In this paper I discuss a prevailing view by which logical terms determine forms of sentences and arguments and therefore the logical validity of arguments. This view is common to those who hold that there is a principled distinction between logical and nonlogical terms and those holding relativistic accounts. I adopt the Tarskian tradition by which logical validity is determined by form, but reject the centrality of logical terms. I propose an alternative framework for logic where logical terms no longer (...) play a distinctive role. This account employs a new notion of semantic. (shrink)

This essay offers a conception of logic by which logic may be considered to be exceptional among the sciences on the backdrop of a naturalistic outlook. The conception of logic focused on emphasises the traditional role of logic as a methodology for the sciences, which distinguishes it from other sciences that are not methodological. On the proposed conception, the methodological aims of logic drive its definitions and principles, rather than the description of scientific phenomena. The notion of a methodological discipline (...) is explained as a relation between disciplines or practices. Logic serves as a methodological discipline with respect to any theoretical practice, and this generality, as well as logic’s reflexive nature, distinguish it from other methodological disciplines. Finally, the evolution of model theory is taken as a case study, with a focus on its methodological role. Following recent work by John Baldwin and Juliette Kennedy, we look at model theory from its inception in the mid-twentieth century as a foundational endeavour until developments at the end of the century, where the classification of theories has taken centre-stage. (shrink)

This collection of new essays presents cutting-edge research on the semantic conception of logic, the invariance criteria of logicality, grammaticality, and logical truth. Contributors explore the history of the semantic tradition, starting with Tarski, and its historical applications, while central criticisms of the tradition, and especially the use of invariance criteria to explain logicality, are revisited by the original participants in that debate. Other essays discuss more recent criticism of the approach, and researchers from mathematics and linguistics weigh in on (...) the role of the semantic tradition in their disciplines. This book will be invaluable to philosophers and logicians alike. (shrink)

In a recent article, “Logical Consequence and Natural Language,” Michael Glanzberg claims that there is no relation of logical consequence in natural language (2015). The present paper counters that claim. I shall discuss Glanzberg’s arguments and show why they don’t hold. I further show how Glanzberg’s claims may be used to rather support the existence of logical consequence in natural language.

In standard model-theoretic semantics, the meaning of logical terms is said to be fixed in the system while that of nonlogical terms remains variable. Much effort has been devoted to characterizing logical terms, those terms that should be fixed, but little has been said on their role in logical systems: on what fixing their meaning precisely amounts to. My proposal is that when a term is considered logical in model theory, what gets fixed is its intension rather than its extension. (...) I provide a rigorous way of spelling out this idea, and show that it leads to a graded account of logicality: the less structure a term requires in order for its intension to be fixed, the more logical it is. Finally, I focus on the class of terms that are invariant under isomorphisms, as they render themselves more easily to mathematical treatment. I propose a mathematical measure for the logicality of such terms based on their associated Löwenheim numbers. (shrink)

Contextualist theories of truth appeal to context to solve the liar paradox: different stages of reasoning occur in different contexts, and so the contradiction is dispelled. The word ‘true’ is relativized by the contextualists to contexts of use. This paper shows that contextualist approaches to the liar are committed to a form of semantic relativism: that the truth value of some sentences depends on the context of assessment, as well as the context of use. In particular, it is shown how (...) Simmons’s and Glanzberg’s contextualist approaches entail relativism. In both cases, the liar sentence gets different semantic evaluations as uttered in a fixed context of use but assessed from different contexts. Shift in context of use alone cannot provide the full explanation of the liar. These contextualist approaches, as originally presented, were thus mischaracterised and they should be re-evaluated according to their full implications. (shrink)

The essay discusses a recurrent criticism of the isomorphism-invariance criterion for logical terms, according to which the criterion pertains only to the extension of logical terms, and neglects the meaning, or the way the extension is fixed. A term, so claim the critics, can be invariant under isomorphisms and yet involve a contingent or a posteriori component in its meaning, thus compromising the necessity or apriority of logical truth and logical consequence. This essay shows that the arguments underlying the criticism (...) are flawed since they rely on an invalid inference from the modal or epistemic status of statements in the metalanguage to that of statements in the object-language. The essay focuses on McCarthy’s version of the argument, but refers to Hanson and McGee’s versions as well. (shrink)

In a recent article, “Logical Consequence and Natural Language”, Michael Glanzberg claims that there is no relation of logical consequence in natural language (2015). The present paper counters that claim. I shall discuss Glanzberg’s arguments and show why they don’t hold. I further show how Glanzberg’s claims may be used to rather support the existence of logical consequence in natural language.

