The aim of this paper is to argue that some objections raised by Jantzen (Synthese, 2010 ) against the separation of the concepts of ‘counting’ and ‘identity’ are misled. We present a definition of counting in the context of quasi-set theory requiring neither the labeling nor the identity and individuality of the counted entities. We argue that, contrary to what Jantzen poses, there are no problems with the technical development of this kind of definition. As a result of being able (...) to keep counting and identity apart for those entities, we briefly suggest that one venerable tradition concerning the nature of quantum particles may be consistently held. According to that tradition, known as the Received View on particles non-individuality, quantum particles may be seen as entities having both features: (i) identity and individuality do not apply to them, (ii) they may be gathered in collections comprising a plurality of them. (shrink)

In order to avoid the problems faced by standard realist analyses of the “relation” of instantiation, Baxter and, following him, Armstrong each analyze the instantiation of a universal by a particular in terms of their partial identity. I introduce two related conceptions of partial identity, one mereological and one non-mereological, both of which require at least one of the relata of the partial identity “relation” to be complex. I then introduce a second non-mereological conception of partial identity, which allows for (...) both relata to be simple. I take these three conceptions to exhaust the plausible ways of construing two entities as being partially identical. I then argue that there is no analysis (including those offered by Baxter and Armstrong) of a universal and a particular as being partially identical consistent with any of these three conceptions that (i) is coherent, (ii) is consistently realist, (iii) does not lead to absurd consequences, and (iv) offers a “solution” to the problem of instantiation that avoids the problems with the other standard realist responses. In so arguing, I offer a criticism of the analysis of instantiation as partial identity that is independent of the standard criticism that it entails the necessity of predication. (shrink)

This paper establishes that the occasional identity relation and the contingent identity relation are both non-transitive and as such are not properly classified as identity relations. This is achieved by appealing to cases where multiple fissions and fusions occur simultaneously. These cases show that the contingent and occasional identity relations do not even satisfy the time-indexed and world-indexed versions of the transitivity requirement and hence are non-transitive relations.

relation between, say, a lump of clay and a statue that it makes up, or between a red and white piece of metal and a stop sign, or between a person and her body? Assuming that there is a single relation between members of each of these pairs, is the relation “strict” identity, “contingent” identity or something else?1 Although this question has generated substantial controversy recently,2 I believe that there is philo- sophical gain to be had from thinking through the (...) issues from scratch. Many of the charges and countercharges are based on the following dichotomy: For any x and y that are related as the lump of clay is to the statue that it makes up, either x is identical to y, or x and y are separate entities, independent of each other. By giving up this dichotomy, we will be able to begin to make sense, I hope, of an intermediate unity relation that holds promise for solving a raft of philosophical problems, including the problem of how persons are related to their bodies.3 And if I am correct, then this relation—constitution without identity—is ubiquitous and interesting in its own right, apart from the light that it sheds on human persons. (shrink)

Attacks on ?closest continuer? and ?best candidate? theories of identity have something correct in them while still failing to discredit the theories they oppose. What follows from Noonan's and Wiggins's objections to such theories is that they need to be so formulated as not to deny the necessity of identity. The best metaphysics for best?candidate theories to adopt is one in which everyday objects are taken to transcend, in a certain sense, their life histories in given worlds. This metaphysics also (...) has the potential for solving problems about contingent identity, transworld identity, and the issue of haecceitism or individual essence. To develop the metaphysics, it is only necessary to follow through the analogy between worlds and times suggested by writers like Plantinga and Schlesinger. (shrink)

Orthodox neural materialists think mental states are neural events or orthodox material properties of neutral events. Orthodox material properties are defining properties of the “physical”. A “defining property” of the physical is a type of property that provides a necessary condition for something’s being correctly termed “physical”. In this paper I give an argument against orthodox neural materialism. If successful, the argument would show at least some properties of some mental states are not orthodox material properties of neural events. Oppositing (...) philosophical orthodoxy, I show there are no posteriori identities -- identities that cannot be known of a priori. (shrink)

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic (...) theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories—having to do with reference, persistence conditions, how they relate, and the epistemology of persistence—are revealed. (shrink)

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold (...) that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts. (shrink)

If there is such a thing as essential reading in metaphysics or in philosophy of language, this is it.

