Both bosons and fermions satisfy a strong version of Leibniz’s Principle of the Identity of Indiscernibles (PII), and so are ontologically on a par with respect to the PII. This holds for non-entangled, non-product states and for physically entangled states—as it has been established in previous work. In this paper, the Leibniz strategy is completed by including the (bosonic) symmetric product states. A new understanding of Pauli’s Exclusion Principle is provided, which distinguishes bosons from fermions in a (...) peculiar ontological way. Finally, the program as a whole is defended against substantial objections. (shrink)

In considering the possibility that the fundamental particles of matter might violate Leibniz's Principle, one is confronted with logical proofs that the Principle is a Theorem of Logic. This paper shows that the proof of that theorem is not universal enough to encompass entities that might not be unique, and also strongly suggests that photons, for example, do violate Leibniz's Principle. It also shows that the existence of non-individuals would imply the breakdown of Quine's criterion of ontological (...) commitment. (shrink)

This paper is concerned with the problem of the validity of Leibniz's principle of the identity of indiscernibles in physics. After briefly surveying how the question is currently discussed in recent literature and which is the actual meaning of the principle for what concerns physics, we address the question of the physical validity of Leibniz's principle in terms of the existence of a sufficient number of naming predicates in the formal language of physics. This approach allows us (...) to obtain in a formal way the result that a principle of the identity of indiscernibles can be justified in the domain of classical physics, while this is not the case in the domain of quantum physics. (shrink)

It is shown that the Hilbert-Bernays-Quine principle of identity of indiscernibles applies uniformly to all the contentious cases of symmetries in physics, including permutation symmetry in classical and quantum mechanics. It follows that there is no special problem with the notion of objecthood in physics. Leibniz's principle of sufficient reason is considered as well; this too applies uniformly. But given the new principle of identity, it no longer implies that space, or atoms, are unreal.

La plupart des commentateurs interprète le principe de l'identité des indiscernables comme principe purement logique, mais avec des implications métaphysiques, et donc, selon l'interprétation commune, comme fausseté ou vérité contingente ou triviale. Je soutiens, au contraire, que le principe, selon Leibniz, est vrai, mais que cette vérité n'est triviale ni contingente, mais nécessaire dans un sens métaphysique. Leibniz tent à démontrer la nécessité du principe dans deux manières : une manière logique et une manière métaphysique . Je soutiens que seule (...) la manière métaphysique peut réussir, et que la négligeance de cette manière aboutit au malentendu de ce principe. (shrink)

Leibniz’s famous Principle of the Identity of Indiscernibles (PII) states that no two things are exactly alike. The PII is commonly thought to be metaphysically necessary for Leibniz: the coexistence of two indiscernibles is metaphysically impossible. This paper argues, against the standard interpretation, that Leibniz’s PII is metaphysically contingent. In other words, while the coexistence of indiscernibles would not imply a contradiction, the PII is true in the actual world because the Principle of Sufficient Reason rules (...) out violations of the PII. God could have created indiscernibles but he did not because he is wise and does nothing without a sufficient reason. Because it is plausible that all Leibnizian possible worlds are unified by a wise plan, this means that the PII is true in all possible worlds. God could create indiscernibles, but the resulting creation would not be a world. To argue for this conclusion, the paper carefully examines Leibniz’s mature account of metaphysical contingency. It shows that for Leibniz, only states of affairs that imply logical contradictions are metaphysically impossible. Next, it argues that the coexistence of indiscernibles would not imply a logical contradiction; it would merely imply what Leibniz calls a “moral absurdity,” that is, a violation of the Principle of Sufficient Reason. This means that the PII is true contingently and—since God can do whatever is metaphysically possible—that God can create two things that are exactly alike. (shrink)

Parkinson schreibt, es sei nicht klar, daß Alexander selbst von Geburt an Merkmale oder Zeichen des Ortes seines zukünftigen Todes in sich getragen haben müsse, weil der vollständige Begriff von Alexander den Begriff des in Babylon Sterbens enthält. Die vorliegende Interpretation des Prinzips der Vorherbestimmtheit der Geschichte verdeutlicht dies mit Hilfe der bildlichen Ausdrücke, Pläne und Dispositionen und mit Hilfe einer aristotelischen Unterscheidung zwischen "going to be" und "will be" , fur welche ein formaler chronologischer Apparat ausgearbeitet ist. Die Arbeit (...) gibt ebenfalls Einblick in den Gedanken, daB die Gegenwart schwanger mit der Zukunft ist, und antwortet auf Reschers Kritik, daß Leibniz' Metaphysik von Grund auf statisch sei. (shrink)

