Non-reflexive logics are systems of logic in which the reflexive law of identity is restricted or violated. The most well-known of such systems are Schrödinger logics and quasi-set theory; both are related with the metaphysics of quantum mechanics, aiming at formalizing the idea that quantum entities are non-individuals. We argue in this paper that non-reflexive logics may be seen as attempting to characterize two metaphysically incompatible notions of non-individuals: (i) non-individuals as violating self-identity and (ii) (...) non-individuals as indiscernible entities. The problem is that any choice between these options brings difficult questions, making the understanding of non-individuals through the apparatus of non-reflexive logics rather implausible. (shrink)

The principle of identity is one of the three basic principles of reason on which classical logic rests. The other two basic principles of reason are principle of noncontradiction and of the excluded middle. These principles were accepted almost unquestionably until the beginning of the twentieth century. Therefore, classical logic, which adhered to these principles, continued to prevail. Today, however, one of the most interesting debates in the field of science is whether these fundamental principles on which classical logic (...) rests can be seen as necessary and invariable truths. With this discussion, a logic emerged in the twentieth century, rejecting the basic principles of reason. In this study, we will examine the logics -non-reflexive logics- that rejects or limits the principle of identity, from which the other two principles of classical logic are derived. First of all, we will talk about the origins of non-reflexive logic. Next, the basic assumptions of the identity principle of classical logic will be discussed. Finally, we will discuss the reasons for which non-reflexive logic rejects or limits the principle of identity, in other words, which assumptions of the identity principle are considered problematic. (shrink)

On the one hand, non-reflexive logics are logics in which the principle of identity does not hold in general. On the other hand, quantum mechanics has difficulties regarding the interpretation of ‘particles’ and their identity, also known in the literature as ‘the problem of indistinguishable particles’. In this article, we will argue that non-reflexive logics can be a useful tool to account for such quantum indistinguishability. In particular, we will provide a particular non-reflexive logic that (...) can help us to analyze and discuss this problem. From a more general physical perspective, we will also analyze the limits imposed by the orthodox quantum formalism to consider the existence of indistinguishable particles in the first place, and argue that non-reflexive logics can also help us to think beyond the limits of classical identity. (shrink)

In this paper we try to justify our way of looking for an alternative approach to quantum mechanics, which is based on a non-classical logic. We consider two specific questions related to quantum theory, namely, entanglement and the indiscernibility of quanta. We characterize individuals, and then explain in what sense entanglement is a concept which can be applied to individuals in a restricted sense only. Then, we turn to indiscernibility and, after realizing that this concept is of a fundamental importance, (...) we mention the ‘traditional’ theory of identity of standard logic and mathematics, which underly the basic formalism of quantum theory. Then we propose to call the Problem of Identity the question whether identity of objects can be justified, and under what conditions. As in the Hume’s celebrated Problem of Induction, we conclude that the attribution of transtemporal identity to an object has no logic justification, and must be considered as a metaphysical hypothesis. Numerical identity is also put aside for similar reasons. Then we guess that identity is just an useful concept, but which in certain fields, mainly in the quantum realm, could be substituted by a weaker concept of indiscernibility. This assumption motivates us to look for an interpretation of quantum mechanics based on a non-classical logic, termed non-reflexive, and the corresponding mechanics is called non-reflexive quantum mechanics. (shrink)

This is a general philosophical paper where I overview some of my ideas concerning the non-reflexive foundations of quantum mechanics. By NRFQM I mean an interpretation of QM that considers an involved on- tology of non-individuals as explained in the text. Thus, I do not endorse a purely instrumentalist view of QM, but believe that it speaks of something, and then I try to show that one of the plausible views of this ‘something’ is as entities devoided of (...) class='Hi'>identity conditions. (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.

This book discusses the philosophical work of Décio Krause. Non-individuality, as a new metaphysical category, was thought to be strongly supported by quantum mechanics. No one did more to promote this idea than the Brazilian philosopher Décio Krause, whose works on the metaphysics and logic of non-individuality are now widely regarded as part of the consolidated literature on the subject. This volume brings together chapters elaborating on the ideas put forward and defended by Krause, developing them in many (...) different directions, commenting on aspects not completely developed so far, and, more importantly, critically addressing their current formulations and defenses by Krause himself. Given that Krause’s ideas do connect directly and indirectly with a wide array of subjects, such as the philosophy of quantum mechanics, more broadly understood, the philosophy of logic and logical philosophy, non-classical logics, metaphysics, and ontology, this volume contains important material for the research on logic and foundations of science, broadly understood. All the invited contributors have already worked with the ideas developed by Décio (some of them still work with them), being also distinct authors and extremely relevant in their areas of expertise. The volume is aimed at philosophers, including those of physics and quantum mechanics. (shrink)

