Ansgar Beckermann's account of self-consciousness can be seen as an attempt to locate the origin of self-conscious states in social cognition. It is assumed that in order to acquire self-consciousness, a cognitive system has to 'see itself through the eyes of the others'. This account, however, is doomed to failure, for principled reasons. It cannot provide a satisfactory explanation of the special, identification-free reference of first-person thoughts and, thus, fails to explain crucial features of attitudes. In addition, Beckermann's account exhibits (...) various other shortcomings. German Ansgar Beckermanns Theorie zur Erklärung von Selbstbewusstsein kann als exemplarischer Versuch verstanden werden, die Wurzeln selbstbewusster Zustände in sozialer Kognition zu suchen. Dabei wird angenommen, dass eine notwendige Bedingung zur Entwicklung von Selbstbewusstsein darin besteht, dass sich kognitive Wesen in sozialer Interaktion ,mit den Augen eines anderen sehen' lernen. Dieser Ansatz scheitert aber aus prinzipiellen Gründen, da er die besondere, identifikationsfreie Referenz von Ich-Gedanken nicht erklären kann und damit eine Erklärung wesentlicher Züge von de-se -Zuständen schuldig bleibt. Zudem ist Beckermanns Theorie im Besonderen durch einige weitere, grundlegende Unzulänglichkeiten gekennzeichnet. (shrink)

Research into voice perception benefits from manipulation software to gain experimental control over acoustic expression of social signals such as vocal emotions. Today, parameter-specific voice morphing allows a precise control of the emotional quality expressed by single vocal parameters, such as fundamental frequency (F0) and timbre. However, potential side effects, in particular reduced naturalness, could limit ecological validity of speech stimuli. To address this for the domain of emotion perception, we collected ratings of perceived naturalness and emotionality on voice morphs (...) expressing different emotions either through F0 or Timbre only. In two experiments, we compared two different morphing approaches, using either neutral voices or emotional averages as emotionally non-informative reference stimuli. As expected, parameter-specific voice morphing reduced perceived naturalness. However, perceived naturalness of F0 and Timbre morphs were comparable with averaged emotions as reference, potentially making this approach more suitable for future research. Crucially, there was no relationship between ratings of emotionality and naturalness, suggesting that the perception of emotion was not substantially affected by a reduction of voice naturalness. We hold that while these findings advocate parameter-specific voice morphing as a suitable tool for research on vocal emotion perception, great care should be taken in producing ecologically valid stimuli. (shrink)

El artículo busca dilucidar algunas características del epistolario en tanto que fuente historiográfica y encontrar claves de comparación con la autobiografía. Con importantes aspectos en común, sus propósitos, sus sesgos y la posición subjetiva de sus autores evidencian importantes diferencias. A partir de esta problemática, se analizará la correspondencia sostenida por Max Weber desde el servicio militar durante la Gran Guerra. En un período en el que no tiene intervención pública alguna, el análisis se centra en la evolución de su (...) perspectiva sobre el papel de Alemania y sobre su actividad específica en los lazaretos. Cada uno de estos aspectos se relaciona respectivamente con dos piedras angulares de la obra weberiana: el problema nacional y el proceso de burocratización. (shrink)

In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to (...) be identified with an infinite sequence of consequence relations holding between increasingly complex relata: formulae, inferences, metainferences, and so on. As a result, the present proposal allows not only to differentiate Classical Logic from ST, but also from other systems sharing with it their valid metainferences. Finally, we show how these results have interesting consequences for some topics in the philosophical logic literature, among them for the debate around Logical Pluralism. The reason being that the discussion concerning this topic is usually carried out employing a rivalry criterion for logics that will need to be modified in light of the present investigation, according to which two logics can be non-identical even if they share the same valid inferences. (shrink)

Visa-se neste artigo definir conceitos e divisões da filosofia elaborados no período chamado Renascimento. Analisa-se obras de Gregor Reisch, Benedetto Varchi e Francisco de Toledo, entre outros, para entender termos centrais como “filosofia”, “ciência” e “arte” e suas relações hierárquicas. Mostra-se que usos desses termos eram significativamente diversos de usos contemporâneos, e o uso de fontes da época visa simplificar e erradicar noções posteriores que não são necessárias para estudos históricos, de modo que se possa explicar questões que disciplinas contemporâneas (...) não explicam. Visa-se também fornecer instrumentos conceituais para pesquisas históricas. (shrink)

Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this (...) logic. In this paper, we show that this logic, once it is adequately understood, is weaker than classical logic. Moreover, the logic is in a way similar to the paraconsistent logic LP. (shrink)

Para explorar las diferencias significativas entre estos dos pensadores, la primera parte de este articulo considerará sus ideas ontológicas. Comenzando con su preocupación común por la multiplicidad, exploraremos el movimiento fundacional de Deleuze hacia diferentes tipos de multiplicidad. La crítica de Badiou a este enfoque estará relacionada con su defensa de los recursos abstractos de la teoría de conjuntos en oposición a las síntesis concretas con las que Deleuze busca comenzar. La segunda parte de este documento explorará las consecuencias de (...) los compromisos ontológicos de Deleuze cuando se trata de la ética del acontecimiento exigido por Badiou. El compromiso de Deleuze con el estoicismo proporcionará el escenario para su explicación de cómo ocurren los acontecimientos y representa una fuente de pensamiento y actividad. En la tercera y última parte se buscará evaluar la explicación de Deleuze sobre el papel de los acontecimientos en situaciones particulares y en las actividades de los sujetos que responden a estos. Esto nos permitirá sacar conclusiones sobre la crítica de Badiou a Deleuze y la capacidad de Deleuze para resistir estas críticas. Argumentaré que Deleuze comparte con Badiou la preocupación de mantener una visión clara del tema como una figura comprometida en la búsqueda de proyectos nuevos e inauditos que responden al llamado de los acontecimientos. (shrink)

Until now, North American and European philosophies have been engaged in debates about the possibility of a postmetaphysical philosophy and the consequences of the linguistic turn for the assessment of modernity; they have done so, however, without departing from the narrow horizons of their respective nationalistic perspectives. In this incisive critique, Dussel demonstrates how most of thse philosophies have either failed to give historically faithful analyses of the genesis of the "myth" of modernity, or have never engaged in a serious (...) questioning of their own Eurocentric presuppositions. He shows how North American and European philosophers have presupposed a no-longer-acceptable philosophy of history that has led them to fall into a "developmental fallacy," the belief that there is a linear sequence that moves from the premodern, underdeveloped, or on the way to industrialization, to the modern, developed, and industrialized. (shrink)

In some recent articles, Cobreros, Egré, Ripley, & van Rooij have defended the idea that abandoning transitivity may lead to a solution to the trouble caused by semantic paradoxes. For that purpose, they develop the Strict-Tolerant approach, which leads them to entertain a nontransitive theory of truth, where the structural rule of Cut is not generally valid. However, that Cut fails in general in the target theory of truth does not mean that there are not certain safe instances of Cut (...) involving semantic notions. In this article we intend to meet the challenge of answering how to regain all the safe instances of Cut, in the language of the theory, making essential use of a unary recovery operator. To fulfill this goal, we will work within the so-called Goodship Project, which suggests that in order to have nontrivial naïve theories it is sufficient to formulate the corresponding self-referential sentences with suitable biconditionals. Nevertheless, a secondary aim of this article is to propose a novel way to carry this project out, showing that the biconditionals in question can be totally classical. In the context of this article, these biconditionals will be essentially used in expressing the self-referential sentences and, thus, as a collateral result of our work we will prove that none of the recoveries expected of the target theory can be nontrivially achieved if self-reference is expressed through identities. (shrink)

In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...) alternative of our own. After that, we consider a number of objections to our account and evaluate a substantially different approach to the same problem. (shrink)

This book explains how the logic of theory change employs formal models in the investigation of changes in belief states and databases. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, and criticism of the model.

Entrevista com o Prof. Eduardo Jardim, Revisor técnico da edição brasileira de "Pensar sem corrimão", mais recente livro de Hannah Arendt no Brasil.