Abstract Thomas Polger has argued in favour of the mind?brain type?identity theory, the view that mental states or processes are type?identical to states of the central nervous system. Acknowledging that the type?materialist must respond to Kripke?s modal anti?materialist argument, Polger insists that Kripke?s argument rests on dubious assumptions concerning the identity conditions of brain states. In brief, Polger claims that one knows that x and y are non?identical when one knows the identity conditions for both x and y. Replace x (...) and y with ?brain states? and ?sensations? and it follows that one can know that brain states and sensations are non?identical only if one knows the identity conditions for brain states. But according to Polger, we do not know the identity conditions for brain states. Hence, we should not be so confident that brain states and sensations are non?identical after all. But Polger?s account is terribly flawed. Ironically, if Polger?s scepticism is warranted, then Polger himself has no good reasons to be a type?materialist. But more importantly, Polger?s scepticism regarding the identity conditions of brain states is deeply defective. We do, I submit, understand the identity conditions of brain states. In the end, I submit, Kripke is safe from Polger. (shrink)

Saul Kripke’s (1971, 1972) modal essentialist argument against materialism remains an obstacle to any prospective Identity Theorist. This paper is an attempt to make room for an Identity Theory without dismissing Kripke’s analytic tools or essentialist intuitions. I propose an explanatory model that can make room for the Identity Theory within the constraints of Kripke’s view; the model is based on ideas from Alan Sidelle’s, “Identity and Identity-like” (1992). My model explains the apparent contingency of some scientific identities by appealing (...) to our epistemic access to the conditions of identity for sensations and brain processes. Pace Kripke, the Identity Theorist can thus explain away the apparent contingency of mind-brain identity claims. (shrink)

coherence of contingent distinctness. Contingent identity follows for free. The theory is Kripkean in that the counterpart relation is in a sense stipulated rather than grounded on similarity, and is such that no object has more than one counterpart at a world. This avoids a number of objections Fara and Williamson have recently levelled against counterpart theory generally; their other objections are addressed by enriching the theory with special quantifiers and actuality operators.

This is a detailed defense of the view that identity is not an eternal, necessary relation: things can be identical at one time and distinct at another; they can be identical in one world and distinct in another. The defense is judicial rather than passionate, as Gallois’s primary goal is to persuade the reader that the view is ‘at least as credible’ as its more fashionable alternatives. But Gallois also aims to show that if the view is credible then it (...) provides a better solution to a wide range of identity puzzles (the ship of Theseus, the problem of material constitution, the puzzle of amoebic fission, and the like). As it turns out, Gallois goes a long way towards establishing the truth of this conditional claim. The real issue, however, is the credibility of the view itself, and in spite of the many sophisticated and original arguments that fill the pages of the book I suspect that many readers will not change their skeptical minds. (shrink)

This paper asks whether persistence can be a matter of convention. It argues that in a rather unexciting de dicto sense persistence is indeed a matter of convention, but it rejects the notion that persistence can be a matter of convention in a more substantial de re sense. However, scenarios can be imagined that appear to involve conventional persistence of the latter kind. Since there are strong reasons for thinking that such conventionality is impossible, it is desirable that our metaphysical-cum-semantic (...) theories of persistence be able to account for such scenarios in terms of conventions of the first kind. Later parts of the article therefore investigate whether three of the currently most influential metaphysical-cum-semantic theories of persistence—the endurance theory, the stage theory, and the perdurance theory—can do this. Fortunately, for them, it turns out that all can, though some philosophers have disputed this. However, when we ask how they account for a typical case of “conventional persistence” some problematic features of the theories —having to do with reference, persistence conditions, how they relate, and the epistemology of persistence — are revealed. (shrink)

Disposition ascription has been discussed a good deal over the last few decades, as has the revisionary metaphysical view of ordinary, persisting objects known as 'fourdimensionalism'. However, philosophers have not merged these topics and asked whether four-dimensional objects can be proper subjects of dispositional predicates. This paper seeks to remedy this oversight. It argues that, by and large, four-dimensional objects are not suited to take dispositional predicates.

