An ontology of Leibnizian relationalism, consisting in distance relations among sparse matter points and their change only, is well recognized as a serious option in the context of classical mechanics. In this paper, we investigate how this ontology fares when it comes to general relativistic physics. Using a Humean strategy, we regard the gravitational field as a means to represent the overall change in the distance relations among point particles in a way that achieves the best combination of being simple (...) and being informative. (shrink)

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

I examine the new defense of the principle of sufficient reason, offered by Michael Della Rocca (_The Journal of Philosophy_, 120 (2023): 220-227). I first identify a crucial premise of Della Rocca’s argument, and argue that it is not justified. I then reformulate his argument, this time with the corresponding crucial premise justified. Finally, although I think the reformed argument is valid, I express some doubts about the propriety of the un-Leibnizian requisite suggested in that paper.

Newton rested his theory of mechanics on distinct metaphysical and epistemological foundations. After Leibniz's death in 1716, the Principia ran into sharp philosophical opposition from Christian Wolff and his disciples, who sought to subvert Newton's foundations or replace them with Leibnizian ideas. In what follows, I chronicle some of the Wolffians' reactions to Newton's notion of absolute space, his dynamical laws of motion, and his general theory of gravitation. I also touch on arguments advanced by Newton's Continental followers, such as (...) Leonhard Euler, who made novel attempts to defend his mechanical foundations against the pro-Leibnizian attack. This examination grants us deeper insight into the fate of Newton's mechanics on the Continent during the early eighteenth century and, more specifically, sheds needed light on the conflicts and tensions that characterized the reception of Newton's philosophy of mechanics among the Leibnizians. (shrink)

Leibniz, it seems, wishes to reduce statements involving relations or extrinsic denominations to ones solely in terms of individual accidents or, respectively, intrinsic denominations. His reasons for this appear to be that relations are merely mental things (since they cannot be individual accidents) and that extrinsic denominations do not represent substances as they are on their own. Three interpretations of Leibniz''s reductionism may be distinguished: First, he allowed only monadic predicates in reducing statements (hard reductionism); second, he allowed also `implicitly (...) relational predicates'' such as `loves somebody'' (soft reductionism); third, he allowed also `explicitly relational predicates'' such as `loves Helen'' (nonreductionism). Hard reductionism is problematic with respect to Leibniz''s doctrines of universal expression and incompossibility (among other things). Nonreductionism, in turn, faces insurmountable problems with Leibniz''s doctrine of self-sufficiency and internal identification of substances, as well as with that of individual accidents. The remaining option, soft reductionism, standing between the other two interpretations, arguably avoids at least some of their problems. (shrink)

I propose a straightforward reconciliation of Leibniz’s conception of bodies as aggregates of simple substances (i.e., monads) with his doctrine that bodies are the phenomena of perceivers, without in the process saddling him with any equivocations. The reconciliation relies on the familiar idea that in Leibniz’s idiolect, an aggregate of Fs is that which immediately presupposes those Fs, or in other words, has those Fs as immediate requisites. But I take this idea in a new direction. Taking notice of the (...) fact that Leibniz speaks of three respects in which one thing may immediately presuppose others--i.e., with respect to its being, its existence, and its reality--I argue that a phenomenon having its being in one perceiving substance (monad) can plausibly be understood to presuppose other perceiving substances (monads) in two of these respects. Accordingly, good sense can be made of both the claim that a phenomenon in one monad is an aggregate of other monads (in Leibniz’s technical sense of 'aggregate') and the (equivalent) claim that the latter monads are constituents of the phenomenon (in his technical sense of 'constituent'). So understood, the two conceptions of body are perfectly compatible, just as Leibniz seems to think. (shrink)

A popular story about Kant's relation to Leibniz presents Kant as a Leibniz-Wolffian by education who, inspired by his encounter with the teachings of Newton and Hume, took on the project of reconciling Leibniz-Wolffian metaphysics with Newtonian science and of responding to epistemological skepticism, a project that led him further and further away from his Leibniz-Wolffian roots and culminated in the total rejection of the Leibniz-Wolffian philosophy in the Critique of Pure Reason. In this essay, four shortcomings of the popular (...) story are identified and several suggestions are made about how to amend and expand the story in order to overcome these shortcomings. Furthermore, some of the most important Leibnizian doctrines that influenced Kant are collected and their role in Kant's philosophy is discussed. (shrink)

In this paper, an interpretation of "necessity", inspired by a Leibnizian idea and based on the method of dialogical logic, is introduced. The semantic rules corresponding to such an account of necessity are developed, and then some peculiarities, and some potential advantages, of the introduced dialogical explanation, in comparison with the customary explanation offered by the possible worlds semantics, are briefly discussed.

