The standard Leibnizian view of identity allows for substitutivity of identicals and validates transitivity of identity within classical semantics. However, in a series of works, Graham Priest argues that Leibnizian identity invalidates both principles when formalized in paraconsistent semantics. This paper aims to show the Leibnizian view of identity validates substitutivity of identicals and transitivity of identity whether the logic is classical or paraconsistent. After presenting Priest's semantics of identity, I show what a semantic expression of Leibnizian identity does amount (...) to. Then, I argue that Priest's semantic definition of identity is not Leibnizian. Finally, I offer a semantics characterization of identity in paraconsistent logic that is truly Leibnizian. I demonstrate that the correct formalization of Leibnizian identity in paraconsistent logic also validates substitutivity of identicals and transitivity of identity. (shrink)

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)

Three different notions of concepts are outlined: one derives from Leibniz, while the other two derive from Frege. The Leibnizian notion is the subject of his "calculus of concepts" (which is really an algebra). One notion of concept from Frege is what we would call a "property", so that when Frege says "x falls under the concept F", we would say "x instantiates F" or "x exemplifies F". The other notion of concept from Frege is that of the notion of (...) sense, which played various roles within Frege's theory. This notion of concept can be generalized and, as such, accounts for our intuitive talk of "x's concept of ...", where the ellipsis can be filled in with a name for individual, a property, or a relation, etc. After outlining these three notions, I then discuss how (axiomatic) object theory offers a distinct, precise regimentation of each of the three notions. (shrink)

This chapter contains sections titled: Introduction The PSR Nonlocal CPs Toward a First Cause The Gap Problem Conclusions and Further Research References.

In this paper, the author develops a theory of concepts and shows that it captures many of the ideas about concepts that Leibniz expressed in his work. Concepts are first analyzed in terms of a precise background theory of abstract objects, and once concept summation and concept containment are defined, the axioms and theorems of Leibniz's calculus of concepts (in his logical papers) are derived. This analysis of concepts is then seamlessly connected with Leibniz's modal metaphysics of complete individual concepts. (...) The fundamental theorem of Leibniz's modal metaphysics of concepts is proved, namely, whenever an object x has F contingently, then (i) the individual concept of x contains the concept F and (ii) there is a (counterpart) complete individual concept y which doesn't contain the concept F and which `appears' at some other possible world. Finally, the author shows how the concept containment theory of truth can be made precise and made consistent with a modern conception of truth. (shrink)

This paper examines the Leibnizian influence in Deleuze's theory of the spatium. Leibniz's critique of Cartesian extension and Newtonian space leads him to a conception of space in terms of internal determination and internal difference. Space is thus understood as a structure of individual relations internal to substances. Making some Nietzschean corrections to Leibniz, Deleuze understands the spatium in terms of individuating differences instead of individual relations. Leibnizian space is thus transformed into a genetic space producing both extension (quantity) and (...) quality. (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)

This article examines Leibniz's philosophy of causation with the aim of clarifying how causes are related to their effects. I argue that, much like J. L. Mackie's INUS conditions, Leibnizian causes are members of complex causal conditions. More precisely, Leibniz identifies causes with elements of complex causal conditions, where the complex condition as a whole is sufficient for the effect, and the cause is a necessary part of that condition. This conception of causation is able to incorporate Leibniz's many other (...) definitions of ‘cause’, thereby resolving what appear to be internal inconsistencies in his philosophy of science. Introduction The ingredients of causation Causes and conditions Causes as INUS conditions Conclusion. (shrink)

