Jonathan Edwards' article “Modern Monads: Leibniz, Continuity, and the Stream of Consciousness” deals with Gottfried Wilhelm Leibniz's (1646– 1716) famous monadology, especially with the perceiving entity, i.e. the subject or monad, and its identity over time. Edwards asks whether it is possible to combine Leibniz's theory of monads with modern biology and physics. His response is affirmative. I will start with some general points about his article, and then I will introduce it in details.

To escape from the labyrinth of the continuum, Leibniz maintains, we must think very differently about the nature of space, time, bodies, and substances; and in particular we must posit an infinity of simple substances or monads. The main aim of this historically rich and interpretively provocative book is to explain why Leibniz says such things by examining his purported solution and how he arrived at it. Each of the book’s seven chapters focuses on a different “Ariadnean thread” that (...) supposedly helped Leibniz find his way out of the labyrinth. They concern the themes of “composition, aggregation, atoms, forms, motion, substance, and continuation in existence” (6). (shrink)

The problematic vagueness inherent to the study of being requires an approach that transcends the use of a methodology pertaining to solely one research area. In the following pages we will explore the categories of being, their metaphysical meaning and their interrelations, approaching them via heuristic methods that incorporate symbolic mathematical abstraction and music theory analogies. We will propose a monadic system for explicating how the modes of being interact with each other, also exposing a harmonic model of the universe (...) derived from these hypotheses (Chapter I). The nature of consciousness and its properties will be investigated in Chapter II, followed by a research concerning possible internal self-adjustments of total-being-for-itself that might offer insights regarding the temporality and necessity of individual consciousnesses. The aim of this paper is to coalesce the categories of being (in-itself, for-itself, the Others) into a comprehensive system that could account as a unified ontological model compatible with inferences related to phenomenal manifestations. (shrink)

In this paper I address a structurally similar tension between phenomenalism and realism about matter in Leibniz and Kant. In both philosophers, some texts suggest a starkly phenomenalist view of the ontological status of matter, while other texts suggest a more robust realism. In the first part of the paper I address a recent paper by Don Rutherford that argues that Leibniz is more of a realist than previous commentators have allowed. I argue that Rutherford fails to show that Leibniz (...) is any less an idealist than his main target, Robert Merrihew Adams, does. I distinguish various kinds of idealism about bodies that Leibniz might have held, and attempt to determine which package of views represents his considered view. In the second part of the paper I situate Kant’s idealism within the same coordinates. I argue that, abstracting from deep differences in their metaphysics and epistemology, Kant and Leibniz have structurally very similar views on the ontological status of matter and bodies. I conclude that the key to understanding the realist strand in their ontology of matter is understanding the way in which, for both thinkers, the forces in bodies are appearances of forces of more fundamental entities, either monads or things in themselves. (shrink)

In this paper, I aim to offer a clear explanation of what monadic domination, understood as a relation obtaining exclusively among monads, amounts to in the philosophy of Leibniz (and this insofar as monadic domination is conceived by Leibniz not to account for the substantial unity of composite substances). Central to my account is the Aristotelian notion of a hierarchy of activities, as well as a particular understanding of the relations that obtain among the perceptions of monads that (...) stand in relations of monadic domination and subordination. (shrink)

Leibniz has almost universally been represented as denying that created substances, including human minds and the souls of animals, can causally interact either with one another or with bodies. Yet he frequently claims that such substances are capable of interacting in the special sense of what he calls 'ideal' interaction. In order to reconcile these claims with their favored interpretation, proponents of the traditional reading often suppose that ideal action is not in fact a genuine form of causation but instead (...) a merely apparent influence which serves to 'save the appearances.' I argue that this traditional reading distorts Leibniz's thought and that he actually considers ideal action a genuine (though non-standard) form of causation. (shrink)

The reconstruction of Leibniz’s metaphysics that Deleuze undertakes in The Fold provides a systematic account of the structure of Leibniz’s metaphysics in terms of its mathematical foundations. However, in doing so, Deleuze draws not only upon the mathematics developed by Leibniz—including the law of continuity as reflected in the calculus of infinite series and the infinitesimal calculus—but also upon developments in mathematics made by a number of Leibniz’s contemporaries—including Newton’s method of fluxions. He also draws upon 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 Weierstrassian theory of analytic continuity, and Poincaré’s theory of automorphic functions. Deleuze then retrospectively maps these developments back onto the structure of Leibniz’s metaphysics. While the Weierstrassian theory of analytic 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. This essay 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)

