The aim of this paper is to render a detailed analysis of the correspondence with Clarke in order to shed some light in the relationship between the Principle of Identity of Indiscernibles and the Principle of Sufficient Reason. Most of the secondary literature takes for granted that Leibniz derives the Principle of Identity of Indiscernible from the Principle of Sufficient Reason in at least some parts of the correspondence. This would render the (...) class='Hi'>Principle of Identity of Indiscernibles a merely contingent truth and not a necessary principle. I will argue that this interpretation is misleading, and that Leibniz never abandoned the idea that the Principle of Identity of Indiscernibles is a necessary truth. Although he is continuously using the Principle of Sufficient Reason in his argumentation, he keeps in parallel a strong argumentation that entails the necessity of the Principle of Identity of Indiscernibles. To achieve this goal, it will be necessary to point out first some contextual facts that may determine a correct understanding of the correspondence. It will be also necessary to frame the discussion about the principles into the broader debate on the possibility of Newtonian space. Finally, it will be shown that the mentioned hypothesis is supported by textual evidence throughout the entire 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)

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)

we propose a revised version of Black's original argument against the principle of identity of indiscernibles. Our aim is to examine a puzzle regarding the intuitiveness of arguments, by showing that the revised version is clearly less intuitive than Black's original one, and appears to be unjustified by our ordinary means of assessment of intuitions.

This paper concerns the question of whether Pauli's Exclusion Principle (EP) vindicates the contingent truth of Leibniz's Principle of the Identity of Indiscernibles (PII) for fermions as H. Weyl first suggested with the nomenclature ‘Pauli–Leibniz principle’. This claim has been challenged by a time-honoured argument, originally due to H. Margenau and further articulated and champione by other authors. According to this argument, the Exclusion Principle—far from vindicating Leibniz's principle—would refute it, since the same (...) reduced state, viz. an improper mixture, can be assigned as a separate state to each fermion of a composite system in antisymmetric state. As a result, the two fermions do have the same monadic state-dependent properties and hence are indiscernibles. PII would then be refuted in its strong version (viz. for monadic properties). I shall argue that a misleading assumption underlies Margenau's argument: in the case of two fermions in antisymmetric state, no separate states should be invoked since the states of the two particles are entangled and the improper mixture—assigned to each fermion by reduction—cannot be taken as an ontologically separate state nor consequently as encoding monadic properties. I shall then conclude that the notion of monadic properties together with the strong version of PII are inapplicable to fermions in antisymmetric state and this undercuts Margenau's argument. (shrink)

The Identity of Indiscernibles is the principle that there cannot be two individual things in nature that are qualitatively identical. The principle is not exactly popular. Michael Della Rocca tries to resurrect it by arguing that we must accept this principle, for otherwise we cannot explain the impossibility of completely overlapping indiscernible objects of the same kind that share all their parts and exist in the same place at the same time. I try to show (...) that his argument goes wrong: we need not embrace the identity of indiscernibles to deal with the co-location problem. (shrink)

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

The Identity of Indiscernibles seems like a good enough way to define identity. Roughly it simply says that if x and y have all and only the same properties, these will be the same object. However the principle has come under attack using a series of thought experiments employing the idea of radical symmetry. I follow the history of the debate including its theological origins to assess the contemporary arguments against the Identity of Indiscernibles. (...) I argue that the principle is viable as a logical truth, and so can be put to work in our idea of objects. (shrink)

A and B continue their conversation concerning the Identity of Indiscernibles. Both are aware of recent critiques of the principle that haven’t received replies; B summarizes those critiques, and A offers the replies that are due. B then raises a new worry.

The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those (...) from classical symmetric universes three main objections put forth against this kind of arguments. (shrink)

The Identity of Indiscernibles is the principle that objects cannot differ only numerically. It is widely held that one interpretation of this principle is trivially true: the claim that objects that bear all of the same properties are identical. This triviality ostensibly arises from haecceities (properties like \textit{is identical to a}). I argue that this is not the case; we do not trivialize the Identity of Indiscernibles with haecceities, because it is impossible to express (...) the haecceities of indiscernible objects. I then argue that this inexpressibility generalizes to all of their trivializing properties. Whether the Identity of Indiscernibles is trivially true ultimately turns on whether we can quantify over properties that we cannot express. (shrink)

