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 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)

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

Im Hinblick auf den Herbrand'schen Satz für die Prädikatenlogik der ersten Stufe und auf die Lehre vom Beweisverfahren mit Rechenautomaten, die daraus folgt, wird ein Beweis als komputazional synthetisch bezeichnet, wenn er sich auf Objekte bezieht, die im erwiesenen Satz nicht erwähnt sind. Die mathematischen Beweise sind aber auch synthetisch in einem begrifflichen Sinne: die Kontrolle oder die Begrenzung der angewandten Begriffe — die sogenannte Methodenreinheit — ist im allgemeinen unerreichbar.

We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...) and Lettieri (Math Logic Q 1:27–43, 2011). (shrink)

Les sciences cognitives poursuivent un objectif fort ancien, qui consiste, sommairement dit, à décrire et à expliquer les comportements intelligents. Elles appliquent à cet effet des principes méthodologiques moins traditionnels, dont l'adoption définit ce qu'il est convenu d'appeler le "tournant cognitif". Je me propose ici d'exposer brièvement ces principes, de les illustrer par des exemples appropriés et d’en discuter la signification philosophique. Pour l’essentiel, j’ai mis en avant un domaine qui me semble particulièrement pertinent pour les philosophes: l'analyse de la (...) catégorisation, c'est-à-dire du processus par lequel un ensemble d'entités (stimuli sonores ou visuels, objets concrets ou abstraits) en vient à être classifié en catégories séparées, qui peuvent être de type perceptif (phonèmes, couleurs) ou conceptuel (espèces naturelles, types d'événements, catégories esthétiques et morales). (shrink)

Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...) characterized. (shrink)

An explicit categorical equivalence is defined between a proper subvariety of the class of \-algebras, as defined by Di Nola and Dvurečenskij, to be called \-algebras, and the category of semi-low \-rings. This categorical representation is done using the prime spectrum of the \-algebras, through the equivalence between \-algebras and \-groups established by Mundici, from the perspective of the Dubuc–Poveda approach, that extends the construction defined by Chang on chains. As a particular case, semi-low \-rings associated to Boolean algebras are (...) characterized. (shrink)

Book Review: Dubucs, J., & Bourdeau, M.. Constructivity and Computability in Historical and Philosophical Perspective. Springer Netherlands, XI. 214, pp. ISBN: 978-94-017-9216-5 978-94-017-9217-2, €83.29.

Since the ground-breaking contributions of M. Dummett (Dummett 1978), it is widely recognized that anti-realist principles have a critical impact on the choice of logic. Dummett argued that classical logic does not satisfy the requirements of such principles but that intuitionistic logic does. Some philosophers have adopted a more radical stance and argued for a more important departure from classical logic on the basis of similar intuitions. In particular, J. Dubucs and M. Marion (?) and (Dubucs 2002) have (...) recently argued that a proper understanding of anti-realism should lead us to the so-called substructural logics (see (Restall 2000)) and especially linear logic. The aim of this paper is to scrutinize this proposal. We will raise two kinds of issues for the radical anti-realist. First, we will stress the fact that it is hard to live without structural rules. Second, we will argue that, from an anti- realist perspective, there is currently no satisfactory justi cation to the shift to substructural logics. (shrink)

The imagery we adopt when recalling the personal past may involve different perspectives. In many cases, we remember the past event from our original point of view. In some cases, however, we remember the past event from an external “observer” perspective and view ourselves in the remembered scene. Are such observer perspective images genuine memories? Are they accurate representations of the personal past? This chapter focuses on such observer perspectives in memory, and outlines and examines proposals about the nature of (...) such imagery. (shrink)

Hasdai Crescas fue un importante pensador, autor y líder comunitario judío de finales del siglo XIV y principios del XV, cuyas obras son estudiadas con detalle en el mundo académico. No obstante, su impacto sobre la comunidad judía tradicional ha sido casi inexistente. Nunca terminó su obra legal, la que podría haber tenido impacto en los judíos tradicionales. Sus escritos filosóficos conservados son difíciles de seguir; solo sobrevive una de las dos polémicas anticristianas vernáculas, en una traducción/paráfrasis hebrea. Aunque Crescas (...) fue bien recordado en el siglo posterior a su muerte, ya en este período se pueden detectar las razones de su posterior olvido. Un examen de la historia de la recepción de la obra de Crescas en el siglo XV demuestra hasta qué punto sus posiciones polémicas, dogmáticas y filosóficas fueron mayoritariamente rechazadas, más allá de que tuvo partidarios, fundamentalmente entre sus alumnos más cercanos. No es de extrañar, entonces, que en los siglos posteriores, la memoria de Crescas fuera casi borrada de la conciencia comunitaria judía. (shrink)

