Abstract -/- The indistinction between repose and uniform movement exposed in the principle of inertia marks one of the most famous dissertations: the discussion between Newton and Leibniz. Through their respective conceptions of space, both seek to solve the problem of indistinction. The relational space of Leibniz, supported by the principle of sufficient reason and the identity of indiscernibles leads to the kinematic solution of the problem of inertia. The objective of this paper is to show the contribution (...) of Leibniz, in terms of relations of order, by distinguishing between equality by identity and equality by equivalence. Under a philosophical approach we link identity, equivalence and equality as relations of order with the indiscernibility between different states of movement. We expose first the principle of sufficient reason and the identity of indiscernibles. Under Bernoulli's principle of indifference, we argue that we distinguish between equality in abstract and equality in concrete. As a third part, we present the relationship between the identity of the indiscernibles and the predicate of equality under logical analysis. Finally we present the conclusions. -/- . (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 following considerations are to be seen in the framework of nontraditional theory of predication (NTP), which stems in its basic features from Sinowjew (cf. Sinowjew 1970, Sinowjew/Wessel 1975), and which is described in detail in Wessel 1989.

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.

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)

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)

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)

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)

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)

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.

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)

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)

I give a critique of the argument against the Identity of Indiscernibles found in Max Black's dialogue "The Identity of Indiscernibles". I begin by postulating and giving existence and individuation conditions for actually existent thought experiment characters on analogy with fictional characters as postulated in Peter van Inwagen's "Creatures of Fiction". I then show that Black's two-spheres thought experiment raises not one but two discernibility questions: 1) Is it true in the two-spheres thought experiment that there (...) exist two indiscernible spheres? NO. 2) Is it true in the actual world that there are two indiscernible sphere-characters? YES. (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 fact of russell's changes of mind over the identity of indiscernibles is not in dispute, but what was his final view? several recent writers have portrayed the late russell as not regarding the identity of indiscernibles as necessary, or at any rate as being indecisive or restrictive about its necessity. the present paper argues that such readings of russell are untenable.

The paper formulates and defends a version of the Identity of Indiscernibles and demonstrates that it entails a non-trivial version of the doctrine of essentialism.

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)

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)

Causal essentialists hold that a property essentially bears its causal and nomic relations. Further, as many causal essentialists have noted, the main motivations for causal essentialism also motivate holding that properties are individuated in terms of their causal and nomic relations. This amounts to a kind of identity of indiscernibles thesis; properties that are indiscernible with respect to their causal and nomic relations are identical. This can be compared with the more well-known identity of indiscernibles thesis, (...) according to which particulars that are qualitatively indiscernible are identical. Robert Adams has developed a well-known objection to this thesis by considering a series of possibilities involving nearly qualitatively indiscernible particulars that naturally leads to a possibility involving qualitatively indiscernible particulars. I argue that we can construct parallel cases involving a series of possibilities involving properties that are nearly indiscernible with respect to their causal and nomic relations that naturally lead to possibilities involving properties that are indiscernible with respect to their causal and nomic relations. The same features that make Adams’ argument forceful also carry over to my cases, giving us a powerful objection to the causal essentialist identity of indiscernibles thesis. (shrink)

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.

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 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.

: 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)

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.