This chapter offers an interpretation of Gottfried Wilhelm Leibniz’s idealism. Despite Leibniz’s frequent claim that the universe ultimately boils down to monads, he also sometimes appears to say that the world’s fundamental furniture includes extended, corporeal substances. Here, I examine Leibniz’s views about the relationship between monads and the material world, especially in connection with material bodies and corporeal substances.

This paper explores various metaphysical aspects of Leibniz’s concepts of space, motion, and matter, with the intention of demonstrating how the distinctive role of force in Leibnizian physics can be used to develop a theory of relational motion using privileged reference frames. Although numerous problems will remain for a consistent Leibnizian relationist account, the version developed within our investigation will advance the work of previous commentators by more accurately reflecting the specific details of Leibniz’s own natural philosophy, especially his handling (...) of the dynamical interactions of plenum bodies. (shrink)

Leibniz often refers to the Principle of Sufficient Reason (PSR) as something like a first principle. In some texts, however, he attempts to give positive arguments in its favor. I examine two such arguments, and find them wanting. The first argument has two defects. First, it is question-begging; and second, when the question-begging step is excised, the principle one can in fact derive is highly counter-intuitive. The second argument is valid, but has the defect of only reaching a nearly trivial (...) conclusion. (shrink)

In the present paper the philosophical and mathematical continuity alleged by A. Robinson in Nonstandard Analysis (1966) between his theory and Leibniz’s calculus is investigated. In Section 1, after a brief overview of the history of analysis, we expose the historical, mathematical and philosophical aspects of Leibniz’s calculus. In Section 2 the main technical aspects of nonstandard analysis are presented, and Robinson’s philosophy is discussed. In Section 2.1 we claim the absence of a complete and direct continuity and the only (...) possibility of a conceptual similarity between Leibniz’s and Robinson’s theories, both at the philosophical and at the mathematical level. (shrink)

This article delves into the mature philosophy of Leibniz, exploring his concepts of life and organism. It aims to establish links between the scientific discoveries of the 17th century and Leibnizian metaphysical assumptions. The paper also highlights how reflections on the Cudworthian system helped the Leipzig philosopher develop his «metaphysics of the organics». The article begins with a brief overview of the querelle sur les natures plastiques to deepen some Leibnizian positions on these topics. It emphasizes Leibniz’s focus on the (...) concept of organism and its fundamental relation and difference with the concept of life. The article also addresses the notion of «nested individuality» and plural individuality in the philosopher’s writings, attempting to determine if such concepts exist. The solution to the coexistence of plural organisms within an organism provided here is mereological. Lastly, the article gathers current research results to demonstrate how the «organism» in the Leibnizian system of maturity is like a fold, leading readers toward different aspects of his metaphysics. (shrink)

It is common to hold that our conscious experiences at a single moment are often unified. But when consciousness is unified, what are the fundamental facts in virtue of which it is unified? On some accounts of the unity of consciousness, the most fundamental fact that grounds unity is a form of singularity or oneness. These accounts are similar to Newtonian views of space according to which the most fundamental fact that grounds relations of co-spatiality between various points (or regions) (...) of a space is the fact that these points (or regions) are parts of the same single space. In this paper, I sketch and defend an alternative account of unity of consciousness. Very roughly, the view holds that experiences are unified when they are connected in the right way. In this respect, the view is analogous to Leibnizian views of space according to which the oneness of space emerges from certain conditions over spatial relations. The Leibnizian alternative has significant implications for our understanding of the metaphysics of conscious experience, the cognitive architecture of the mind and our assessment of the conditions under which unity of consciousness breaks. (shrink)

