Jonas R. B. Arenhart

This paper examines whether grounding can be naturalized. We adopt a tripartite framework—Ocat (scientific catalogue of existents), Otyp (ontological types), and metaphysics (natures/modal profiles)—and show that classifying as such the relata of putative grounding claims forces a dilemma. When the relata belong to Ocat, ‘ground’ merely paraphrases logical or scientific explanatory relations already available and adds no explanatory value. When they belong to Otyp or to metaphysics, the relation floats free of empirical warrant and cannot be naturalized. Surveying canonical cases (Fine; Schaffer) and general programs (monism; ontic structural realism), we conclude that naturalistic grounds of grounding are unavailable: the notion is either otiose to the scientific discourse, adding nothing to it, or detrimental if competing with it.

In the recent literature, moderate naturalistic metaphysicians have been attempting to justify the existence of ‘free range’ analytic metaphysics by employing an analogy with pure mathematics: just as pure mathematics is justified by its potential applications to science, so too, they argue, is analytic metaphysics justified by its potential applications in philosophy of science. Employing standard textbook logical tools to evaluate analogies, we argue that the analogy doesn’t hold: there are relevant dissimilarities between the two disciplines. The grounds and domain of application of metaphysics and mathematics to science is ultimately different, and arguments intended to justify the epistemic value of metaphysics for science often presuppose its value rather than demonstrate it. This is why metaphysics is not like mathematics.

Intuitively, an individual is a unity, having identity and being such that it is possible at least in principle to discern it from any other individual. But when we leave the intuitive realm and attempt a logical analysis, we find a cluster of problems that are difficult to overcome within standard logico-mathematical apparatuses. This chapter is concerned with some aspects of this intuitive concept of an individual and some related facts about individuation taken from recent discussions that arise in quantum theory, pushing the discussion to a “logical” view. It characterizes individuals by means of invariance by automorphisms. The final part of the chapter proposes a metaphysics where the notion of identity is substituted, for some objects, by a weaker notion of indiscernibility, and the chapter tries to motivate and justify such a move.

It is a widespread consensus among metaphysicians that the bundle and substratum theories are substantially different metaphysical theories of individuality. In a realist stance towards metaphysics, they cannot both track the truth when describing fundamental reality, thus they’re rival metaphysical theories. Against that consensus, Jiri Benovsky has advanced a metametaphysical thesis that they are in fact metaphysically equivalent. This paper challenges Benovsky’s equivalence thesis with two counter-arguments based on the metaphysics of quantum mechanics: quantum metaphysical indeterminacy and wavefunction realism. As we shall argue, while both substratum and bundle theories arguably fail in standard quantum mechanics, they fail in different ways. Hence, given Benovsky’s own notion of metaphysical equivalence, they are not equivalent.

It is a widespread consensus among metaphysicians that the bundle and substratum theories are substantially different metaphysical theories of individuality. In a realist stance towards metaphysics, they cannot both track the truth when describing fundamental reality, thus they’re rival metaphysical theories. Against that consensus, Jiri Benovsky has advanced a metametaphysical thesis that they are in fact metaphysically equivalent. This paper challenges Benovsky’s equivalence thesis with two counter-arguments based on the metaphysics of quantum mechanics: quantum metaphysical indeterminacy and wavefunction realism. As we shall argue, while both substratum and bundle theories arguably fail in standard quantum mechanics, they fail in different ways. Hence, given Benovsky’s own notion of metaphysical equivalence, they are not equivalent.

This article critically examines the challenges of developing a metaphysics of non-individuals in the context of quantum mechanics. It investigates the Received View, which posits that quantum entities are non-individuals, and highlights several unresolved issues. Through these challenges, it is shown that a coherent metaphysics of non-individuals remains an ongoing project. Section 2 outlines the historical motivations behind a metaphysics of non-individuals in quantum mechanics, providing insight into how physics seems to necessitate such a framework. Section 3 discusses how these motivations have been articulated in the traditional approach (referred to here as the ‘non-reflexive proposal’), which characterizes non-individuality as a failure of the identity relation to apply. Section 4 situates the problem within a broader context, extracting methodological insights and clarifying the issue. Section 5 elaborates on the challenges that a metaphysics of non-individuals must still overcome, positioning this text as a prolegomenon to future formulations of such a metaphysics grounded in quantum mechanics, and section 6 wraps it all up.