This article discusses the problem of the influence of the Leibniz' continuity principle on the concept of structural plan and homology formation in biology. The concept of body plan was established for the justification of the thesis about the structural sameness of the all living objects at the organismal level. However, the continuity hypothes is testing which was made on the comparative anatomical material has showed the impossibility of reducing the animals structure explanation to the single plan. The idea (...) of organic evolution has made it possible to present the continuity of the organic world as a historical consistency. From an evolutionary point of view homology was interpreted as a homogeny. That made it possible to consider the continuity of the organic world on the suborganismal level. This hypothesis was tested on the embryological material. The results, however, showed that the morphological structures, which seemed to be identical according to the first criterion of the Remane homology and occurred epigenetically, are not really gomogenic. This fact does not allow us to recognize the continuity ofthe organic world on the suborganismal level. The key concepts of classical biological disciplines (comparative anatomy, systematics, evolutionism) could be reconciled only on the basis ofthe discrete principle. (shrink)

The Principle of the Identity of Indiscernibles —the principle that no two numerically distinct things are perfectly similar—features prominently in Leibniz’s metaphysics. Despite its centrality to his philosophical system, it is surprisingly difficult to determine what modal status Leibniz ascribes to the PII. On many occasions Leibniz appears to endorse the necessity of the PII. There are a number of passages,however, where Leibniz seems to imply that numerically distinct indiscernibles are possible, which suggests that he subscribes to (...) a merely contingent version of the PII. In this paper I attempt to resolve this apparent inconsistency. I argue that Leibniz consistently takes the PII to be necessary and that this view of his shines through even in his correspondence with Clarke. I also show that competing interpretations, on which Leibniz’s PII is contingent, misread a number of crucial passages from this correspondence. (shrink)

Gonzalo Rodriguez-Pereyra presents an original study of the place and role of the Identity of Indiscernibles in Leibniz's philosophy. The Principle of the Identity of Indiscernibles rules out numerically distinct but perfectly similar things; Leibniz derived it from more basic principles and used it to establish important philosophical theses. Rodriguez-Pereyra aims to establish what Leibniz meant by the Principle of Identity of Indiscernibles, what his arguments for and from it were, and to assess those arguments and Leibniz's claims (...) about the Principle of Identity of Indiscernibles. He argues that Leibniz had a very strong version of the principle, according to which no possibilia are intrinsically perfectly similar, where this excludes things that differ in magnitude alone. The book discusses Leibniz's arguments for the Identity of Indiscernibles in the Meditation on the Principle of the Individual, the Discourse on Metaphysics, Notationes Generales, Primary Truths, the letter to Casati of 1689, the correspondence with Clarke, as well as the use of the Identity of Indiscernibles in Leibniz's arguments against the Cartesian conception of the material world, atoms, absolute space and time, the Lockean conception of the mind as a tabula rasa, and freedom of indifference. Rodriguez-Pereyra argues that the Identity of Indiscernibles was a central but inessential principle of Leibniz's philosophy. (shrink)

How many formulations of Principle of Sufficient Reason can one find in Leibniz's works? This paper suggests that there are at least two different formulations, which start from different basic concepts, trying to sketch the relations between them and the evolution from the more ancient formulation to the mature one.

Kant rejects Leibniz’s Principle of the Identity of Indiscernibles. In quantum mechanics, Leibniz’s principle is also apparently violated. However, both ways of rejecting the PII differ significantly. In particular, Kant denies that spatiotemporal objects are unique individuals and establishes appearances as merely singular ones. The distinction between ‘unique’ and ‘singular’ individuals is crucial for the role that intuition plays in cognition: it will be shown that Kant’s way of rejecting the PII goes against the standard versions (...) of conceptualism and non-conceptualism which, in turn, points out the relevance of this issue for the understanding of transcendental idealism. Finally, the systematic relevance will be checked by defending a Kantian interpretation of quantum individuality. (shrink)