The oft-told story of Leibniz’s doctrine of the best world, or optimism, is that it enjoyed a great deal of popularity in the eighteenth century until the massive earthquake that struck Lisbon on 1 November 1755 destroyed its support. Despite its long history, this story is nothing more than a commentators’ fiction that has become accepted wisdom not through sheer weight of evidence but through sheer frequency of repetition. In this paper we shall examine the reception of Leibniz’s doctrine of (...) the best world in the eighteenth century in order to get a clearer understanding of what its fate really was. As we shall see, while Leibniz’s doctrine did win a good number of adherents in the 1720s and 1730s, especially in Germany, support for it had largely dried up by the mid-1740s; moreover, while opponents of Leibniz’s doctrine were few and far between in the 1710s and 1720s, they became increasing vocal in the 1730s and afterwards, between them producing an array of objections that served to make Leibnizian optimism both philosophically and theologically toxic years before the Lisbon earthquake struck. (shrink)

I argue that the key dynamical concepts and laws of Newton's Principia never gained a solid foothold in Germany before Kant in the 1750s. I explain this absence as due to Leibniz. Thus I make a case for a robust Leibnizian legacy for Enlightenment science, and I solve what Jonathan Israel called “a meaningful historical problem on its own,” viz. the slow and hesitant reception of Newton in pre-Kantian Germany.

This essay examines the metaphysical foundation of Leibniz’s theory of space against the backdrop of the subtantivalism/relationism debate and at the ontological level of material bodies and properties. As will be demonstrated, the details of Leibniz’ theory defy a straightforward categorization employing the standard relationism often attributed to his views. Rather, a more careful analysis of his metaphysical doctrines related to bodies and space will reveal the importance of a host of concepts, such as the foundational role of God, the (...) holism of both geometry and the material world’s interconnections, and the viability and adequacy of a property theory in characterizing his natural philosophy of space. (shrink)

This essay examines the relationship between monads and space in Kant’s early pre-critical work, with special attention devoted to the question of ubeity, a Scholastic doctrine that Leibniz describes as “ways of being somewhere”. By focusing attention on this concept, evidence will be put forward that supports the claim, held by various scholars, that the monad-space relationship in Kant is closer to Leibniz’ original conception than the hypotheses typically offered by the later Leibniz-Wolff school. In addition, Kant’s monadology, in conjunction (...) with God’s role, also helps to shed light on further aspects of his system that are broadly Leibnizian, such as monadic activity and the unity of space. (shrink)

Much has been made of Deleuze’s Neo-Leibnizianism,3 however not very much detailed work has been done on the specific nature of Deleuze’s critique of Leibniz that positions his work within the broader framework of Deleuze’s own philo- sophical project. The present chapter undertakes to redress this oversight by providing an account of the reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold. Deleuze provides a systematic account of the structure of Leibniz’s metaphys- ics in terms of its mathematical (...) underpinnings. However, in doing so, Deleuze draws upon not only the mathematics developed by Leibniz – including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus – but also the developments in mathematics made by a number of Leibniz’s contemporaries – including Newton’s method of fluxions – and a number of subsequent developments in mathematics, the rudiments of which can be more or less located in Leibniz’s own work – including the theory of functions and singularities, the theory of continuity and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the theory of continuity serves to clarify Leibniz’s work, Poincaré’s theory of automorphic functions offers a solution to overcome and extend the limits that Deleuze identifies in Leibniz’s metaphysics. Deleuze brings this elaborate conjunction of material together in order to set up a mathematical idealization of the system that he considers to be implicit in Leibniz’s work. The result is a thoroughly mathematical explication of the structure of Leibniz’s metaphysics. What is provided in this chapter is an exposition of the very mathematical underpinnings of this Deleuzian account of the structure of Leibniz’s metaphysics, which, I maintain, subtends the entire text of The Fold. (shrink)

Leibniz developed several arithmetical interpretations of the assertoric syllogistic in a series of drafts from April 1679. In this article, I present what I take to be one of his most mature articulations of the arithmetical semantics from that series. I show that the assertoric syllogistic can be characterized exactly not only in the full divisibility lattice, as Leibniz implicitly suggests, but in a certain four-element sublattice thereof. This refinement is also shown to be optimal in the sense that the (...) assertoric syllogistic is not complete with respect to any smaller sublattice using Leibniz’s truth conditions. (shrink)