This book discusses the philosophical work of Décio Krause. Non-individuality, as a new metaphysical category, was thought to be strongly supported by quantum mechanics. No one did more to promote this idea than the Brazilian philosopher Décio Krause, whose works on the metaphysics and logic of non-individuality are now widely regarded as part of the consolidated literature on the subject. This volume brings together chapters elaborating on the ideas put forward and defended by Krause, developing them in many (...) different directions, commenting on aspects not completely developed so far, and, more importantly, critically addressing their current formulations and defenses by Krause himself. Given that Krause’s ideas do connect directly and indirectly with a wide array of subjects, such as the philosophy of quantum mechanics, more broadly understood, the philosophy of logic and logical philosophy, non-classical logics, metaphysics, and ontology, this volume contains important material for the research on logic and foundations of science, broadly understood. All the invited contributors have already worked with the ideas developed by Décio (some of them still work with them), being also distinct authors and extremely relevant in their areas of expertise. The volume is aimed at philosophers, including those of physics and quantum mechanics. (shrink)

Using the Hilbert-Bernays account as a spring-board, we first define four ways in which two objects can be discerned from one another, using the non-logical vocabulary of the language concerned. Because of our use of the Hilbert-Bernays account, these definitions are in terms of the syntax of the language. But we also relate our definitions to the idea of permutations on the domain of quantification, and their being symmetries. These relations turn out to be subtle---some natural conjectures about them are (...) false. We will see in particular that the idea of symmetry meshes with a species of indiscernibility that we will call `absolute indiscernibility'. We then report all the logical implications between our four kinds of discernibility. We use these four kinds as a resource for stating four metaphysical theses about identity. Three of these theses articulate two traditional philosophical themes: viz. the principle of the identity of indiscernibles, and haecceitism. The fourth is recent. Its most notable feature is that it makes diversity weaker than what we will call individuality : two objects can be distinct but not individuals. For this reason, it has been advocated both for quantum particles and for spacetime points. Finally, we locate this fourth metaphysical thesis in a broader position, which we call structuralism. We conclude with a discussion of the semantics suitable for a structuralist, with particular reference to physical theories as well as elementary model theory. (shrink)

The notion of an individual and the related issues on individuation are topics that appear in the philosophical discussion ever since the antiquity. The idea of an individual thing is intuitively clear: an individual is something of a specific kind that is a unity, having its own identity, and being so that it is possible at least in principle to discern it from any other individual, even of similar species. But when we try to leave the intuitive realm and (...) push this idea to a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical contexts. In this work, we shall be concerned with some aspects of this intuitive concept of an individual and on some related facts about individuation taken from recent discussions that arose ever since the inception of quantum theory, pushing the discussion to a “logical” view, which in our opinion is still lacking in the usual debates on such issues. In the final part of the paper, we propose a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and we try to justify such a move. In most of the uses of the expression “quantum theory”, we shall not make explicit the distinction between the non-relativistic and the relativistic approaches, although they of course are quite different, for we think that the problems as we shall present them appear in both versions. But, as the text goes, the context will distinguish between them and these questions will become clear to the reader. (shrink)

Noneism a is form of Meinongianism, proposed by Richard Routley and developed and improved by Graham Priest in his widely discussed book Towards Non-Being. Priest's noneism is based upon the double move of building a worlds semantics including impossible worlds, besides possible ones, and admitting a new comprehension principle for objects, differerent from the ones proposed in other kinds of neo-Meinongian theories, such as Parsons' and Zalta's. The new principle has no restrictions on the sets of properties that can deliver (...) objects, but parameterizes the having of properties by objects to worlds. Modality is therefore explicitly built in - so the approach can be conveniently labeled as "modal noneism". In this paper, I put modal noneism to work by testing it against classical issues in modal logic and semantics. It turns out that - perhaps surprisingly - the theory performs well in problems of transworld identity, which are frequently considered to be the difficult ones in the literature; faces a limitation, albeit not a severe one, when one comes to transworld individuation, which is often taken as an easy issue, if not a pseudo-problem; and may stumble upon a real trouble when dealing with what I shall call 'extensionally indiscernible entities' - particular nonexistent objects modal noneism is committed to. (shrink)

