Jonas R. B. Arenhart

In one of his papers, JC Beall advanced a new and interesting interpretation of Weak Kleene logic, in terms of on-topic/off-topic. In brief, Beall suggests to read the third value as off-topic, whereas the two classical values are read as true and on-topic and false and on-topic. Building on Beall’s new interpretation, the aim of this paper is threefold. First, we discuss two motivations to enrich Beall’s interpretation, and offer an alternative semantic framework that reflects our motivations. Second, by making use of our new framework, we will offer a new interpretation of the logic of Catuskoti which combines Beall’s proposal of having FDE as the correct logic with the on-topic/off-topic divide. Finally, we will offer a general result that will allow us to make sense of a family of infectious logics in terms of Beall’s on-topic/off-topic reading.

Ever since its beginnings, standard quantum mechanics has been associated with a metaphysical view according to which the theory deals with non-individual objects, i.e., objects deprived of individuality in some sense of the term. We shall examine the grounds of the claim according to which quantum mechanics is so closely connected with a metaphysics of non-individuals. In particular, we discuss the attempts to learn the ‘metaphysical lessons’ required by quantum mechanics coming from four distinct roads: from the formalism of the theory, treating separately the case of the physics and the underlying logic; from the ontology of the theory, understood as the furniture of the world according to the theory; and, at last, we analyze whether a metaphysics of non-individuals is indispensable from a purely metaphysical point of view. We argue that neither non-individuality nor individuality is to be found imposed on us in any of these levels so that it should be seen as a metaphysical addition to the theory, rather than as a lesson from it.

In this paper, we analyze the epistemic approach to paraconsistency. This approach is advanced as an alternative to dialetheism on what concerns interpreting paraconsistency and contradictions; instead of having to accept that there are true contradictions, it is suggested that we may understand such situations as involving only conflicting evidence, which restricts contradictions to a notion of evidence weaker than truth. In this paper, we first distinguish two conflicting programs entangled in the proposal: interpreting paraconsistency in general through the notion of evidence, and modeling reasoning with evidence by using paraconsistent logic. The first part of the program, we argue, does not succeed, on the grounds that it does not lead to a uniform proposal to the understanding of paraconsistency, and fails to engage with dialetheism in a legitimate dispute about interpretation of paraconsistency. Also, when seen through the lights of the second kind of approach, a ‘logic as modeling’ approach, weaknesses of dealing with evidence through paraconsistency come to light, basically because evidence does not seem to suggest the need of a paraconsistent treatment. As a result, one can neither approach paraconsistency in general through evidence, nor approach evidence with the use of paraconsistent logics.

In this paper, we critically discuss the idea of a ‘philosophical interpretation’ of paraconsistent logics. We do so by considering the epistemic approach to paraconsistency, by Carnielli and Rodrigues, according to which paraconsistent logics should be interpreted exclusively in terms of non-conclusive evidence, and also, by considering counter-arguments by Barrio and Barrio and Da Re, according to whom paraconsistent logics are not specially tied to any specific interpretation. We begin by presenting the positions involved, and by arguing that the debate may be profitably understood in terms of the distinction between pure and applied logics. We argue that dialetheism is not an interpretation of paraconsistent logics, but rather a view on truth and negation which requires use of paraconsistent logics. Something similar may be said about the epistemic approach itself. The result is that there is nothing distinctive to be called a philosophical interpretation of paraconsistent logics, but rather what we have are distinct applications of paraconsistent logics. Arguments by Barrio and Barrio and Da Re may be then re-framed more effectively.

ABSTRACT Traditionally, being a realist about something means believing in the independent existence of that something. In this line of thought, a scientific realist is someone who believes in the objective existence of the entities postulated by our best scientific theories. In metaphysical terms, what does that mean? In ontological terms, i.e., in terms of what exists, scientific realism can be understood as involving the adoption of a scientifically informed ontology. But according to some philosophers, a realistic attitude must go beyond ontology. The way in which this requirement has been understood involves providing a metaphysics for the entities postulated by science, that is, answering questions about the nature of what ontology admits to exist. We discuss how two fashionable approaches face the challenge of providing a metaphysics for science: a form of naturalism and the Viking/Toolbox approach. Finally, we present a third way, which adopts the best of both approaches: the meta-Popperian method, which focuses on discarding the wrong alternatives, or better saying, the metaphysical profiles incompatible with certain theories. We present the meta-Popperian method, a metametaphysical method capable of objectively assessing which metaphysical profiles are incompatible with certain scientific theories. For this, we will use quantum mechanics as a case study, presenting some previously obtained results. As our focus is on methodological questions about the relationship between metaphysics and science; with this method, we can see how science can be used to avoid error in metaphysical issues. In our opinion, this would be a way to develop a productive relationship between science and metaphysics.