In den „Fundamenta praedemonstrabilia“ der Theoria motus abstracti entwickelt Leibniz den Versuch, das Kontinuum als aus grundsätzlich unteilbaren Einheiten in einer Weise aufgebaut zu denken, die seine Kontinuität bewahrt - durch die systematische Unterscheidung der Verhältnisse von ,unum ad infinitum‘ und von ,nullius ad unum‘ versucht er hier Balance zu halten. Zwar komme ich zu dem Ergebnis, daß Leibniz' Auffassung vom Kontinuum in der Theoria motus abstracti letztlich inkohärent bleibt, gleichwohl bildet er Begriffe, die sein weiteres Bemühen, den Zugang zum (...) Unendlich-Kleinen neu zu legen, zum Mittel seiner Lösung des ,labyrinthus de compositione continui‘ gestalten. Im zweiten Teil der Arbeit konfrontiere ich die hier vorgelegte Interpretation der Position von Leibniz einer Deutung, die unlängst Philip Beeley gab. (shrink)

This paper explores systematic parallels between the criticisms of Kantian cognitive dualism provided by Salomon Maimon within his 'Essay on Transcendental Philosophy' of 1790 and F.W.J. Schelling within his 'General Overview of the Most Recent Philosophical Literature' of 1797. It discusses how both Maimon and Schelling suggest that the difficulties with Kant's cognitive dualism are so severe that they can only be resolved by recourse to a Leibnizian position, in which sensibility and understanding, and matter and form, arise from one (...) and the same cognitive source. It thus shows how Maimon and Schelling – within 1790 and 1797, respectively – sketch systems of transcendental philosophy explicitly modelled on the Leibnizian philosophy, which both of them interpret as claiming that God is immanently contained within the human soul. (shrink)

Most accounts of miracles assume that a necessary condition for an event's being miraculous is that it be, as Hume put it, “a violation of the laws of nature.” However, any account of this sort will be ill-suited for defending the major Western religious traditions because, as I will argue, classical theists should not believe in violations of the laws of nature. In place of the rejected Humean accounts, this paper seeks to develop and defend a Leibnizian conception of miracles (...) on which an event is said to be miraculous just in case we can discover its final cause but not its efficient cause. (shrink)

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)

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. (shrink)

Leibniz’s philosophy enjoyed a Russian fandom that endured from the eighteenth century to the death of the last exiled Russian philosophers in the twentieth century. There was, to begin with, Leibniz’s direct impact on Peter the Great and on the scientific development of Saint Petersburg. Then there was, still in the eighteenth century, Mikhail Lomonosov, who was sent to study with Christian Wolff in Marburg, and who came back to Saint Petersburg with a watered-down Leibnizian worldview, which he applied to (...) the study of chemistry and physics. Another eighteenth century philosopher, Alexander Radishchev, who studied in Leipzig, displayed acquiescence with a number of key elements from Leibniz’s philosophy. Russian Lebnizianism as a continuous philosophical movement was considerably reinvigorated in the 1870s when the Leibnizian German philosopher Gustav Teichmüller took a position at the University of Dorpat (nowadays Tartu, Estonia), which was then located within the Russian Empire. Teichmüller influenced a number of Russian philosophers into adopting a “Teichmüllerian” version of Leibnizianism. Among these philosophers were Evgeny Bobrov and Alexei Kozlov. In Saint Petersburg, Kozlov influenced his own son, Askoldov, and the latter’s friend — Nikolai Lossky. In the meanwhile, in Moscow Lev Lopatin, Nikolai Bugaev, and Petr Astafiev developed their own Leibnizianism in seemingly relative independence from Teichmüller’s influence and presumably, in some cases, under the partial influence of Vladimir Solovyov. Despite this relative independence, however, the fact remains that there was in late nineteenth and early twentieth century Russia a network of more or less loosely interconnected Leibnizian philosophers who read each other and wrote about each other, who exchanged ideas, and who constituted a movement that we might characterize as “Russian Leibnizianism” or “Russian Neo-Leibnizianism.” In this chapter, I tell the story of the intellectual lineage of Russian Leibnizianism. (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)

