-
251Structural realism and the nature of structureEuropean Journal for Philosophy of Science 5 (1): 111-139. 2015.Ontic Structural Realism is a version of realism about science according to which by positing the existence of structures, understood as basic components of reality, one can resolve central difficulties faced by standard versions of scientific realism. Structures are invoked to respond to two important challenges: one posed by the pessimist meta-induction and the other by the underdetermination of metaphysics by physics, which arises in non-relativistic quantum mechanics. We argue that difficult…Read more
-
71Does weak discernibility determine metaphysics?Theoria: Revista de Teoría, Historia y Fundamentos de la Ciencia 32 (1): 109-125. 2017.Two entities are weakly discernible when an irreflexive and symmetric relation holds between them. That weak discernibility holds in quantum mechanics is fairly uncontroversial nowadays. The ontological consequences of weak discernibility, however, are far from clear. Part of the literature seems to imply that weak discernibility points to a definite metaphysics to quantum mechanics. In this paper we shall discuss the metaphysical contribution of weak discernibility to quantum mechanics and argu…Read more
-
30New Logics for Quantum Non-individuals?Logica Universalis 12 (3-4): 375-395. 2018.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 …Read more
-
42On Material Exclusion and Absolute ContradictionAxiomathes 29 (4): 413-425. 2019.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 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…Read more
-
173Is Identity Really so Fundamental?Foundations of Science 24 (1): 51-71. 2019.We critically examine the claim that identity is a fundamental concept. According to those putting forward this thesis, there are four related reasons that can be called upon to ground the fundamental character of identity: identity is presupposed in every conceptual system; identity is required to characterize individuality; identity cannot be defined; the intelligibility of quantification requires identity. We address each of these points and argue that none of them advances compelling reasons…Read more
-
51Classical Negation Strikes Back: Why Priest’s Attack on Classical Negation Can’t SucceedLogica Universalis 11 (4): 465-487. 2017.Dialetheism is the view that some true sentences have a true negation as well. Defending dialetheism, Graham Priest argues that the correct account of negation should allow for true contradictions and \) without entailing triviality. A negation doing precisely that is said to have ‘surplus content’. Now, to defend that the correct account of negation does have surplus content, Priest advances arguments to hold that classical Boolean negation does not even make sense without begging the question …Read more
-
105Full-blooded anti-exceptionalism about logicAustralasian Journal of Logic 15 (2): 362-380. 2018.Problems of logical theory choice are current being widely dis- cussed in the context of anti-exceptionalist views on logic. According to those views, logic is not a special science among others, so, in particular, the methodology for theory choice should be the same in logic as for other scientific disciplines. Richard Routley advanced one such methodology which meshes well with anti-exceptionalism, and argued that it leads one to choosing one single logic, which is a kind of ultralogic. We arg…Read more
-
105A Discussion on Finite Quasi-cardinals in Quasi-set TheoryFoundations of Physics 41 (8): 1338-1354. 2011.Quasi-set theory Q is an alternative set-theory designed to deal mathematically with collections of indistinguishable objects. The intended interpretation for those objects is the indistinguishable particles of non-relativistic quantum mechanics, under one specific interpretation of that theory. The notion of cardinal of a collection in Q is treated by the concept of quasi-cardinal, which in the usual formulations of the theory is introduced as a primitive symbol, since the usual means of cardin…Read more
-
72Finite Cardinals in Quasi-set TheoryStudia Logica 100 (3): 437-452. 2012.Quasi-set theory is a ZFU-like axiomatic set theory, which deals with two kinds of ur-elements: M-atoms, objects like the atoms of ZFU, and m-atoms, items for which the usual identity relation is not defined. One of the motivations to advance such a theory is to deal properly with collections of items like particles in non-relativistic quantum mechanics when these are understood as being non-individuals in the sense that they may be indistinguishable although identity does not apply to them. Acc…Read more
-
153Metaphysics Within Science: Against Radical NaturalismMetaphilosophy 47 (2): 159-180. 2016.In Every Thing Must Go James Ladyman and Don Ross argue for a radical version of naturalistic metaphysics and propose that contemporary analytic metaphysics is detached from science and should be discontinued. The present article addresses the issues of whether science and metaphysics are separable, intuitions and understanding should be excluded from scientific theory, and Ontic Structural Realism satisfies the criteria of the radical version of naturalism advanced by Ladyman and Ross. The poin…Read more
-
65Making Sense of Non-Individuals in Quantum MechanicsIn Olimpia Lombardi, Sebastian Fortin, Cristian López & Frederico Holik (eds.), Quantum Worlds. Different Perspectives about the ontology of quantum mechanics, Cambridge University Press. forthcoming.In this work, we focus on a very specific case study: assuming that quantum theories deal with “particles” of some kind, what kind of entity can such particles be? One possible answer, the one we shall examine here, is that they are not the usual kind of object found in daily life: individuals. Rather, we follow a suggestion by Erwin Schrödinger, according to which quantum mechanics poses a revolutionary kind of entity: non-individuals. While physics, as a scientific field, is not concerned with…Read more
-
66Following J.-Y.Béziau in his pioneer work on non-standard interpretations of the traditional square of opposition, we have applied the abstract structure of the square to study the relation of opposition between states in superposition in orthodox quantum mechanics in [1]. Our conclusion was that such states are contraries, contradicting previous analyzes that have led to different results, such as those claiming that those states represent contradictory properties. In this chapter we bring the …Read more
-