An alternative to the standard endurance/perdurance accounts of persistence has recently been developed: the stage theory (Sider, T. Four-Dimensionalism: an Ontology of Persistence and Time. Oxford: Oxford University Press, 2001; Hawley, K. How Things Persist. Oxford: Oxford University Press, 2001). According to this theory, a persisting object is identical with an instantaneous stage (temporal part). On the basis of Leibniz's Law, I argue that stage theorists either have to deny the alleged identity (i.e., give up their central thesis) or hold (...) that stages are both instantaneous and continuants. I subsequently show that, although stage theory is flexible enough to accommodate the latter claim, the cost for accommodating it is an excessive proliferation of persistence concepts. (shrink)

Recently, there has been a debate as to whether or not the principle of the identity of indiscernibles (the PII) is compatible with quantum physics. It is also sometimes argued that the answer to this question has implications for the debate over the tenability of ontic structural realism (OSR). The central aim of this paper is to establish what relationship there is (if any) between the PII and OSR. It is argued that one common interpretation of OSR is undermined if (...) the PII turns out to be false, since it is committed to a version of the bundle theory of objects, which implies the PII. However, if OSR is understood as the physical analogue of (sophisticated) mathematical structuralism then OSR does not imply the PII. It is further noted that it is (arguably) a virtue of OSR that it is compatible with a version of the PII for possible worlds. (shrink)

Philosophers have long believed that if the Principle of the Identity of Indiscernibles were logically true, there would be no problem of individuation. I show (a) that if spatial relations are, as seems plausible, of such a nature that it makes no sense to say of one thing that it is related to itself, then the Principle is a logical truth, asserting that a certain kind of state of affairs is impossible because the kind of sentence purporting to express it (...) is ill-formed and (b) that even if the Principle were such a truth the problem of individuation would remain. I then examine some of what Leibniz and Wittgenstein have said about the notions of individuation, difference and nonidentity. (shrink)

One of the oldest topics in foundational metaphysics is the issue how particulars are to be individuated. To individuate a particular, x, means to find criteria that are necessary and sufficient to ensure the assertibility of x ≠ y, for all and only y that are distinct from x. One can distinguish two separate issues that are run under the heading of individuation. One is the question: what is it about a particular that makes it distinct from all other particulars? (...) The other is the question: how do we single out a particular qua distinct from all other particulars? The distinction closely resembles the one put forward by Hector- Neri Castañeda (1975), except that Castañeda talks about the first question in terms of the issue of the ‘internal constitution’ of objects. This way of speaking is misleading, as it insinuates that it is only intrinsic facts about particulars that could serve as candidates for individuation. Instead, in this essay, I will put forward a theory of individuation in which both questions are treated on equal footing, with the implication that both intrinsic and extrinsic, as well as some special properties that I will introduce play a role in individuating particulars. I call the theory ‘derivational contextualism’. It is an elaboration of some ideas I have put forward in an earlier work (Author forthcoming), regarding some basic conditions for individuation, with a structuralist component. I will.. (shrink)

If ordinary particulars are bundles of properties, and if properties are said to be universals, then three well-known objections arise : no particular can change, all particulars have all of their properties essentially (even the most insignificant ones), and there cannot be two numerically distinct but qualitatively indiscernible particulars. In this paper, I try to make a little headway on these issues and see how the objections can be met, if one accepts a certain view about persistence through time and (...) across possible worlds – namely, four-dimensionalism and its modal analogue. The paper is especially devoted to the second and third of the three objections. (shrink)

The other aim of the volume is to show that there is a close semantic connection between the concepts of individual, mind and body in Leibniz.

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)

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.

In ‘Two Spheres, Twenty Spheres, and the Identity of Indiscernibles,’ Della Rocca argues that any counterexample to the PII would involve ‘a brute fact of non-identity [. . .] not grounded in any qualitative difference.’ I respond that Adams's so-called Continuity Argument against the PII does not postulate qualitatively inexplicable brute facts of identity or non-identity if understood in the context of Kripkean modality. One upshot is that if the PII is understood to quantify over modal as well as non-modal (...) properties, the qualitative explicability of numerical distinctness requires not the PII but a principle of the identity of necessary indiscernibles. (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)

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)

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.

1. The Bundle Theory I shall discuss is a theory about the nature of substances or concrete particulars, like apples, chairs, atoms, stars and people. The point of the Bundle Theory is to avoid undesirable entities like substrata that allegedly constitute particulars. The version of the Bundle Theory I shall discuss takes particulars to be entirely constituted by the universals they instantiate.' Thus particulars are said to be just bundles of universals. Together with the claim that it is necessary that (...) particulars have constituents, the fundamental claim of the Bundle Theory is: (BT) Necessarily, for every particular x and every entity y, y constitutes x if and only ify is a universal and x instantiates y. 2 The standard and supposedly devastating objection to the Bundle Theory is that it entails or is committed to a false version of the Principle of Identity of Indiscernibles (Armstrong 1978: 91, Loux 1998: 107), namely: (Pll) Necessarily, for all particulars x and y and every universal z, if z is instantiated by x if and only if z is instantiated byy, then x is numerically identical with y. The most famous counterexample to the Identity of Indiscernibles is that put forward by Max Black, consisting of a world where there are only two iron spheres two miles apart from each other, having the same diameter, temperature, colour, shape, size, etc (Black 1952: 156). Let us from now on think of the properties of the spheres in this world as universals. The possibility of this world, which I shall hereafter refer to as 'Black's world', makes (Pll) false.' And according to common philosophical opinion this means that the Bundle Theory is false.. (shrink)