The so-called Principle of Plenitude was ascribed to Leibniz by A. O. Lovejoy in The Great Chain of Being: A Study of the History of an Idea. Its temporal version states that what holds always, holds necessarily. This temporal formulation is the subject of the current paper. Lovejoy’s idea was criticised by Hintikka. The latter supported his criticisms by referring to specific Leibnizian notions of absolute and hypothetical necessities interpreted in a possible-worlds semantics. In the paper, Hintikka’s interpretative suggestions are (...) developed and enriched with a temporal component that is present in the characteristics of the real world given by Leibniz. We use in our approach the Leibnizian idea that change is primary to time and the idea that there are possible laws that characterize worlds other than the real one. We formulate a modal propositional logic with three primitive operators for change, temporal constancy, and possible lawlikeness. We give its axiomatics and show that our logic is complete with respect to the given semantics of possible worlds. Finally, we show that the counterparts of the considered versions of the Principle of Plenitude are falsified in this semantics and the same applies to the counterpart of Leibnizian necessarianism. (shrink)

Leibniz is an eclectic and ecumenical philosopher. He often worked out philosophical positions that reconciled seemingly opposed theoretical systems and chastised people for rejecting certain views too quickly. In this paper, I describe one episode of Leibnizian reconciliation. My target is the phenomenon of deliberation. Traditionally, philosophers have offered two different accounts of deliberation based on two different accounts of the compatibility of freedom and determinism. Leibniz, I argue, cannot accept either account because of his broader theoretical commitments. This leads (...) Leibniz to formulate an interesting account of deliberation that adopts certain elements from each account while excising the untoward aspects of each one. I outline the various mechanisms involved in deliberation on Leibniz’s view and show how deliberation fits into a broader theory of free action. I close with an assessment of whether Leibniz in fact succeeds in offering an account of deliberation that is distinct from the traditional positions. (shrink)

I argue that we can learn quite a lot about Leibniz’s metaphysics, in particular about monads and their relationship to time, by viewing Leibniz through a McTaggartian lens. After presenting McTaggart’s highly influential two basic conceptions of time, the A- (or tensed) and B- (or tenseless) conceptions, I distinguish four possible models of the relationship between monads and time: the fi rst two invoke tenses, differing in whether they treat non-present states as “real,” while the latter two are tenseless, differing (...) in whether we construe the monad as (tenselessly) manifesting distinguishable perceptual states or as being in one indivisible but complex perceptual state representing the world as varying over time. A detailed study of the relative merits and demerits of the four models supports, I argue, the last model. Along the way I provide a Leibnizian account of the conscious illusion of temporal fl ow. (shrink)

The mature Leibniz frequently uses the phrase “moral necessity” in the context of discussing free choice. In this essay I provide a seventeenth century geneology of the phrase. I show that the doctrine of moral necessity was developed by scholastic philosophers who sought to retain a robust notion of freedom while purging bruteness from their systems. Two sorts of bruteness were special targets. The first is metaphysical bruteness, according to which contingent events or states of affairs occur without a sufficient (...) explanation. The second is semantic bruteness according to which a proposition can be true without a truth maker. Denying eithersort of bruteness was thought by some to raise problems for freedom. Defenders of moral necessity thought the notion solved these problems without having to invoke bruteness. (shrink)

The mature Leibniz frequently uses the phrase “moral necessity” in the context of discussing free choice. In this essay I provide a seventeenth century geneology of the phrase. I show that the doctrine of moral necessity was developed by scholastic philosophers who sought to retain a robust notion of freedom while purging bruteness from their systems. Two sorts of bruteness were special targets. The first is metaphysical bruteness, according to which contingent events or states of affairs occur without a sufficient (...) explanation. The second is semantic bruteness according to which a proposition can be true without a truth maker. Denying eithersort of bruteness was thought by some to raise problems for freedom. Defenders of moral necessity thought the notion solved these problems without having to invoke bruteness. (shrink)