Tarski characterized logical notions as invariant under permutations of the domain. The outcome, according to Tarski, is that our logic, which is commonly said to be a logic of extension rather than intension, is not even a logic of extension—it is a logic of cardinality. In this paper, I make this idea precise. We look at a scale inspired by Ruth Barcan Marcus of various levels of meaning: extensions, intensions and hyperintensions. On this scale, the lower the level of meaning, (...) the more coarse-grained and less “intensional” it is. I propose to extend this scale to accommodate a level of meaning appropriate for logic. Thus, below the level of extension, we will have a more coarse-grained level of form. I employ a semantic conception of form, adopted from Sher, where forms are features of things “in the world”. Each expression in the language embodies a form, and by the definition we give, forms will be invariant under permutations and thus Tarskian logical notions. I then define the logical terms of a language as those terms whose extension can be determined by their form. Logicality will be shown to be a lower level analogue of rigidity. Using Barcan Marcus’s principles of explicit and implicit extensionality, we are able to characterize purely logical languages as “sub-extensional”, namely, as concerned only with form, and we thus obtain a wider perspective on both logicality and extensionality. (shrink)

This paper deals with the adequacy of the model-theoretic definition of logical consequence. Logical consequence is commonly described as a necessary relation that can be determined by the form of the sentences involved. In this paper, necessity is assumed to be a metaphysical notion, and formality is viewed as a means to avoid dealing with complex metaphysical questions in logical investigations. Logical terms are an essential part of the form of sentences and thus have a crucial role in determining logical (...) consequence. Gila Sher and Stewart Shapiro each propose a formal criterion for logical terms within a model-theoretic framework, based on the idea of invariance under isomorphism. The two criteria are formally equivalent, and thus we have a common ground for evaluating and comparing Sher and Shapiro philosophical justification of their criteria. It is argued that Shapiro's blended approach, by which models represent possible worlds under interpretations of the language, is preferable to Sher’s formal-structural view, according to which models represent formal structures. The advantages and disadvantages of both views’ reliance on isomorphism are discussed. (shrink)

Invariance criteria are widely accepted as a means to demarcate the logical vocabulary of a language. In previous work, I proposed a framework of “semantic constraints” for model theoretic consequence which does not rely on a strict distinction between logical and nonlogical terms, but rather on a range of constraints on models restricting the interpretations of terms in the language in different ways. In this paper I show how invariance criteria can be generalized so as to apply to semantic constraints (...) on models. Some obviously unpalatable semantic constraints turn out to be invariant under isomorphisms. I shall connect our discussion to known counterexamples to invariance criteria for logical terms, and so the generalization will also shed light on the current existing debate on logicality. I analyse the failure of invariance to fulfil its role as a criterion for logicality, and argue that invariance conditions should best be thought of as merely methodological meta-constraints restricting the ways the model-theoretic apparatus should be used. (shrink)

In his new book, Logical Form, Andrea Iacona distinguishes between two different roles that have been ascribed to the notion of logical form: the logical role and the semantic role. These two roles entail a bifurcation of the notion of logical form. Both notions of logical form, according to Iacona, are descriptive, having to do with different features of natural language sentences. I agree that the notion of logical form bifurcates, but not that the logical role is merely descriptive. In (...) this paper, I focus on formalization, a process by which logical form, on its logical role, is attributed to natural language sentences. According to some, formalization is a form of explication, and it involves normative, pragmatic, as well as creative aspects. I present a view by which formalization involves explicit commitments on behalf of a reasoner or an interpreter, which serve the normative grounds for the evaluation of a given text. In previous work, I proposed the framework of semantic constraints for the explication of logical consequence. Here, I extend the framework to include formalization constraints. The various constraints then serve the role of commitments. I discuss specific issues raised by Iacona concerning univocality, co-reference and equivocation, and I show how our views on these matters diverge as a result of our different starting assumptions. (shrink)

Is there a relation of logical consequence in natural language? Logicality, in the philosophical literature, has been conceived of as a restrictive phenomenon that is at odds with the unbridled richness and complexity of natural language. This article claims that there is a relation of logical consequence in natural language, and moreover, that it is the subject matter of the bulk of current theories of formal semantics. I employ the framework of _semantic constraints_ (Sagi in Log Anal 57(227):259–276, 2014), (...) which generalizes the Tarskian definition of logical consequence. I apply the widely accepted criterion of invariance under isomorphisms (Sher in J. Symb Log 61(2):653–686, 1996) generalized to the framework of semantic constraints (Sagi in Bull Symb Log 28(1):104–132, 2022b), combined with a theory of Glanzberg (in Metasemantics: new essays on the foundations of meaning, 2014) to delineate the relation of logical consequence in natural language. (shrink)

One True Logic is a rare contribution to the most fundamental issues in the philosophy of logic. The book pushes a remarkably clear and uncompromising monistic.