According to Leibniz, there is no death in the sense that the human being or animal is destroyed completely. This is due to his metaphysical pluralism which would suffer if the number of substances decreased. While animals transform into other animals after “death”, human beings are rewarded or punished of their behavior in this life. This paper presents a comprehensive account of how Leibniz thought the “death” to take place and discusses his often unclear views on the life after death. (...) I will also present a new, naturalistic reading of Leibniz’s views on afterlife. (shrink)

This article explores the later Schleiermacher’s metaphysics of substance and what it entails concerning the question of transcendental freedom. I show that in espousing a metaphysics of substance, Schleiermacher also abandoned an understanding of nature as a mere mechanism, a view implying what I call a “state-state view of causation” (“SSV” for short). Adoption of the view of the self as substance was motivated by the primacy of practical and religious concerns in Schleiermacher’s later work: in Christian Faith, an analysis (...) of self-consciousness from a first person point of view grounds this understanding of the self. In fact, in Christian Faith, ontology, and thereby theology, is only possible through such a first person analysis. The development of Schleiermacher’s views over time, and the reasons accompanying this development, can be fully understood only the in the context of his engagement with the work of Spinoza, Leibniz, and Kant. In what follows I trace this development through an analysis of the philosophical problems and influences shaping Schleiermacher’s mature view, and shed light on his understanding of self-consciousness and its relation to God. My own account should also serve to correct some recent misunderstandings that have made their way into the secondary literature. (shrink)

This paper attempts to resolve the puzzle associated with the non-spatiality of monads by investigating the possibility that Leibniz employed a version of the extension of power doctrine, a Scholastic concept that explains the relationship between immaterial and material beings. As will be demonstrated, not only does the extension of power doctrine lead to a better understanding of Leibniz’ reasons for claiming that monads are non-spatial, but it also supports those interpretations of Leibniz’ metaphysics that accepts the real (...) extension of bodies. (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)

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)

This paper is a discussion of the treatment of Leibniz's conception of substance in Heidegger's The Metaphysical Foundations of Logic. I explain Heidegger's account, consider its relation to recent interpretations of Leibniz in the Anglophone secondary literature, and reflect on the ways in which Heidegger's methodology may illuminate what it is to read Leibniz and other figures in the history of philosophy.

The purpose of this essay is to make the case for a heterodox reading of Leibniz’s The Monadology (published 1720) through the lens of Professor John Wheeler’s hypothesis of the one-electron universe (proposed in 1940). My conjecture is this: That there exists in the knowable universe only one monad; that this monad traverses time in both directions, eventually criss-crossing the entire past and future history of the universe; and that this singular monad interacts with itself countless times, thereby filling the (...) universe with simultaneous appearances of itself. In the course of this article I will consider the possibility that our solitary monad is synonymous with Leibniz’s God, or if the monad in question is rather a created substance that is alone with God, a notion that gains some traction thanks to Leibniz’s admiration for the solipsism of Saint Teresa of Avila. I will also consider whether the one-monad hypothesis is consistent with Leibniz’s own views on harmony, simplicity and perfection. (shrink)

Written in 1714, the “Monadology” is widely regarded as a classic statement of much of Leibniz’s mature philosophical system. In just 90 numbered paragraphs, Leibniz outlines—and argues for—the core features of his system, starting with his famous doctrine of monads (simple substances) and ending with the uplifting claim that God is concerned not only for the world as a whole but for the welfare of the virtuous in particular. This chapter begins by considering the circumstances of composition of the (...) “Monadology” and its publication history before offering a detailed analysis of the claims and arguments found therein; I suggest the text is best read as dealing with three distinct realms, the metaphysical (§§1–-60), the physical (§§61–-82), and lastly the moral (§§83–-90). The chapter concludes with a consideration of the fate and influence of this seminal text. (shrink)

