Identity of Indiscernibles

I argue that there is an ambiguity in the concept of indiscernibility as applied to objects, because there are two different categories of properties, associated with two different ways in which all of the pre-theoretical 'properties' of an object may be identified. In one structural way, identifications of properties are independent of any particular spatial orientation of the object in question, but in another 'field' way, identifications are instead dependent on an object's particular spatial orientation, so that its properties as (...) thus identified in one orientation are distinct from its properties as identified in any other orientation--all of which ‘field’ properties must hence also be distinct from the previous structurally defined properties. -/- To accommodate the two kinds of intrinsic properties, the standard concept of indiscernibility is redefined as structural indiscernibility, while a new concept of field indiscernibility is introduced. I argue among other things that, though two objects may be structurally indiscernible under all orientational (and other) conditions, those objects may nevertheless fail to have field indiscernibility with each other under some orientational conditions. I also briefly discuss the implications of these results for general issues about the nature of properties, and of realist versus nominalist approaches to them. -/- . (shrink)

An attempt to vindicate naive set theory by postulating a universal set V which is describable in two distinct description languages: predicative and extensional. The extensional description of a set consists of describing all its elements whereas its predicative description consists of describing what sets it is an element of. -/- Extensionally described V has an uncapturable description length, akin to its cardinality. But predicatively described, in virtue of being the set that is not contained in any set whatsoever, V (...) has a minimal description length, a counterbalance to its cardinality. -/- Descriptive efficiency can genuinely be attributed to V (achieved in a third description language) only if it contains predicatively indiscernible but extensionally discernible sets. (shrink)

x and y are at least weakly indiscernible if they are distinct with respect to two predicates F and G (FxGy or FyGx and not both) but for all z except x and y, Fz if and only if Gz.

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)

De Clercq (2012) proposes a strategy for denying purported graph-theoretic counterexamples to the Principle of the Identity of Indiscernibles (PII), by assuming that any vertex is contained by multiple graphs. Duguid (2016) objects that De Clercq fails to show that the relevant vertices are discernible. Duguid is right, but De Clercq’s strategy can be rescued. This note clarifies what assumptions about graph ontology are needed by De Clercq, and shows that, given those assumptions, any two vertices are weakly discernible, and (...) so are not counterexamples to the version of PII that requires only weak discernibility. (shrink)

Is identity fundamental to every conceptual systems? In this article I intend to present reasons against the claim that every conceptual system presupposes the notion of identity. To address this debate I analyze the positions of Bueno (2014; 2016) and Krause and Arenhart (2015). While Bueno argues that identity is necessary for all conceptual systems, Krause and Arenhart present a series of objections against such position, thus defending that identity is not fundamental. I intend to show that the main objections (...) presented by Krause and Arenhart do not affect Bueno’s theory because of a misinterpretation of his arguments. Finally, I will present some objections against Bueno that, hopefully, does not miss the target. (shrink)

In this paper, we introduce a quasi-set theory without atoms. The quasi-sets (qsets) can have as elements completely indiscernible things which do not turn out to be the very same thing as it would be implied if its underlying logic was classical logic. A quasi-set can have a cardinal, called its quasi-cardinal, but this is made so that, at least for the finite case, the quasi-cardinal is not an ordinal, and hence the indistinguishable elements of a quasi-set cannot be ordered. (...) In the last sections, we show how the theory can be used to ground a quantum metaphysics of properties, which sees the quantum entities as bundles of properties, and we also introduce a new approach for the use of quantifiers in quantum physics. (shrink)

According to anti-haecceitism, facts about particular things are modally fixed by qualitative matters. According to qualitativism, such facts are metaphysically second-rate, perhaps because grounded in qualitative matters. Qualitativism seems to imply anti-haecceitism, so objections to the latter threaten the former. The most powerful sort of apparent counterexample to anti-haecceitism, I think, consists in a pair of situations that seem the same, and qualitatively symmetric, for a stretch of time, but that differ in how that symmetry breaks. I examine this sort (...) of candidate counterexample in depth, and argue that the prospects for resisting it are heavily sensitive to broader metaphysical considerations, specifically ones about ontology, time, and causation. So, anti-haecceitism’s and qualitativism’s prospects are heavily sensitive to such considerations. (shrink)