Leibniz desenvolve uma intensa actividade filosófico-científica ao longo de um período de mais de cinquenta anos, na procura de uma via da modernidade mais complexa do que o mecanicismo vulgar, que reduz significativamente o campo do saber. A correspondência com Jacob Thomasius, seu professor mais influente, permitiu ao jovem Filósofo uma cuidada reflexão sobre dois tópicos nucleares da sua elaboração teórica – o da continuidade e o da forma –, que são, simultaneamente, motivo de afinidade e de divergência entre ambos. (...) De facto, tal como Thomasius, Leibniz assume a tarefa de conciliar antigos e modernos, mas, diferentemente do seu Mestre, entende que a matriz dessa ciência eclética é a ciência moderna e não a aristotélica. No que diz respeito à forma e mais precisamente à forma subs­tancial, Leibniz concorda com Thomasius que ela é imprescindível na filosofia natural, mas explica a sua génese de modo mecânico, através do movimento. Por seu lado, em virtude do estatuto fenomenal do movimento, a sua causa primordial não poderá ser outra que o próprio espírito. Por conseguinte, a primeira filosofia de Leibniz conjuga mecanicismo e espiritualismo. (shrink)

Purdue University and Syracuse University.

Purdue University and Syracuse University.

I argue that we can learn quite a lot about Leibniz’s metaphysics, in particular about monads and their relationship to time, by viewing Leibniz through a McTaggartian lens. After presenting McTaggart’s highly influential two basic conceptions of time, the A- (or tensed) and B- (or tenseless) conceptions, I distinguish four possible models of the relationship between monads and time: the fi rst two invoke tenses, differing in whether they treat non-present states as “real,” while the latter two are tenseless, differing (...) in whether we construe the monad as (tenselessly) manifesting distinguishable perceptual states or as being in one indivisible but complex perceptual state representing the world as varying over time. A detailed study of the relative merits and demerits of the four models supports, I argue, the last model. Along the way I provide a Leibnizian account of the conscious illusion of temporal fl ow. (shrink)

This paper is devoted to the late Leibnizian doctrine of vinculum substantiale. In the first section I sketch the old problem of possibility of composite substances. This possibility is refuted on the ground of Monadism (presented in section two). However Leibniz’s correspondence with Des Bosses contains new thoughts concerning composite substances. A vinculum enters the stage as a real unifier, transforming aggregates of monads into genuine substances (section three). In the last section I give a systematic interpretation of a vinculum.I (...) start with the thesis that every composed thing, which is not a pure plurality of objects, must have two structures: the whole-parts structure and the subject-properties structure. In the case of substances the latter is ontologically prior over the former. A vinculum is a subject-of-properties (accidents) determining such a way of composition which makes a compound entity a true substance. Since Leibniz still thought a vinculum unifies independent (existentially and with regard to activity) substances he was inclined to separate a vinculum from the integrated monads and finally conceived it as an additional relatively independent monad-like substance. (shrink)

It is argued that from a genuine Leibnizian point of view the well-known thought experiment, call it BTE, involving a possible world with only two exactly similar objects, cannot be used to refute Leibniz's Principle of the Identity of Indiscernibles (LIdI). If the claim that there are two objects in BTE is based on primitive thisnesses, the Leibnizian objection is that there are no such things; and even if there were, then, quite generally, something true of one object – that (...) it has its primitive thisness – would not be true of the other. Secondly, if the duality claim is based on a primitive, irreducible relation of distinctness, the Leibnizian objection is that there are no irreducible relations. Finally, if it is said that the (putatively) two objects in BTE cannot be separately individuated, then BTE is not a counter-example to LIdI, because if there is no individuation, there are no individuals either, while LIdI presupposes that there are individuals. (shrink)

A model is said to be Leibnizian if it has no pair of indiscernibles. Mycielski has shown that there is a first order axiom LM (the Leibniz-Mycielski axiom) such that for any completion T of Zermelo-Fraenkel set theory ZF, T has a Leibnizian model if and only if T proves LM. Here we prove: THEOREM A. Every complete theory T extending ZF + LM has $2^{\aleph_{0}}$ nonisomorphic countable Leibnizian models. THEOREM B. If $\kappa$ is aprescribed definable infinite cardinal of a (...) complete theory T extending ZF + V = OD. then there are $2^{\aleph_{1}}$ nonisomorphic Leibnizian models $\mathfrak{M}$ of T of power $\aleph_{1}$ such that $(\kappa^{+})^\mathfrak{M}$ is $\aleph_{1}-like$ . THEOREM C. Every complete theory T extending ZF + V = OD has $2^{\aleph_{1}}$ nonisomorphic \aleph_{1}-like$ Leibnizian models. (shrink)

I explicate and defend leibniz's argument from "eternal truths" to the existence of god. I argue that necessary beings can be caused to exist, Showing how one can apply a counterfactual analysis to such causation, Then argue that if such beings can be caused to exist, They are.