Gottfried Wilhelm Leibniz presents the idea of monads, as non-communicative, self-actuating system of beings that are windowless, closed, eternal, deterministic and individualistic. For him, the whole universe and its constituents are monads and that includes humans. In fact, any ‘body’, such as the ‘body’ of an animal or man has, according to Leibniz, one dominant monad which controls the others within it. This dominant monad, he often refers to as the soul. If Leibniz’s conception of monads is (...) accepted, it merely establishes human subjectivity, idiosyncrasies, biases, prejudices and individual points of view as the norm. How then do we ensure inter-subjectivity and the kind of social interaction requisite for the achievement of social order, since Leibniz’s system forecloses the possibility of interaction and communication among monads? In this essay, we argue that just as Leibniz’s monads synchronize only through the Supreme Monad (Monas Monadum), humans as social monads should also interact through a matrix of ideals like truth, honesty, sincerity, integrity, altruism, impartiality, compassion and trust. Since social order is actualised only within the context of linked social structures, relations and values, these utopian ideals would form the fulcrum through which humans relate and the very foundation that would anchor a viable social order. Our aim here is to establish a relationship between Leibniz’s metaphysics and the physical domains of life by showing that metaphysical constructs can impinge on human social relations and wellbeing. The study employed the qualitative method of research through critical analysis of texts, library and archival materials. (shrink)

Deferential Monadic Panpsychism is a view that accepts that physical science is capable of discovering the basic structure of reality. However, it denies that reality is fully and exhaustively de- scribed purely in terms of physical science. Consciousness is missing from the physical description and cannot be reduced to it. DMP explores the idea that the physically fundamental features of the world possess some intrinsic mental aspect. It thereby faces a se- vere problem of understanding how more complex mental states (...) emerge from the mental features of the fundamental features. Here I explore the idea that a new form of aggregative emergence, which I call 'combinatorial infusion', could shed light on this problem and bolster the prospects for this form of panpsychism. (shrink)

The Russian philosopher Nikolai Onufrievich Lossky considered himself a Leibnizian of sorts. He accepted parts of Leibniz’s doctrine of monads, although he preferred to call them ‘substantival agents’ and rejected the thesis that they have neither doors nor windows. In Lossky’s own doctrine, monads have existed since the beginning of time, they are immortal, and can evolve or devolve depending on the goodness or badness of their behavior. Such evolution requires the possibility for monads to reincarnate into (...) the bodies of creatures of a higher level on the scala perfectionis. According to this theory, a monad can evolve by being progressively reincarnated multiple times through a sort of process of metamorphosis from the level of the most elementary particles all the way up to the level of human beings or even higher. Lossky argues that the works of Leibniz contain scattered elements of such a systematic doctrine of reincarnation. He attempts to reconstitute this doctrine in an article that appeared both in Russian and German in 1931. The Russian version, ‘Ученiе Лейбница о перевоплощенiи какъ метаморфозѣ’, was published in the Сборникъ Русскаго института въ Прагѣ, vol. 2, 1931, pp. 77–88. The German version appeared under the title ‘Leibniz’ Lehre von der Reinkarnation als Metamorphose,’ in Archiv für Geschichte der Philosophie, vol. 40, n. 2, 1931, pp. 214–226. The content of the Russian and German versions is roughly the same, except for the omission, in the German version, of a mention of David Hume in the second sentence and of one paragraph and a half at the end of the article. The following is a translation of this article. I translated the text from the Russian version, which was in all appearances written first, but I also took the German version into account. The original pagination is added in angle brackets. Angle brackets are used wherever the additions are mine. — Frédéric Tremblay. (shrink)

One of the most intriguing – and arguably counter-intuitive – doctrines defended by environmental philosophers is that of positive aesthetics, the thesis that all of nature is beautiful. The doctrine has attained philosophical respectability only comparatively recently, thanks in no small part to the work of Allen Carlson, one of its foremost defenders. In this paper, we argue that the doctrine can be found much earlier in the work of Gottfried Wilhelm Leibniz who devised and defended a version of positive (...) aesthetics in the early modern period, grounded in a conception of the world as a world of monads, each of which individually fulfils the rationalist aesthetic criteria of multiplicity-in-unity and that taken together ensure that the world as a whole is a harmoniously ordered system of multiple and diverse individuals, whose intelligible order and variety is made known to us through natural scientific endeavour. In showing this, we advance two further theses: first, that Leibniz's vers.. (shrink)

The quest to understand the natural and the mathematical as well as philosophical principles of dynamics of life forms are ancient in the human history of science. In ancient times, Pythagoras and Plato, and later, Copernicus and Galileo, correctly observed that the grand book of nature is written in the language of mathematics. Platonism, Aristotelian logism, neo-realism, monadism of Leibniz, Hegelian idealism and others have made efforts to understand reasons of existence of life forms in nature and the underlying principles (...) through the lenses of philosophy and mathematics. In this paper, an approach is made to treat the similar question about nature and existential life forms in view of mathematical philosophy. The approach follows constructivism to formulate an abstract model to understand existential life forms in nature and its dynamics by selectively combining the elements of various schools of thoughts. The formalisms of predicate logic, probabilistic inference and homotopy theory of algebraic topology are employed to construct a structure in local time-scale horizon and in cosmological time-scale horizon. It aims to resolve the relative and apparent conflicts present in various thoughts in the process, and it has made an effort to establish a logically coherent interpretation. (shrink)