The Received View on quantum non-individuality is, roughly speaking, the view according to which quantum objects are not individuals. It seems clear that the RV finds its standard expression nowadays through the use of the formal apparatuses of non-reflexive logics, mainly quasi-set theory. In such logics, the relation of identity is restricted, so that it does not apply for terms denoting quantum particles; this “lack of identity” formally characterizes their non-individuality. We face then a dilemma: (...) on the one hand, identity seems too important to be given up, on the other hand the RV seems to require that identity be given up. In this paper we shall discuss how the specific characterization of the RV through non-reflexive logics came to be framed. We examine some of the main objections to this version of the RV and argue that they are misguided under this specific “non-reflexive” understanding of the RV. Finally, we shall also argue that this non-reflexive view is not the only option for a metaphysical articulation of the RV: less radical approaches to identity and logic are open. In particular, some of these alternative approaches to the RV we present may be immune to most of the criticisms presented against the non-reflexive approach. (shrink)

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of –1 are indiscernible: anything true of one of them is true (...) of the other. I suggest that ‘i’ functions like a parameter in natural deduction systems. I gave an early version of this paper at a workshop on structuralism in mathematics and science, held in the Autumn of 2006, at Bristol University. Thanks to the organizers, particularly Hannes Leitgeb, James Ladyman, and Øystein Linnebo, to my commentator Richard Pettigrew, and to the audience there. The paper also benefited considerably from a preliminary session at the Arché Research Centre at the University of St Andrews. I am indebted to my colleagues Craige Roberts, for help with the linguistics literature, and Ben Caplan and Gabriel Uzquiano, for help with the metaphysics. Thanks also to Hannes Leitgeb and Jeffrey Ketland for reading an earlier version of the manuscript and making helpful suggestions. I also benefited from conversations with Richard Heck, John Mayberry, Kevin Scharp, and Jason Stanley. CiteULike Connotea Del.icio.us What's this? (shrink)

In this paper I consider some logical and mathematical aspects of the discussion of the identity and individuality of quantum entities. I shall point out that for some aspects of the discussion, the logical basis cannot be put aside; on the contrary, it leads us to unavoidable conclusions which may have consequences in how we articulate certain concepts related to quantum theory. Behind the discussion, there is a general argument which suggests the possibility of a metaphysics of non-individuals, (...) based on a reasonable interpretation of quantum basic entities. I close the paper with a suggestion that consists in emphasizing that quanta should be referred to by the cardinalities of the collections to which they belong, for which an adequate mathematical framework seems to be possible. (shrink)

Our aim is to provide a sequent calculus whose external consequence relation coincides with the three-valued paracomplete logic `of nonsense' introduced by Dmitry Bochvar and, independently, presented as the weak Kleene logic K3W by Stephen C. Kleene. The main features of this calculus are (i) that it is non-reflexive, i.e., Identity is not included as an explicit rule (although a restricted form of it with premises is derivable); (ii) that it includes rules where no variable-inclusion conditions are attached; (...) and (iii) that it is hybrid, insofar as it includes both left and right operational introduction as well as elimination rules. (shrink)

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)

Quasi-set theory has been proposed as a means of handling collections of indiscernible objects. Although the most direct application of the theory is quantum physics, it can be seen per se as a non-classical logic (a non-reflexive logic). In this paper we revise and correct some aspects of quasi-set theory as presented in [12], so as to avoid some misunderstandings and possible misinterpretations about the results achieved by the theory. Some further ideas with regard to quantum field theory are (...) also advanced in this paper. (shrink)