This book addresses the logical aspects of the foundations of scientific theories. Even though the relevance of formal methods in the study of scientific theories is now widely recognized and regaining prominence, the issues covered here are still not generally discussed in philosophy of science. The authors focus mainly on the role played by the underlying formal apparatuses employed in the construction of the models of scientific theories, relating the discussion with the so-called semantic approach to scientific theories. The book describes the role played by this metamathematical framework in three main aspects: considerations of formal languages employed to axiomatize scientific theories, the role of the axiomatic method itself, and the way set-theoretical structures, which play the role of the models of theories, are developed. The authors also discuss the differences and philosophical relevance of the two basic ways of aximoatizing a scientific theory, namely Patrick Suppes’ set theoretical predicates and the "da Costa and Chuaqui" approach. This book engages with important discussions of the nature of scientific theories and will be a useful resource for researchers and upper-level students working in philosophy of science.

In his “The simple argument for subclassical logic,” Jc Beall advances an argument that led him to take FDE as the one true logic (the latter point is explicitly made clear in his “FDE as the One True Logic”). The aim of this article is to point out that if we follow Beall’s line of reasoning for endorsing FDE, there are at least two additional reasons to consider that FDE is too strong for Beall’s purposes. In fact, we claim that Beall should consider another weaker subclassical logic as the logic adequate for his project. To this end, we first briefly present Beall’s argument for FDE. Then, we discuss two specific topics that seem to motivate us to weaken FDE. We then introduce a subsystem that will enjoy all the benefits of Beall’s suggestion.

It is not an exaggeration to say that quantum mechanics is at odds with most of our received metaphysical notions. In particular, an alleged revision is brought about by the theory on the metaphysical notion of ‘individuality’. Certainly, this should figure as being of great interest for metaphysicians and philosophers of science alike. What makes issues even more interesting is that some of the founding fathers of the theory, with their typical philosophical inclinations, suggested that the entities dealt with by the theory had something different regarding individuality: according to them, quantum entities somehow fail individuality.

In this paper, we generalize the ordered-pair semantics advanced by Matthew Clemens for the Logic of Paradox to n-tuple semantics, for each fixed n. Moreover, we show that the resulting semantics can accommodate not only LP, but also classical logic as well as strong Kleene logic depending on the set of designated values that one chooses. Building on the technical observations, we offer intuitively plausible readings for the semantics, and we also discuss some weaknesses of the original intuitive reading advanced by Clemens.

In this paper, I discuss the relation between logical theory and evidence in the context of an anti-exceptionalist approach to logic. I hold not only that current versions of anti-exceptionalism failed to appreciate the fact that logical evidence is theory laden, but also that benefits for the view are expected when we engage with the appropriate philosophy of science. I make the discussion more vivid by considering the cases of both the Liar and Russell paradoxes, and disputes between the classical and dialetheist approaches to them. Disputes between these parties involve different understandings of the logical terminology involved in the evidence (the paradoxes), and they illustrate how the data gets contaminated with theory. As a result of the discussion, I conclude that pragmatical considerations are better guides to evaluate disputes in such cases, with scientific fertility being the criterion of legitimacy for a logical system.

Quasi-truth is a formal approach to a pragmatically-oriented view of truth. The basic plan motivating the framework consists in providing for a more realistic account of truth, accommodating situations where there is incomplete information, as typically happens in the practice of science. The historical sciences are a case in hand, where incomplete information is the rule. It would seem, then, that the quasi-truth approach would be the most appropriate one to deal with historical sciences, then. In this paper, we explore this possibility and use the historical sciences as a test case for the approach of quasi-truth. Our claim is that, on what concerns historical sciences, the quasi-truth approach fails in two basic senses; first, by misrepresenting some cases concerning incomplete information, and second, by falling short of accounting for many features of incomplete information peculiar to historical sciences. We conclude that, despite its stated goals, quasi-truth must be either amended or substituted if the goal of a more faithful representation of scientific practice is to be achieved.

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

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 conception ofreality grounded in some relations he claims to hold between some featuresof quantum mechanics, mainly the collapse of the wave function, with thephilosophies of Plotino and A. N. Whitehead. We end our discussion pointingto some diculties in the author's approach.A mec^anica qu^antica levanta profundas quest~oes acerca de nossaconcepc~ao de realidade. Neste ensaio discutiremos uma possvel soluc~ao paraalgumas destas diculdades proposta por Shimon Malin em seu livro NatureLoves to Hide. Primeiramente discutiremos a exposic~ao de Malin sobre omodo como a teoria qu^antica acarreta uma profunda revis~ao de nossa concepc~ao da realidade, derrogando certas formas de realismo. Aqui, o principalponto centra-se no fato de a teoria violar das desigualdades de Bell. Depois,apresentaremos de modo mais breve a proposta do autor de uma novaconcepc~ao da realidade baseada em certas relac~oes que arma existir entrealgumas caractersticas da mec^anica qu^antica, principalmente o colapso dafunc~ao de onda, com as losoas de Plotino e A. N. Whitehead. Finalizamos apontando algumas diculdades na abordagem do autor