Do theories of quantum mechanics and quantum gravity require spacetime to be a basic ground-level feature, or can spacetime be seen as an emergent element of these theories? While several commentators have raised serious doubts about the prospects of forgoing the standard spacetime backdrop, we will argue that a defence of these emergent spacetime interpretations of quantum mechanics and quantum gravity hypotheses can be made whether as an inference as to what the best explanation is or using another strategy. Furthermore, (...) the idea that space and time can arise from a quite different, non-spatiotemporal level of reality will be shown to have various historical precedents, especially in the seventeenth and eighteenth centuries. This realization may help dispel some of the mystery associated with these types of hypotheses. (shrink)

A contribution to the history of a formerly hotly discussed, but short-lived scientific project: neurophenomenology , the proposal of weaving together Husserlian phenomenology of consciousness and the neuroscience of brain functioning, this article traces back the opening and closing of an apparent window of opportunity, both in phenomenology and in neuroscience, for the eventually unfulfilled realization of that project.

Pure shape dynamics (PSD) is a novel implementation of the relational framework originally proposed by Julian Barbour and Bruno Bertotti. PSD represents a Leibnizian/Machian approach to physics in that it completely describes the dynamical evolution of a physical system without resorting to any structure external to the system itself. The chapter discusses how PSD effectively describes a de Broglie-Bohm N-body system and the conceptual benefits of such a relational description. The analysis will highlight the new directions in the quest for (...) an understanding of the nature of the wave function that are opened up by a modern relationalist elaboration on de Broglie's and Bohm's original insights. (shrink)

Leibniz’s account of moral necessity does double heavy-duty: it aims a) to provide explanations of divine choices without rendering these divine choices metaphysically necessary, thus permitting for divine freedom; and b) to ground the conviction that God did the best God could have done in creating the world, or Leibnizian Optimism. I present a novel interpretation of what Leibniz calls ‘the principle of the best’ as a second-order will to do what is best (read de dicto) that grounds a set (...) of subjunctive conditionals of divine freedom. These conditionals encode what God would do (namely the best) if God were to deliberate about creating one of a set of mutually exclusive options which are metaphysically possible for God to create. I argue that this reading of the principle of the best enables Leibnizian moral necessity to do the mentioned double heavy-duty. (shrink)

Time as the key to a theory of everything became recently a renewed topic in scientific literature. Social constructivism applied to physics abandons the inevitable essentials of nature. It adopts uncertainty in the scope of the existential activity of scientific research. We have enlightened the deep role of social constructivism of the predetermined Newtonian time and space notions in natural sciences. Despite its incompatibility with determinism governing the Newtonian mechanics, randomness and entropy are inevitable when negative localized energy is transformed (...) into spatially dissipative heat. In sharp contrast to the Newtonian notion, social constructivism makes room for the temporal twin of cyclic conservation and pseudo-linearly structural evolution both reconciling mechanical order and thermodynamic chaos in Leibnizian space-time. In the broad scope of natural sciences this triad nature of time produces a multiple reality and gives appropriate answers on virtual physical paradoxes. (shrink)

Modern rationalism transformed the modern homeland to a discursive space and time by means of institutes governing the modern society in all its walks. Based on the Newtonian and Kantian conception of space and time the discursive field is just a scene wherein any human individual adopts stewardship to create progress by reducing landscape and non-human life to auxiliary items for human’s benefit. In contrast, Aldo Leopold considered humans, non human life and the landscape as mutually influencing participants and enlarged (...) ethical care to all living participants and the landscape, called ´the land´. Integrity and autonomy of the homeland are the central topics of Leopold’s land ethics. Baird Callicott suggested to complete it with new metaphysical conceptions of space and time. -/- We formulated a metaphysical background for Leopold’s land ethics by phenomenology of space and time based on the Leibnizian conception of space-time. The latter is constructed by particular places and events called ´ecotopois´ embracing all human participants, locals and foreigners in a varying symbolic temporal and spatial field of dynamic process of identification and self consciousness. Adopting Warwick Fox´ transpersonal identification idea non-human life and landscape enriches these processes. Finally, it is not a matter of conquering the land, it is matter of making a community. -/- Though landscape and participants are particular, integrity and autonomy of the homeland claim the universal status of the land. Adopting Gadamer hermeneutical way of understanding, we reject mutual and equally understanding. Only acceptance of mutual prejudice makes room for asymmetric praxis between locals and foreigners as well as between humans and non-humans. What is more, Gadamer´s hermeneutics makes an ontological status of the foreigner possible and recognizes the interest of homeland’s particularity. This universal status is guaranteed as a priori space-time that links subject’s tradition and that of the land to actual contact with the foreigner. Transpersonal identification is a consequence of converging hermeneutical understanding of foreigner’s particularity and that of the landscape. Ethics of the land evolves from the ethical status of any foreigner in the own homeland. -/- . (shrink)