How is it possible that a thing singled out not exist? How is it possible that two things singled out be numerically identical? How is one to understand the relationship between, say, a quality of a thing and what this quality is? And how is one to understand the relation between this quality and the thing which happens to be thus qualified? Trying to answer these four questions involves investigation of the four senses of the verb "to be," or of (...) the concepts of existence, identity, essential and accidental predication. Butchvarov’s thesis is that these four questions admit of a common answer, that the cornerstone of this comprehensive theory is an answer to the second question, and that this crucial answer depends on making some such distinction as his between "objects" and "entities." The bare bones of his argument are these: We commonly make statements of the form "a is b" where "a" and "b" are used referringly. A "material identity" statement of this form may be true. If true, it is about one thing; yet what it is about appears to be distinct things. This distinctness is not a real distinction among existents, nor does it arise solely or primarily from features of language. Butchvarov’s account is based on a distinction "of reason" between objects and entities. An entity is an existent, a constituent of the world. An object is whatever can be singled out once, and only once, in perception or imagination or in "thought". Entities as such cannot be singled out, yet they may be recognized through applications of a conceptual apparatus to objects. A material identity statement, then, states that two objects are one entity. If true, it is both about two distinct objects and about the one entity which each is. When two objects are judged to be one entity, then indiscernibility is enforced. Seeming counterexamples to the indiscernibility of identicals are explained in terms of the distinction between objects and entities. Though some applications of the concept of identity are relative to sortal characteristics, others are not. The latter are prior to the former. These primary judgments constitute the backbone of "thought" and discourse. They are governed by impersonal, nonhuman "paradigms." There are entities, of course; and there are objects, though as objects none exists. Some objects are entities, some are not. The notion of existence, like the notion of identity in its material role, is then a principle of classification, a concept. Butchvarov examines nine objections to this claim, and elaborates his distinction between objects and entities. He concludes that identifiability, hence indefinite reidentifiability, is the logically sufficient condition of applicability of the concept of existence. A statement such as "Socrates is white" is a disguised conjunction, viz., "Socrates has this color, and this color is white." The second conjunct is an "essential" statement; it says of an object singled out that it is a certain entity; or, to allow for essences of nonexistent objects, it states what entity the object would be were it an entity. An essential statement is not a material identity statement, for only one of its terms is used referringly. The essence of an object is not a property of it, for it is what the object is or would be. Whereas logically prior consciousness of objects is intentional and non-conceptual, consciousness of entities is conceptual and nonintentional; it consists in recognizing that a thing can be identified by oneself or by others. What is accidentally white, say, cannot be a material substance or bare particular; therefore it is a "cluster" of qualities. The Resemblance Theory, according to which qualities are particulars, is not a coherent alternative to the Identity Theory; therefore the qualities an individual happens to have are themselves universals. The Bradleyan critique of ontological atomism is cogent; therefore an individual is a cluster of qualities each of which depends for its "formal identity" on its being together with the rest. An individual’s having qualities is then to be understood in terms of the necessary togetherness of the qualities constitutive of it. Since in addition each of these qualities is essentially a universal, and specific universals are contingently coinstantiated, the predication in question is properly regarded as accidental. The problem of identifying quality-clusters through space and time is discussed. (shrink)

This paper is a continuation of the authors' attempts to deal with the notion of indistinguishability (or indiscernibility) from a logical point of view. Now we introduce a two-sorted first-order modal logic to enable us to deal with objects of two different species. The intended interpretation is that objects of one of the species obey the rules of standard S5, while the objects of the other species obey only the rules of a weaker notion of indiscernibility. Quantum mechanics motivates the (...) development. The basic idea is that in the ‘actual’ world things may be indiscernible but in another accessible world they may be distinguished in some way. That is, indistinguishability needs not be seen as a necessary relation. Contrariwise, things might be distinguished in the ‘actual’ world, but they may be indiscernible in another world. So, while two quantum systems may be entangled in the actual world, in some accessible world, due to a measurement, they can be discerned, and on the other hand, two initially separated quantum systems may enter in a state of superposition, losing their individualities. Two semantics are sketched for our system. The first is constructed within a standard set theory (the ZFC system is assumed at the metamathematics). The second one is constructed within the theory of quasi-sets, which we believe suits better the purposes of our logic and the mathematical treatment of certain situations in quantum mechanics. Some further philosophically related topics are considered. (shrink)

This paper is about the nature of God’s pre-creation knowledge of possible creatures. I distinguish three theories: non-qualitative singularism, qualitative singularism, and qualitative generalism, which differ in terms of whether the relevant knowledge is qualitative or non-qualitative, and whether God has singular or merely general knowledge of creatures. My main aim is to argue that qualitative singularism does not depend on a version of the Principle of Identity of Indiscernibles to the effect that, necessarily, qualitatively indiscernible individuals are identical. (...) It follows that qualitative singularism does not depend on the view that possible creatures categorically have qualitative individual essences. (shrink)