A good argument is one whose conclusions follow from its premises; its conclusions are consequences of its premises. But in what sense do conclusions follow from premises? What is it for a conclusion to be a consequence of premises? Those questions, in many respects, are at the heart of logic (as a philosophical discipline). Consider the following argument: 1. If we charge high fees for university, only the rich will enroll. We charge high fees for university. Therefore, only the rich (...) will enroll. There are many different things one can say about this argument, but many agree that if we do not equivocate (if the terms mean the same thing in the premises and the conclusion) then the argument is valid, that is, the conclusion follows deductively from the premises. This does not mean that the conclusion is true. Perhaps the premises are not true. However, if the premises are true, then the conclusion is also true, as a matter of logic. This entry is about the relation between premises and conclusions in valid arguments. (shrink)

We show that there is a restriction, or modification of the finite-variable fragments of First Order Logic in which a weak form of Craig's Interpolation Theorem holds but a strong form of this theorem does not hold. Translating these results into Algebraic Logic we obtain a finitely axiomatizable subvariety of finite dimensional Representable Cylindric Algebras that has the Strong Amalgamation Property but does not have the Superamalgamation Property. This settles a conjecture of Pigozzi [12].

In this paper I present an interpretation of Deleuze's concept of the virtual. I argue that this concept is best understood in relation to the problematic of individuation or differentiation, which Deleuze inherits from Duns Scotus. After analysing Scotus' critique of Aristotelian or hylomorphic approaches to the problem of individuation, I turn to Deleuze's account of differentiation and his interpretation of the calculus in chapter 4 of Difference and Repetition. The paper seeks thereby to explicate Deleuze's dialectics or theory of (...) Ideas, his approach to the principle of sufficient reason, and the concept of the virtual itself. (shrink)

The medical profession is observing a rising number of calls to action considering the threat that climate change poses to global human health. Theory-led bioethical analyses of the scope and weight of physicians’ normative duty towards climate protection and its conflict with individual patient care are currently scarce. This article offers an analysis of the normative issues at stake by using Korsgaard’s neo-Kantian moral account of practical identities. We begin by showing the case of physicians’ duty to climate protection, before (...) we succinctly introduce Korsgaard’s account. We subsequently show how the duty to climate protection can follow from physicians’ identity of being a healthcare professional. We structure conflicts between individual patient care and climate protection, and show how a transformation in physicians’ professional ethos is possible and what mechanisms could be used for doing so. An important limit of our analysis is that we mainly address the level of individual physicians and their practical identities, leaving out important measures to respond to climate change at the mesolevels and macrolevels of healthcare institutions and systems, respectively. (shrink)

Spoofing is the act of placing orders to buy or sell a financial contract without the intention to have those orders fulfilled in order to create the impression that there is a large demand for that contract at that price. In this article, I deny the view that spoofing in financial markets should be viewed as morally permissible analogously to the way bluffing is permissible in poker. I argue for the pro tanto moral impermissibility of spoofing and make the case (...) that spoofing is disanalogous from bluffing in at least one important regard—speculative trading serves an important economic role, whereas poker does not. (shrink)

We present four new change detection methods that create an automated change map from a probability map. In this case, the probability map was derived from a 3D model. The primary application of interest is aerial photographic applications, where the appearance, disappearance or change in position of small objects of a selectable class (e.g., cars) must be detected at a high success rate in spite of variations in magnification, lighting and background across the image. The methods rely on an earlier (...) derivation of a probability map. We describe the theory of the four methods, namely Bernoulli variables, Markov Random Fields, connected change, and relaxation-based segmentation, evaluate and compare their performance experimentally on a set probability maps derived from aerial photographs. (shrink)