In this paper, I discuss the work of W. E. B. Du Bois to expose the disastrous effects of white supremacy in the U.S. and the world. While his early works suggest that white supremacy might be rehabilitated by the careful presentation of contrary evidence, in later works he catalogs the primary features of whiteness, including an infantile comportment, a pathological attachment to innocence, and an epistemic incapacity to absorb evidence of its own error. To capture the scope of the (...) delusion of whiteness on Du Bois’s account, I suggest the term “irrevocable license.” The remainder of the paper uses Du Bois’s account to examine the case of a “Karen”—a white woman who obliviously and inappropriately interferes with the lawful actions of a family of color—and further considers police violence against people of color as an outgrowth of white irrevocable license. (shrink)

We present PhrasIS, a benchmark dataset composed of natural occurring Phrase pairs with Inference and Similarity annotations for the evaluation of semantic representations. The described dataset fills the gap between word and sentence-level datasets, allowing to evaluate compositional models at a finer granularity than sentences. Contrary to other datasets, the phrase pairs are extracted from naturally occurring text in image captions and news headlines. All the text fragments have been annotated by experts following a rigorous process also described in the (...) manuscript achieving high inter annotator agreement. In this work we analyse the dataset, showing the relation between inference labels and similarity scores. With 10K phrase pairs split in development and test, the dataset is an excellent benchmark for testing meaning representation systems. (shrink)

Polyphony of Anxiety. The Interview with Stefano Micali about His Book Phenomenology of Anxiety.

In lieu of an abstract, here is a brief excerpt of the content:570 BOOK REVIEWS like reasonable rule for economic life. This effort is worthy of more attention than is possible here, but let it be noted that it must inevitably suffer the same fate as any ethical calculus: someone must decide for others what is their due and what is not. How much wealth, for example, makes for a concentration [of wealth] that would be " demonstrably detrimental to some (...) people's exercise of their generic rights "? His is ultimately an entitlement or rights ethic, rather than an aitial ethic of goal-purposive fulfillment for the individual, projected outwards for a common good scenario. While his rejection of goal ethics's inability to detail principles for distribution of goods is noteworthy, it does not appear that a tightened version of generic rights theory will come closer to either of Phillips's desiderata: a justification of moral reasoning apart from any theory of nature or a calculus for its application. Desan and Phillips wish to think against the limits of the human situation. For Desan, rising above limitation is a moral task and obligation facing us each, if there is to be a common future. His call is to be World Citizen in a Polis of Nations. Phillips's vision is more concrete, a distribution of benefits to benefit all with well-being and freedom. But this mundane task is no less difficult than Desan's transcendent one. Indeed, according to Augustine, even the Divine Mind must utilize an artifice in dealing with human creation: "He loves each of us as though there were only one of us." Both ethicists have striven to show us how we might think this vision for ourselves, i.e., for each other of us. ]OIIN B. DAVIS, O.P. ' Detroit, Michigan Catholics, Anglicans, and Puritans: Seventeenth-Century Essays. By HUGH TREVOR-ROPER. Chicago: The University of Chicago Press, 1988. Pp. xiii + 317. $27.50 (hardbound). Even to list the changes and events which occurred in seventeenth century England is a difficult task: the century spans the period from the death of Queen Elizabeth to the Glorious Revolution and beyond, through the Civil War, the accession and exile (twice) of the Stuarts, the rise of science, the transformation of the theological and religious issues of the English Reformation, to name only the most obvious. To conceive a book, in the form of occasional essays, which not only addresses these changes and events but does so by establishing the connections which were present with European currents at the same time surely tempts fate, even when it does not tempt reviewers. BOOK REVIEWS 571 But Hugh Trevor-Roper is a master, both of the period under survey and of the form of the essay. With one exception, each of these essays began as a lecture or seminar paper, and the pleasantly legible style in which they are written must bear some trace of that origin. The occasional flashes of wit, mixed with rthe fairly non-technical style, make the book a joy to read and a welcome escape from the usually constipated style of scholarly prose. In his Introduction, the essayist clearly sets forth his thesis that English intellectual history does not exist apart from the currents of European intellectual history (a thesis for which Trevor-Roper has already staked a claim). That leads to what may very well be the major problem with these essays: its end is in its beginning. The list of names cited in these essays only partially coincides with the list of names in the index; the former is much longer than the latter. And while the style of the essay welcomes the reader to the period, it also throws up more names and places and events than can be explained or even annotated adequately. This occurs both on a large and on a small scale. The first essay, on "Nicholas Hill, the English Atomist" contains such a vast array of names that at times it becomes the prosopo· graphical equivalent of a telephone book. On a large scale, there is the problem with a definition of Arminianism. No definition, at least no formal definition, is attempted-and this is probably wise. But, particularly in... (shrink)

