Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A∪B holds at the current time instant w iff either B holds at w or there exists a time instant w' in the future at which B holds and such that A holds in all the time instants between the current one and ẃ. This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in (...) contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and ẃ. This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL∇) for a linear-time logic LTL∇ endowed with the new history operator. We show that LTL∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL∇ into LTL via temporal logics with past operators; such a result provides an upper bound to the problem of satisfiability for LTL∇ formulas. (shrink)

We present an extension of the mosaic method aimed at capturing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5-like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique not only in obtaining a proof of decidability and a proof of completeness (...) for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system. (shrink)

Neste artigo, propõe-se uma leitura das categorias no tratado aristotélico homônimo como um primeiro esboço de uma ontologia regional, centrada nas substâncias sensíveis. Tendo por foco substância, quantidade, qualidade, relativo, agir e sofrer, este trabalho busca expor as duas estratégias principais que Aristóteles parece empregar para chegar a uma lista das categorias: (a) características básicas, cuja satisfação ou não satisfação de cada uma determina a natureza categorial de cada item e (b) a propriedade única que caracteriza cada categoria em contraste (...) com todas as outras. São, então, feitas considerações para vincular esse primeiro esboço ontológico a temas discutidos nos livros Lambda e Zeta da Metafísica, de modo a sugerir as direções principais que a sua ontologia nova (e geral) seguirá ao evoluir para uma teoria unificada da substância. (shrink)

Proposed educational outcomes for the health humanities in medical education range from empathy to visual thinking skills to social accountability. This lack of widely agreed-upon high-level curricular goals limits humanities educators’ ability to design purposeful curricula toward clear, common ends and threatens justifications for scarce curricular time. We propose a novel approach to the hoped-for outcomes of health humanities training in medical schools, which has the potential to encompass traditional health humanities knowledge, skills, and behaviors while also being concrete and (...) measurable: humanistic practice. Humanistic practice, adapted from the concept of ethical sensitivity, is an intentional process of applying humanities knowledge and skills to a clinical scenario by 1) noticing that the scenario requires humanities knowledge or skills, 2) informing one’s clinical and interpersonal strategy and behavior with humanities knowledge or skills, 3) reflecting on the effectiveness of the strategy and behavior, and 4) reorienting to develop new approaches for future practice. The construct of humanistic practice may help address some of the foundational problems in health humanities outcomes research since it transcends the traditional diverse content domains in the health humanities, can link patient and provider experiences, and may bridge the divide among the additive, curative, and intrinsic epistemic positions of humanities to medical education. (shrink)

Numenius is one of the most important authors who, in the Imperial Age, deal with the figure of Socrates. Socrates is important in the Platon­ic tradition, in particular in the sceptical tradition, when the Socratic dubitative “spirit” of the first Platonic dialogues became important to justify the “suspension of judgement.” Numenius criticises the whole Academic tradition by saying that the Academics (particularly the sceptics) betrayed the original doctrine of Plato and formulated a new image of Socrates. For Numenius, Socrates plays (...) a central role because Plato would have inherited his doctrine. What does Socrates’s doctrine consist in? According to Numenius, Socrates theorised a “doctrine of three Gods” (which can be likely found in the second Platonic epistle) which is strictly bound up with the main aspect of Plato’s thought. In fact, in Numenius’s view, Plato belongs to a genealogy which can be linked to Pythagoras himself. From this perspective, Numenius says that Socrates’s original thought is a theology which also belongs to the Pythagorean tradition and which Plato further developed. For Nume­nius, Socrates is not the philosopher of doubt, but a theologian who first theorised the existence of three levels of reality (Gods), which is also the kernel of Numenius’s metaphysical system. For this reason, Numenius puts Socrates within a theological genealogy that begins with Pythago­ras and continues with Socrates and Plato, and that the Academics and the Socratics failed to understand. (shrink)