A theory of magnitudes involves criteria for their equivalence, comparison and addition. In this article we examine these aspects from an abstract viewpoint, by focusing on the so-called De Zolt’s postulate in the theory of equivalence of plane polygons (“If a polygon is divided into polygonal parts in any given way, then the union of all but one of these parts is not equivalent to the given polygon”). We formulate an abstract version of this postulate and derive it from some (...) selected principles for magnitudes. We also formulate and derive an abstract version of Euclid’s Common Notion 5 (“The whole is greater than the part”), and analyze its logical relation to the former proposition. These results prove to be relevant for the clarification of some key conceptual aspects of Hilbert’s proof of De Zolt’s postulate, in his classicalFoundations of Geometry(1899). Furthermore, our abstract treatment of this central proposition provides interesting insights for the development of a well-behaved theory ofcompatiblemagnitudes. (shrink)

When discussing Logical Pluralism several critics argue that such an open-minded position is untenable. The key to this conclusion is that, given a number of widely accepted assumptions, the pluralist view collapses into Logical Monism. In this paper we show that the arguments usually employed to arrive at this conclusion do not work. The main reason for this is the existence of certain substructural logics which have the same set of valid inferences as Classical Logic—although they are, in a clear (...) sense, non-identical to it. We argue that this phenomenon can be generalized, given the existence of logics which coincide with Classical Logic regarding a number of metainferential levels—although they are, again, clearly different systems. We claim this highlights the need to arrive at a more refined version of the Collapse Argument, which we discuss at the end of the paper. (shrink)

Many authors have considered that the notions of paraconsistency and dialetheism are intrinsically connected, in many cases, to the extent of confusing both phenomena. However, paraconsistency is a formal feature of some logics that consists in invalidating the rule of explosion, whereas dialetheism is a semantical/ontological position consisting in accepting true contradictions. In this paper, we argue against this connection and show that it is perfectly possible to adopt a paraconsistent logic and reject dialetheism, and, moreover, that there are examples (...) of non-paraconsistent logics that can be interpreted in a dialetheic way. (shrink)

In this paper, we present a non-trivial and expressively complete paraconsistent naïve theory of truth, as a step in the route towards semantic closure. We achieve this goal by expressing self-reference with a weak procedure, that uses equivalences between expressions of the language, as opposed to a strong procedure, that uses identities. Finally, we make some remarks regarding the sense in which the theory of truth discussed has a property closely related to functional completeness, and we present a sound and (...) complete three-sided sequent calculus for this expressively rich theory. (shrink)

From a scientific standpoint, the world is more prepared than ever to respond to infectious disease outbreaks; paradoxically, globalization and air travel, antimicrobial resistance, the threat of bioterrorism, and newly emerging pathogens driven by ecological, socioeconomic, and environmental factors, have increased the risk of global epidemics.1,2,3 Following the 2002–2003 severe acute respiratory syndrome (SARS), global efforts to build global emergency response capabilities to contain infectious disease outbreaks were put in place.4,5,6 But the recent H1N1, Ebola, and Zika global epidemics have (...) shown unnecessary delays and insufficient coordination in response efforts.7,8,9,10 In a thoughtful and compelling essay,11 Thana C. de Campos argues that greater clarity in the definition of pandemics would probably result in more timely effective emergency responses, and pandemic preparedness. In her view, a central problem is that the definition of pandemics is based solely on disease transmission across several countries, and not on spread and severity together, which conflates two very different situations: emergency and nonemergency disease outbreaks. A greater emphasis on severity, such that pandemics are defined as severe and rapidly spreading infectious disease outbreaks, would make them “true global health emergencies,” allowing for priority resource allocation and effective collective actions in emergency response efforts. Sympathetic to the position taken by de Campos, here I highlight some of the challenges in the definition of severity during an infectious disease outbreak. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

O artigo busca abordar o pensamento de Auerbach quanto ao romance do século XX, especificamente o que ele chama de romance realista. Realismo, representação, historicismo são alguns dos conceitos-chave para a compreensão do pensamento auerbachiano e cuja apresentação serve como abertura do artigo. A seguir há uma investigação das características do romance entreguerras tal como Auerbach o pensa. Finalmente faço a relação entre o projeto filológico e o tratamento que o filólogo dá ao romance do século XX.