Department of History and Philosophy of Science. University of Cambridge, Free School Lane, Cambridge CB2 3RH This paper is concerned with the question of whether atomic particles of the same species, i. e. with the same intrinsic state-independent properties of mass, spin, electric charge, etc, violate the Leibnizian Principle of the Identity of Indiscernibles, in the sense that, while there is more than one of them, their state-dependent properties may also all be the same. The answer depends (...) on what exactly the state-dependent properties of atomic particles are taken to be. On the plausible interpretation that these should comprise all monadic and relational properties that can be expressed in terms of physical magnitudes associated with self-adjoint operators that can be defined for the individual particles, then the weakest form of the Principle is shown to be violated for bosons, fermions and higher-order paraparticles, treated in first quantization *Some of the arguments inn this paper appeared in a thesis submited by one of us (S.F.) In partial fulfilment of the requirements for the PhD degree of the University of London, in 1984. entitled 'Identity and ‘Individuality in Classical and Quantum Physics’. (shrink)

SummaryOne form of the principle of the identity of indiscernibles asserts that for any two distinct entities it is necessarily the case that there is a description which distinguishes between them, in that it applies to one but not to the other. In this paper it is argued that this form of the principle is false. The argument is based upon the nature of language, in particular the need for ostensive definition of terms which are not (...) verbally definable. It is concluded that the identity of indiscernibles, in its linguistic form, requires a power of discrimination which no language could possess. Other versions of the principle, however, formulated in terms of properties rather than descriptions, are unaffected by the argument and may well be true. (shrink)

The strongest version of the principle of the Identity of Indiscernibles states that of necessity, there are no distinct things with all their universals in common (where such putative haecceities as being Aristotle do not count as universals: I use 'universal' rather than 'property' here and in what follows for the simple reason that 'universal' is the term of art that most safely excludes haecceities from its instances). It is commonly supposed that Max Black's famous paper 'The (...) identity of indiscernibles' (2) refutes this thesis. (Armstong's [1], chapter 9 is representative here.) Black argues ([2], p. 156) that it is perfectly possible that there be a world consisting solely of two indiscernible spheres at some distance to each other and that this world constitutes a counterexample to the principle above. The strongest version of the bundle theory of substance claims that of necessity, the substances that make up the world are bundles of universals.1 It is commonly supposed that a consequence of Black's defeat of the principle of the Identity of Indiscernibles is that this bundle theory of substance is mistaken. (Again, Armstong's [1] is representative.) I shall argue that Black's thought experiment does not defeat the bundle theory and that, as a result, the bundle theory can be used to salvage the principle of the Identity of Indiscernibles. (shrink)

Putative counterexamples to the Principle of Identity of Indiscernibles (PII) are notoriously inconclusive. I establish ground rules for debate in this area, offer a new response to such counterexamples for friends of the PII, but then argue that no response is entirely satisfactory. Finally, I undermine some positive arguments for PII.

The principle of Identity of Indiscernibles has been challenged with various thought experiments involving symmetric universes. In this paper, I describe a fractal universe and argue that, while it is not a symmetric universe in the classical sense, under the assumption of a relational theory of space it nonetheless contains a set of objects indiscernible by pure properties alone. I then argue that the argument against the principle from this new thought experiment resists better than those (...) from classical symmetric universes three main objections put forth against this kind of arguments. (shrink)

It is argued that recent discussion of the principle of the identity of indiscernibles (PII) and quantum mechanics has lost sight of the broader philosophical motivation and significance of PII and that the `received view' of the status of PII in the light of quantum mechanics survives recent criticisms of it by Muller, Saunders, and Seevinck.

The mathematical field of graph theory has recently been used to provide counterexamples to the Principle of the Identity of Indiscernibles. In response to this, it has been argued that appeal to relations between graphs allows the Principle to survive the counterexamples. In this paper, I aim to show why that proposal does not succeed.

Leibniz’s short letter to the mathematician and physicist Ludovico Casati of 1689 is a short but interesting text on the Principle of Identity of Indiscernibles, to which it is entirely dedicated. Since there is no watermark in the paper of the letter, the letter is difficult to date, but it is likely that it was written during Leibniz’s stay in Rome, sometime between April and November of 1689 (A 2 2 287–8). When addressing the letter, Leibniz wrote (...) ‘Casani’, but this seems to be a mistake and the real addressee is thought to be Ludovico Casati, nephew of Paolo Casati, the Jesuit mathematician. The letter, reproduced in the Berlin’s Academy edition of Leibniz’s works, was first published by Gerhardt in the Archiv für Geschichte der Philosophie in 1892 (Gerhardt 1892: 53–54). It also appears in Robinet’s Iter Italicum (Robinet 1988: 134–35). But neither Gerhardt nor Robinet provide a philosophical discussion of the letter, and I am not aware of any other philosophical discussion of it. Furthermore, as far as I know, the letter has never been translated into any language. Thus I shall here provide a transcription (from A 2 2 288–89) and a translation of the letter into English, and a philosophical discussion of its treatment of the Identity of Indiscernibles. (shrink)