Two of the most well-known belief contraction operators are partial meet contractions (PMCs) and kernel contractions (KCs). In this paper we propose two new classes of contraction operators, namely the class of generalized partial meet contractions (GPMC) and the class of generalized kernel contractions (GKC), which strictly contain the classes of PMCs and of KCs, respectively. We identify some extra conditions that can be added to the definitions of GPMCs and of GKCs, which give rise to some interesting subclasses of (...) those classes of functions, namely the classes of extensional and of uniform GPMCs/GKCs. In the context of contractions on belief sets the classes of partial meet contractions, uniform GPMCs and extensional GPMCs are all identical. Nevertheless, when considered as operations on belief bases, the class of uniform GPMCs coincides with the class of partial meet contractions, but the extensional GPMCs constitute a new kind of belief base contraction functions whose characterizing postulate of irrelevance of syntax is extensionality—the same postulate of irrelevance of syntax which occurs in the classical axiomatic characterization of partial meet contractions for belief sets—rather than the postulate of uniformity—which is the irrelevance of syntax postulate used in the axiomatic characterization for partial meet contractions on belief bases. Analogous results are obtained regarding the classes of extensional and of uniform GKCs. We present the interrelations in the sense of inclusion among all the new classes of operators presented in this paper and several well known classes of PMCs and of KCs. (shrink)

This essay will discuss how the Theory of Communicative Action incorporates the systemic complexification process and the Systems and Life World duality. Part of this process will be carried out with the discussion of communicative action, as a space for dialogue between people seeking understanding. The process of new forms of understanding and construction of knowledge is possible through the integrative structure of the lifeworld, such as semantic dimension, social space, and historical time. However, there is the other side, the (...) Systems, where the manifestations of crisis and disturbances, the pathologies of society, which in cultural reproduction appear as a loss of meaning of culture, loss of legitimacy of society and in personality, there is a crisis of belonging. (shrink)

Why are mistaken beliefs about COVID-19 so prevalent? Political identity, education and other demographic variables explain only part of the differences between people in their susceptibility to COVID-19 misinformation. This paper focuses on another explanation: epistemic vice. Epistemic vices are character traits that interfere with acquiring, maintaining, and transmitting knowledge. If the basic assumption of vice epistemology is right, then people with epistemic vices such as indifference to the truth or rigidity in their belief structures will tend to be more (...) susceptible to believing COVID-19 misinformation. We carried out an observational study (US adult sample, n = 998) in which we measured the level of epistemic vice of participants using a novel Epistemic Vice Scale that captures features of the current competing analyses of epistemic vice in the literature. We also asked participants questions eliciting the extent to which they subscribe to myths and misinformation about COVID-19. We find overwhelming evidence to the effect that epistemic vice is associated with susceptibility to COVID-19 misinformation. In fact, the association turns out to be stronger than with political identity, educational attainment, scores on the Cognitive Reflection Test, personality, dogmatism, and need for closure. We conclude that this offers evidence in favor of the empirical presuppositions of vice epistemology. (shrink)

The Oscar Wilde trials (1895) have usually been interpreted either as a historical document which gives insight into the regulation of sexuality in the late nineteenth century, or as literary biography explicating the playwright's life and works. Taking its cue from recent scholarship in ‘law and literature’, and also from Wilde's own conception of the relationship between art and life, this article proposes a reading of the trials which blurs the distinction between legal history and literary criticism by considering them (...) as a form of literature. It argues that the trial transcripts enact and reflect Wilde's vision of what literature is and how it should be read, and as such should be given a place amongst his literary works, alongside such aesthetic manifestos as ‘The Decay of Lying’ and ‘The Critic as Artist’. (shrink)

Disagreement plays an important role in several philosophical debates, with intuitions about ordinary or exotic cases of agreement and disagreement being invoked to support or undermine competing semantic, epistemological and metaphysical views. In this paper we discuss cases of interworld doxastic disagreement, that is to say, cases of doxastic disagreement supposedly obtaining between individuals inhabiting different possible worlds, in particular between an individual inhabiting the actual world and his/her counterpart in another possible world. We draw a distinction between propositional and (...) attitudinal disagreement, bring it to bear on the issue of the conditions of this kind of disagreement, and raise some metaphysical and epistemological worries about the claim that an individual inhabiting the actual world can disagree with an attitude or a speech act of his/her own counterpart, or of another individual, in a different possible world. (shrink)

