Juan Pablo Jorge

Standard quantum mechanics poses serious challenges to some principles deeply entrenched in traditional metaphysics. In particular, the theory defies the ontological category of individual object through three of its features: contextuality, non-separability, and indistinguishability. The difficulties have prompted the development of non-traditional ontological frameworks intended to account for the quantum domain. Some approaches advocate replacing the classical conception of a realm of objects endowed with properties by an ontology that either dispenses with the category of object altogether or treats it as a derivative notion. The Modal-Hamiltonian Interpretation (MHI) of quantum mechanics and Ontic Structural Realism (OSR) exemplify this position. MHI proposes an ontology in which quantum systems are non-objectual bundles of properties linked by definite physical relations. The OSR defends the ontological primacy of structures, within which objects are construed as nodes of relations. The aim of this article is to compare these two ontological approaches, highlighting both their points of convergence and their divergences, particularly in light of the ontological challenges posed by quantum mechanics. With this aim, the article is structured as follows. Section 2 outlines the ontology of MHI, introducing the distinction between type-properties and case-properties, characterizing quantum systems as non-objectual bundles, and analyzing the role of symmetry groups in providing physical content to the theory and governing actualization. Section 3 turns to OSR, examining its motivations, its distinction between physical and mathematical structures, and the modal character of structures. Section 4 offers a systematic comparison of the two approaches, considering their respective motivations and scope, their shared commitment to an object-free ontology, the role played by symmetry groups within each framework, and their contrasting interpretations of modality. Finally, Section 5 presents some concluding remarks.

This book provides a comprehensive overview of different logics from a metainferential standpoint. It starts with a metainferential presentation of Classical Logic, and then moves onto other systems where one or more structural metainferences fail. These logics maybe considered non-classical in a robust sense, since they allow to build theories which are non-transitive, non-reflexive, non-monotonic and non-contractive. In some other sense, though, they also preserve many desirable features of classical logics, and thus may have an advantage over other non-classical alternatives. The authors show how these logics can be characterized both model and proof-theoretically. Besides some standard inferential properties, emphasis is placed on metainferential theorems, some of them quite standard, such as Cut-elimination, and other more idiosyncratic, such as metainferential Soundness and Completeness. It ends with a philosophical chapter which intends to illustrate some of these logics' applications, mainly regarding non-classical treatments of paradoxes. Each chapter comes with exercises which help fix the central concepts, learn to use some of the formal tools, and problematize the philosophical issues at stake. This book is aimed to anyone interested in the question of reasoning, argumentation and theory-building in the presence of contradictions, paradoxes and other puzzles.

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.

According to quantifier generalism, all facts about the world can be expressed in a language devoid of proper names, whose only referential expressions are variables bound by quantifiers. This paper considers and repels some of the recently raised objections against this position. The central part of the paper presents a critical analysis of the claim advanced by Ted Sider that quantifier generalism is inevitably holistic and therefore requires unusually strong expressive resources when applied to infinite domains. Using an example of arithmetic, it is shown that there is a simple generalistic description of natural numbers that does not resort to any infinitary conjunctions or quantifiers. Such generalistic accounts also exist in many cases involving continua (such as descriptions of matter distribution in a continuous space). Moreover, these accounts are arguably superior to their individualistic counterparts due to their parsimony. In addition to that, Sider’s argument alleging that generalism cannot account for the difference between non-isomorphic models of arithmetic is repelled.

According to Daniel Dennett, some non-human animals are “Popperian creatures” who possess internal representational models that allow them to simulate different responses offline, evaluate their consequences, and discard bad options in advance. There are, however, some discrepancies, both in Dennett’s writings and those of his critics, regarding what animals can be classified as Popperian. While some defend a very inclusive view, which counts all mammals and even some invertebrates as Popperian animals, others think that humans might be the only animals qualifying as such. This disagreement suggests significant discrepancies in understanding what it means to be a Popperian creature. In light of such disputes, in this paper, I aim to clarify which cognitive abilities should be considered critical to being a Popperian animal. Based on that analysis, I then focus on a specific cognitive ability – instrumental or means-end reasoning – and argue that possessing it suffices to count as a Popperian animal in a robust understanding of this notion. Finally, I discuss some empirical evidence and argue, based on it, that at least some non-human animals – the most compelling evidence coming from great apes and New Caledonian crows – count as genuine instrumental reasoners and, therefore, also as genuine Popperian creatures.

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.