In this paper we discuss James Buchanan’s contribution in the narrow domain of understanding committee voting under majority rule. We then go on to discuss Charles Plott’s seminal experimental work on the topic that sparked a wave of public choice experimental work. However, given Plott’s claims that Buchanan influenced him significantly, it is puzzling that his work with Morris Fiorina explores a question outside of those which Buchanan and Tullock found interesting. We suggest several ways to resolve this tension. Our (...) chapter concludes by discussing a lacuna in the experimental public choice literature in which Buchanan was particularly interested—logrolling, or vote trading. (shrink)

The global Covid-19 pandemic has resulted in social and economic disruption unprecedented in the modern era. Many countries have introduced severe measures to contain the virus, including travel restrictions, public event bans, non-essential business closures and remote work policies. While digital technologies help governments and organizations to enforce protection measures, such as contact tracing, their rushed deployment and adoption also raises profound concerns about surveillance, privacy and data protection. This article presents two critical cases on digital surveillance technologies implemented during (...) the Covid-19 pandemic and delineates the privacy implications thereof. We explain the contextual nature of privacy trade-offs during a pandemic and explore how regulatory and technical responses are needed to protect privacy in such circumstances. By providing a multi-disciplinary conversation on the value of privacy and data protection during a global pandemic, this article reflects on the implications digital solutions have for the future and raises the question of whether there is a way to have expedited privacy assessments that could anticipate and help mitigate adverse privacy implications these may have on society. (shrink)

Available corpora for Argument Mining differ along several axes, and one of the key differences is the presence (or absence) of discourse markers to signal argumentative content. Exploring effective ways to use discourse markers has received wide attention in various discourse parsing tasks, from which it is well-known that discourse markers are strong indicators of discourse relations. To improve the robustness of Argument Mining systems across different genres, we propose to automatically augment a given text with discourse markers such that (...) all relations are explicitly signaled. Our analysis unveils that popular language models taken out-of-the-box fail on this task; however, when fine-tuned on a new heterogeneous dataset that we construct (including synthetic and real examples), they perform considerably better. We demonstrate the impact of our approach on an Argument Mining downstream task, evaluated on different corpora, showing that language models can be trained to automatically fill in discourse markers across different corpora, improving the performance of a downstream model in some, but not all, cases. Our proposed approach can further be employed as an assistant tool for better discourse understanding. (shrink)

Downward causation exercised by emergent properties of wholes upon their lower-level constituents’ properties has been accused of conceptual and metaphysical incoherence. Only upward causation is usually peacefully accepted. The aim of this paper is to criticize and refuse the traditional hierarchical-vertical way of conceiving both types of causation, although preserving their deepest ontological significance, as well as the widespread acceptance of the traditional atomistic-combinatorial view of the entities and the relations that constitute the so-called ‘emergence base’. Assuming those two perspectives (...) with no reserves, we are condemned to confine our debate to the question of whether reified wholes can have the power to downwardly change or influence their lower-level parts, a question which seems profoundly misleading to me. I therefore propose an alternative relational ontological view, assuming a straightforward horizontal and intra-level way of representing those putative cases of cross-level causation. I finally confront two recent replies to Kim’s well-known objections to DC—Craver and Bechtel and Kistler :595–609, 2009)—, emphasizing their global positive approaches, as well as the reasons why their accounts still seem insufficient to me. I conclude arguing that both Kim’s principle of the causal closure of the physical domain and its allegation of an overdetermination in cases of DC can be surpassed by the new relational ontological perspective presented here. (shrink)

This book is an attempt to read the totality of Camus s oeuvre as a voyage, in which Camus approaches the fundamental questions of human existence: What is the meaning of life? Can ultimate values be grounded without metaphysical presuppositions? Can the pain of the other penetrate the thick shield of human narcissism and self-interest? Solipsism and solidarity are among the destinations Camus reaches in the course of this journey. This book is a new reading of one of the towering (...) humanists of the twentieth century, and sheds new light on his spiritual world.". (shrink)

Among others we will prove that the equational theory of ω dimensional representable polyadic equality algebras (RPEA ω 's) is not schema axiomatizable. This result is in interesting contrast with the Daigneault-Monk representation theorem, which states that the class of representable polyadic algebras is finite schema-axiomatizable (and hence the equational theory of this class is finite schema-axiomatizable, as well). We will also show that the complexity of the equational theory of RPEA ω is also extremely high in the recursion theoretic (...) sense. Finally, comparing the present negative results with the positive results of Ildiko Sain and Viktor Gyuris [12], the following methodological conclusions will be drawn: The negative properties of polyadic (equality) algebras can be removed by switching from what we call the "polyadic algebraic paradigm" to the "cylindric algebraic paradigm". (shrink)