Galvano Della Volpe was the dominant philosopher of Italian Marxism for twenty years after the Liberation. His most important book was a work of aesthetic theory—Critique of Taste. Della Volpe, proponent of a robust materialism in all his writings, was concerned to rehabilitate the inherently rational and intellectual nature of art. Opposing both the sociological reductionism of Plekhanov or Lukács, and the formalist irrationalism of Croce or New Criticism, Della Volpe's aim was to demonstrate that conceptual meaning (...) is always inseparable from aesthetic effect. Whether he is discussing Pindar or Góngora, Cleanth Brooks or Roland Barthes, Goethe or Mallarmé, Della Volpe is always challenging, always illuminating. Critique of Taste represents one of the major crossroads of twentieth-century aesthetics. (shrink)

The value of solidarity, which implies mutual concern and support, is often conveyed in our everyday moral and political language. But what is its conceptual relationship with justice? Influential positions in this debate may argue for the opposition between the two concepts: justice is impartial and universal, while solidarity is partial and limited. The present paper aims to shortly explore a range of theories that may exemplify possible answers to this position, from communitarian and realist views, which ultimately confirm the (...) opposition, to political solidarities, which claim an instrumental need for solidarity as a reaction to injustices. Special attention will be paid to Habermas’s compatibilist account of solidarity as the “reverse side” of justice. The paper contends that a compelling answer should preserve the difference between the two spheres and the essential features of solidarity by also sketching a concept of solidarity as a social duty arising from our moral interdependence. (shrink)

A spatial logic is a formal language interpreted over any class of structures featuring geometrical entities and relations, broadly construed. In the past decade, spatial logics have attracted much attention in response to developments in such diverse fields as Artificial Intelligence, Database Theory, Physics, and Philosophy. The aim of this handbook is to create, for the first time, a systematic account of the field of spatial logic. The book comprises a general introduction, followed by fourteen chapters by invited authors. Each (...) chapter provides a self-contained overview of its topic, describing the principal results obtained to date, explaining the methods used to obtain them, and listing the most important open problems. Jointly, these contributions constitute a comprehensive survey of this rapidly expanding subject. (shrink)

This article gives a practice-based overview of the implementation aspects of Corporate Responsibility. After discussing the success factors for implementing Corporate Responsibility, the article describes a model for implementing Corporate Responsibility. Special attention is given to the success factors in the subsequent phases of implementation (sensitivity to the organizational environment, awareness of core values and clear leadership), to ensure that the most optimal results attainable for the organization can be reached. The implementation-model is clarified by looking at experiences in implementing (...) Corporate Responsibility at Chiquita. (shrink)

Ongoing evaluation of a clinical ethics consultation service (ECS) allows for continuous quality improvement, a process-based, data-driven approach for improving the quality of a service. Evaluations by stakeholders involved in a consultation can provide realtime feedback about what is working well and what might need to be improved. Although numerous authors have previously presented data from research studies on the effectiveness of clinical ethics consultation, few ECSs routinely send evaluations as an ongoing component of their everyday clinical activities. The primary (...) purpose of this article is to equip and encourage others to engage in ongoing evaluation of their own ECS. Toward that end, the following resources are shared: (1) the survey tool used to gather the evaluation data, (2) the procedure used to elicit and collate responses, and (3) how the resulting data are used to support continuous quality improvement and justify the continued financial support of the ECS to hospital administration. (shrink)

In this paper I outline an account of the structure of perceptual justification that develops Wittgenstein’s thought that the possibility of acquiring any degree of justification for our beliefs depends on placing certain propositions outside the route of empirical inquiry, turning them into the ‘hinges’ of our rational evaluations. The proposal is akin to ‘moderate’ accounts of the structure of perceptual justification, but it conjoins Wittgenstein’s insight with explanationist and contrastivist ideas, and so differs in important respects both from such (...) accounts and from other versions of hinge epistemology. I maintain that the basic presuppositions of the epistemic practice of taking experience at face value are not totally refractory to evidential assessment, arguing that they can receive some degree of second-order empirical justification via inference to the best explanation. And I address the worry that the account may face the problem of ‘easy knowledge’ by helping myself to the contrastivist view that empirical knowledge is best understood as a three-place, contrastive relation between an agent, a proposition (or fact) and a contrast. This leads me to replace the usual closure principles for epistemic justification and knowledge with corresponding contrastive principles, filling in the final details of contrastive hinge epistemology. (shrink)