Leibnizian metaphysics is traditionally held to be idealistic. It means that reality is composed of soul-like substances whereas material bodies are mere phenomena. The traditional interpretation presupposes that Leibniz’s view has not changed during the mature period (from 1683 onward). Some commentators have recently challenged this view. They claim that either Leibniz (despite inconsistency) was both a realist and an idealist (Hartz), or changed his view on the nature of substance (Garber). The aim is to defend the traditional interpretation and (...) to reply to the arguments by realist commentators. (shrink)

For the last forty years, Hume's Newtonianism has been a debated topic in Hume scholarship. The crux of the matter can be formulated by the following question: Is Hume a Newtonian philosopher? Debates concerning this question have produced two lines of interpretation. I shall call them ‘traditional’ and ‘critical’ interpretations. The traditional interpretation asserts that there are many Newtonian elements in Hume, whereas the critical interpretation seriously questions this. In this article, I consider the main points made by both lines (...) of interpretations and offer further arguments that contribute to this debate. I shall first argue, in favor of the traditional interpretation, that Hume is sympathetic to many prominently Newtonian themes in natural philosophy such as experimentalism, criticality of hypotheses, inductive proof, and criticality of Leibnizian principles of sufficient reason and intelligibility. Second, I shall argue, in accordance with the critical interpretation, that in many cases Hume... (shrink)

Some philosophers respond to Leibniz’s “shift” argument against absolute space by appealing to antihaecceitism about possible worlds, using David Lewis’s counterpart theory. But separated from Lewis’s distinctive system, it is difficult to understand what this doctrine amounts to or how it bears on the Leibnizian argument. In fact, the best way of making sense of the relevant kind of antihaecceitism concedes the main point of the Leibnizian argument, pressing us to consider alternative spatiotemporal metaphysics.

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition, based on discernibility, and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that—contrary to a widespread consensus—‘naturalised’ metaphysics supports both the acceptability (...) of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, by assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality. The kind of individuality that prevails in a certain context and at a given level can be ascertained only on the basis of the specific scientific theory at hand. (shrink)

This paper argues that Wolff’s rejection of Leibnizian monads is rooted in a disagreement concerning the general notion of substance. Briefly, whereas Leibniz defines substance in terms of activity, Wolff retains a broadly scholastic and Cartesian conception of substance as that which per se subsists and sustains accidents. One consequence of this difference is that it leads Wolff to interpret Leibniz’s concept of a constantly striving force as denoting a feature of substance separate from its static powers, and not as (...) their replacement. For Wolff, powers are essential possibilities of acting in subjects suited for independent existence. Force is a further ingredient that provides a reason for the contingent operation of powers. Unlike Leibniz, Wolff conceives force narrowly as a principle of actuality, which he calls the “nature” of substance, as distinct from its principle of possibility, or essence. (shrink)

The category of ‘organism’ has an ambiguous status: is it scientific or is it philosophical? Or, if one looks at it from within the relatively recent field or sub-field of philosophy of biology, is it a central, or at least legitimate category therein, or should it be dispensed with? In any case, it has long served as a kind of scientific “bolstering” for a philosophical train of argument which seeks to refute the “mechanistic” or “reductionist” trend, which has been perceived (...) as dominant since the 17th century, whether in the case of Stahlian animism, Leibnizian monadology, the neo-vitalism of Hans Driesch, or, lastly, of the “phenomenology of organic life” in the 20th century, with authors such as Kurt Goldstein, Maurice Merleau-Ponty, and Georges Canguilhem. In this paper I try to reconstruct some of the main interpretive ‘stages’ or ‘layers’ of the concept of organism in order to critically evaluate it. How might ‘organism’ be a useful concept if one rules out the excesses of ‘organismic’ biology and metaphysics? Varieties of instrumentalism and what I call the ‘projective’ concept of organism are appealing, but perhaps ultimately unsatisfying. (shrink)