Here we investigate the classes RCA $^\uparrow_\alpha$ of representable directed cylindric algebras of dimension α introduced by Nemeti[12]. RCA $^\uparrow_\alpha$ can be seen in two different ways: first, as an algebraic counterpart of higher order logics and second, as a cylindric algebraic analogue of Quasi-Projective Relation Algebras. We will give a new, "purely cylindric algebraic" proof for the following theorems of Nemeti: (i) RCA $^\uparrow_\alpha$ is a finitely axiomatizable variety whenever α ≥ 3 is finite and (ii) one can obtain (...) a strong representation theorem for RCA $^\uparrow_\alpha$ if one chooses an appropriate (non-well-founded) set theory as foundation of mathematics. These results provide a purely cylindric algebraic solution for the Finitization Problem (in the sense of [11]) in some non-well-founded set theories. (shrink)

Physicians frequently encounter situations in which their professional practice is intermingled with moral affordances stemming from other domains of the physician’s lifeworld, such as family and friends, or from general morality pertaining to all humans. This article offers a typology of moral conflicts ‘at the margins of professionalism’ as well as a new theoretical framework for dealing with them. We start out by arguing that established theories of professional ethics do not offer sufficient guidance in situations where professional ethics overlaps (...) with moral duties of other origins. Therefore, we introduce the moral theory developed by Christine M. Korsgaard, that centres around the concept of practical identity. We show how Korsgaard’s account offers a framework for interpreting different types of moral conflicts ‘at the margins of professionalism’ to provide either orientation for solving the conflict or an explanation for the emotional and moral burden involved in moral dilemmas. (shrink)

Feelings are conscious mental events that represent body states as they undergo homeostatic regulation. Feelings depend on the interoceptive nervous system (INS), a collection of peripheral and central pathways, nuclei and cortical regions which continuously sense chemical and anatomical changes in the organism. How such humoral and neural signals come to generate conscious mental states has been a major scientific question. The answer proposed here invokes (1) several distinctive and poorly known physiological features of the INS; and (2) a unique (...) interaction between the body (the ‘object’ of interoception) and the central nervous system (which generates the 'subject' of interoception). The atypical traits of the INS and the direct interactions between neural and non‐neural physiological compartments of the organism, neither of which is present in exteroceptive systems, plausibly explain the qualitative and subjective aspects of feelings, thus accounting for their conscious nature. (shrink)

Often institutions or individuals are faced with decisions where not all claims can be satisfied. Sometimes, these claims will be of differing strength. In such cases, it must be decided whether or not weaker claims can be aggregated in order to collectively defeat stronger claims. Many are attracted to a view, which this chapter calls Limited Aggregation, where this is sometimes acceptable and sometimes not. A new version of this view, Local Relevance, has recently emerged. This chapter seeks to explore (...) and evaluate this view. In order to do so, the chapter offers a more precise interpretation of this basic approach, calling it ‘Sequential Claims-Matching’. The chapter shows how Sequential Claims-Matching avoids problems that dog other Limited Aggregation views but suffers from difficulties and ambiguities of its own. In particular, the chapter shows that it is hard to accommodate some core Limited Aggregation intuitions around tie-break cases within the Local Relevance view. (shrink)

Let be a countable first order structure and endow the universe of with the discrete topology. Then the automorphism group of becomes a topological group. A tuple of automorphisms is defined to be weakly generic iff its diagonal conjugacy class (in the algebraic sense) is dense (in the topological sense) and the ‐orbit of each is finite. Existence of tuples of weakly generic automorphisms are interesting from the point of view of model theory as well as from the point of (...) view of finite combinatorics.The main results of the present work are as follows. In Theorem 2.6 we characterize the existence of tuples of weakly generic automorphisms with the aid of the profinite topology of free groups. In Corollary 2.12 we will show that if has finite topological rank r (and satisfies a further, mild technical condition) then the existence of a weakly generic tuple in implies the existence of weakly generic tuples in for all natural number. Finally, in Theorem 3.2 we show that if is a countable model of an ℵ0‐categorical, simple theory in which all types over the empty set are stationary and has a pair of weakly generic automorphisms then it has tuples of weakly generic automorphisms of arbitrary finite length.At the technical level we will combine elementary investigations about the profinite topology of free groups with the results of [11] about topological ranks of the automorphism groups of some structures. (shrink)