I propose a novel metaphysical explanation of identity and distinctness facts called the Modal Proposal. According to the Modal Proposal, for each identity fact – that is, each fact of the form a=b – that fact is metaphysically explained by the fact that it is necessary that the entities involved are indiscernible, and for each distinctness fact –that is, each fact of the form a≠b – that fact is metaphysically explained by the fact that it is possible for the entities (...) involved to be discernible. I argue that the Modal Proposal has greater payoffs at less cost than any of its competitors. It gives simple, uniform, and intuitive explanations of identity and distinctness that conserve longstanding philosophical insights about identity that go back to Leibniz. It does this while making our fundamental base more parsimonious, determining whether controversial cases of identity or distinctness are possible, and expanding our understanding of these central philosophical relations. It does all this while avoiding controversial ontological commitments. (shrink)

I discuss the idea that the objects of Wittgenstein’s Tractatus are propertyless bare particulars, an idea defended by Leonard Goddard and Brenda Judge in their monograph, The Metaphysics of the Tractatus. I present the difficulties that Goddard and Judge raise for this construal concerning the idea that Tractarian objects have natures that determine their possibilities of combination, and I assess the solution they propose. I offer an alternative construal of the notion with which these difficulties can be overcome.

In my fourth year, I completed a research paper critically analyzing writing on Endurance and Perdurance by testing these theories of how objects persist through change with Einstein’s Relativity to present a thesis. I then compared these metaphysical accounts of persistence for how well they conform to applied physical principles of Special Relativity.

This chapter argues that the general philosophy of science should learn metaphilosophical lessons from the case of metaphysical underdetermination, as it occurs in non-relativistic quantum mechanics. Section presents the traditional discussion of metaphysical underdetermination regarding the individuality and non-individuality of quantum particles. Section discusses three reactions to it found in the literature: eliminativism about individuality; conservatism about individuality; eliminativism about objects. Section wraps it all up with metametaphysical considerations regarding the epistemology of metaphysics of science.

Few Star Wars characters are more beloved than Luke Skywalker, Jedi Knight, son of Darth Vader, and mentor to Rey. Fictional characters like Luke are wholly defined by how people understand, interpret, and evaluate their depictions within the fictions in which they appear. This chapter explores various ways to provide identity conditions for fictional characters. It examines a more sophisticated, but again ultimately incorrect, account of fictional character identity: the Say‐So Account, in which authors determine whether two characters, from two (...) fictional works, are identical. The Perspectival Account avoids the problems seen in the earlier accounts and provides the authors with an adequate account of identity conditions for fictional characters. Further, the Perspectival Account allows the authors to explain how the truth‐value of fictional character identity claims can change over time. (shrink)

The Principle of Identity of Indiscernibles (PII) is the focus of much controversy in the history of Metaphysics and in contemporary Physics. Many questions rover the debate about its truth or falsehood, for example, to which objects the principle applies? Which properties can be counted as discerning properties? Is the principle necessary? In other words, which version of the principle is the correct and is this version true? This thesis aims to answer this questions in order to show that PII (...) is a necessarily true principle of metaphysics. To accomplish this task, the reader will find, in this thesis, an encyclopaedical introduction to the history of PII and to the reasons it matters so much, followed by a presentation of the most famous arguments against it and the defences used against these arguments. Then, the reader finds in-depth discussion of the minutiae involved in postulating the principle as to make clear what is in fact being attacked and defended. With these preliminaries solved, a deeper analysis of these defences is presented aiming to discover which is the most appropriate example to use against the attacks to the principle. This analysis allowed a classification of these defences in four families with different strategies within them. Finally, with these defensive strategies at hand we are able to confront alleged counterexamples to PII in Mathematics with the intention to test these defences. (shrink)

I systematically defend a novel account of the grounds for identity and distinctness facts: they are all uniquely zero‐grounded. First, this Null Account is shown to avoid a range of problems facing other accounts: a relation satisfying the Null Account would be an excellent candidate for being the identity relation. Second, a plenitudinist view of relations suggests that there is such a relation. To flesh out this plenitudinist view I sketch a novel framework for expressing real definitions, use this framework (...) to give a definition of identity, and show how the central features of the identity relation can be deduced from this definition. (shrink)