This paper has three aims: first, to present in a clear way Newton da Costa’s argument against the necessity of logical laws. In order to do so, we need to clearly advance his views on the idea that logic is context-relative, and not known a priori. Doing so, however, requires that we present his methodology for the development of counter-examples to logical laws: the use of hypothetical models in logic. Given that this method has been overlooked in most discussions on the epistemology of logic, our second goal is to present da Costa’s views on it carefully. The discussion of some tensions resulting from the relation of a system of logic and the context it governs, in da Costa’s approach, is our third goal. Basically, da Costa seems to swing between two incompatible views on such relation, requiring sometimes that a logic is dependent on a context, and in other cases, that the nature of the context is dependent on a logic. Bringing this to light may also benefit current discussions on logical relativism.

The Weak Principle of the Identity of Indiscernibles (weak PII), states that numerically distinct items must be discernible by a symmetrical and irreflexive relation. Recently, some authors have proposed that weak PII holds in non relativistic quantum mechanics, contradicting a long tradition claiming PII to be simply false in that theory. The question that arises then is: are relations allowed in the scope of PII? In this paper, we propose that quantum mechanics does not help us in deciding matters concerning that problem, since that is a metaphysical problem rather than a quantum mechanical one. We argue further that weak PII is unmotivated on metaphysical grounds. We examine three metaphysical theses (bundle theory, counting, empiricism) that may provide reasons for one to sustain PII, and we conclude that weak PII gets no independent motivation from them.

Francesco Berto has argued that a primitive concept of material exclusion could be employed to formulate a notion of absolute contradiction that not even dialetheists could accept. The machinery of material exclusion and absolute contradiction could then be employed as a common (non-question-begging) ground by both dialetheists as well as their opponents in debates about negation and truth. In this paper, we first put the idea on a clear basis, and then present some criticism to it. We shall argue that the concepts of material exclusion and absolute contradiction hardly help with a clear basis for the debate on dialetheism; furthermore, the introduction of material exclusion threatens the coherence of dialetheism by allowing one to express the opposition between designated and undesignated values, with unwanted conclusions.

The so-called Received View (RV) on quantum non-individuality states, basically, that quantum particles are not individuals. It has received an amount of criticism in the recent literature, most of it concerning the relation between the RV and the relation of identity. In this chapter we carefully characterise a family of concepts involved in clarifying the view, indicating how the very idea of failure of identity, commonly used to define the RV, may be understood. By doing so, we hope to dissipate some misunderstandings about the RV, which shall also be seen as evidence of its tenability.

This book provides new approaches to the debate on individuality and non-individuality in quantum mechanics, with chapters written by leading experts in the field. A significant issue in the philosophy of quantum mechanics, the choice between individuality and non-individuality, and the well-known metaphysical underdetermination between these options in quantum theory, receive here new treatment, including metaphysical, logical, and methodological analyses. Scholars and students engaged in the philosophy of quantum mechanics and the metaphysics of science, as well as philosophers concerned with the impact of quantum mechanics on their disciplines will find this book to not only new proposals and arguments for the various sides of the debate, but also new venues for exploring the subject further.

The theory of quasi-truth was developed by Newton da Costa and collaborators as a more realistic account of truth, encompassing the incompleteness and inconsistency of scientific knowledge. Intuitively, the idea is that truth is reached when consensus is established at the end of inquiry; until that is reached, we have something less than the whole truth, we have partial or quasi-truth. Formally, the view faces some challenges that have been recently addressed in the literature; they concern a mismatch between the offered formalism and the expected claims to be formalized. In this paper we use inspiration from quasi-truth theory to develop an account of consensus in science encompassing the notion of quasi-truth. We not only present the formal system capturing the idea of a scientific consensus, but also show how quasi-truth may be represented within it too. We compare the original quasi-truth approach to ours, and argue that the latter is able to face some of the difficulties that plagued the former.

Scientific realism is the philosophical stance that science tracks truth, in particular in its depiction of the world’s ontology. Ontologically, this involves a commitment to the existence of entities posited by our best scientific theories; metaontologically, it includes the claim that the theoretical framework itself is true. In this article, we examine wave function realism as a case study within this broader methodological debate. Wave function realism holds that the wave function, as described by quantum mechanics, corresponds to a real physical entity. We focus on a recent formulation of this view that commits to the ontology of the wave function while deliberately avoiding the metaontological question of the framework’s truth. Instead, the view is defended on pragmatic, non-truth-conductive grounds. This, we argue, raises tensions for the purported realism of wave function realism and its compatibility with scientific realism more broadly.