The paper takes off from the problem of finding a proper content for the relation of identity as it holds or fails to hold among ordinary things or substances. The necessary conditions of identity are familiar, the sufficient conditions less so. The search is for conditions at once better usable than the Leibnizian Identity of Indiscernibles (independently suspect) and strong enough to underwrite all the formal properties of the relation.It is contended that the key to this problem (...) rests at the level of metaphysics and epistemology alike with a sortalist position. Sortalism is the position which insists that, if the question is whether a and b are the same, it has to be asked what are they? Any sufficiently specific answer to that question will bring with it a principle of activity or functioning and a mode of behaviour characteristic of some particular kind of thing by reference to which questions of persistence or non-persistence through change can be adjudicated.These contentions are illustrated by reference to familiar examples such as the human zygote, the Ship of Theseus and Shoemaker's Brown-Brownson. The first example is hostage for a mass of unproblematical cases. The problems presented by the second and third sort of examples arise chiefly (it is claimed) from an incompleteness in our conceptions of the relevant sort—the what the thing in question is. That incompleteness need not prevent us from knowing perfectly well which thing we are referring to. In the concluding section, sortalism is defended against various accusations of anthropocentrism.The paper touches on the interpretation of Heraclitus, Leibniz's theory of clear indistinct ideas, the difficulties of David Lewis's ‘perdurantist’ or stroboscopic view of persistence, four-dimensionalism, and the relation of personal identity both to experiential memory and to the particular bodily physiognomy of a subject. At some points—as in connection with the so-called Only a and b rule—the paper corrects, supplements or extends certain theses or formulations proposed in the author's Sameness and Substance Renewed (2001). (shrink)

According to strong composition as identity, the logical principles of one–one and plural identity can and should be extended to the relation between a whole and its parts. Otherwise, composition would not be legitimately regarded as an identity relation. In particular, several defenders of strong CAI have attempted to extend Leibniz’s Law to composition. However, much less attention has been paid to another, not less important feature of standard identity: a standard identity statement is true (...) iff its terms are coreferential. We contend that, if coreferentiality is dropped, indiscernibility is no help in making composition a genuine identity relation. To this aim, we analyse as a case study Cotnoir’s theory of general identity, in which indiscernibility is obtained thanks to a revisionary semantics and true identity statements are allowed to connect non-coreferential terms. We extend Cotnoir’s strategy for indiscernibility to the relation of comaternity, and we show that, neither in the case of composition nor in that of comaternity, indiscernibility contibutes to show that they are genuine identity relations. Finally, we compare Cotnoir’s approach with other versions of strong CAI endorsed by Wallace, Bøhn, and Hovda, and canvass the extent to which they violate coreferentiality. The comparative analysis shows that, in order to preserve coreferentiality, strong CAI is forced to adopt a non-standard semantic treatment of the singular/plural distinction. (shrink)

This paper examines a variety of contexts in metaphysics which employ a strategy I consider to be suspect. In each of these contexts, ‘The Suspect Strategy’ (TSS) aims at excluding a series of troublesome contexts from a general principle whose truth the philosopher in question wishes to preserve. We see (TSS) implemented with respect to Leibniz’s Law (LL) in the context of Gibbard’s defense of contingent identity, Myro and Gallois’ defense of temporary identity, as well as Terence Parsons’ (...) defense of indeterminate identity. Our example of (TSS) as implemented with respect to the Existence Principle (EP) is Terence Parsons’ defense of non-existent objects. Finally, the coincidence-theorist’s analysis of the problem of constitution as given by Baker, Fine and Yablo, as well as Deutsch’s recent defense of the relative-identity theory provide examples of (TSS) as implemented with respect to restricted indiscernibility principles of the form in (RI). While we of course cannot conclude from our exposure to extant versions of (TSS) that no exclusion-procedure could ever overcome the troubling features we encountered, my remarks in this paper should, I think, at least give us reasons to be skeptical that any strategy which proceeds by means of purely formal (e.g., syntactic) individuation-criteria could achieve its intended purpose; for we have seen that such strategies are in general too coarse-grained to individuate contexts correctly into those that should and those that should not be excluded from the reaches of the general principle under discussion. I suspect, moreover, though I do not argue for this stronger claim, that any strategy which does not proceed by means of purely formal criteria would in some way succumb to the charge of circularity. As a result, I recommend that we should learn to become accustomed to a universe populated with a surprising multitude of numerically distinct yet almost indiscernible objects, such as statues and the lumps of clay that constitute them. Given the large amounts of overlap among these almost indiscernible objects, such a densely populated universe is actually quite easy to live with, but that’s a story for a separate occasion. (shrink)

We begin by discussing some logical constraints on the psychological approach to personal identity. We consider a problem for the psychological approach that arises in fission cases. The problem engenders the need for a non-branching clause in a psychological account of the co-personality relation. We look at some difficulties in formulating such a clause. We end by rejecting a recently proposed formulation of non-branching. Our criticism of the formulation raises some interesting questions about the individuation of person stages.