Much of the debate about identity in recent decades has been about personal identity, and specifically about personal identity over time, but identity generally, and the identity of things of other kinds, have also attracted attention. Various interrelated problems have been at the centre of discussion, but it is fair to say that recent work has focussed particularly on the following areas: the notion of a criterion of identity; the correct analysis of identity over time, and, in particular, the disagreement (...) between advocates of perdurance and advocates of endurance as analyses of identity over time; the notion of identity across possible worlds and the question of its relevance to the correct analysis of de re modal discourse; the notion of contingent identity; the question of whether the identity relation is, or is similar to, the composition relation; and the notion of vague identity. A radical position, advocated by Peter Geach, is that these debates, as usually conducted, are void for lack of a subject matter: the notion of absolute identity they presuppose has no application; there is only relative identity. Another increasingly popular view is the one advocated by Lewis: although the debates make sense they cannot genuinely be debates about identity, since there are no philosophical problems about identity. Identity is an utterly unproblematic notion. What there are, are genuine problems which can be stated using the language of identity. But since these can be restated without the language of identity they are not problems about identity. (For example, it is a puzzle, an aspect of the so-called “problem of personal identity”, whether the same person can have different bodies at different times. But this is just the puzzle whether a person can have different bodies at different times. So since it can be stated without the language of personal “identity”, it is not a problem about identity, but about personhood.) This article provides an overview of the topics indicated above, some assessment of the debates and suggestions for further reading. (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)

How superposition explains the human mind. And, also, the Universe.

What does it mean for an object to persist through time? Consider the statement, ‘My car is filthy, I need to wash it.’ Consider the response, ‘How did it get that way?’ The answer is that dirt, dust and other particles have collected on the car’s surface thus making it filthy. Its properties have changed. At one point in the car’s career, none of that dirt and grime existed on its surface and the car was said to be clean. The (...) fact is that for a car to get dirty, the extension of time is necessary. The standard view of identity is that each thing is entirely itself at any given time. So how can an object remain identical with itself over time, if it changes its properties? In many ways I have different properties now than those I had last week. But if I am different, how then can I be the same? The objective of this article is to answer the question of what it means to say that we and other things persist through time. First I’ll lay out two popular philosophical views of persistence through time, then I will present possible problems with both views. After that, I will outline another possible answer that lies outside of these views. Finally, I will providemy own answer. (shrink)

According to strong pluralism, objects distinct by virtue of their modal properties can coincide. The most common objection towards such view invokes the so-called Grounding Problem according to which the strong pluralist needs to explain what the grounds are for supposed modal differences between the coincidents. As recognized in the literature, the failure to provide an answer to the Grounding Problem critically undermines the plausibility of strong pluralism. Moreover, there are strong reasons to believe that strong pluralists cannot provide an (...) explanation of the Grounding Problem. In this paper, we argue that strong pluralism can be motivated independently of the successful answer to the Grounding Problem. In order to achieve that aim, we provide a haecceitistic interpretation of strong pluralism according to which strong pluralism should be read as a position committed to the existence of primitive individuals, i.e., the individuals that have their criteria of individuation independently of their qualitative profiles. That said, we do not aim at defending haecceitism. Instead, our aim is rather modest: we want to provide a new way for the strong pluralist to supplement his view to make it more watertight. (shrink)

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

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

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)

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

ABSTRACTI present a new objection to Bundle Theory. The objection rests on the repeatability of universals, and targets every version of Bundle Theory that assumes that concrete particulars constituted by the same universals are numerically identical. The only way that bundle theorists can elude this objection is to admit the possibility of distinct bundles constituted by the same universals. If even this view is untenable, then Bundle Theory as such is hopeless. Finally, I show how the present inquiry reshapes the (...) dialectical relationship between Bundle Theory and the principle of Identity of Indiscernibles. (shrink)

Philosophy and model theory frequently meet one another. Philosophy and Model Theory aims to understand their interactions -/- Model theory is used in every ‘theoretical’ branch of analytic philosophy: in philosophy of mathematics, in philosophy of science, in philosophy of language, in philosophical logic, and in metaphysics. But these wide-ranging appeals to model theory have created a highly fragmented literature. On the one hand, many philosophically significant mathematical results are found only in mathematics textbooks: these are aimed squarely at mathematicians; (...) they typically presuppose that the reader has a significant background in mathematics; and little clue is given as to their philosophical significance. On the other hand, the philosophical applications of these results are then scattered across disconnected pockets of papers, separated by decades or more. -/- The first aim of Philosophy and Model Theory, then, is to consider the philosophical uses of model theory. On a technical level, we try to show how philosophically significant results connect to one another, and also to state the best version of a result for philosophical purposes. On a philosophical level, we show how similar dialectical situations arise repeatedly, across fragmented debates in varied philosophical areas. -/- The second aim of Philosophy and Model Theory, though, is to consider the philosophy of model theory. Model theory itself is rarely taken as the subject matter of philosophising (contrast this, say, with the philosophy of biology, or the philosophy of set theory). But model theory is a beautiful part of pure mathematics, and worthy of philosophical study in its own right. (shrink)