Dialetheism is the thesis that some contradictions are true. In this paper, we explore claims to such a thesis to be found in some early philosophical writings of Newton da Costa, most notably in his book Ensaio Sobre os Fundamentos da Lógica (hereafter mentioned as the Essay). We present and explore da Costa’s claims that, in a certain sense, abstract notions such as ‘set’ and ‘truth’ may clearly involve true contradictions. Additionaly, we reconstruct da Costa’s argument to the effect that some contradictions may also be true of concrete reality. In a nutshell, da Costa suggests that some paradoxes, the aporias, are so deeply problematic that they may be pointing to reality as the source of the contradiction; i.e. aporias may ground a form of metaphysical dialetheism. This goes further than most dialetheistic claims found in the current literature. We compare these claims to a standard approach to dialetheism as Graham Priest’s, and conclude that da Costa offers a version of dialetheism too in the Essay. This opens the door for interesting explorations of some valuable yet often overlooked contributions of da Costa’s thought to the contemporary debate on dialetheism.

This book provides new approaches to the debate on individuality and non-individuality in quantum mechanics, with chapters written by leading experts in the field. A significant issue in the philosophy of quantum mechanics, the choice between individuality and non-individuality, and the well-known metaphysical underdetermination between these options in quantum theory, receive here new treatment, including metaphysical, logical, and methodological analyses. Scholars and students engaged in the philosophy of quantum mechanics and the metaphysics of science, as well as philosophers concerned with the impact of quantum mechanics on their disciplines will find this book to not only new proposals and arguments for the various sides of the debate, but also new venues for exploring the subject further.

Scientific realism is, currently, one of the most well-entrenched background assumptions of some relevant versions of anti-exceptionalism about logic. We argue that this is a sort of sociological contingency rather than a metaphilosophical necessity. Drawing parallels with the metaphysics of science (as applied to quantum foundations), we try to bring the realist assumptions of anti-exceptionalism to light, to demotivate the necessary connection between realism and anti-exceptionalism, briefly exploring the possibility of adopting antirealism as the background default view of science instead.

With the rise of paraconsistent logics, contradictions need no longer be seen as a threat to rationality: one may embrace them, without going trivial. This, however, brings a methodological challenge when one is facing a paradox. Broadly speaking, paradoxes are derivations leading from the plausible to the implausible; when the conclusion is a contradiction, the implausible is an explicit contradiction. Now, with paraconsistent logics, such implausibility need no longer be seen as logically trivializing. As a result, the paradox may be embraced as plausible reasoning, with the contradiction accommodated in our overall system. This conflicts with more traditional approaches, requiring that contradictions be eliminated by revision of the derivation. Given that now two paths are available, do we have any reason to prefer one option over the other? In this paper, we argue that the accommodation camp faces difficulties when a form of methodological naturalism is embraced.

In this paper we argue that physical theories, including quantum mechanics, refer to some kind of ‘objects’, even if only implicitly. We raise questions about the logico-mathematical apparatuses commonly employed in such theories, bringing to light some metaphysical presuppositions underlying such apparatuses. We point out to some incongruities in the discourse holding that quantum objects would be entities of some ‘new kind’ while still adhering to the logico-mathematical framework we use to deal with classical objects. The use of such apparatus would hinder us from being in complete agreement with the ontological novelties the theories of quanta seem to advance. Thus, we join those who try to investigate a ‘logic of quantum mechanics’, but from a different point of view: looking for a formal foundation for a supposed new ontology. As a consequence of this move, we can revisit Einstein’s ideas on physical reality and propose that, by considering a new kind of object traditionally termed ‘non-individuals’, it is possible to sustain that they still obey some of Einstein’s conditions for ‘physical realities’, so that it will be possible to talk of a ‘principle of separability’ in a sense which is not in complete disagreement with quantum mechanics. So, Einstein’s departure from quantum mechanics might be softened at least concerning a form of his realism, which sees separated physical objects as distinct ‘physical realities’.

The Received View on quantum non-individuality (RV) 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.

‘Shallow’ and ‘deep’ versions of scientific realism may be distinguished as follows: the shallow realist is satisfied with belief in the existence of the posits of our best scientific theories; by contrast, deep realists claim that realism can be legitimate only if such entities are described in metaphysical terms. We argue that this methodological discussion can be fruitfully applied in Everettian quantum mechanics, specifically on the debate concerning the existence of worlds and the recent dispute between Everettian actualism and quantum modal realism. After presenting what is involved in such dispute, we point to a dilemma for realists: either we don’t have the available metaphysical tools to answer the deep realist’s demands, and realism is not justified in this case, or such demands of metaphysical dressing are not mandatory for scientific realism, and deep versions of realism are not really required.