Leibniz's principle of sufficient reason (PSR) is the claim that everything has a sufficient reason. But is Leibniz committed to the necessity or to the contingency of his great principle? I argue that Leibniz is committed to its contingency, given that he allows for the absolute possibility of entities that he claims violate the PSR. These are all cases of qualitatively indiscernible entities, such as indiscernible atoms, vacua, and bodies. However, Leibniz's commitment to the contingency of the PSR (...) seems to stand in tension with his inference of the PSR from his theory of truth. I argue that this apparent tension can be resolved satisfactorily. When it comes to his modal views on the PSR, Leibniz's position is entirely consistent. (shrink)

It is surprisingly difficult to determine what modal strength Leibniz wants to ascribe to his principle of the identity of indiscernibles (PII). I consider this question by examining (i) some direct textual evidence, (ii) Leibniz's main arguments for PII, (iii) Leibniz's presumable response to a prominent contemporary defense of the necessity of PII against Max Black style counterexamples, and (iv) Leibniz's views about the possibility of primitive haecceities. I conclude that Leibniz probably takes PII to be necessary.

The aim of this paper is to shed light on Leibniz’s justification of the Principle of Sufficient Reason. It approaches this issue through a close textual analysis of the correspondence with Samuel Clarke and a more abstruse and lesser-known writing, ‘Leibniz’s Philosophical Dream’.

About the text and translation -- The Monadology -- The structure of the Monadology -- The Monadology : text with running commentary -- Appendix: Theodicy -- The principles of nature and grace, founded on reason -- Leibniz to Nicole Remond : appendix on monads.

Although scholars have often settled upon 1686 as the year in which the central elements of Leibniz’s philosophy first appear in systematic form, certain of his positions appear to have been firmly in place at least ten years earlier. Papers written in 1676 reveal that Leibniz had already by that time established the fundamental feature of his single-substance metaphysics: the insubstantiality of matter. As he defines it, matter is a mode, but a mode of peculiar status, a sort of (...) “top mode,” which, together with change, is requisite to the existence of any other modes, or “things.” Things for Leibniz include all bodies and their qualities, and in some places also appear to include minds, although Leibniz for religious reasons equivocates here, and wants to resist. Nevertheless, Leibniz’s desire to move toward a version of the Aristotelian notion of matter as the principle of individuation is clearly in evidence as he works to set out a view which can accommodate mechanistic physics while avoiding the perceived atheistic threat inherent in both Cartesian dualism and Spinozistic monism. (shrink)

This book explicates Leibnizian analysis as a search for conditions of intelligibility, and reconsiders his use of principles and methods as well as his account of truth in this way. Via careful reading of well-known, lesser known, and previously unedited texts, it gives a more accurate picture of his philosophical intentions, as well as the relevance of his project to contemporary debate. Two case studies are included, one concerning logic and the other arithmetic; they illustrate a theory of intelligibility that (...) takes as its central notion "possibility for thought", a notion which allows Leibniz to escape certain traps of psychologism, the pseudo-ontology of empiricism, and the empty forms of logicism, and suggests new approaches for contemporary philosophy. "In this remarkable study, Grosholz and Yakira offer a fresh interpretive and conceptual angle on Leibniz's metaphysics. [...] this study deserves high marks for its subtlety, novelty, and creative insight into Leibniz's modes of inquiry as well as for its philosophical acumen." Annals of Science. (shrink)

Larry Jorgensen aims to show that "Leibniz offers a fully natural theory of mind", recommending Leibniz to our contemporary discussion of naturalism. Readers of Leibniz will, however, hesitate to call him a naturalist. After all, he considered natural laws to be subordinated rules below general divine laws and rejected explaining the soul's action by bodily motion. Jorgensen does have a point, though, when he refers to Leibniz's frequent pleas for natural explanations and his continuity principle.Jorgensen's project unfolds in four (...) parts. The first offers a discussion of Leibniz's concept of nature and a clear presentation of Leibniz's principles, above all the... (shrink)

Leibniz’s religious cosmopolitanism is one of the main ways in which his thought foreshadows the Enlightenment. Of the controversial issues of his time, it is the one on which he was boldest. His commitment to it is discussed here in relation to both the Chinese Rites Controversy and the reunion of Christendom, and the main features of his conception of religion are discussed. (1) It is a religious and normative conception. (2) Its main principle is “the love of (...) God above all things.” (3) It involves a principled pragmatism on many, perhaps most, religious issues. The implications of this pragmatism are traced for (4) Leibniz’s ecclesiology and (5) his strategies for interpreting religious concepts. (6) The relatively abstract and ahistorical character of religious essentials on Leibniz’s view is acknowledged. (shrink)