This paper examines the view that ordinary particulars are complexes of universals. Russell's attempt to develop such a theory is articulated and defended against some common misinterpretations and unfounded criticisms in Section I. The next two sections address an argument which is standardly cited as the primary problem confronting the theory: (1) it is committed to the necessary truth of the principle of the identity of indiscernibles; (2) the principle is not necessarily true. It is argued (...) in Section II that a proponent of the theory need not accept (1) and an argument against (2) is presented in Section III. The final section attempts to show that Russell's theory ultimately fails because of inadequacies in its treatment of space and time. The paper closes with a suggestion for remedying this difficulty. (shrink)

A number of commentators (especially French and Redhead, 1988, and Butterfield, 1993) have investigated the status of the principle of the identity of indiscernibles (PII) for bosons and fermions. In this paper I extend that investigation to the full range of quantum particles of any allowed kind of statistics -- `quarticles', that is. I show that for any kind (except bosons and fermions) there are states in which PII is violated by every pair of particles, some pairs (...) and not others, and by no pairs. (shrink)

In his well-known 1952 dialogue Max Black describes a counterexample to the Principle of the Identity of Indiscernibles (PII). The counterexample is a world containing nothing but two purportedly indiscernible iron spheres. Reflecting on Black's example, Robert Adams uses the possibility of a world containing two almost indiscernible spheres to argue for the possibility of the indiscernible spheres world. One of Adams's almost indiscernible spheres has a small impurity, and, Adams writes, "Surely... the absence of the impurity (...) would not make such a universe impossible." The appeal to "surely" constitutes a gap in Adams's argument. This paper bridges the gap with a premise that exploits the counterfactual conditional and the related notion of causal independence. The paper then argues that causal independence bears in a similar way on an issue Nathan Salmon raises concerning Kripke's argument for the Essentiality of Origins. (shrink)

There is a certain argument against the principle of the indiscernibility of identicals, or the thesis that whatever is true of a thing is true of anything identical with that thing. In this argument, PInI is used together with the self-evident principle of the necessity of self-identity to reach the conclusion, which is held to be paradoxical and, thus, fatal to PInI. My purpose is to show that the argument in question does not have this consequence. Further, (...) I argue that PInI is a universally valid principle which can be used to prove the necessity of identity. (shrink)

The identity of indiscernibles states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to (...) a number of well-known and recent objections to the PII. (shrink)

In Section 21 of his fifth letter to Clarke Leibniz attempts to derive the Identity of Indiscernibles from an application of the Principle of Sufficient Reason to God´s act of creation, namely that God has a reason to create the world he creates. In this paper I argue that this argument fails, not just because the Identity of Indiscernibles is false, but because there is a counterexample to one of the premises that Leibniz cannot satisfactorily (...) rule out. (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)

: Hegel is commonly thought to affirm Leibniz’s principle of the identity of indiscernibles, which states that no two things are exactly alike. I argue that this interpretation is mistaken: it cannot accommodate passages in which Hegel rejects PII, and the texts cited in favor of this interpretation admit of another reading, which I provide. On my view, Hegel distinguishes between different senses of PII, and the sense of PII he accepts only entails that determinacy is immanent (...) to individuals qua concrete particulars. (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.

In this paper I defend the claim that quantum theory, Specifically quantum field theory (qft), Is incompatible with leibniz's principle of the identity of indiscernibles. This is in response to r. Barnette's criticism ("philosophy of science" 45:466-470) of an argument given by alberto cortes ("philosophy of science" 43:491-505) intended to establish this claim. I show that, Using the qft point of view, Cortes' argument can be restated in a way that leaves it immune to barnette's criticism.

Faced with strong arguments to the effect that Leibniz''sPrinciple of the Identity of Indiscernibles (PII) is not a necessary truth, many supporters of the Principle have staged a strategic retreat to the claim that it is contingently true in this, the actual, world. The purpose of this paper is to examine the status of the various forms of PII in both classical and quantum physics, and it is concluded that this latter view is at best doubtful, at (...) worst, simply wrong. (shrink)

Paul (Noûs 36:578–596, 2002; Noûs 40:623–659, 2006, The Handbook of Mereology, forthcoming) has argued for a bundle theory of objects that analyzes the bundling relation between properties and objects in terms of parthood relations. In this paper I argue that any mereological bundle theory with the explanatory power of Paul’s theory will entail the principle of the identity of indiscernibles (PII). This is problematic, since similar bundle theories seem to fall to Max Black’s two sphere counterexample to (...) (PII). I argue, however, that a fully developed mereological bundle theory provides a new way of interpreting Black’s two sphere universe that dispels the counterexample. I argue that this solution to Black’s puzzle is superior to other solutions on offer, and consequently that mereological bundle theory is an attractive ontological strategy for friends of (PII). (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)

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)

The relationship of the identity of indiscernibles principle to other major metaphysical principles (e.g., relational doctrine of space and time, elimination of singular terms) is discussed, the aim being to outline the necessary requirements of a systematic metaphysics incorporating the former principle. the conclusion is that no adequate systematic metaphysics of this sort is defensible. throughout special attention is paid to modern logical formulation of the principle and to its role in quine's philosophy.