Rejecting the Cut rule has been proposed as a strategy to avoid both the usual semantic paradoxes and the so-called v-Curry paradox. In this paper we consider if a Cut-free theory is capable of accurately representing its own notion of validity. We claim that the standard rules governing the validity predicate are too weak for this purpose and we show that although it is possible to strengthen these rules, the most obvious way of doing so brings with it a serious (...) problem: an internalized version of Cut can be proved for a Curry-like sentence. We also evaluate a number of possible ways of escaping this difficulty. (shrink)

I argue against Matthew Slater’s rejection of what he calls the grounding claim in his stable property cluster account of natural kinds. This claim states that the epistemic value of natural kinds depends on the existence of some ground to bind together a kind’s properties. Using two test cases from academic medicine, I show that grounds are genuinely explanatory of scientific epistemic practices and that the SPC account should not do without them in its philosophical analysis of natural kinds.

We study the algebraizability of the logics constructed using literal-paraconsistent and literal-paracomplete matrices described by Lewin and Mikenberg in [11], proving that they are all algebraizable in the sense of Blok and Pigozzi in [3] but not finitely algebraizable. A characterization of the finitely algebraizable logics defined by LPP-matrices is given.We also make an algebraic study of the equivalent algebraic semantics of the logics associated to the matrices ℳ32,2, ℳ32,1, ℳ31,1, ℳ31,3, and ℳ4 appearing in [11] proving that they are (...) not varieties and finding the free algebra over one generator. (shrink)

Why do humpback whales sing? This paper considers the hypothesis that humpback whales may use song for long range sonar. Given the vocal and social behavior of humpback whales, in several cases it is not apparent how they monitor the movements of distant whales or prey concentrations. Unless distant animals produce sounds, humpback whales are unlikely to be aware of their presence or actions. Some field observations are strongly suggestive of the use of song as sonar. Humpback whales sometimes stop (...) singing and then rapidly approach distant whales in cases where sound production by those whales is not apparent, and singers sometimes alternately sing and swim while attempting to intercept another whale that is swimming evasively. In the evolutionary development of modern cetaceans, perceptual mechanisms have shifted from reliance on visual scanning to the active generation and monitoring of echoes. It is hypothesized that as the size and distance of relevant events increased, humpback whales developed adaptive specializations for long-distance echolocation. Differences between use of songs by humpback whales and use of sonar by other echolocating species are discussed, as are similarities between bat echolocation and singing by humpback whales. Singing humpback whales are known to emit sounds intense enough to generate echoes at long ranges, and to flexibly control the timing and qualities of produced sounds. The major problem for the hypothesis is the lack of recordings of echoes from other whales arriving at singers immediately before they initiate actions related to those whales. An earlier model of echoic processing by singing humpback whales is here revised to incorporate recent discoveries. According to the revised model, both direct echoes from targets and modulations in song-generated reverberation can provide singers with information that can help them make decisions about future actions related to mating, traveling, and foraging. The model identifies acoustic and structural features produced by singing humpback whales that may facilitate a singer’s ability to interpret changes in echoic scenes and suggests that interactive signal coordination by singing whales may help them to avoid mutual interference. Specific, testable predictions of the model are presented. (shrink)

In 1997, I introduced the concept and the phrase “bio art”, originally in relation to my artwork “Time Capsule”. This work approached the problem of wet interfaces and human hosting of digital memory through the implantation of a microchip. The work consisted of a microchip implant, seven sepia-toned photographs, a live television broadcast, a webcast, interactive telerobotic webscanning of the implant, a remote database intervention, and additional display elements, including an X-ray of the implant. While “bio art” is applicable to (...) a large gamut of in vivo works that employ biological media, made by myself and others, in 1998, I started to employ the more focused term “transgenic art”. Republished in Ars Electronica ‘99—Life Science, ed. Gerfried Stocker and Christine Schopf, 289–296.) to describe a new art form based on the use of genetic engineering to create unique living beings. Art that manipulates or creates life must be pursued with great care, with acknowledgment of the complex issues it raises and, above all, with a commitment to respect, nurture, and love the life created. I have been creating and exhibiting a series of transgenic artworks since 1999. I have also been creating bio art that is not transgenic. The implications of this ongoing body of work have particular esthetic and social ramifications, crossing several disciplines and providing material for further reflection and dialog. What follows is an overview of theses works, the issues they evoke, and the debates they have elicited. (shrink)