How to reconcile monadic simplicity with the successive plurality of the monadic states ? The doctrine of continued creation seems to entail the existence of independent temporal parts and thus lead to the thesis that the world contains only transitory things. I try to show how Leibniz has the resources to get out of this quandary. The analysis of the concept of extension shows that a plurality of states does not constitute a divisible aggregate. Then I examine the Leibnizian interpretation (...) of continued creation, by com- paring it to the scholastic and Cartesian Background. From thence I conclude that Leibniz’s final thesis is that monads are wholly present at each moment of their duration. (shrink)

The orthodox monadic determination thesis holds that we represent colour relations by virtue of representing colours. Against this orthodoxy, I argue that it is possible to represent colour relations without representing any colours. I present a model of iconic perceptual content that allows for such primitive relational colour representation, and provide four empirical arguments in its support. I close by surveying alternative views of the relationship between monadic and relational colour representation.

Over the course of the past ten-plus years, Peter Hanks and Scott Soames have developed detailed versions of Act-Based views of propositions which operate with the notions of reference to objects, indicating properties, predication, and judgment (or entertaining). In this paper I discuss certain foundational aspects of the Act-Based approach having to do with the relations between these notions. In particular, I argue for the following three points. First, that the approach needs both an atomistically understood thin notion of reference, (...) a bare act of thinking of o, as well as a more involved notion, something like making o a target of predication. Second, that the acts of thinking of o and indication of the property of being F are in no sense parts of the acts of predication of being F of o and judgment that o is F. Rather, the former are simply necessary preconditions for the performance of the latter. The acts of predication or judgment are emphatically not structured sequences of separate acts but unities in and of themselves. Finally, that we should understand the Act-Based theorists’ claim that to predicate is to judge as the claim that judgment can be reductively analyzed in terms of predication. Furthermore, while predication is metaphysically a multiple relation between a predicator, a target, and the property predicated, judgment is a monadic property, just one that has propositional content. (shrink)

Scholars have wrestled with "consciousness", one writer calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a form (...) of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the relationship. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

A fresh translation and in-depth commentary of Leibniz's seminal text, the Monadology. -/- Written in 1714, the Monadology is widely considered to be the classic statement of Leibniz's mature philosophy. In the space of 90 numbered paragraphs, totalling little more than 6000 words, Leibniz outlines - and argues for - the core features of his philosophical system. Although rightly regarded as a masterpiece, it is also a very condensed work that generations of students have struggled to understand. -/- Lloyd Strickland (...) presents a new translation of the Monadology, alongside key parts of the Theodicy, and an in-depth, section-by-section commentary that explains in detail not just what Leibniz is saying in the text but also why he says it. The sharp focus on the various arguments and other justifications Leibniz puts forward makes possible a deeper and more sympathetic understanding of his doctrines. (shrink)

Scholars have wrestled with "consciousness", a major scholar calling it the "hard problem". Some thirty-plus years after the Towards a Science of Consciousness, we do not seem to be any closer to an answer to "What is consciousness?". Seemingly irresolvable metaphysical problems are addressed by bootstrapping, provisional assumptions, not unlike those used by logicians and mathematicians. I bootstrap with the same ontology and epistemology applicable to everything we apprehend. Here, I argue for a version of the unity of opposites, a (...) form of neutral monism. Something exists because of what it is not; nothing can exist by itself, singularities (analogous to monads), expressing the model. Applying this most fundamental law to the consciousness problem, the physical (movement) comes into being simultaneously as the mental (stasis), each displayed by a field that is variegated (ranging from creative to entropic processes). Such is in keeping with how the singularity emerged as our universe, the same form that may account for sub-Planck-scale phenomena. Overall, like the most fundamental law, deep structures are imminent in our universe, both as objects and processes. (shrink)

Contrary to widely shared opinion in analytic metaphysics, E.J. Lowe argues against the existence of relations in his posthumously published paper There are probably no relations (2016). In this article, I assess Lowe’s eliminativist strategy, which aims to show that all contingent “relational facts” have a monadic foundation in modes characterizing objects. Second, I present two difficult ontological problems supporting eliminativism about relations. Against eliminativism, metaphysicians of science have argued that relations might well be needed in the best a posteriori (...) motivated account of the structure of reality. Finally, I argue that, by analyzing relational inherence, trope theory offers us a completely new approach to relational entities and avoids the hard problems motivating eliminativism. (shrink)