The view that propositional knowledge is knowledge of facts is prima facie rather appealing, especially for realistically minded philosophers, but it is difficult to square with the referential opacity of knowledge attributions of the form ‘S knows that p’. For how could Lois Lane know that Superman can fly and ignore that Clark Kent can fly if knowledge is a two-place relation between an agent and a fact and the fact that Superman can fly just is the fact that Clark (...) Kent can fly? Giorgio Volpe reviews some attempts to tackle the problem and then proposes a new solution which exploits the contrastivist claim that knowledge is a three-place relation between an agent, a fact and a contrast. (shrink)

This article gives a practice-based overview of the implementation aspects of Corporate Responsibility. After discussing the success factors for implementing Corporate Responsibility, the article describes a model for implementing Corporate Responsibility. Special attention is given to the success factors in the subsequent phases of implementation (sensitivity to the organizational environment, awareness of core values and clear leadership), to ensure that the most optimal results attainable for the organization can be reached. The implementation-model is clarified by looking at experiences in implementing (...) Corporate Responsibility at Chiquita. (shrink)

The twenty‐six‐year‐old patient requested a prophylactic bilateral mastectomy with reconstruction because of an extensive family history of cancer. She reported that she had developed melanoma at twenty‐five; that her mother, sister, aunts, and a cousin all had breast cancer; that a cousin had ovarian cancer at nineteen; and that a brother was treated for esophageal cancer at fifteen. The treating team was skeptical about this history, and they could find no documentation of the patient's reported melanoma. The surgeon wrote the (...) patient's primary care physician, explaining that he had seen the patient and planned to proceed with the bilateral mastectomy and reconstruction. The primary care physician responded that he was unable to substantiate several of the patient's claims; some of his colleagues believed the family history to be fabricated. Trying to make sense of the discrepancies, the genetic counselor called a counselor colleague who had met with this patient. The colleague suggested that the in‐house genetic counselor “google” the patient. The search revealed two Facebook pages linked to the patient. In one, apparently a personal profile, the patient stated that in addition to battling stage four melanoma, she had recently been diagnosed with breast cancer. She provided a link to a site where she solicited donations to attend a summit for young cancer patients. The other Facebook page featured numerous pictures of her with a bald head, as though she has been through chemotherapy. The genetic counselor showed the Facebook pages to the surgeon, who then decided not to operate. Should health care professionals “google” their patients? (shrink)

Gutes und Guter, Leben, Leib, Tugend - in diesem Band werden die Vortrage der ersten vier Symposien der Mainz Moral Meetings aus den Jahren 2009-2011 zu diesen Themen zusammengefasst. Ein interdisziplinarer Zugang durch Bibelwissenschaft, Judaistik, Altphilologie, Philosophie, Patristik, Systematische Theologie und weiteren Disziplinen eroffnet einen Blick auf die ethischen Normen des fruhen Christentums. Die Autoren der Beitrage fragen nach den Moglichkeiten von Norm und Normbegrundung einer fruhchristlichen Ethik in ausgewahlten Bereichen sowohl im Kontext antiker Philosophie als auch in gegenwartiger Verantwortung. (...) Mit Beitragen von: Jochen Althoff, Frederick D. Aquino, Wilhelm Blumer, Maximilian Forschner, Christian Hengstermann, Christoph Horn, Friedrich W. Horn, David Horrell, Manfred Lang, Sebastian Moll, Maren Niehoff, Jorg Roder, Eckart David Schmidt, Nikolaus Schneider, Lorenzo Scornaienchi, Notger Slenczka, Mira Stare, Gerd Theissen, Ulrich Volp, Jan G. van der Watt, Werner Zager, Ruben Zimmermann. (shrink)