_Blood_, according to Gil Anidjar, maps the singular history of Christianity. As a category for historical analysis, blood can be seen through its literal and metaphorical uses as determining, sometimes even defining Western culture, politics, and social practices and their wide-ranging incarnations in nationalism, capitalism, and law. Engaging with a variety of sources, Anidjar explores the presence and the absence, the making and unmaking of blood in philosophy and medicine, law and literature, and economic and political thought from ancient Greece (...) to medieval Spain, from the Bible to Shakespeare and Melville. The prevalence of blood in the social, juridical, and political organization of the modern West signals that we do not live in a secular age into which religion could return. Flowing across multiple boundaries, infusing them with violent precepts that we must address, blood undoes the presumed oppositions between religion and politics, economy and theology, and kinship and race. It demonstrates that what we think of as modern is in fact imbued with Christianity. Christianity, Blood fiercely argues, must be reconsidered beyond the boundaries of religion alone. (shrink)

This study aims to enhance the understanding about the influence of perceived ethical work climate dimensions on employees’ trust in co-workers. The instrument used was Victor and Cullen’s (1988) questionnaire containing five empirically derived types of ethical climate (caring, law and code, rules, instrumentalism, and independence). As hypothesized, the study revealed that the instrumental ethical climate dimension was negatively related, and independent climate was positively related to co-worker trust. Thus, two ethical climate dimensions (independent and instrumental) account for the 22.7 (...) percent variation taking place in co-worker trust while the remaining climate types had no significant impact. The findings may be of help particularly to human resource staff in developing policies to better off relations among employees acknowledging differing potential of ethical climate types. (shrink)

"Alexandre Matheron is considered one of the most important interpreters of Spinoza's philosophy in the 20th century. These 20 essays, translated into English for the first time, focus on ontology, knowledge, politics and ethics in Spinoza, his predecessors and his contemporaries."--Publisher description.

To advance current knowledge on ethical decision-making in organizations, we integrate two perspectives that have thus far developed independently: the organizational identification perspective and the ethical climate perspective. We illustrate the interaction between these perspectives in two studies, in which we presented participants with moral business dilemmas. Specifically, we found that organizational identification increased moral decision-making only when the organization’s climate was perceived to be ethical. In addition, we disentangle this effect in Study 2 from participants’ moral identity. We argue (...) that the interactive influence of organizational identification and ethical climate, rather than the independent influence of either of these perspectives, is crucial for understanding moral decision-making in organizations. (shrink)

According to what I call the ‘argument from public bads’, if a researcher deceived subjects in the past, there is a chance that subjects will discount the information that a subsequent researcher provides, thus compromising the validity of the subsequent researcher’s experiment. While this argument is taken to justify an existing informal ban on explicit deception in experimental economics, it can also apply to implicit deception, yet implicit deception is not banned and is sometimes used in experimental economics. Thus, experimental (...) economists are being inconsistent when they appeal to the argument from public bads to justify banning explicit deception but not implicit deception. (shrink)

Buchanan’s work, and in particular The Calculus of Consent, which he wrote with Gordon Tullock, has been foundational in the field of public choicePublic choice. One of his students, Charles Plott, became a pioneer with multiple seminal contributions in the field of experimental public choice. In this chapter we focus on Buchanan’s work on decision making under majority rule, and any influence it may have had on Plott. While Buchanan and Tullock address environments with single decisions, they focus much more (...) on decision making under repeated votes, a topic they found of great interest. Plott’s seminal 1978 paper with Morris Fiorina, however, focuses on single decisions. It may seem puzzling, then, that Plott has often suggested Buchanan’s influence on his work. We offer a resolution to this puzzle. (shrink)

Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...) prove that every involutive bisemilattice is representable as the Płonka sum over a direct system of Boolean algebras. We then study PWK from the viewpoint of AAL. We show that \ is not the equivalent algebraic semantics of any algebraisable logic and that PWK is neither protoalgebraic nor selfextensional, not assertional, but it is truth-equational. We fully characterise the deductive filters of PWK on members of \ and the reduced matrix models of PWK. Finally, we investigate PWK with the methods of second-order AAL—we describe the class \ of PWK-algebras, algebra reducts of basic full generalised matrix models of PWK, showing that they coincide with the quasivariety generated by WK—which differs from \—and explicitly providing a quasiequational basis for it. (shrink)