In seiner traditionellen Auffassung besagt der Superessentialismus, daß alle Eigenschaften einer Person dieser Person wesentlich sind, und daß jedes Individuum genau einer möglichen Welt zugeordnet ist. Dies impliziert, daß eine Person alle Eigenschaften haben muß, die ihr vollständiger Begriff angibt, andernfalls kann diese Person nicht existieren. Diese Lehre ist eine offensichtliche Bedrohung für den Leibnizschen Freiheitsbegriff, der erfordert, daß Handlungen sowohl kontingent als auch ein Produkt von Einsicht sein müssen. Ich behandle zwei Interpretationen der Kontingenz und behaupte, daß nur eine (...) dieser Interpretationen sowohl mit Freiheit als auch mit Superessentialismus in Einklang zu bringen ist. Weiter behaupte ich, daß eine auf erwägender Einsicht beruhende Handlung, die für Freiheit notwendig ist, Betrachtungen von Handlungsabläufen beinhaltet, die dieser Person wirklich möglich sind. Dies bringt mich zu dem Schluß, daß Superessentialismus unvereinbar ist mit dem Leibnizschen Freiheitsbegriff, daß Personen eine Mehr-Welten-Identität besitzen, und daß der vollständige Begriff eines Individuums sowohl aktuale als auch nur mögliche Eigenschaften beinhaltet. (shrink)

This paper paper will examine some very different positions that Leibniz held or explored on monism, force, and substance during his long philosophical life. For reasons to be explained, positions drawn from Leibniz’s youth as well as his maturity will be considered. It will prove useful to consider these Leibnizian positions on these issues in relation to some of the leading alternatives of his age, in particular, those of Descartes, Spinoza and Malebranche. A guiding idea of this paper is that (...) by meditating seriously on some key ideas explored by Leibniz on our topics, one can gain new insight into the philosophical options of his era. A few introductory remarks on Descartes, followed by an overview of the main divisions and aims of the present paper, will help set the stage for these Leibnizian meditations. (shrink)

This paper paper will examine some very different positions that Leibniz held or explored on monism, force, and substance during his long philosophical life. For reasons to be explained, positions drawn from Leibniz’s youth as well as his maturity will be considered. It will prove useful to consider these Leibnizian positions on these issues in relation to some of the leading alternatives of his age, in particular, those of Descartes, Spinoza and Malebranche. A guiding idea of this paper is that (...) by meditating seriously on some key ideas explored by Leibniz on our topics, one can gain new insight into the philosophical options of his era. A few introductory remarks on Descartes, followed by an overview of the main divisions and aims of the present paper, will help set the stage for these Leibnizian meditations. (shrink)

This paper paper will examine some very different positions that Leibniz held or explored on monism, force, and substance during his long philosophical life. For reasons to be explained, positions drawn from Leibniz’s youth as well as his maturity will be considered. It will prove useful to consider these Leibnizian positions on these issues in relation to some of the leading alternatives of his age, in particular, those of Descartes, Spinoza and Malebranche. A guiding idea of this paper is that (...) by meditating seriously on some key ideas explored by Leibniz on our topics, one can gain new insight into the philosophical options of his era. A few introductory remarks on Descartes, followed by an overview of the main divisions and aims of the present paper, will help set the stage for these Leibnizian meditations. (shrink)

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)

In this paper, I argue a position that has almost never been held: that Leibniz was a materialist. At the conclusion of my article, I consider whether the difficulty of reconciling Leibnizs idea of concluding that there is instead a Leibnizian idea of which does a better job.