Anti-exceptionalism about logic states that logical theories have no special epistemological status. Such theories are continuous with scientific theories. Contemporary anti-exceptionalists include the semantic paradoxes as a part of the elements to accept a logical theory. Exploring the Buenos Aires Plan, the recent development of the metainferential hierarchy of ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-logics shows that there are multiple options to deal with such paradoxes. There is a whole ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-based hierarchy, of which LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document} and ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} themselves are only the first steps. This means that the logics in this hierarchy are also options to analyze the inferential patterns allowed in a language that contains its own truth predicate. This paper explores these responses analyzing some reasons to go beyond the first steps. We show that LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {LP}}$$\end{document}, ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document} and the logics of the ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-hierarchy offer different diagnoses for the same evidence: the inferences and metainferences the agents endorse in the presence of the truth-predicate. But even if the data are not enough to adopt one of these logics, there are other elements to evaluate the revision of classical logic. Which is the best explanation for the logical principles to deal with semantic paradoxes? How close should we be to classical logic? And mainly, how could a logic obey the validities it contains? From an anti-exceptionalist perspective, we argue that ST\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {ST}}$$\end{document}-metainferential logics in general—and STTω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbf {STT}}_{\omega }$$\end{document} in particular—are the best available options to explain the inferential principles involved with the notion of truth. (shrink)

Who Comes After the Subject offers the most comprehensive overview to date of contemporary French thinking on the question of the "subject." Nineteen philosophers and critics offer diverse perspectives on the subject as it has manifested itself in our modern discourses: the subject of philosophy, of the State, of history, of psychoanalysis. Each contribution asks What has become of the subject? or What has the subject become? in the wake of its critiques and deconstructions .

The paper outlines an interpretation of one of the most important and original contributions of David Hilbert’s monograph Foundations of Geometry , namely his internal arithmetization of geometry. It is claimed that Hilbert’s profound interest in the problem of the introduction of numbers into geometry responded to certain epistemological aims and methodological concerns that were fundamental to his early axiomatic investigations into the foundations of elementary geometry. In particular, it is shown that a central concern that motivated Hilbert’s axiomatic investigations (...) from very early on was the aim of providing an independent basis for geometry. Accordingly, these concerns about an independent grounding for elementary geometry determined very clear methodological constraints in the process of embedding it into a formal axiomatic system. It is argued that Hilbert not only sought to show that geometry could be considered a pure mathematical theory, once it was presented as a formal axiomatic system; he also aimed at showing that in the construction of such an axiomatic system one could proceed purely geometrically, avoiding concept formations borrowed from other mathematical disciplines like arithmetic or analysis. (shrink)

In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...) a sheaf of MV-chains on a compact topological space. This result is intimately related to McNaughton’s theorem, and we explain why our representation theorem can be viewed as a vast generalization of McNaughton’s theorem. In spite of the language used in this abstract, we have written this paper in the hope that it can be read by experts in MV-algebras but not in sheaf theory, and conversely. (shrink)

In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other. Moreover, he also show that any such group G can be recovered from its segment since \^*}\), establishing an equivalence of categories. In “Interpretation of AF C (...) *-algebras in Lukasiewicz sentential calculus” Mundici extended this result to arbitrary MV-algebras and l-groups with strong unit. He takes the representation of A as a sub-direct product of chains A i, and observes that \ where \. Then he let A * be the l-subgroup generated by A inside \. He proves that this idea works, and establish an equivalence of categories in a rather elaborate way by means of his concept of good sequences and its complicated arithmetics. In this note, essentially self-contained except for Chang’s result, we give a simple proof of this equivalence taking advantage directly of the arithmetics of the the product l-group \, avoiding entirely the notion of good sequence. (shrink)