I would like to attack a certain view: The view that the concept of identity can fail to apply to some things although, for some positive integer n, we have n of them. The idea of entities without self-identity is seriously entertained in the philosophy of quantum mechanics. It is so pervasive that it has been labelled the Received View. I introduce the Received View in Section 1. In Section 2 I explain what I mean by entity, and I argue (...) that supporters of the Received View should agree with my characterization of the corresponding notion of entity. I also explain what I mean by identity, and I show that supporters of the Received View agree with my characterization of that notion. In Section 3 I argue that the concept of identity, so characterized, is one with the concept of oneness. Thus, it cannot but apply to what belongs to a collection with n elements, n being a positive integer. In Section 4 I add some considerations on the primitiveness of identity or unity and the status of the Identity of Indiscernibles. In Section 5 I address the problem of how reference to indiscernible objects with identity can be achieved. (shrink)

There are several relations which may fall short of genuine identity, but which behave like identity in important respects. Such grades of discrimination have recently been the subject of much philosophical and technical discussion. This paper aims to complete their technical investigation. Grades of indiscernibility are defined in terms of satisfaction of certain first-order formulas. Grades of symmetry are defined in terms of symmetries on a structure. Both of these families of grades of discrimination have been studied in some detail. (...) However, this paper also introduces grades of relativity, defined in terms of relativeness correspondences. This paper explores the relationships between all the grades of discrimination, exhaustively answering several natural questions that have so far received only partial answers. It also establishes which grades can be captured in terms of satisfaction of object-language formulas and draws connections with definability theory. (shrink)

Two kinds of individuals are distinguished: abstract and concrete. Whereas abstract individuals belong to our conceptual sphere, concrete individuals (i.e. particulars) individuate the world of matter. A subject investigating the external world projects abstract individuals onto concrete ones. The proposal offers a solution to various metaphysical and epistemological puzzles concerned with individuals, e.g., the Ship of Theseus, the Polish Logician, problems with reidentification, or proper names.

Interactionists hold that non-spatial objects causally interact with physical objects. Interactionists have traditionally grappled with the puzzle of how such interaction is possible. More recently, Jaegwon Kim has presented interactionists with a more daunting threat: the pairing argument, which purports to refute interactionism by showing that non-spatial objects cannot stand in causal relations. After reviewing that argument, I develop a challenge to it on behalf of the interactionist. The challenge poses a dilemma: roughly, either haecceities exist or they do not. (...) I argue that the pairing argument fails in either case. While the challenge does not explain exactly how the pairing argument goes wrong, it shows that the argument fails. The challenge also explains the difficulty in pinpointing the pairing argument’s failure: exactly how the pairing argument fails depends on difficult issues concerning the nature of objects. (shrink)

In this paper I show that a novel ontic reading of explanation, intending to capture the de re essential features of individuals, can support the qualitative view of individual essences. It is argued further that the putative harmful consequences of the Leibniz Principle and its converse for the qualitative view can be avoided, provided that individual essences are not construed in the style of the naïve bundle theory with set-theoretical identity- conditions. Adopting either the more sophisticated two-tier BT or, alternatively, (...) the neo-Aristotelian position of taking essences as natures in the Aristotelian sense, can help to evade these main charges against the qualitative view. The functional parallels with the alternative haecceitistic view of individuation and individual essence will also be considered. (shrink)

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous (...) to identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself,... (shrink)

This is a brief sequel to Max Black 's classic dialogue on the Identity of Indiscernibles. Interlocutor A defends the bundle theory by endorsing the view according to which Black 's world does not contain two indiscernible spheres but rather a single, bi-located sphere. His opponent, B, objects that A cannot distinguish such a world from a world with a single, uniquely located sphere, hence that the view in question adds nothing to A's original response to Black 's challenge. A (...) is simply denying that there can be worlds with two or more indiscernible entities. (shrink)

In my review of Steven French's The structure of the world. Metaphysics & Representation. OUP, Oxford, 2014 I argue that the author is forced to navigate between the Scilla of Tegmark’s Pitagoreanism (2008) and the Carybdis of “blobobjectivism” (Horgan and Potrč 2008), namely the claim that the whole physical universe is a single concrete structurally complex but partless cosmos (a “blob”).