The lives of children who live at the intersectional nexus between childhood autism and race may be considered as “shadow stories” that have remained silenced in autism literature. We explored the experiences of racialized parents who provide care to autistic children. We drew on a theoretical framework known as DisCrit and decolonizing arts-based methodologies. Racialized parents of autistic children demonstrated resistance along various themes, including fighting the system, protecting my child, and creating cultural communities. We join black girlhood studies, critical (...) race theory, and disabled children’s childhood studies by continuing the journey of decentering Whiteness in childhood disability research. We demonstrate how disabled racialized communities engage in activism and social justice while forming powerful counter-discourses. (shrink)

This book explores both scientific and humanistic theoretical traditions in anthropology through the lens of ontology. The first part of the book examines different methods for generating valid anthropological knowledge, and proposes a shift in current consensus. Drawing on western scholars of antiquity and the medieval period and moving away from twentieth century theorists, it argues that we must first make ontological assumptions about the kinds of things that can exist (or not) before we can then develop epistemologies that study (...) those kinds of things. The book goes on to apply the ontology-first theory to a set of case studies in modern day conspiracy theories, misinformation, and magical thinking. It asserts that we need to move away from unneeded metaphysical assumptions of conspiracy theories being misinformation, and argues that reconstructing particular historical events can be a fruitful zone for application of quantitative methods to humanistic questions. Theorizing the Anthropology of Belief is an excellent supplementary suitable for upper-level undergraduate and graduate courses in anthropological theory. (shrink)

Republicans consider freedom as non-domination an attractive political ideal for a modern pluralistic society that cannot be found in liberalism. This book shows how this view is untenable. By analysing freedom as non-domination as it is understood by contemporary republicans, the book rejects the widely held view that this freedom concept is superior to liberal understandings of freedom as non-interference. In fact, setting up institutions to promote non-domination is shown to also promote non-interference. The book demonstrates how it is the (...) focus on making an ideal suitable for a modern society that leads republicans to a view of freedom with no normative insight that cannot also be found in liberalism. However, the book also shows how republicans can adjust their freedom ideal so that it actually offers a distinctly republican contribution to political philosophy. By understanding freedom to require that citizens commit to an especially high level of political participation to deny powerholders opportunities to act against the common good, republicans can reject liberalism and freedom as non-interference. But this freedom ideal does not respect the many citizens in a modern society whose conceptions of a good life do not involve such a high level of political engagement. Republicans therefore face a dilemma: They can promote a freedom ideal suited for modern conditions, but they then end up endorsing a liberal theory promoting freedom as non-interference. Alternatively, they can promote a distinct freedom ideal, but this ideal will be unsuited for a modern society. (shrink)

This chapter examines so-called body image disorders, focusing on body dysmorphic disorder, anorexia nervosa, bulimia nervosa, and binge eating disorder. These disorders have been studied extensively by psychologists and psychiatrists from both the "body image" and "body shame" research orientations. Body image disorders have also proved, for feminist thinkers mindful of the gender imbalance in many of these disorders, to be an important locus for cultural criticism, including criticism of psychological and psychiatric perspectives. Those philosophers and anthropologists with a phenomenological (...) bent, particularly those with an interest in the lived body and embodiment, have also found a fruitful terrain in body image disorders. These different disciplines and approaches provide multiple perspectives which are often complementary, occasionally in some tension with one another, but always mutually enriching, and all of them are sketched here. (shrink)