A critical review of Gonzalo Rodriguez-Pereyra’s Two Arguments for the Identity of Indiscernibles.

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)

One of the key questions in the contemporary analytic ontology concerns the relation between the Principle of Identity of Indiscernibles (PII) and the Bundle Theory (BT). The majority of authors believe that BT implies PII. Therefore, it is widely believed that the world violating PII presented by Max Black (1952. “The Identity of Indiscernibles.” Mind 61 (242): 153–64) is also devastating for BT. However, this has been questioned by Rodriguez-Pereyra (2004. “The Bundle Theory is Compatible (...) with Distinct but Indiscernible Particulars.” Analysis 64 (1): 72–81), who formulated an interpretation of BT with instances. Recently Robert (2019. “Can the Realist Bundle Theory Account for the Numerical Difference between Qualitavely Non-discernible Concrete Particulars?” Theorema 38 (1): 25–39) argued that this version of BT is not a constituent ontology and, therefore, Rodriguez-Pereyra’s solution comes at a price of excluding bundle theory from the domain of constituent ontologies, and, in this sense, it fails. I question Robert’s point by claiming that his account of constituent ontologies is too demanding. In particular, I show that the instance version of BT is compatible with the constrains defining constituent ontologies in general, and therefore Rodriguez-Pereyra’s argument is correct. (shrink)

It is shown that typical arguments from intensionality against the Principle of Indiscernibility of Identicals (InI) misconstrue this principle, confusing it with the Principle of Substitution (PS). It has been proposed that Leibniz, in his statements like, "If A is the same as B, then A can be substituted for B, salva veritate, in any proposition", is not applying InI to objects nor PS to signs, but is talking about substitution of concepts in propositions, or applying InI (...) to concepts. It is shown in the paper that since Leibniz holds that there are exceptions to the principle thus stated, either the proposal in question is misguided, or else Leibniz is mistaken in thinking that there are such exceptions. (shrink)

Recently, several authors have claimed to have found graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles. In this paper, I argue that their counterexamples presuppose a certain view of what unlabeled graphs are, and that this view is optional at best.

It is well known that the manner in which a definitely descriptive term contributes to the meaning of a sentence depends on the place the term occupies in the sentence. A distinction is accordingly drawn between ordinary contexts and contexts variously termed non-referential, intensional, oblique, or opaque. The aim of the present article is to offer a general account of the phenomenon, based on transparent intensional logic. It turns out that on this approach there is no need to say (as (...) Frege does) that descriptive terms are referentially ambiguous or to deny (as Russell does) that descriptive terms represent self-contained units of meaning. There is also no need to tolerate (as Montague does) exceptions to the Principle of Functionality. The notion of an ordinary (i.e., non-intensional) context is explicated exclusively in terms of logical structure and it is argued that two aspects of ordinariness (termed hospitality and exposure) must be distinguished. (shrink)

In this paper it is argued that The Principle of the Identity of Indiscernibles can be justified as a concrete application of Ockham’s Razor, the maxim which enjoins us not to multiply entities beyond necessity. First, a statement of the Principle is presented, according to which the Principle, while interesting enough, is not logically necessary. It is then argued that the assumption of the falsity of the Principle prescribes an epistemological situation where it seems (...) to be impossible to find grounds for thinking that the Principle is indeed false. Hence it is to be accepted as an epistemological necessity of sorts, one that recommended by the desire not to multiply entities beyond need. (shrink)

The goal of this paper is to set out the structure and order of Leibniz’s discussion of the so-called “static shift,” in his correspondence in Clarke. The immediate point of this exercise is to determine precisely how Leibniz puts to use his two famous principles – the Principle of Sufficient Reason (PSR) and the Principleof Identity of Indiscernibles (PII) – in constructing, and defending his relational view of space, while providing a refutation of Absolute Space. In specific, (...) it is to set out an interpretation of this argument contrary to the generally accepted one – here represented by Chernoff – about the use of the PII. (shrink)