In a series of recent articles, the problem of individuality in quantum theory was addressed from a radical position: there are neither individuals nor quasi-individuals in the quantum ontology; the quantum world is populated by quantum properties that form bundles which, nevertheless, do not acquire the features necessary to be characterized by the ontological category of individual.The aim of the present article is to relate this view with the symmetries of quantum theories. First, we will argue that, although quantum systems are non-individual bundles, the group of symmetry of non-relativistic quantum mechanics, the Galilei group, introduces in the bundle the difference between essential and contingent properties. Under certain conditions, those essential properties generate the illusion of the presence of an individual. Nevertheless, this is not the case when the behavior of the bundle is considered in its relation with other bundles, for instance, when statistical reasoning is involved. Second, we will extrapolate this idea to other quantum theories. For instance, in relativistic quantum mechanics and in quantum field theory, the space-time symmetry represented by the Poincaré group and the gauge symmetries also define the essential properties of the non-individual bundles, which are precisely the properties that define the different kinds of the so-called fundamental “particles”.

In previous publications, it was shown that finite non-deterministic matrices are quite powerful in providing semantics for a large class of normal and non-normal modal logics. However, some modal logics, such as those whose axiom systems contained the Löb axiom or the McKinsey formula, were not analyzed via non-deterministic semantics. Furthermore, other modal rules than the rule of necessitation were not yet characterized in the framework.In this paper, we will overcome this shortcoming and present a novel approach for constructing semantics for normal and non-normal modal logics that is based on restricted non-deterministic matrices. This approach not only offers a uniform semantical framework for modal logics, while keeping the interpretation of the involved modal operators the same, and thus making different systems of modal logic comparable. It might also lead to a new understanding of the concept of modality.

Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.

Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst affording the theoretical resources for a defence of Boffa set theory as a faithful description of set-theoretic reality.

We approach the sorites paradox through an observer-based and time-dependent approach to truth of vague assertions. Formally the approach gives rise to a semantics, called fluxing-object semantics (FOS), because it involves models that contain “fluxing objects”, that is, entities changing with time and observer. The models are equipped with agents (observers) and a linear and discrete time axis for time. The changing entities are represented by partial functions of time and agent, and this partiality causes truth-value gaps. If we interpret a truth-value gap as a third truth value, then FOS becomes a three-valued logic, which, quite interestingly, is proved identical to strong Kleene three-valued logic. The sorites phenomena can be represented in a structure of FOS as special objects that change imperceptibly with respect to an observer and with respect to a particular attribute. In this account the key point that eliminates the paradoxical character of sorites is the partiality of functions. When the observer is fixed the partiality corresponds to interrupted watching on his part. The interruption creates watching gaps during which the attributed property of the object as understood by the observer may change, without violating the imperceptibility condition. Interrupted watching has, according to experts on visual attention and focusing capabilities of humans, a firm physiological justification. The relationship of watching gaps with horizon crossing is also discussed.

Some philosophers of physics have addressed criticisms of the so-called Received View (RV) of non-individual quantum objects, also called the orthodox view. Dennis Dieks made a very good resume of these criticisms in Dieks (in: Non-reflexive logics, non-individuals, and the philosophy of quantum mechanics: essays in honor of the philosophy of Décio Krause, Synthese Library, Springer, 2023) and Bigaj (Identity and indiscernibility in quantum mechanics. New directions in the philosophy of science, Palgrave Macmillan, 2022) has a more detailed account. In considering (mainly) these works and with some additional mentions, I hope to dissipate some misunderstandings about the RV and clarify what is happening with such a view. According to Dieks, the RV doesn’t fit the practice of physics since, in some situations, the physicist assumes that quantum objects can be treated individually, imitating standard objects (individuals) of classical physics. Dieks also proposes an Alternative View (AV), generally called the heterodox view, which would give a view of the fundamental ontology of quantum physics and which would be more by the way physicists usually proceed. I think that the AV cannot be viewed as the fundamental ontological theory despite being suitable for practical purposes. Furthermore, I think that it does not conflate the RV but is complementary to it, substituting it when quantum objects are sufficiently apart and can be treated in conformity with the classical way. From my point of view, in the practice of physics, one can adopt AV. Still, the RV is more adequate when we are looking for logical and foundational analyses, at least when the supposed metaphysics comprises non-individuals.

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.

Any scientific theory (here we consider physical theories only) has an underlying logic, even if it is not totally made explicit. The role of the underlying logic of a theory T is mainly to guide the proofs and the accepted consequences of the theory’s principles, mainly when described by its axioms. In this sense, the theorems of the underlying logic are also theorems of the theory. In most cases, if pressed, the scientist will say that the underlying logic of most physical theories is classical logic or some fragment of a set theory suitable for accommodating the theory’s mathematical and logical concepts. We argue that no physical theory and no philosophical discussion based on the theory should dismiss its underlying logic, so the arguments advanced by some philosophers of physics in that certain entities (the considered case deals with quantum entities) can be only weakly discerned or be just ‘relational’ and that they cannot be absolutely identified by a monadic property, are fallacious once one remains within a ‘standard’ logico-mathematical framework, grounded on classical logic. We also discuss the (to us) unjustifiable claim that some properties (such as those that came from logic) would be ‘illegitimate’ for discerning these entities. Thus, this paper may interest logicians, physicists, and philosophers.