This article provides a thorough introduction into the problem arising in Leibniz’s philosophical system of whether God’s act of will in creation is rendered necessary following the system’s doctrine of truth and Principle of the Best. Several items necessary for a grasp of the subject are discussed first in summary fashion: §1 relevant elements of Leibniz’s logic and the nature of truth, §2 the meaning of freedom, and §3 the principle of perfection, or the best. In (...) the final section, the author defends the view that Leibniz effectively responds, within the framework of his logic, to the main objections against his position. It is argued that Leibniz is able to vindicate the system’s position on the freedom of God’s act of will in creating the order of nature, whereby the ‘root of contingency’ in his system is at once derived from God’s will and yet completely intelligible through the system’s modern Rationalism, logic and doctrine of truth. (shrink)

The fundamental principle of Leibniz's idealism is that “there is nothing in things except simple substances, and in them perception and appetite.” He held that bodies are not simple, and therefore must be constructed out of the simple, perceiving substances. He held indeed that bodies are aggregates of substances, and also that they are merely phenomena. Leibniz's consistency and constancy in holding these two theses are defended in this chapter against highly influential objections. It considers in what sense he (...) regarded bodies as phenomena, and why he thought their being aggregates of substances a reason for rather than against counting them as phenomena. (shrink)

By now widely read, Catherine Wilson’s book on Leibniz’s metaphysics needs no introduction to Leibniz scholars. This volume, like its companions in the ‘Studies in Intellectual History and the History of Philosophy’ series, succeeds in meeting high standards of historical and textual scholarship; of special note are Wilson’s remarkable grasp of the contribution that relatively minor figures made to Leibniz’s thought, and her familiarity with the European secondary literature. The book is, as a consequence, broader and historically richer (...) than other books on Leibniz in English. Contributing to this historical flavor is also a more strategic feature of Wilson’s project—namely its exploration of Leibniz’s metaphysics “[not] as a collection of theses and principles, but developmentally and thematically”. The distinction seems to imply that while one could view Leibniz’s metaphysics as a collection of principles and theses, exactly “which principles and theses?” threatens to get wrongly answered: the “governing assumption” of a developmental approach is that “what the words of a [long-dead philosopher] mean cannot be determined by an internal inspection of the texts”. Or anyway, not precisely determined, with a high confidence of Leibniz’s intentions, and for some projects this may well matter. Surely it may well matter for someone inclined—as Wilson is not—to see the largest part of Leibniz’s metaphysics as a relatively unified system of theses and principles: the governing assumption, which beckons us to read Leibniz against the backdrop of his ancient, medieval, and modern heritage, is consistent with exploring the internal coherence of the theses and principles making up his metaphysical system. If much of the older secondary literature was mistaken in doing almost to the exclusion of, Wilson’s book can scarcely be charged with the same mistake. Were I asked to complain about Wilson’s approach, I would only suggest that her eagerness and ability to do has sometimes obscured the extent to which an internal inspection of the texts is needed in fairly doing. (shrink)

Leibniz viewed the principle of continuity, the principle that all natural changes are produced by degrees, as a useful heuristic for evaluating the truth of a theory. Since the Cartesian laws of motion entailed discontinuities in the natural order, Leibniz could safely reject it as a false theory. The principle of continuity has similar implications for analyses of Leibniz's theory of consciousness. I briefly survey the three main interpretations of Leibniz's theory of consciousness and argue that the (...) standard account entails a discontinuity that Leibniz could not allow. I argue that the principle of continuity and the textual data favor an interpretation according to which a conscious mental state just is a perception that is distinct to a sufficient degree. (shrink)

I have shown (to my satisfaction) that Leibniz's final attempt at a generalized syllogistico-propositional calculus in the Generales Inquisitiones was pretty successful. The calculus includes the truth-table semantics for the propositional calculus. It contains an unorthodox view of conjunction. It offers a plethora of very important logical principles. These deserve to be called a set of fundamentals of logical form. Aside from some imprecisions and redundancies the system is a good systematization of propositional logic, its semantics, and a correct account (...) of general syllogistics. For 1686 it was quite an accomplishment. It is a pity that Leibniz himself did not fully appreciate what he had achieved. It does seem to me that this was due in part, as the Kneales urge (Note 4), to his having kept the focus of his attention on traditional syllogistics. It is a great pity that he did not polish GI 195–200 for publication. The publication of GI 195, 198, and 200 would have most likely promoted further research. MAJR- Humanities, Social Sciences and Law. (shrink)