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

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

Goetz outlined legal models of identical entities that include natural persons who are identical to a coregency and natural persons who are identical to a general partnership. Those entities cohere with the formula logic of relative identity. This essay outlines the coexistence of relative identity and numerical identity in the models of identical legal entities, which is impure relative identity. These models support the synthesis of Relative Trinitarianism and Social Trinitarianism, which I call Relative-Social Trinitarianism.

(Abstract - Inglês) Identity is traditionally taken to be a fundamental notion of our conceptual framework as well as a fundamental metaphysical component of entities. But as far as we make this claim we face ourselves with two problems: what is identity? And why would it be fundamental? These questions will guide us towards a discussion put forward by Bueno (2014), Krause and Arenhart (2015). Bueno holds that there are four aspects that make identity being fundamental: (1) identity is assumed (...) in every conceptual system; (2) it is required for a minimal characterisation of being an individual; (3) it cannot be defined; and (4) identity is required for quantification. On the other hand, Krause and Arenhart refuse the thesis that identity is fundamental replying to Bueno's arguments. In this dissertation we will deal with this debate. In the introduction we will deal with the first problem – what is identity? –, showing how this concept is traditionally understood, either for its metaphysical characteristics as for its formal account. After that we will deal with each of the four aspects defended by Bueno and challenged by Krause and Arenhart. After a critical presentation of each position we will also provide other arguments for the current debate. Finally we will outline an alternative view to those defended throughout this work. -/- (Resumo - Português) Tradicionalmente a identidade é adotada como uma noção fundamental de nosso arcabouço conceitual e como um componente metafísico fundamental das entidades. Mas logo ao fazermos essa afirmação nos deparamos com dois problemas: O que é a identidade? E por que ela seria fundamental? Estas perguntas irão nos guiar à discussão conduzida por Otávio Bueno (2014), Décio Krause e Jonas Arenhart (2015). Bueno defende que há quatro aspectos que fazem a identidade ser fundamental: (1) A identidade é pressuposta em todo sistema conceitual; (2) é requerida para uma caracterização mínima de indivíduo; (3) não pode ser definida; e (4) a identidade é requerida para a quantificação. Por outro lado, Krause e Arenhart recusam a tese de que a identidade seja fundamental, respondendo aos argumentos de Bueno. Neste trabalho iremos tratar desse debate. Na introdução iremos tratar do primeiro problema – O que é a identidade? –, mostrando como este conceito é tradicionalmente compreendido, tanto suas características metafísicas como também seu tratamento formal. Posteriormente iremos tratar de cada um dos quatro aspectos defendidos por Bueno e atacados por Krause e Arenhart. Além da exposição crítica de cada posição iremos também oferecer outros argumentos para o debate atual. Ao final iremos esboçar uma posição alternativa às defendidas ao longo do texto. (shrink)

This paper addresses the issue of the multiplicity of various grades of discernibility that can be defined in model theory. Building upon earlier works on the subject, I first expand the known logical categorizations of discernibility by introducing several symmetry-based concepts of discernibility, including one I call “witness symmetry-discernibility”. Then I argue that only grades of discernibility stronger than this one possess certain intuitive features necessary to individuate objects. Further downsizing of the set of non-equivalent grades of discernibility can be (...) achieved by stipulating that any relation of discernibility should be applied only to those pairs of objects which have been previously distinguished from the rest of the universe. Restricting discernibility to pairs of objects satisfying this condition gives an additional bonus in the form of restoring the transitivity of some types of indiscernibility which have been known to be non-transitive. (shrink)