Décio Krause has achieved a thorough reconstruction of logic and set theory, to account for the unusual objects or quasi-objects of quantum physics. How can one cope with the (partial) lack of criteria of individualization and re-identification of quantum objects, when the elementary operations of counting them, and constituting sets of them, are to be performed? Here, I advocate an alternative strategy, that consists in going below the level of logic and set theory to inquire how their categories are generated (...) in the experience and activity of knowing subjects, and whether this mode of category generation is still relevant in the field of experimental quantum physics. This project of a “genealogy of logic” is borrowed from Husserl’s last treatise, entitled Experience and Judgment. It is transposed to the case of quantum physics by way of a QBist approach of Mott’s theorization of quasi-“trajectories” in Wilson cloud chambers. It is also shown that one of the most appropriate ontologies for quantum objects or quasi-objects involves reversing the (grammatical) roles of subject and predicate, as advocated by Japanese philosopher Nishida Kitarô in reasonable agreement with both Schrödinger’s and Krause’s approaches of the concept of “particle”. (shrink)

The present article deals with the not very common opinion among medieval philosophers according to which the identity principle is the true first principle, undermining the primacy of the principle of non-contradiction. Following a refutation of this position in the logical work of the Franciscan Geraldus Odonis, we intend to investigate its target as well as other cases of the same dispute in 14th century authors: Antoine Andre, John of Buridan, John of Baconthorpe and Nicolas of Autrecourt. We defend (...) that Odonis presents a successful response to this position. (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)

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)

We begin by discussing some logical constraints on the psychological approach to personal identity. We consider a problem for the psychological approach that arises in fission cases. The problem engenders the need for a non-branching clause in a psychological account of the co-personality relation. We look at some difficulties in formulating such a clause. We end by rejecting a recently proposed formulation of non-branching. Our criticism of the formulation raises some interesting questions about the individuation of person stages.

An argument against multiply instantiable universals is considered in neglected essays by Stanislaw Lesniewski and I.M. Bochenski. Bochenski further applies Lesniewski's refutation of universals by maintaining that identity principles for individuals must be different than property identity principles. Lesniewski's argument is formalized for purposes of exact criticism and shown to involve both a hidden vicious circularity in the form of impredicative definitions and explicit self-defeating consequences. Syntactical restrictions on Leibnizian indiscernibility of identicals are recommended to forestall Lesniewski's paradox.

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)

The distinction between qualitative and non-qualitative properties should be familiar from discussions of the principle of the identity of indiscernibles: two otherwise exactly similar individuals, Castor and Pollux, might share all their qualitative properties yet differ with respect to their non-qualitative properties—for while Castor has the property being identical to Castor, Pollux does not. But while this distinction is familiar, there has not been much critical attention devoted to spelling out its precise nature. I argue that the class of (...) non-qualitative properties is broader than it is often taken to be. When properly construed, it will not only include properties such as being identical to Castor, which somehow make reference to particular individuals, it will also include more general properties such as identity, composition, set membership, as well as various peculiarly ontological properties. Given that some of these more general properties help to explain objective similarity, we have reason to believe that there are fundamental non-qualitative properties. (shrink)

Recently, in the debate about the ontology of quantum mechanics some authors have defended the view that quantum particles are individuals in a primitive sense, so that individuality should be preferred over non-individuality (the alternative option). Primitive individuality involves two main claims: (1) every item is identical with itself and (2) it is distinct from every other item. Non-relativistic quantum mechanics is said to provide positive evidence for that position, since in every situation comprising multiple particles there (...) is a well-defined number of them to begin with, and so they must be distinct from each other. We argue that the link between a well-defined number of items and the relation of identity that is being claimed to hold is not imposed by quantum mechanics, but rather by a metaphysical view. Formal evidence is advanced in favor of the thesis that counting may be performed for items without identity (non-individuals), so that quantum mechanics needs not be viewed as endorsing an ontology of individuals. (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)

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)

Description: Contents: Preface 1. General Remarks on the Vedanta 2. Fundamental Distinction Between The Self and the Ego 3. The Vital Centre of the Human Being, Seat of Brahma 4. Purusha and Prakriti 5. Purusha Unaffected by Individual Modifications 6. The Degrees of Individual Manifestation 7. Buddhi or the Higher Intellect 8. Manas or the Inward Sense : The Ten External Faculties of Sensation and Action 9. The Envelopes of the Self ; The Five Vayus or Vital Functions 10. The (...) Essential Unity and Identity of the Self in all the States of the Being 11. The Different Conditions of Atma in the Human Being 12. The Waking State or the Condition of Vaishwanara 13. The Dream State or the Condition of Taijasa 14. The State of Deep Sleep or the Condition of Prajna 15. The Unconditioned State of Atma 16. The Symbolical Representation of Atma and its Conditions by the Sacred Monosyllable Om 17. The Posthumous Evolution of the Human Being 18. The Reabsorption of the Individual Faculties 19. Differences in the Posthumous Conditions According to the Degrees of Knowledge 20. The Coronal Artery and the Solar Ray 21. The Divine Journey of the Being on the Path of Liberation 22. Final Deliverance 23. Videha-mukti and Jivana-mukti 24. The Spiritual State of the Yogi : The Supreme Identity. (shrink)