1. A substance is a being that is capable of action. It is either •simple, meaning that it has no parts, or •composite, meaning that it is a collection of simple substances or monads. (Monas is a Greek word meaning ‘unity’ or ‘oneness’.) Any composite thing—any body—is a multiplicity, ·a many, but simple substances are unities, ·or ones·. There must be simple substances everywhere, because without simples there would be no composites—·without ones there could not be manies·. And simple substances (...) are lives, souls, minds—·where there is a simple substance there is life·—and the world’s being full of such substances means that the whole of nature is full of life. (shrink)

I show that Leibniz’s account of divine concurrence is constrained in a surprising way by his commitment to the Principle of Sufficient Reason, where a sufficient reason for the existence of an entity or a state of affairs is understood to be the totality of requisites for its existence. I argue first that Leibniz endorses, in both his early and later metaphysics, the ‘totality of requisites’ conception of sufficient reason. I then show that this conception gives rise to (...) a distinctive and underappreciated logical redundancy problem. Finally, I show that the logical redundancy problem can be side-stepped if we attribute to Leibniz the view that the states of any created substance are caused by God in a single act. On this view, God’s concurrence with creaturely activity is irreducibly plural: the natural effects or states of any created substance are brought about together, as a collective. I show that there are both philosophical and textual grounds for attributing such a view to Leibniz. (shrink)

Leibniz sought to solve the metaphysical problem of reality, avoiding ontological premises. His intensional method was aimed at the logical solution of the problem, preserving the objectivity and unobstructed metaphysical research. Metaphysics can provide a certain level of coherence to the phenomena of physics and make them more real. Leibniz was convinced that physics, for its part, should be grounded in metaphysical principles. This promotes a reciprocal relationship between physics and metaphysics, where metaphysical principles derive their reality from physical principles, (...) and the two fields are interrelated. If we recognize the reality of the laws of physics, then we must also recognize the reality of the concept of substance. His position is that the laws of mathematical physics predict the existence of real substances, which makes it possible to move from mathematical objects to real substances. This method of substantiating the reality of substance and metaphysical principles can be considered as the foundations of the transcendental method. Leibniz's metaphysical approach is that necessary truths exist by themselves and do not depend on specific objects of study or perception. He regarded these truths as eternal. (shrink)

The monumental works of Bertrand Russell and Louis Couturat have set a firm pattern of interpretation which many follow in their approach to the Philosophy of Leibniz. In the Preface to the second edition of The Philosophy of Leibniz , Russell reaffirms his contention that “Leibniz’s philosophy was almost entirely derived from his logic”. He welcomes the support provided in Couturat’s La Logique de Leibniz . Russell remarks “No candid reader—can doubt that Leibniz’s metaphysic was derived by him (...) from the subject-predicate logic. This appears, for example, from the paper ‘Primae Veritates’ where all the main doctrines of the Monadology are deduced, with terse logical rigor from the premises; ‘Always therefore the predicate or consequent adheres in the subject or antecedent, and in this fact consists the nature of truth in general—But this is true in every affirmative truth, universal or singular, necessary or contingent’.” Referring further to Couturat, he points out that in his book the “Principle of Sufficient Reason” and “The Identity of Indiscernibles” are “expressly deduced—from the analytic character of all true propositions”. In short, Russell is contending that in formulating his metaphysics Leibniz used the rigorous methods of deductive logic and employed “models” drawn from logic to construct his “picture of reality”, i.e. his metaphysics. (shrink)

Leibniz’s claim that it is possible for us to gain metaphysical knowledge through reflection on the self has intrigued many commentators, but it has also often been criticized as flawed or unintelligible. A similar fate has beset Leibniz’s arguments against materialism. In this paper, I explore one of Leibniz’s lesser-known arguments against materialism from his reply to Bayle’s new note L, and argue that it provides us with an instance of a Leibnizian “argument from reflection”. This argument, (...) I further show, does not constitute a flawed appeal to mere introspection, but is in fact securely grounded in an important corollary of the Principle of Sufficient Reason: Leibniz’s Principle of Intelligibility. (shrink)