María del Rosario Martínez-Ordaz

Here I discuss the legitimacy of the cluster of logics that are considered to be relating logics. I argue that even if the cluster ⌜Relating logics⌝ satisfies the basic theoretical criteria for legitimate clusters, logicians and philosophers of logic have failed at providing the corresponding pragmatic backing. In response to this, I propose to provide the pragmatic justification of the cluster by showing a domain of application for which ⌜Relating logics⌝ fit more adequately the evidence than any of their rivals do; such a domain is the phenomenon of scientific understanding. Finally, I argue that the characterization of scientific understanding as a relating phenomenon provides a description of it that is more accurate than the ones offered by rival views.

We critically examine Vickers’ project of future-proof science, which aims to identify scientific facts based upon a solid international scientific consensus. Vickers claims that second-order evidence—specifically a 95% consensus among a diverse, international scientific community—provides a principled criterion for identifying future-proof science. We challenge both the motivation behind this project and Vickers’ account of scientific consensus. Our analysis raises concerns about the methodological validity of the 30 alleged examples of future-proof science, questioning the selection, isolation, and interpretation of such scientific claims. We argue that the dissimilarities among these examples expose potential flaws, such as lack of simplicity and semantic opacity, which undermine their effectiveness in supporting the project. Furthermore, we criticize the assumption that a solid international scientific consensus is a reliable indicator of future-proof science. Given that consensus in science is multifactorial, we contend that second-order evidence is insufficient to support any scientific claim as an instance of future-proof science. We also object that scientific consensus cannot be correlated to future-proof science, provided its mechanism is driven by social factors that are not necessarily aligned with the reliability required for claims about established scientific facts. Our analysis thus reveals that Vickers fails to tackle the so-called threshold problem afflicting his proposed criterion for future-proof science.

Here, we aim at elucidating the epistemic grounds by which scientists traverse the path from ignorance to insight to scientific understanding- within the realm of empirical sciences, specifically focusing on cases marked by the existence of recalcitrant anomalies. We contend that scientific understanding is structuralist. Furthermore, we contend that the partial overcoming of anomalies between scientific theory and observation resides in the finding of some structures that allow for reconciliation and integration of the resulting inconsistencies and explanatory gaps by providing novel inferential pathways and ways of making sense of dependency relations. Moreover, we claim that this type of understanding is gradual in that it begins with insight, understood in our view as a way of grasping what type of structure might be helpful in overcoming the above difficulties and leading eventually to a more full-blown understanding involving systematic integration and subsumption of theoretical posits and empirical observations within theoretical structures.

Nowadays there is a growing tendency in the philosophy of science to think that some phenomena cannot be exhaustively explained, or even described, by a single theory or a particular approach. Thus, we are occasionally required to use various approaches in order to give account of the phenomenon we are analyzing. And sometimes, we can appreciate this as an invitation to be pluralist in certain respects about our understanding of a particular aspect in science. During the last decade applications of pluralism have increased and led to several other relevant debates in the philosophy of science. By the strengthening of pluralism, new questions have emerged, and more importantly, new alternatives have been offered in dealing with problems about how to interpret the ontology and the ontological commitments of particular theories, or how to apply strategies to analyze and understand specific episodes from the history of science, or how to work within different, and sometimes incompatible, explanations about a particular phenomenon, among others. In general, pluralism seems to be a very rich and yet not enough explored path for the philosophy of science in general. Today, it is recognized that, at least for methodological purposes, the application of pluralism to the study of science can offer a great number of benefits. One of them would be the opportunity of analyzing the role that some epistemic virtues -such as scope, fruitfulness, consistency, and simplicity, to name just a few- play in the scientific activity. From the different pluralist positions, a lot has been said about empirical adequacy, refutability and explanatory power yet consistency power, yet, consistency has not been equally dealt with. As a matter of fact, the lack of consistency and its philosophical implications have been studied from an angle that does not necessarily involve a pluralism of any kind. At the moment, it is commonly accepted that inconsistencies are more frequent in scientific development that the traditional philosophy of science could have expected and the idea that inconsistency is not always a synonym of logical anarchy, as it was suggested in the classical literature of logic and the philosophy of science, has been gaining support. All this has been possible, mostly, thanks to the emergence of paraconsistent logics and the availability of case studies that show how inconsistency is not an uncommon phenomenon in science. But pluralism does not necessarily entail inconsistency toleration nor vice versa. Accordingly the main motivation for this volume is to explore the links between pluralism and inconsistency toleration in science, in order to connect the reflections on inconsistency toleration with broader and major issues in philosophy of science. In order to do so, we will suggest two different lines of investigation: first, to focus on the implication of some pluralistic accounts in the philosophy of science, regarding inconsistency; and second to analyze the implications of some paraconsistent approaches regarding pluralism in science.

Here, we deal with the question of under which circumstances can scientists achieve a legitimate understanding of defective theories qua defective. We claim that scientists understand a theory if they can recognize the theory’s underlying inference pattern(s) and if they can reconstruct and explain what is going on in specific cases of defective theories as well as consider what the theory would do if non-defective—even before finding ways of fixing it. Furthermore, we discuss the implications of this approach to understanding the meta-metaphysics of Quantum Mechanics, specifically with regard to Quasi-set theory. We illustrate this by employing Quasi-set theory to structure a defective scientific theory and make possible the understanding of the theory.