We prove that the category of Nachbin’s compact ordered spaces and order-preserving continuous maps between them is dually equivalent to a variety of algebras, with operations of at most countable arity. Furthermore, we observe that the countable bound on the arity is the best possible: the category of compact ordered spaces is not dually equivalent to any variety of finitary algebras. Indeed, the following stronger results hold: the category of compact ordered spaces is not dually equivalent to any finitely accessible (...) category, any first-order definable class of structures, and any class of finitary algebras closed under products and subalgebras. An explicit equational axiomatisation of the dual of the category of compact ordered spaces is obtained; in fact, we provide a finite one, meaning that our description uses only finitely many function symbols and finitely many equational axioms. In preparation for the latter result, we establish a generalisation of a celebrated theorem by Mundici: our result—whose proof is independent of Mundici’s theorem—asserts that the category of unital commutative distributive lattice-ordered monoids is equivalent to the category of what we call MV-monoidal algebras.Abstract taken directly from the thesis.E-mail: marco[email protected]: https://air.unimi.it/retrieve/handle/2434/812809/1698986/phd_unimi_R11882.pdf. (shrink)

This symposium explores the boldest recommendation of the Institute of Medicine’s Committee on Increasing Rates of Organ Donation, namely, the recommendation that the U.S. consider a new population of potential donors. In its 2006 report, Organ Donation: Opportunities for Action, the committee recommended pilot programs in socalled “uncontrolled” donation after a circulatory determination of death. Potential uDCD donors have died from an unexpected loss of circulation, either due to sudden cardiac arrest or excessive blood loss following traumatic injury. Because circulation (...) is lost before death is determined and long before organ procurement could begin, potentially transplantable organs will die from oxygen starvation unless they are quickly preserved by cooling or other means. (shrink)

This symposium explores the boldest recommendation of the Institute of Medicine’s Committee on Increasing Rates of Organ Donation, namely, the recommendation that the U.S. consider a new population of potential donors. In its 2006 report, Organ Donation: Opportunities for Action, the committee recommended pilot programs in socalled “uncontrolled” donation after a circulatory determination of death. Potential uDCD donors have died from an unexpected loss of circulation, either due to sudden cardiac arrest or excessive blood loss following traumatic injury. Because circulation (...) is lost before death is determined and long before organ procurement could begin, potentially transplantable organs will die from oxygen starvation unless they are quickly preserved by cooling or other means. (shrink)

This article examines whether people share the Gettier intuition (viz. that someone who has a true justified belief that p may nonetheless fail to know that p) in 24 sites, located in 23 countries (counting Hong Kong as a distinct country) and across 17 languages. We also consider the possible influence of gender and personality on this intuition with a very large sample size. Finally, we examine whether the Gettier intuition varies across people as a function of their disposition to (...) engage in “reflective” thinking. (shrink)

Purpose – Does copyright protection reduce or foster intellectual and industrial creation? Based on a case study from history of science, the aim is to provide more controversial evidence to this debate. Design/methodology/approach – The investigation used primary and secondary sources from the history of science and made the link to the actual debate on copyright, piracy and scientific communication. Findings – The paper describes how Elzevier, through non-authorized exploitation of a new product and without consideration of the editor's legitimate (...) interests, in a context of missing copyright protection, largely contributed to the dissemination of the French Journal de Savants and its content, and finally to the success of scientific journals. Obviously, rights infringement can not only promote the interest and objective of the rights holder but also and above all contribute to the emergence and development of new forms of scientific life. Sometimes, when barriers to communication and debate are too strong, tolerated and calculated infringement may be an option to move the lines/change the situation. Research limitations/implications – In the post-Gutenberg galaxy, made up of open access, common goods and public domain, open data and e-Science, evaluation, innovation, sustainability, communication and sharing, copyright is not necessarily the option to develop scientific communication. At least, the authors have to study lessons from academic publishing, copyright protection and piracy very carefully. Originality/value – The paper sheds light on a surprising and not very well-known part of the history of academic publishing. (shrink)