Consider an infinite series whose items are each explained by their immediate successor. Does such an infinite explanation explain the whole series or does it leave something to be explained? Hume arguably claimed that it does fully explain the whole series. Leibniz, however, designed a very telling objection against this claim, an objection involving an infinite series of book copies. In this paper, I argue that the Humean claim can, in certain cases, be saved from the Leibnizian “infinite book copies” (...) objection, and that this provides an interesting way to defuse some cosmological arguments for the existence of God and to give a non-theistic but complete explanation of the Universe. In the course of my argumentation, I also show that circular explanations can be “self-explanatory” as well: explaining two items by each other can explain the couple of items tout court. (shrink)

In this paper, I draw attention to various doctrines common to different Vedāntic traditions. In particular, I pay close attention to the doctrine of beginningless _karman_. I also note that this doctrine seems to stand in tension with Leibnizian Cosmological Arguments (LCAs) and Kalām Cosmological Arguments (KCAs). This tension arises because defenders of these arguments argue that an infinite causal regress or an actual infinite cannot be physically instantiated and because the doctrine of beginningless _karman_ seems to imply that such (...) a regress or actual infinite can be physically instantiated. I address this tension by showing that not all interpretations of beginningless _karman_ involve an infinite causal regress or an actual infinite. I close this paper by highlighting a few features that Vedāntic traditions have that make them more resistant to some objections to LCAs and KCAs. (shrink)

Since his Metaphysische Anfangsgründe der Naturwissenschaft was first published in 1786, controversy has surrounded Immanuel Kant’s conception of matter. In particular, the justification for both his dynamical theory of matter and the related dismissal of mechanical philosophy are obscure. In this paper, I address these longstanding issues and establish that Kant’s dynamism rests upon Leibnizian, metaphysical commitments held by Kant from his early pre-Critical texts on natural philosophy to his major critical works. I demonstrate that, throughout his corpus and inspired (...) by Leibniz, Kant endorses the a priori law of continuity of alteration as a truth of metaphysics, according to which all alterations in experience must occur gradually through all intervening degrees. The principle thus legislates against mechanical philosophy’s absolutely impenetrable atoms, as they would would involve instantaneous changes of velocity in impact. This reveals the metaphysical incoherencies in mechanical philosophy and leaves Kant’s own dynamical theory of matter, grounded on material forces, as the only viable approach to physical explanation. Subsequently, I demonstrate that Kant nevertheless made conceptual space in his system for the theoretical consideration of mechanical explanations, which makes manifest one of the positive roles that the faculty of reason can play with respect to natural science. (shrink)

Leibniz endorses several tenets regarding explanation: (1) causes provide contrastive explanations of their effects, (2) the past and the future can be read from the present, and (3) primitive force and derivative forces drive and explain changes in monadic states. I argue that, contrary to initial appearances, these tenets do not preclude an intelligible conception of contingency in Leibniz’s system. In brief, an agent is free to the extent that she determines herself to do that which she deliberately judges to (...) be the best from several considered options that she could have brought about, had she come to the deliberative conclusion that these options were best. I develop a model which illustrates how Leibnizian agents could have come to different deliberative conclusions, and which thus illustrates how Leibnizian agents could have acted differently. (shrink)

This paper examines the origin, range and meaning of the Principle of Action and Reaction in Kant’s mechanics. On the received view, it is a version of Newton’s Third Law. I argue that Kant meant his principle as foundation for a Leibnizian mechanics. To find a ‘Newtonian’ law of action and reaction, we must look to Kant’s ‘dynamics,’ or theory of matter. I begin, in part I, by noting marked differences between Newton’s and Kant’s laws of action and reaction. I (...) argue that these are explainable by Kant’s allegiance to a Leibnizian mechanics. I show (in part II) that Leibniz too had a model of action and reaction, at odds with Newton’s. Then I reconstruct how Jakob Hermann and Christian Wolff received Leibniz’s model. I present (in Part III) Kant’s early law of action and reaction for mechanics. I show that he devised it so as to solve extant problems in the Hermann-Wolff account. I reconstruct Kant’s views on ‘mechanical’ action and reaction in the 1780s, and highlight strong continuities with his earlier, pre-Critical stance. I use these continuities, and Kant’s earlier engagement with post-Leibnizians, to explain the un-Newtonian features of his law of action and reaction. (shrink)

