just a special case of what makes ability-ascriptions true: compossibility. The novelty of our compossibility theory of epistemic modality lies in its subsuming epistemic modality under agentive modality, the modality characterizing what agents can do.