Many have contended that non-classical logicians have failed at providing evidence of paraconsistent logics being applicable in cases of inconsistency toleration in the sciences. With this in mind, my main concern here is methodological. I aim at addressing the question of how should we study and explain cases of inconsistent science, using paraconsistent tools, without ruining into the most common methodological mistakes. My response is divided into two main parts: first, I provide some methodological guidance on how to approach cases of inconsistent science; and second, I focus on a peculiar type of formal methodologies for the scrutiny of inconsistent reasoning, the _Paraconsistent Alternative Approach_ (henceforth, PAA) and argue that PAA can enhance a more accurate understanding of sensible reasoning in inconsistent contexts.

Two of the most important outcomes of The Contradictory Christ include: identifying Christ as an unproblematically contradictory being as well as laying the foundations of an investigation of the logical consequences of the existence of Christ, qua contradictory, within a particular 'theory'. In light of the enormous reluevance of Beall’s The contradictory Christ for the study of inconsistency, my main concern here is to explore the effect of some methodological choices behind Beall’s proposal -this in order to recognize in more detail the scope of Beall’s contribution. To do so, I will focus on three main questions: 1. What is required for the identification of a contradiction? 2. How can we recognize a true contradiction from either an apparent or a temporal contradiction? 3. If we identify a true contradiction within a theory, where can we actually go from there?

Recently there has been a tendency on the part of some scientific realists to weaken their philosophical theses with respect to the success of science. Some of them have suggested that a satisfactorily realist standpoint should be a highly modest approach to scientific success, leaving many with the impression that scientific realism nowadays is nothing that we once thought it was. In light of that, the main concern of this paper is methodological, here I want to answer the question how far can we push the boundaries of our realist commitments and still be in control of our philosophical claims. In particular, I deal with the issue of how a certain type of weak version of selective realism will necessarily allow for true contradictions, dialetheias –even if that is not desirable. Here I argue that if one presents a very weak characterization of selective realism, one that is in line with contemporary projects, this type of realism will not forbid the possibility of things such as dialetheias. I also claim that, if that is the case, we face the following dilemma: or our general characterization of selective realism is mistaken or selective realists cannot provide a satisfactory explanation of why and how to forbid dialetheias in science.

Inconsistency toleration is the phenomenon of working with inconsistent information without threatening one’s rationality. Here I address the role that ignorance plays for the tolerance of contradictions in the empirical sciences. In particular, I contend that there are two types of ignorance that, when present, can make epistemic agents to be rationally inclined to tolerate a contradiction. The first is factual ignorance, understood as temporary undecidability of the truth values of the conflicting propositions. The second is what I call “ignorance of theoretical structure”, which is lack of knowledge of relevant inference patterns within a specific theory. I argue that these two types of ignorance can be explanatory of the scientists’ rational disposition to be tolerant towards contradictions, and I illustrate this with a case study from neutrino physics.

It has recently been argued by Davey (2014) that inconsistency is never tolerated in science, but only discretely isolated. But when talking about inconsistencies in science, not much attention has been paid to the inconsistencies between theory and observation. Here I will argue that inconsistency toleration actually takes place in science, and that when we examine actual inconsistent theories, inconsistencies between theory and observation look anything but homogeneous. I will argue, appealing to certain properties of empirical theories, especially holism, that at least two sub-types of inconsistencies regarding theory and observation can be distinguished: those that satisfy a criterion of observational independence and those that do not.

Most scientific theories are globally inconsistent. Chunk and Permeate is a method of rational reconstruction that can be used to separate, and identify, locally consistent chunks of reasoning or explanation. This then allows us to justify reasoning in a globally inconsistent theory. We extend chunk and permeate by adding a visually transparent way of guiding the individuation of chunks and deciding on what information permeates from one chunk to the next. The visual representation is in the form of bundle diagrams. We then extend the bundle diagrams to include not only reasoning in the presence of inconsistent information or reasoning in the logical sense of deriving a conclusion from premises, but more generally reasoning in the sense of trying to understand a phenomenon in science. This extends the use of the bundle diagrams in terms of the base space and the fibres. We then apply this to a case in physics, that of understanding binding energies in the nucleus of an atom using together inconsistent models: the liquid drop model and the shell model. We draw some philosophical conclusions concerning scientific reasoning, paraconsistent reasoning, the role of logic in science and the unity of science.

Like theories, reconstructions of episodes in the history of science can possess, or lack, certain virtues such that, when we face two or more different reconstructions of the same episode, we assume that we should choose the most “virtuous one”. However, we will argue that, with dissimilar reconstructions of the same episode, it is not always necessary to separate the “good ones” from the “wrong ones”, and that, as a matter of fact, each reconstruction could provide different but perhaps equally relevant data about the episode, about science in general, and about particular philosophical theses. In order to help us to identify these benefits, we will present a criterion that guides the search for historiographical reinforcement of philosophical theses and we will use it to evaluate three different reconstructions of the same scientific episode.

Five major stances on the problems of the possibility and fruitfulness of a debate on the principle of non-contradiction (PNC) are described: Detractors, fierce supporters, demonstrators, methodologists and calm supporters. We show what calm supporters have to say on the other parties wondering about the possibility and fruitfulness of a debate on PNC. The main claim is that one can find all the elements of calm supporters already in Aristotle’s works. In addition, we argue that the Aristotelian refutative strategy, originally used for dealing with detractors of PNC in Metaphysics, has wider implications for the possibility and fruitfulness of an up-to-date debate on PNC, at least in exhibiting some serious difficulties for the other parties.