This article presents a trope bundle theory of simple substances, the Strong Nuclear Theory[SNT] building on the schematic basis offered by Simons's (1994) Nuclear Theory[NT]. The SNT adopts Ellis's (2001) dispositional essentialist conception of simple substances as powerful particulars: all of their monadic properties are dispositional. Moreover, simple substances necessarily belong to some natural kind with a real essence formed by monadic properties. The SNT develops further the construction of substances the NT proposes to obtain an adequate trope bundle theory (...) of powerful particulars. The SNT allows for co-located powerful particulars. However, every powerful particular is necessarily co-located with its constituent tropes, which determine its causal powers. Every constituent trope of substance i is part of a trope aggregate (the n-bundle or c-bundle) that forms an individual figuring in the basic spatio-temporal relations. The location of these individuals determines the location of individual tropes. Since they are necessarily co-located with substance i when they exist, every trope t of i is necessarily co-located with i when it exits. Every simple substance has nuclear tropes necessary to it. It belongs to certain primary natural kind K because its nuclear tropes belong to certain distinct determinate kinds. (shrink)

The question I want to explore is whether experience supports an antireductionist ontology of time, that is, whether we should take it to support an ontology that includes a primitive, monadic property of nowness responsible for the special feel of events in the present, and a relation of passage that events instantiate in virtue of literally passing from the future, to the present, and then into the past.

The trope bundle theories of objects are capable of analyzing monadic inherence (objects having tropes), which is one of their main advantage. However, the best current trope theoretical account of relational tropes, namely, the relata specific view leaves relational inherence (a relational trope relating two or more entities) primitive. This article presents the first trope theoretical analysis of relational inherence by generalizing the trope theoretical analysis of inherence to relational tropes. The analysis reduces the holding of relational inherence to the (...) obtaining of certain other facts about entities of the trope theoretical category system. Moreover, I show that the analysis can deal with asymmetric and non-symmetric relations by assuming that all relation-like tropes are quantities. Finally, I provide an account of the spatial location of tropes in the difficult case in which tropes contribute to determining of the location of other entities. (shrink)

Metaphysics should follow science in postulating laws alongside properties. I defend this claim against the claim that natural properties conceived as powers make laws of nature redundant. Natural properties can be construed in a “thin” or a “thick” way. If one attributes a property in the thin sense to an object, this attribution does not conceptually determine which other properties the object possesses. The thin construal is underlying the scientific strategy for understanding nature piecemeal. Science explains phenomena by cutting reality (...) conceptually in properties attributed to space-time points, where these properties are conceived of independently of each other, to explore then, in a separate step, how the properties are related to each other; those determination relations between properties are laws. This is compatible with the thesis that laws are metaphysically necessary. According to the thick conception, a property contains all its dependency relations to other properties. The dependency relationships between properties (which appear as laws in the thin conception) are parts of the properties they relate. There are several reasons to resist the thick conception of properties. It makes simple properties “holistic”, in the sense that each property contains many other properties as parts. It cannot account for the fact that properties constrain each other’s identity; it can neither explain why natural properties are linked to a unique set of dispositions, nor why and how this set is structured nor why the truth-maker of many disposition attributions is relational although the disposition is grounded on a monadic property. (shrink)

Heinrich Behmann (1891-1970) obtained his Habilitation under David Hilbert in Göttingen in 1921 with a thesis on the decision problem. In his thesis, he solved - independently of Löwenheim and Skolem's earlier work - the decision problem for monadic second-order logic in a framework that combined elements of the algebra of logic and the newer axiomatic approach to logic then being developed in Göttingen. In a talk given in 1921, he outlined this solution, but also presented important programmatic remarks on (...) the significance of the decision problem and of decision procedures more generally. The text of this talk as well as a partial English translation are included. (shrink)

We argue that if one wishes to be a realist, one should adopt a Neo-Aristotelian ontology involving tropes instead of a Russellian ontology of property universals and objects. Either Russellian realists should adopt the relata-specific relational tropes of instantiation instead of facts, or convert to Neo-Aristotelian realism with monadic tropes. Regarding Neo-Aristotelian realism, we have two novel points why it fares better than Russellian realism. Instantiation of property universals by tropes and characterization or inherence between tropes and objects are more (...) transparent ontological notions than relational inherence, which is assumed in Russellian realism with the relational tropes of instantiation. Neo-Aristotelian realism makes better sense about abstract universals, which are a more viable option than concrete universals. (shrink)

In terms of validity in Kripke frames, a modal formula expresses a universal monadic second-order condition. Those modal formulae which are equivalent to first-order conditions are called elementary. Modal formulae which have a certain persistence property which implies their validity in all canonical frames of modal logics axiomatized with them, and therefore their completeness, are called canonical. This is a survey of a recent and ongoing study of the class of elementary and canonical modal formulae. We summarize main ideas and (...) results, and outline further research perspectives. (shrink)

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.