A prominent version of mathematical structuralism holds that mathematical objects are at bottom nothing but "positions in structures," purely relational entities without any sort of nature independent of the structure to which they belong. Such an ontology is often presented as a response to Benacerraf's "multiple reductions" problem, or motivated on hermeneutic grounds, as a faithful representation of the discourse and practice of mathematics. In this paper I argue that there are serious difficulties with this kind of view: its proponents (...) rely on a distinction between "essential" and "nonessential" features of mathematical objects, and there's no good way to articulate this distinction which is compatible with basic structuralist commitments. But all is not lost. For I further argue that the insights motivating structuralism (or at least those worth preserving) can be preserved without formulating the view in ontologically committal terms. (shrink)

Is identity fundamental to formal systems? Even if a system have no the identity relation, is that concept is not assumed in any way – whether in a metalinguistic or intuitive level? In this paper we shall discuss this issue. Otávio Bueno (2014, 2016) argues against the elimination of identity, holding that this concept is fundamental and non-eliminable (even in does systems that claim to do so). Décio Arenhart Krause and Jonas (2015), by the other hand, have a number of (...) objections to Bueno’s thesis. Firstly, we look at how the concept of identity was accounted in the philosophical tradition, as well as part of its formal account. We will also examine the notion of indiscernibility that, according to the traditional approach to identity, is equivalent to the notion of identity, but (arguably) is not it logically equivalent. Thus, we shall state Krause and Arenhart’s strategy, according to, in a formal system we can eliminate identity in favor of the indiscernibility notion. Finally, we shall expose Bueno’s criticism to such strategy, and then to put forward some objections against it. (shrink)

It is argued that from a genuine Leibnizian point of view the well-known thought experiment, call it BTE, involving a possible world with only two exactly similar objects, cannot be used to refute Leibniz's Principle of the Identity of Indiscernibles (LIdI). If the claim that there are two objects in BTE is based on primitive thisnesses, the Leibnizian objection is that there are no such things; and even if there were, then, quite generally, something true of one object – that (...) it has its primitive thisness – would not be true of the other. Secondly, if the duality claim is based on a primitive, irreducible relation of distinctness, the Leibnizian objection is that there are no irreducible relations. Finally, if it is said that the (putatively) two objects in BTE cannot be separately individuated, then BTE is not a counter-example to LIdI, because if there is no individuation, there are no individuals either, while LIdI presupposes that there are individuals. (shrink)

This chapter has a twofold aim. First, to look at the debate about identity and individuality in nonrelativistic quantum mechanics and offer a limited defense of the view according to which identity facts are primitive in that domain. Second, to contribute to the clarification of the relationship between science and metaphysics, in particular with respect to what a proper “naturalistic” methodology should and should not be taken to entail as far as the theme of individuality is concerned. The guiding idea (...) is that taking identity and individuality facts as basic is not necessarily in conflict with naturalism. The overall picture that emerges, however, is that of a “pluralistic” approach, whereby different scientific domains and theories are likely to allow, and in fact to ask for, different forms of individuality. (shrink)

Some authors have attempted to defend Leibniz’s Identity of Indiscernibles through weak discernibility. The idea is that if there is a symmetric, nonreflexive physical relation that holds between two particles, then those particles cannot be identical. In this article I focus only on Muller and Saunders’s account and argue that the means by which they achieve weak discernibility is not through a quantum mechanical observable but an alternate mathematical construction that is both unorthodox and incomplete.

Ladyman and Ross argue that quantum objects are not individuals and use this idea to ground their metaphysical view, ontic structural realism, according to which relational structures are primary to things. LR acknowledge that there is a version of quantum theory, namely the Bohm theory, according to which particles do have denite trajectories at all times. However, LR interpret the research by Brown et al. as implying that "raw stuff" or haecceities are needed for the individuality of particles of BT, (...) and LR dismiss this as idle metaphysics. In this paper we note that Brown et al.'s research does not imply that haecceities are needed. Thus BT remains as a genuine option for those who seek to understand quantum particles as individuals. However, we go on to discuss some problems with BT which led Bohm and Hiley to modify it. This modified version underlines that, due to features such as context-dependence and non-locality, Bohmian particles have a very limited autonomy in situations where quantum effects are non-negligible. So while BT restores the possibility of quantum individuals, it also underlines the primacy of the whole over the autonomy of the parts. The later sections of the paper also examine the Bohm theory in the general mathematical context of symplectic geometry. This provides yet another way of understanding the subtle, holistic and dynamic nature of Bohmian individuals. We finally briefly consider Bohm's other main line of research, the "implicate order", which is in some ways similar to LR's structural realism. (shrink)