This paper deals with the identity and individuality of material objects. In particular, the view that identity is derivative on the qualities of things, based on the endorsement of the Principle of the Identity of the Indiscernibles, is studied in detail. This provides what seems to be a much-needed unitary look at, and up-to-date critical analysis of, the vast literature on the Identity of the Indiscernibles. It is concluded that the ‘reductionist’ view, dating back to (...) Quine and, earlier, to Leibniz, possesses no compelling justification, neither from the conceptual, a priori point of view, nor from the methodological perspective, nor as far as empiricalevidence (as the latter is described by our best current science) is concerned. That is to say, the Principle has not been (perhaps, cannot be) shown to be either a necessary or a contingent truth. Therefore, it can be argued that the whole reductionist view of the individuality of material entities can be dispensed with in favour of an interpretation of reality in terms of objects provided with primitive identity. A suggestion in this latter sense that preserves the appeal of a property-based ontology is very briefly made. (shrink)

According to a very widespread interpretation of the metaphysical nature of quantum entities—the so-called Received View on quantum non-individuality—, quantum entities are non-individuals. Still according to this understanding, non-individuals are entities for which identity is restricted or else does not apply at all. As a consequence, it is said, such approach to quantum mechanics would require that classical logic be revised, given that it is somehow committed with the unrestricted validity of identity. In this paper we examine (...) the arguments to the inadequacy of classical logic to deal with non-individuals, as previously defined, and argue that they fail to make a good case for logical revision. In fact, classical logic may accommodate non-individuals in that specific sense too. What is more pressing for the Received View, it seems, is not a revision of logic, but rather a more adequate metaphysical characterization of non-individuals. (shrink)

The treatment of identical particles in quantum mechanics rests on two (related) principles: the spin-statistics connection and the Symmetrization Postulate. In light of recent theories (such as q-deformed commutators) that allow for ‘small’ violations of the spin-statistics connection and the Symmetrization Postulate, we revisit the issue of how quantum mechanics deals with identical particles and how it supports or fails to support various philosophical stances concerning individuality. As a consequence of the expanded possibilities for quantum statistics, we argue that (...) permutation symmetry is best formulated as a formal property of the state function describing the system of particles rather than as a property of the individual particles. 1 Introduction 2 Philosophical background 2.1 Important terminology 2.1.1 Identity 2.1.2 Indistinguishability 2.1.3 Indiscernibility 2.2 When are particles indistinguishable? 2.3 The Principle of the Identity of Indiscernibles and quantum mechanics 2.4 The Principle of the Identity of Indiscernibles and logic 2.5 Particle history 2.6 Transcendental individuality 3 Some quantum formalism 3.1 The Principle of Permutation Invariance and the Symmetrization Postulate 3.2 The configuration-space approach 3.3 Commutators and anticommutators, and identical particle statistics 3.4 Q-mutators 4 Identical particle statistics: a holistic point of view 5 Conclusions. (shrink)

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure (...) is not to be accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view. We want to thank Leon Horsten, Jeff Ketland, Øystein Linnebo, John Mayberry, Richard Pettigrew, and Philip Welch for valuable comments on drafts of this paper. We are especially grateful to Fraser MacBride for correcting our interpretation of two of his papers and for other helpful comments. CiteULike Connotea Del.icio.us What's this? (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)

We consider the claim by Dorato and Morganti 591–610) that primitive individuality should be attributed to the entities dealt with by non-relativistic quantum mechanics. There are two central ingredients in the proposal: in the case of non-relativistic quantum mechanics, individuality should be taken as a primitive notion and primitive individuality is naturalistically acceptable. We argue that, strictly understood, naturalism faces difficulties in helping to provide a theory with a unique principle of individuation. We also hold that even (...) when taken in a loose sense, naturalism does not provide any sense in which one could hold that quantum mechanics endorses primitive individuality over non-individuality. Rather, we argue that non-individuality should be preferred based on the grounds that such a view fits better the claims of the theory. (shrink)

Relative Identity contains a sustained attack on the classical or absolute theory of identity and a defense of a non-classical or relative theory of identity. According to the absolute theory of identity each thing is identical with itself and with nothing other than itself. The fundamental principle of this theory is Leibniz' Law:From a variety of characteristic principles about identity can be derived, including The Indiscernibility of Identicals, The Identity of Indiscernibles, and the symmetry, (...) reflexivity, and transitivity of identity. (shrink)