Powers ontologies are currently enjoying a resurgence. This would be dispiriting news for the moderns; in their eyes, to imbue bodies with powers is to slide back into the scholastic slime from which they helped philosophy crawl. I focus on Descartes’s ‘little souls’ argument, which points to a genuine and, I think persisting, defect in powers theories. The problem is that an Aristotelian power is intrinsic to whatever has it. Once this move is accepted, it becomes very hard to see (...) how humble matter could have such a thing. It is as if each empowered object were possessed of a little soul that directs it and governs its behavior. Instead of attempting to resurrect the Aristotelian power theory, contemporary philosophers would be best served by taking their inspiration from its early modern replacement, devised by John Locke and Robert Boyle. On this view, powers are internal relations, not monadic properties intrinsic to their bearers. This move at once drains away the mysterious directedness of Aristotelian powers and solves the contemporary version of the little souls argument, Neil Williams’s ‘problem of fit.’. (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)

In the correspondence with Arnauld, Leibniz contends that each corporeal substance has a substantial form. In support he argues that to be real a corporeal substance must be one and indivisible, a true unity. I will show how this argument precludes a tempting interpretation of corporeal substances as composite unities. Rather it mandates the interpretation that each corporeal substance is a single monad.

In the paper we will employ set theory to study the formal aspects of quantum mechanics without explicitly making use of space-time. It is demonstrated that von Neuman and Zermelo numeral sets, previously efectively used in the explanation of Hardy’s paradox, follow a Heisenberg quantum form. Here monadic union plays the role of time derivative. The logical counterpart of monadic union plays the part of the Hamiltonian in the commutator. The use of numerals and monadic union in the classical probability (...) resolution of Hardy’s paradox [1] is supported with the present derivation of a commutator for sets. (shrink)

There are at least five ‘core’ notions of community found in Kant's works: 1. The scientific notion of interaction. This concept is introduced in the Third Analogy and developed in the Metaphysical Foundations of Natural Science. 2. A metaphysical idea. The idea of a world of individuals (monads) in interaction. This idea was developed in Kant’s precritical period and can be found in his metaphysics lectures. 3. A moral ideal. The idea of a realm of ends. 4. A political (...) ideal. The idea of a juridical community (or community of communities) governed by juridical laws. 5. A theological ideal. What Kant calls ‘the kingdom of heaven’, and which can be thought of as a community of holy beings, or angels. In this paper I focus on the relationship between the first, second and fourth of these notions. My argument is that Kant’s notion of a juridical community governed by juridical laws is modelled on the metaphysical idea of the world. This metaphysical idea of a world is, in turn, modelled on the category of community introduced in the first Critique and developed in his logic lectures. (shrink)

This paper aims to show that a proper understanding of what Leibniz meant by “hypercategorematic infinite” sheds light on some fundamental aspects of his conceptions of God and of the relationship between God and created simple substances or monads. After revisiting Leibniz’s distinction between (i) syncategorematic infinite, (ii) categorematic infinite, and (iii) actual infinite, I examine his claim that the hypercategorematic infinite is “God himself” in conjunction with other key statements about God. I then discuss the issue of whether (...) the hypercategorematic infinite is a “whole”, comparing the four kinds of infinite outlined by Leibniz in 1706 with the three degrees of infinity outlined in 1676. In the last section, I discuss the relationship between the hypercategorematic infinite and created simple substances. I conclude that, for Leibniz, only a being beyond all determinations but eminently embracing all determinations can enjoy the pure positivity of what is truly infinite while constituting the ontological grounding of all things. (shrink)