There are, familiarly, a range of distinct and competing accounts of the methodological underpinnings of Menger' s work. These include Leibnizian, Kantian, Millian, and even Popperian readings; but they include also readings of an Aristotelian sort, and I have myself made a number of contributions in clarification and defence of the latter. Not only, I have argued, does the historical situation in which Menger found himself point to the inevitability of the Aristotelian reading; this reading fits also very naturally to (...) the text of Menger's works. (shrink)

Leibniz was a philosopher of principles: the principles of Contradiction, of Sufficient Reason, of Identity of Indiscernibles, of Plenitude, of the Best, and of Continuity are among the most famous Leibnizian principles. In this article I shall focus on the first three principles; I shall discuss various formulations of the principles (sect. 1), what it means for these theses to have the status of principles or axioms in Leibniz’s philosophy (sect. 2), the fundamental character of the Principles of Contradiction and (...) Sufficient Reason (sect. 3), some attempts to demonstrate the Principles of Contradiction and Sufficient Reason (sect. 4), and one attempt to demonstrate the Principle of Identity of Indiscernibles (sect. 5). The main results of the chapter are summarized in a short conclusion (sect. 6). (shrink)

I defend the Contingent Spotlight Theory, a theory of modality analogous to the Moving Spotlight Theory in the philosophy of time. My defence of the theory consists in developing responses to three objections that have been raised against it, two of which are due to David Lewis. I also argue that the version of the contingent spotlight theory I develop in response to these objections has some advantages over its closest rival, Philip Bricker's ‘Leibnizian Realism’.

I will present and criticise the two theories of truthmaking David Armstrong offers us in Truth and Truthmakers (Armstrong 2004), show to what extent they are incompatible and identify troublemakers for both of them, a notorious – Factualism, the view that the world is a world of states of affairs – and a more recent one – the view that every predication is necessary. Factualism, combined with truthmaker necessitarianism – ‘truthmaking is necessitation’ – leads Armstrong to an all-embracing totality state (...) of affairs that necessitates not only everything that is the case but also everything else – that which is not the case, that which is merely possible or even impossible. All the things so dear to realists – rocks, natural properties, real persons – become mere abstractions from this ontological monster. The view that every predication is necessary does in some sense the opposite: it does away with totality states of affairs and, arguably, also with states of affairs. We have particulars and universals, partially identical and necessarily connected to everything else. Just by the existence of anything, everything is necessitated – the whole world mirrored in every monad. Faced with the choice between these two equally unappealing alternatives, I suggest returning to Armstrong’s more empiricist past: the world is not an all-inclusive One, nor necessitated by every single particular and every single universal, but a plurality of particulars and universals, interconnected by a contingent and internal relation of exemplification. While a close variant, truthmaker essentialism, can perhaps be saved, this means giving up on truthmaker necessitarianism. This, I think, what it takes to steer a clear empiricist course between the Scylla of Spinozist general factness and the Charybdis of a Leibnizian overdose of brute necessities. (shrink)

The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristotelian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian voluntarist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Cantor’s thought with (...) reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspectives on the Actual Infinite”) (1885). (shrink)

The book discusses the structure, content, and evaluation of cosmological arguments. The introductory chapter investigates features essential to cosmological arguments. Traditionally, cosmological arguments are distinguished by their appeal to change, causation, contingency or objective becoming in the world. But none of these is in fact essential to the formulation of cosmological arguments. Chapters 1-3 present a critical discussion of traditional Thomistic, Kalam, and Leibnizian cosmological arguments, noting various advantages and disadvantages of these approaches. Chapter 4 offers an entirely new approach (...) to the cosmological argument - the approach of theistic modal realism. The proper explananda of cosmological arguments on this approach is not change, causation, contingency or objective becoming in the world. The proper explananda is the totality of metaphysical reality - all actualia and all possibilia. The result is the most compelling and least objectionable version of the cosmological argument. (shrink)

Leibniz endorses the world apart doctrine, according to which a substance is that which is independent of all other things except God. However, I will argue that in what appears to be a radical departure from the causal version of the world apart doctrine, Du Châtelet—whose metaphysics appears to be Leibnizian from a distance—embraces the causal connectedness of created substances. I further show that Du Châtelet’s rejection of Leibniz’s claim that a substance is causally independent of all other created substances (...) can be traced back to a more fundamental antiLeibnizian commitment on Du Châtelet’s part concerning the in-principle accessibility of natural (i.e., non-divine) sufficient reasons by finite minds and to her commitment to a causal theory of intentionality. (shrink)