In the philosophy of science, identity over time emerges as a central concern both as an ontological category in the interpretation of physical theories, and as an epistemological problem concerning the conditions of possibility of knowledge. In Reichenbach and subsequent writers on the problem of indistinguishable quantum particles we see the return of a contrast between Leibniz and Aquinas on the subject of individuation. The possibility of rejecting the principle of the identity of indiscernibles has certain logical difficulties, (...) leading us inexorably from ontology into epistemology. For the epistemological problem we attend to the differences that emerged between the (neo-)Kantian and logical empiricist traditions, also saliently displayed in Reichenbach's writings. After examining the contrast between Kant's and Leibniz's conceptions of empirical knowledge, specifically with respect to the irreducibility of spatiotemporal determinations, we explore an application of a neo-Kantian view to the same problem of indistinguishable quantum particles. (shrink)

Lowe has recently argued that quantum particles offer examples of vague objects. While accepting the premise of the argument that such particles can be regarded as individuals, we point out that there is a lacuna here, to be filled by a detailed analysis of the nature of the entangled states which they enter into. We then elaborate the alternative view, according to which such particles should be regarded as non- individuals' and situate it in the context of recent developments of (...) a logic of non- individuality. Our conclusion is that it is here that one encounters genuine ontic vagueness. (shrink)

One recent debate in philosophy of physics has centered whether quantum particles are individuals or not. The received view is that particles are not individuals and the standard methodology is to approach the question via the structure of quantum theory. I challenge both the received view and the standard methodology. I contend not only that the structure of quantum theory is not the right place to look for conditions of individuality that quantum particles may or may not satisfy, but (...) also that there is an important role for traditional metaphysics to play. Consequently, my work brings together the philosophy of physics and traditional metaphysics literatures to shed new light on the debate over the individuality of quantum particles. I defend a set of conditions of individuality and argue that quantum particles satisfy these conditions thereby defending the view that particles are individuals in opposition to the received view. I also challenge a second feature of the standard methodology insofar as I challenge the significance of the Principle of the Identity of Indiscernibles in terms of which much discussion in the philosophy of physics literature is framed. My work is significant in a number of additional ways as well. My work implies that the dominant explanation for quantum statistics in terms of non-individuality is incorrect and it also undermines the ontic-structural realists metaphysical underdetermination challenge to the scientific realist. (shrink)

This essay examines an argument of perennial importance against naive Leibnizian absolute identity theory, originating with Ruth Barcan in 1947 (Barcan, R. 1947. ?The identity of individuals in a strict functional 3 calculus of second order?, Journal of Symbolic Logic, 12, 12?15), and developed by Arthur Prior in 1962 (Prior, A.N. 1962. Formal Logic. Oxford: The Clarendon Press), presented here in the form offered by Nicholas Griffin in his 1977 book, Relative Identity (Griffin, N. 1977. Relative (...) class='Hi'>Identity. Oxford: The Clarendon Press). The objection considers the property of being necessarily identical to a specific object a as a counterexample to Leibnizian identity conditions, and more particularly to the indiscernibility of identicals, when it is only contingently true that a=b. The inquiry eliminates necessity and reference to a specifically designated object as responsible for the counterexample, leaving only identity. The requirements for an exact reinterpretation of Leibniz's Law in light of counterexamples involving converse intentional properties and the family of properties suggested by the property of being necessarily identical to a where a=b (or an equivalent definite descriptor variation) is only logically contingently true, are formalized in a more powerful, counterexample-resistant version of Leibniz's Law that does not succumb to relative identity as a necessary alternative motivated by desperation over the failure of the absolute identity principle. (shrink)

Décio Krause is one of the staunchest defenders of the “Received View” of “identical quantum particles”, i.e. quantum particles of the same kind. According to the Received View identical quantum particles do not possess individuating properties: they are entities without identity. Still, they are “different” from each other in the weak sense that there can be more than one of them. As Décio Krause has pointed out, such identity-less objects must be handled by a non-standard set theory—quasi-set theory, (...) a subject to which he has made important contributions.In this Chapter we compare and contrast the ideas of the Received View with those of a rival interpretation that has recently started to attract attention. According to this Alternative View quantum particles are emerging entities—at a fundamental level, the world does not consist of particles. But once emerged, quantum particles of the same kind are distinguishable and possess identity, so that they can be dealt with by standard set theory and ordinary mathematics. (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.