The perpetual secretary of the Berlin Academy Johann Heinrich Samuel Formey is best known as a populariser of Christian Wolff’s doctrines. As of Formey’s activity in the Berlin Academy, scholars have mostly emphasized his role in the controversy over monads with Leonhard Euler, while overlooking other interesting contributions Formey presented in the “speculative philosophy” class of the Academy. In this paper, I analyse two articles Formey published in 1747 on the Mémoires de l’Académie de Berlin, namely the Preuves de (...) l’existence de Dieu, ramenées aux notions communes and the Examen de la preuve qu’on tire des fins de la nature, pour établir l’existence de Dieu. In these texts, Formey presents some of Wolff’s methodological and metaphysical ideas, in an implicit dialogue with other members of the Academy – in particular, with the president Pierre-Louis Moreau de Maupertuis – who were also interested in metaphysics and the philosophical method. Formey reworks the Wolffian arguments as to make them more accessible, in order to promote an open confrontation over core philosophical questions. Far from adopting a controversial tone, Formey’s attitude is rather conciliatory: any disagreement, as he thinks, can be easily settled once the true method for philosophizing is made available to everybody. (shrink)

Gottfried Wilhelm Leibniz (1646–1716) was a universal genius, making original contributions to law, mathematics, philosophy, politics, languages, and many areas of science, including what we would now call physics, biology, chemistry, and geology. By profession he was a court counselor, librarian, and historian, and thus much of his intellectual activity had to be fit around his professional duties. Leibniz’s fame and reputation among his contemporaries rested largely on his innovations in the field of mathematics, in particular his discovery of the (...) calculus in 1675. Another of his enduring mathematical contributions was his invention of binary arithmetic, though the significance of this was not recognized until the 20th century. These days, a good proportion of scholarly interest in Leibniz is focused on his philosophy. Among his signature philosophical doctrines are the pre-established harmony, the theory of monads, and the claim that ours is the best of all possible worlds, which forms the central plank of his theodicy. For Leibniz, philosophy was not the discovery of deep truths of interest only to other philosophers, but a practical discipline with the means to increase happiness and well-being. Philosophical truths, he believed, revealed the beauty and rational order of the universe, and the justice and wisdom of its creator, and accordingly could inspire contentment and peace of mind. Leibniz’s other intellectual projects were likewise geared toward the improvement of the human condition. He lobbied tirelessly for the establishment of scientific societies, devised measures to improve public health, and was actively engaged in projects to unite the churches and so end the religious strife that marred the Europe of his day. He was also engaged in politics for much of his career, and often took on a diplomatic role, sometimes officially and other times not. In the political sphere, Leibniz did not wield true power but was a man with influence, obtained in no small part by his cultivation of relationships with leaders and sovereigns both inside and outside Germany. The sheer range of Leibniz’s interests, projects, and activities can make him a difficult figure to study, and the vast quantity of his writings only compounds the problem (around fifty thousand of his writings survive). Nevertheless, even a sampling of Leibniz’s work is enough to get a sense of his vision, originality, and intellectual depth, and good secondary literature will only enhance this. The items in this bibliography were chosen with this in mind. (shrink)

This blog post begins by showing the pejorative connotations inherent in the term 'Hindu' and goes on to lay bare the differences between Hinduism and other religions including Jainism and the Abrahamic religions. So that this necessary project of dialogues is not hijacked by celibates of various traditions; the post ends with these reflections: "The Hare Krishna movement, and all other prominent movements within the Sanatana Dharma including the various well known cults of hero-worship are all structured around centralised superstructures (...) which we acquired during our long history of colonisation. Many of these movements appeal to the Western mind because they are authoritarian with strict rules. But these rules have been negated within the Sanatana Dharma by thinkers ranging from Sri Utpaladeva to Sri Abhinavagupta to Sri Kshemraja. The Sanatana Dharma stresses marriage over celibacy not because it is akin to Protestantism. There is none to protest against. Nor is it better to marry than to burn. It is simply this; marriage is not a lower state than other choices in life. It is a first step towards recognising that one can indeed be two who form a monad.". (shrink)

One of the greatest philosophical controversies of the eighteenth century was the competition organized in 1746 by the Berlin Academy of Sciences. Although the specific object of the competition was the theory of monads, this particular question nevertheless referred to a deeper and more radical opposition between the two contending parties, Newtonians and Wolffians. In this contribution, we will first focus on the reasons for Newtonian opposition to Wolff’s philosophy. In this context, particular attention will be paid to the (...) positions of Euler and Maupertuis. We will then proceed to a comparison between the positions of Wolff and Maupertuis on the crucial question of the relationship between mathematical and philosophical method. Our analysis will attempt to show the existence, in Maupertuis’s thought, of an effort to apply the mathematical method to disciplines other than mathematics itself, which will allow us to determine his opposition to Wolffian philosophy. Finally, we will clarify the affinities and divergences between Wolff and Maupertuis, trying to show that the real reasons for their opposition should be sought in their respective epistemologies and metaphysics. (shrink)