The view that numerical difference entails qualitative difference has come under attack from various quarters. One classical attack, advanced by Black, involves possible worlds which are symmetrical. In a symmetrical world, it is claimed, the identity of indiscernibles is false. I argue that such attacks are mistaken, basically because they confuse epistemological issues (such as, how to specify a quality difference) with ontological ones (such as, whether there is such a quality difference). In brief, though there may be some reasons (...) for doubting the necessity of the Identity of lndiscernibles, the possibility of a symmetrical world is not one of them. (shrink)

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.

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)

Orthodox neural materialists think mental states are neural events or orthodox material properties of neutral events. Orthodox material properties are defining properties of the “physical”. A “defining property” of the physical is a type of property that provides a necessary condition for something’s being correctly termed “physical”. In this paper I give an argument against orthodox neural materialism. If successful, the argument would show at least some properties of some mental states are not orthodox material properties of neural events. Oppositing (...) philosophical orthodoxy, I show there are no posteriori identities -- identities that cannot be known of a priori. (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.

Newton's arguments for the immobility of the parts of absolute space have been claimed to licence several proposals concerning his metaphysics. This paper clarifies Newton, first distinguishing two distinct arguments. Then, it demonstrates, contrary to Nerlich ([2005]), that Newton does not appeal to the identity of indiscernibles, but rather to a view about de re representation. Additionally, DiSalle ([1994]) claims that one argument shows Newton to be an anti-substantivalist. I agree that its premises imply a denial of a kind of (...) substantivalism, but I show that they are inconsistent with Newton's core doctrine that not all motion is the relative motions of bodies, and so conclude that they are not part of his considered views on space. The Arguments The Identity Argument 2.1 Identity of indiscernibles for individuals 2.2 Identity of indiscernibles for worlds and states 2.3 Representation de re Kinematic Relationism Conclusion CiteULike Connotea Del.icio.us What's this? (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)

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. *Received July 2009; revised September 2009. †To contact the authors, please write to: James Ladyman, Department of Philosophy, University of Bristol, 9 Woodland Road, Bristol (...) BS8 1TB, United Kingdom; e‐mail: james.ladyman@bristol.ac.uk. (shrink)

There has been much debate in philosophy about the relation between identity and distinctness on the one hand, and various forms of discernibility on the other. For instance, philosophers have debated the truth of the Principle of the Identity of Indiscernibles (PII), which is naturally formulated using a second-order quantifier ranging over some class of properties of particular philosophical significance.

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)

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)

This paper offers a critical assessment of the current state of the debate about the identity and individuality of material objects. Its main aim, in particular, is to show that, in a sense to be carefully specified, the opposition between the Leibnizian ‘reductionist’ tradition based on discernibility and the sort of ‘primitivism’ that denies that facts of identity and individuality must be analysable has become outdated. In particular, it is argued that – contrary to a widespread consensus - ‘naturalised’ metaphysics (...) supports both the acceptability of non-qualitatively grounded (both ‘contextual’ and intrinsic) identity and a pluralistic approach to individuality and individuation. A case study is offered that focuses on non-relativistic quantum mechanics, in the context of which primitivism about identity and individuality, rather than being regarded as unscientific, is on the contrary suggested to be preferable to the complicated forms of reductionism that have recently been proposed. More generally, assuming a plausible form of anti-reductionism about scientific theories and domains, it is claimed that science can be regarded as compatible with, or even as suggesting, the existence of a series of equally plausible grades of individuality - the kind of individuality that prevails in a certain context and at a given level being ascertainable only on the basis of the specific scientific theory at hand. (shrink)