Crispin Wright’s “Unified Strategy” for addressing some familiar sceptical paradoxes exploits a subtle distinction between two different ways in which we can be related to a proposition: (full-blown) belief and (mere) acceptance. The importance of the distinction for his strategy stems from his conviction that we cannot acquire any kind of evidence, either empirical or a priori, for the “cornerstones” of our cognitive projects, i.e., for those basic presuppositions of our inquiries that we must be warranted to endorse if we (...) are to claim warrant for any of the beliefs formed as a result of such inquiries: regarding the idea of a non-evidential warrant to believe a proposition as a kind of “conceptual solecism”, he doesn’t set himself the task of showing that we are evidentially warranted to believe such presuppositions, but only that of showing that we are non-evidentially warranted to accept them. In the present paper, I argue that such choice involves a fatal departure from a basic principle governing doxastic commitment—a principle that requires that we regard cornerstones propositions as propositions we are rationally committed to believe, not just entitled to accept. I press the point by presenting the Acceptance Argument, a sceptical paradox whose consideration leads to the conclusion that the Unified Strategy is caught between the Scylla of incoherently invoking a rather dubious form of epistemic alchemy and the Charybdis of placing an unexpected and apparently ad hoc restriction on the doxastic commitments we undertake by believing the things we believe. My final suggestion is that the Unified Strategy might be spared this dilemma only by undergoing a rather radical revision—a revision that would require setting aside the distinction between belief and acceptance to re-conceptualise its goal unabashedly in terms of (non-evidentially) warranted belief. (shrink)

Mr. Galanas, an eighty‐six‐year‐old man, intentionally shot himself in the chest and abdomen. Surprisingly, the bullet damaged only his distal pancreas and part of his colon, requiring a diverting colostomy to prevent leakage of bowel fluids into his abdomen. After being admitted, he lies intubated in the intensive care unit awaiting surgery to repair his colon. He is responsive but does not demonstrate clear decision‐making capacity. He grudgingly accepts pain medications but refuses antibiotics and antidepressants. He has a living will (...) that gives his wife durable power of attorney and also explicitly states a desire to refuse all medical interventions if he is permanently unconscious or in an end‐stage condition. Mrs. Galanas reports frequent conversations in which her husband said he would not want to be sustained on life support. She also says that he often mentioned he would not want an ostomy bag—a likely, albeit temporary, outcome of the proposed surgery. His physicians are nervous about withholding medical interventions when Mr. Galanas's injury is the result of a suicide attempt and his prognosis is good. Should the care team surgically repair his injured colon, regardless of the patient's capacity, his advance directive, and his wife's statement that he would not want surgery or other life‐sustaining treatment? (shrink)

Debates on the moral status of human embryos have been highly and continuously controversial. For many, these controversies have turned into a fruitless scholastical endeavor. However, recent developments and insights in cellular biology have cast further doubt on one of the core points of dissent: the argument from potentiality. In this article we want to show in a nonscholastical way why this argument cannot possibly survive. Getting once more into the intricacies of status debates is a must in our eyes. (...) Not merely intellectual coherence but the standing and self-understanding of current stem cell research might profit from finally taking leave of the argument from potentiality. (shrink)

This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...) to define the deductive limit to this hierarchy, that is, its greatest lower deductive bound. The calculus $ \mathcal {C}$min, stronger than $ \mathcal {C}$$\scriptstyle \omega$, is first presented as a step toward this limit. As an alternative to the bivaluation semantics of $ \mathcal {C}$min presented thereupon, possible-translations semantics are then introduced and suggested as the standard technique both to give this calculus a more reasonable semantics and to derive some interesting properties about it. Possible-translations semantics are then used to provide both a semantics and a decision procedure for $ \mathcal {C}$Lim, the real deductive limit of da Costa's hierarchy. Possible-translations semantics also make it possible to characterize a precise sense of duality: as an example, $ \mathcal {D}$min is proposed as the dual to $ \mathcal {C}$min. (shrink)