Necessity is a touchstone issue in the thought of Charles Peirce, not least because his pragmatist account of meaning relies upon modal terms. We here offer an overview of Peirce’s highly original and multi-faceted take on the matter. We begin by considering how a self-avowed pragmatist and fallibilist can even talk about necessary truth. We then outline the source of Peirce’s theory of representation in his three categories of Firstness, Secondness and Thirdness, (monadic, dyadic and triadic relations). These have modal (...) purport insofar as the first category corresponds to possibility, the second to mechanical necessity and the third to a kind of semantic or intentional necessity. We then turn to Peirce’s explicit modal epistemology and show how it began as information-relative, with different modalities (e.g. logical, physical, practical) distinguished in terms of respective ‘designated states of information’, and shifted later in his life towards a more robust realism founded in direct perception of ideas in their relations. We then turn to Peirce’s formal logic, focusing on his diagrammatic system of Existential Graphs where he did his most serious logical research. Finally we discuss Peirce’s modal metaphysics and its implications for determinism and realism about universals. (shrink)

In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998) criticized by Imamura were never utilized since they were improved shortly after but he omits to tell their development, and that in real world applications we need to convert/approximate the NonStandard Analysis hyperreals, monads and binads to tiny intervals with the desired accuracy – otherwise (...) they would be inapplicable. We point out several errors and false statements by Imamura [21] with respect to the inf/sup of nonstandard subsets, also Imamura’s “rigorous definition of neutrosophic logic” is wrong and the same for his definition of nonstandard unit interval, and we prove that there is not a total order on the set of hyperreals (because of the newly introduced Neutrosophic Hyperreals that are indeterminate), whence the Transfer Principle from R to R* is questionable. After his criticism, several response publications on theoretical nonstandard neutrosophics followed in the period 2018-2022. As such, I extended the NonStandard Analysis by adding the left monad closed to the right, right monad closed to the left, pierced binad (we introduced in 1998), and unpierced binad - all these in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of NonStandard Unit Interval and NonStandard Neutrosophic Logic, together with NonStandard Neutrosophic Operators are presented. (shrink)

The author investigates greek ontologies that apparently rely on a conflation of "binary" (x is f) and "monadic" (x is) uses of 'is'. He uses Aristotelian and other texts to support his proposal that these ontologies are explained by the Greeks using two alternative semantic analyses for 'x is F'. The first views it as asserting a relation between x and F, the second as asserting that a "predicative complex" exists, where a predicative complex is a complex consisting of x (...) and F. The article concludes by indicating some uses for the novel concept of predicative complex in aristotelian interpretation. (shrink)

In the fifth version of our reply article [26] to Imamura's critique, we recall that Neutrosophic Non-Standard Logic was never used by the neutrosophic community in any application, that the quarter-century old (1995-1998) neutrosophic operators criticized by Imamura were never used as they were improved soon after, but omits to talk about their development, and that in real-world applications we need to convert/approximate the hyperreals, monads and bi-nads of Non-Standard Analysis to tiny intervals with the desired precision; otherwise they (...) would be inapplicable. We pointed out several errors and false statements by Imamura [21] regarding the inf/sup of nonstandard subsets, also Imamura's "rigorous definition of neutrosophic logic" is incorrect, as is his definition of nonstandard unit interval, and we showed that there is no total order in Neutrosophic Computing and Machine Learning , Vol. 23, 2022 Florentin Smarandache, Definición mejorada de la lógica neutrosófica no estándar e introducción a los hiperreales neutrosóficos (Quinta versión) 2 the set of hyperreals (due to the recently introduced Neutrosophic Hyperreals which are indeterminate), so the Transfer Principle from R to R* is questionable. After his critique, several reply posts on non-standard theoretical neutrosophy followed in 2018-2022. As such, I extended the Nonstandard Analysis by adding the right-closed left monad, the left-closed right monad, the punctured binad (which we introduced in 1998), and the nonpunctured binad - all in order to close the newly extended nonstandard space (R*) under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations [23, 24]. Improved definitions of the Nonstandard Unitary Interval and Nonstandard Neutrosophic Logic are presented, along with Nonstandard Neutrosophic Operators. (shrink)