In this chapter, I demonstrate the several fundamental and original aspects of Bamgarten's concpetion of metaphyics that have been overlooked or at least insufficiently investigated. Baumgarten departs from his predecessors, and from many of his contemporaries, by regarding metaphysics as a uniquely human science whose essential purpose is to provide the best instruments for knowing and realising perfection in human life, given that we are subject to essential limitations. This instrumental view of metaphysics leads him to develop seveal Leibnizian ideas (...) regarding perfection and the best possible world into highly articulated metaphysical doctrines that are able to serve as universal guiding principles for all other sciences. In the final part of the chapter, I illustrate three ways in which metaphysics plays this role through an examination of the foundations of Baumgarten's own practical philosophy. (shrink)

This chapter traces the origins of Kant's perfectionism, and so of his moral law, to the formal conception of 'nature' that emerges from his reflection on the work of Wolff and Baumgarten. The conceptual preparation for this move turns upon two hinges, both of which trace to Baumgarten's subtle modifications of Wollffian perfectionism, namely, his fuller articulation of a non-consequentialist, internal morality of actions and what I call a 'hyper-Leibnizian' account of the idea and formal structure of nature itself. The (...) fourth section shows how Kant discovers a new account of the a priori origin of this formal structure, which, when combined with his conception of unconditioned or transcendental freedom, allows him to locate an unconditioned, hence genuinely moral law, in freedom's lawlike unconditioned, intetentional imiposition of this same formal strcture, this homologia, on all its actions. In this way, the neo-Stoicism found in the earlier rationalist tradition, which bits us to 'live according to nature,' becomes in Kant the absolute duty to live according to reason's pure, a priori idea of a nature. (shrink)

While the problem of the philosophical significance of Riemann's theorem on conditionally convergent series has been discussed in detail for some time, specific versions of it have appeared in the literature very recently, over which there have been widespread disagreements. I argue that such discrepancies can be clarified by introducing a rather conventional type of composition rule for the treatment of some infinite systems (as well as supertasks) while analysing and clarifying the role of the concept of continuity by stripping (...) it of the excesses that its application by the Leibnizian tradition has led to. The conclusion reached is that the indeterminacy associated with conditional convergence has a clear philosophical significance, but no fundamental ontological significance. (shrink)

In this extended critical discussion of 'Kant's Modal Metaphysics' by Nicholas Stang (OUP 2016), I focus on one central issue from the first chapter of the book: Stang’s account of Kant’s doctrine that existence is not a real predicate. In §2 I outline some background. In §§3-4 I present and then elaborate on Stang’s interpretation of Kant’s view that existence is not a real predicate. For Stang, the question of whether existence is a real predicate amounts to the question: ‘could (...) there be non-actual possibilia?’ (p.35). Kant’s view, according to Stang, is that there could not, and that the very notion of non-actual or ‘mere’ possibilia is incoherent. In §5 I take a close look at Stang’s master argument that Kant’s Leibnizian predecessors are committed to the claim that existence is a real predicate, and thus to mere possibilia. I argue that it involves substantial logical commitments that the Leibnizian could reject. I also suggest that it is danger of proving too much. In §6 I explore two closely related logical commitments that Stang’s reading implicitly imposes on Kant, namely a negative universal free logic and a quantified modal logic that invalidates the Converse Barcan Formula. I suggest that each can seem to involve Kant himself in commitment to mere possibilia. (shrink)

The article examines Kant's various criticisms of the broadly Cartesian ontological argument as they are developed in the Critique of Pure Reason. It is argued that each of these criticisms is effective against its intended target, and that these targets include—in addition to Descartes himself—Leibniz, Wolff, and Baumgarten. It is argued that Kant's most famous criticism—the charge that being is not a real predicate—is directed exclusively against Leibniz. Kant's argument for this thesis—the argument proceeding from his example of a hundred (...) thalers—although it may seem to beg the question, in fact succeeds against Leibniz. It does so because the charge of begging the question can be rebutted if one makes certain Leibnizian assumptions. (shrink)