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert spaces, is not in conflict with Leibniz's Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical relations, i.e. relations independent of the quantum-mechanical probabilities. If, indeed, probabilistic relations are permitted as well, we argue that similar bosons can also be discerned in all (...) their admissible states; but their categorical discernibility turns out to be a state-dependent matter. In all demonstrated cases of discernibility, the fermions and the bosons are discerned (i) with only minimal assumptions on the interpretation of quantum mechanics; (ii) without appealing to metaphysical notions, such as Scotusian haecceitas, Lockean substrata, Postian transcendental individuality or Adamsian primitive thisness; and (iii) without revising the general framework of classical elementary predicate logic and standard set theory, thus without revising standard mathematics. This confutes: (a) the currently dominant view that, provided (i) and (ii), the quantum-mechanical description of such composite physical systems always conflicts with PII; and (b) that if PII can be saved at all, the only way to do it is by adopting one or other of the thick metaphysical notions mentioned above. Among the most general and influential arguments for the currently dominant view are those due to Schrödinger, Margenau, Cortes, Dalla Chiara, Di Francia, Redhead, French, Teller, Butterfield, Giuntini, Mittelstaedt, Castellani, Krause and Huggett. We review them succinctly and critically as well as related arguments by van Fraassen and Massimi. Introduction: The Currently Dominant View 1.1 Weyl on Leibniz's principle 1.2 Intermezzo: Terminology and Leibnizian principles 1.3 The rise of the currently dominant view 1.4 Overview Elements of Quantum Mechanics 2.1 Physical states and physical magnitudes 2.2 Composite physical systems of similar particles 2.3 Fermions and bosons 2.4 Physical properties 2.5 Varieties of quantum mechanics Analysis of Arguments 3.1 Analysis of the Standard Argument 3.2 Van Fraassen's analysis 3.3 Massimi's analysis The Logic of Identity and Discernibility 4.1 The language of quantum mechanics 4.2 Identity of physical systems 4.3 Indiscernibility of physical systems 4.4 Some kinds of discernibility Discerning Elementary Particles 5.1 Preamble 5.2 Fermions 5.3 Bosons Concluding Discussion CiteULike Connotea Del.icio.us What's this? (shrink)

We maximally extend the quantum‐mechanical results of Muller and Saunders ( 2008 ) establishing the ‘weak discernibility’ of an arbitrary number of similar fermions in finite‐dimensional Hilbert spaces. This confutes the currently dominant view that ( A ) the quantum‐mechanical description of similar particles conflicts with Leibniz’s Principle of the Identity of Indiscernibles (PII); and that ( B ) the only way to save PII is by adopting some heavy metaphysical notion such as Scotusian haecceitas or Adamsian primitive thisness. We (...) take sides with Muller and Saunders ( 2008 ) against this currently dominant view, which has been expounded and defended by many. *Received July 2008; revised May 2009. †To contact the authors, please write to: F. A. Muller, Faculty of Philosophy, Erasmus University Rotterdam, Burg. Oudlaan 50, H5–16, 3062 PA Rotterdam, The Netherlands; e‐mail: f.a.muller@fwb.eur.nl , and Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: f.a.muller@uu.nl . M. P. Seevinck, Institute for the History and Foundations of Science, Utrecht University, Budapestlaan 6, IGG–3.08, 3584 CD Utrecht, The Netherlands; e‐mail: m.p.seevinck@uu.nl. (shrink)

We extend the work of French and Redhead [1988] further examining the relation of quantum statistics to the assumption that quantum entities have the sort of identity generally assumed for physical objects, more specifically an identity which makes them susceptible to being thought of as conceptually individuatable and labelable even though they cannot be experimentally distinguished. We also further examine the relation of such hypothesized identity of quantum entities to the Principle of the Identity of Indiscernibles. We conclude that although (...) such an assumption of identity is consistent with the facts of quantum statistics, methodological considerations show that we should take quantum entities to be entirely unindividuatable, in the way suggested by a Fock space description. (shrink)

I argue that the standard counterexamples to the identity of indiscernibles fail because they involve a commitment to a certain kind of primitive or brute identity that has certain very unpalatable consequences involving the possibility of objects of the same kind completely overlapping and sharing all the same proper parts. The only way to avoid these consequences is to reject brute identity and thus to accept the identity of indiscernibles. I also show how the rejection of the identity of indiscernibles (...) derives some of its support from its affinity with a Kripkean account of trans-world identity and theories of direct reference. (shrink)

In this paper I reconstruct Leibniz's argument for the Identity of Indiscernibles in his *Primary Truths*. I criticise the alternative interpretation put forward by Cover and O'Leary-Hawthorne and defend my own interpretation, both on philosophical and hermeneutical grounds.