Scientific realism is typically associated with metaphysics. One current incarnation of such an association concerns the requirement of a metaphysical characterization of the entities one is being a realist about. This is sometimes called “Chakravartty’s Challenge”, and codifies the claim that without a metaphysical characterization, one does not have a clear picture of the realistic commitments one is engaged with. The required connection between metaphysics and science naturally raises the question of whether such a demand is appropriately fulfilled, and how metaphysics engages with science in order to produce what is called “scientific metaphysics”. Here, we map some of the options available in the literature, generating a conceptual spectrum according to how each view approximates science and metaphysics. This is done with the purpose of enlightening the current debate on the possibility of epistemic warrant that science could grant to such a metaphysics, and how different positions differently address the thorny issue concerning such a warrant.

Este artigo discute dois tratamentos dados por Charles Sanders Peirce ao paradoxo do Mentiroso, estabelecendo conexões com o debate atual acerca do tema. Nas Harvard Lectures de 1865, Peirce considera que a proposição do mentiroso é tanto verdadeira quanto falsa, o que, de acordo com sua visão sobre a lógica, torna a proposição sem sentido. Esse tratamento antecipa parcialmente a posição dialeteísta contemporânea, que considera que o Mentiroso é uma evidência de que algumas proposições são verdadeiras e falsas. Em textos posteriores, Peirce revisa seu tratamento do problema, considerando que a contradição do Mentiroso é falsa, alinhando-se à tradição da lógica de sua época. A discussão deste artigo evidencia que concepções lógicas específicas pressupostas na investigação de Peirce são as responsáveis pelas interpretações que ele fornece para a contradição envolvida no paradoxo. A partir dessa discussão, este artigo argumenta que o tratamento dado ao Mentiroso depende das concepções lógicas de fundo. Assim, as limitações encontradas por Peirce em suas abordagens ao problema são introduzidas pela lógica tradicional, que, diferentemente de algumas lógicas contemporâneas, não oferece aparato compatível com contradições verdadeiras.

Anti‐exceptionalism about logic is the view that logic is not special; it is just like empirical sci‐ ence in many respects. In particular, it is thought that an anti‐exceptionalist must also hold that logical theories are completely a posteriori. However, it is not clear what it means to say that logical theories are a posteriori, for the a priori/a posteriori divide has been explored from different perspectives in contemporary philosophy. The central claim of this paper is to argue that logical anti‐exceptionalism is quite compatible with the a priori, if the a priori/a posteriori divide is understood in the lines recently developed by Tuomas Tahko. The con‐ ception advanced by Tahko is characterized by an interplay between a priori and a posteriori knowledge, generating a bootstrapping relation in which one kind of knowledge constantly substantiates the other. We further present some of the advantages of the bootstrapping approach over the current epistemology associated with anti‐exceptionalism.

Philosophers of science commonly connect ontology and science, stating that these disciplines maintain a two-way relationship: on the one hand, we can extract ontology from scientific theories; on the other hand, ontology provides the realistic content of our scientific theories. In this article, we will critically examine the process of naturalizing ontology, i.e., confining the work of ontologists merely to the task of pointing out which entities certain theories commit themselves to. We will use non-relativistic quantum mechanics as a case study. We begin by distinguishing two roles for ontology: the first would be characterized by cataloging existing entities according to quantum mechanics; the second would be characterized by establishing more general ontological categories in which existing entities must be classified. We argue that only the first step is available for a naturalistic approach; the second step not being open for determination or anchoring in science. Finally, we also argue that metaphysics is still a step beyond ontology, not contained in either of the two tasks of ontology, being thus even farther from science.

Nosso objetivo neste artigo é duplo. Primeiramente, desejamos expor uma versão de platonismo em filosofia da matemática defendida por Newton da Costa. A filosofia da matemática e da lógica de da Costa ainda é pouco conhecida, de modo que este artigo busca preencher parcialmente esta lacuna. Da Costa amplia o escopo do platonismo tradicional em filosofia da lógica e da matemática para todos os sistemas não-triviais, de modo a incorporar em seu realismo um pluralismo lógico e matemático. O resultado é chamado de realismo multivalente. Em segundo lugar, proporemos uma lista de problemas que a versão de platonismo aqui apresentada deverá enfrentar. Focamos em dificuldades específicas da versão multivalente de platonismo, evidenciando que se trata de concepção interessante e merecedora de mais estudos.