61In this paper we deal with two applications of the square of opposition to controversial issues in the philosophy of quantum mechanics. The first one concerns the kind of opposition represented by states in superposition. A superposition of “spin up” and “spin down” for a given spatial direction, for instance, is sometimes said to originate particular kinds of opposition such as contradictoriness. The second application concerns the problem of identical particles. Identity and indiscernibility a…Read more
-
209Ontological Frameworks for Scientific TheoriesFoundations of Science 17 (4): 339-356. 2012.A close examination of the literature on ontology may strike one with roughly two distinct senses of this word. According to the first of them, which we shall call traditional ontology , ontology is characterized as the a priori study of various “ontological categories”. In a second sense, which may be called naturalized ontology , ontology relies on our best scientific theories and from them it tries to derive the ultimate furniture of the world. From a methodological point of view these two se…Read more
-
33Dialetheists’ Lies About the LiarPrincipia: An International Journal of Epistemology 22 (1): 59-85. 2018.Liar-like paradoxes are typically arguments that, by using very intuitive resources of natural language, end up in contradiction. Consistent solutions to those paradoxes usually have difficulties either because they restrict the expressive power of the language, or else because they fall prey to extended versions of the paradox. Dialetheists, like Graham Priest, propose that we should take the Liar at face value and accept the contradictory conclusion as true. A logical treatment of such contrad…Read more
-
92We discuss the idea that superpositions in quantum mechanics may involve contradictions or contradictory properties. A state of superposition such as the one comprised in the famous Schrödinger’s cat, for instance, is sometimes said to attribute contradictory properties to the cat: being dead and alive at the same time. If that were the case, we would be facing a revolution in logic and science, since we would have one of our greatest scientific achievements showing that real contradictions exis…Read more
-
53Nonreflexive quantum mechanics is a formulation of quantum theory based on a non- classical logic termed nonreflexive logic. In these logics, the standard notion of identity, as encapsulated in classical logic and set theories, does not hold in full. The basic aim of this kind of approach to quantum mechanics is to take seriously the claim made by some authors according to whom quantum particles are non-individuals in some sense, and also to take into account the fact that they may be absolutely…Read more
-
43In this paper we consider the notions of structure and models within the semantic approach to theories. To highlight the role of the mathematics used to build the structures which will be taken as the models of theories, we review the notion of mathematical structure and of the models of scientific theories. Then, we analyse a case-study and argue that if a certain metaphysical view of quantum objects is adopted, namely, that which sees them as non-individuals, then there would be strong reasons…Read more
-
36The 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, w…Read more
-
106Separability and Non-Individuality: Is It Possible to Conciliate (At Least A Form Of) Einstein’s Realism with Quantum Mechanics?Foundations of Physics 44 (12): 1269-1288. 2005.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 de…Read more
-
38Ontology and the Mathematization of the Scientific EnterprisePhainomenon 25 (1): 109-130. 2012.In this basically expository paper we discuss the role oflogic and mathematics in researches concerning the ontology of scientific theories, and we consider the particular case of quantum mechanics. We argue that systems of logic in general, and classical logic in particular, may contribute substantially with the ontology of any theory that has this logic in its base. In the case of quantum mechanics, however, from the point of view of philosophical discussions conceming identity and individuali…Read more
-
The Price of True Contradictions About the WorldIn Walter Carnielli & Jacek Malinowski (eds.), Contradictions, from Consistency to Inconsistency, Springer. 2018.
-
57In this paper we consider the phenomenon of superpositions in quantum mechanics and suggest a way to deal with the idea in a logical setting from a syntactical point of view, that is, as subsumed in the language of the formalism, and not semantically. We restrict the discussion to the propositional level only. Then, after presenting the motivations and a possible world semantics, the formalism is outlined and we also consider within this schema the claim that superpositions may involve contradic…Read more
-
A Natureza Ama Esconder-se? Ensaio Sobre “nature Loves To Hide”Manuscrito 33 (1): 381-391. 2010.Quantum mechanics raises deep questions about our conceptionof reality. In this essay we discuss a possible solution proposed by ShimonMalin in his book Nature Loves to Hide to some of these diculties. Firstlywe discuss Malin's exposition about how the quantum theory entails a deeprevision of our conception of reality, overthrowing some kinds of realism.Here, the main focus is quantum mechanics' violation of Bell's inequalities.After that, we briey present the author's proposal of a new concepti…Read more
-
22Resenha de Filosofias da matemática de autoria de Jairo José da Silva (Unesp, 2007)Manuscrito 33 (2): 531-550. 2010.
-
83The received view on quantum non-individuality: formal and metaphysical analysisSynthese 194 (4). 2017.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 d…Read more
-
113Axiomatization and Models of Scientific TheoriesFoundations of Science 16 (4): 363-382. 2011.In this paper we discuss two approaches to the axiomatization of scientific theories in the context of the so called semantic approach, according to which (roughly) a theory can be seen as a class of models. The two approaches are associated respectively to Suppes’ and to da Costa and Chuaqui’s works. We argue that theories can be developed both in a way more akin to the usual mathematical practice (Suppes), in an informal set theoretical environment, writing the set theoretical predicate in the…Read more
-
82From primitive identity to the non-individuality of quantum objectsStudies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 46 (2): 273-282. 2014.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 princ…Read more
Jonas R. B. Arenhart
Universidade Federal de Santa Catarina
-
Universidade Federal de Santa CatarinaAssociate Professor
Areas of Specialization
Logic and Philosophy of Logic |
Metaphilosophy |
Metaphysics |
Quantum Mechanics |