The logic of proofs was introduced by Artemov in order to analize the formalization of the concept of proof rather than the concept of provability. In this context, some operations on proofs play a very important role. In this paper, we investigate some very natural operations, paying attention not only to positive information, but also to negative information (i.e. information saying that something cannot be a proof). We give a formalization for a fragment of such a logic of proofs, and (...) we prove that our fragment is complete and decidable. (shrink)

Answering a question raised by Shavrukov and Visser :569–582, 2014), we show that the lattice of \-sentences ) over any computable enumerable consistent extension T of \ is uniformly dense. We also show that for every \ and \ refer to the known hierarchies of arithmetical formulas introduced by Burr for intuitionistic arithmetic) the lattices of \-sentences over any c.e. consistent extension T of the intuitionistic version of Robinson Arithmetic \ are uniformly dense. As an immediate consequence of the proof, (...) all these lattices are also locally universal. (shrink)

In the eighties of the nineteenth century Ubu comes into the world. Thanks to Alfred Jarry, in around ten years this imaginary tyrant with unrestrained longings will rise to an outstanding position in the Parisian theatrical arena. Ubu, anyway, is not a mere culture phenomenon: he is also – better, he is first of all – the outcome of an unprecedented and primitive reflection on power. So Ubu, from the beginning, is the embodiment of the excess, the expression of tyranny (...) as the childish power par excellence, driven by a bulimic imagination and dragged by overwhelming yearnings, always associated with the denial of any decorum and mediation. Ubu is, to a certain extent, one of the most prophetic and accurate anticipations of that imbalance between the autocrat’s longings and the endurance degree of the environment around him: a political pathology which will be the eminent and dramatic feature of the terrible catastrophes of the 20th century. Jarry’s work is even more significant when, in the last of its plays, describes an institutional system protected by a brittle glass bell, unbreakable only by those who hesitate to strike it, and an administrative apparatus so much subject to arbitrary power that it seems built «by the tyrant himself». (shrink)

It is universally recognized that in the fragments of Hipponax there are many references to Homer, in both language and content. In this paper I analyse the relationship between Hipponax’ poetic persona and the character of Odysseus.

This article reconstructs Habermas hypothesis that in the sacral complexity the rite precedes the myth and that could explain the permanence of religion as archaic source of solidarity even in the context of the secular world. Mythical narratives, in confrontation with science, shall lose the capacity to explain the world while the religious rites are still able to produce social integration and to collaborate for the construction of identities, at least for those who manifest such sensibility. Confrontation is stablished with (...) Charles Taylor positions, not directly about the hypothesis mentioned above but about the assumptions, that inspires it. Taylor sees the religious experience as generated in the present, an opening to transcendence of the internal modern immanent order, capable to offer therapy to pathologies of a modernity that, even accomplished great advances, has the risk of self-encapsulation. (shrink)

Journal Name: Philologus Issue: Ahead of print.

In this paper I analyze the rhetorical function of compositional neologisms in Cercidas’ versification, in order to provide a new semantical and/or syntactical explanation for single words that have not been correctly interpreted before. In particular I analyze the fragments 1.41–50 Lom., 2.25–7 Lom. and 60 Lom., focusing especially on the correct interpretation of τεθνακοχαλκίδης, συοπλουτοσύνη and μεταμελλοδύνη. At the end of the paper, final considerations on the rhetorical function of neologism in Cercidas’ text are offered.

Different summarized shape indices, like mean shape index (MSI) and area weighted mean shape index (AWMSI) can change over multiple size scales. This variation is important to describe scale heterogeneity of landscapes, but the exact mathematical form of the dependence is rarely known. In this paper, the use of fractal geometry (by the perimeter and area Hausdorff dimensions) made us able to describe the scale dependence of these indices. Moreover, we showed how fractal dimensions can be deducted from existing MSI (...) and AWMSI data. In this way, the equality of a multiscale tabulated MSI and AWMSI dataset and two scale-invariant fractal dimensions has been demonstrated. (shrink)

Guaspari (J Symb Logic 48:777–789, 1983) conjectured that a modal formula is it essentially Σ1 (i.e., it is Σ1 under any arithmetical interpretation), if and only if it is provably equivalent to a disjunction of formulas of the form ${\square{B}}$ . This conjecture was proved first by A. Visser. Then, in (de Jongh and Pianigiani, Logic at Work: In Memory of Helena Rasiowa, Springer-Physica Verlag, Heidelberg-New York, pp. 246–255, 1999), the authors characterized essentially Σ1 formulas of languages including witness comparisons (...) using the interpretability logic ILM. In this note we give a similar characterization for formulas with a binary operator interpreted as interpretability in a finitely axiomatizable extension of IΔ 0 + Supexp and we address a similar problem for IΔ 0 + Exp. (shrink)

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a natural mechanism (...) of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)

In her recent article “The Ontology of Social Groups”, Thomasson (Synthese 196:4829–4845, 2019) argues that social groups can be characterized in terms of the norms that surround them. We show that according to Thomasson’s normativity-based criterion, the dead constitute a social group, since there are widespread and well-defined social norms as to how to treat the dead, such as the norm expressed in the title (“Speak no ill of the dead”). We argue that the example of the dead must not (...) be interpreted as a counterexample to this criterion, and that, rather, there are good reasons to think of the dead as a genuine social group. Furthermore, the dead as a social group exist, regardless of whether or not the dead (i.e. the members of this social group) exist as persons. This view is clearly incompatible with the idea that social groups can be explained by citing features of their members, which is why we take the case of the dead to pose a challenge for the thesis of individualism. We consider the ontological implications of this example and suggest that social groups ought to be seen as reifications of social norms. Another implication of taking the dead to be a social group is that the presence of external norms is sufficient for the existence of a social group, and therefore internal norms are not necessary. We defend this implication against some potential theoretical and moral problems. (shrink)

Adrian Stokes , long admired by a small, highly distinguished, mostly English circle, was the natural successor to Pater and Ruskin. But though his place in cultural history is important, what is of particular interest now to art historians is his theory of the presentness of painting, a theory which offers a challenging critique of the practice of artwriting. From Vasari to the present, the most familiar rhetorical strategy of the art historian is the narrative of “the form, prophet-saviour-apostles,” in (...) which the first artist poses some problem that his successors develop and their successors solve.1 Such very different books as Art and Illusion and Art and Culture deploy that plan. The three periods of naturalism in E. H. Gombrich’s narrative—antiquity, Renaissance religious narrative, nineteenth-century landscape—function like Clement Greenberg’s sequence—old master art, early French modernism, American abstract expressionism. Gombrich and Greenberg disagree about how to narrate art’s history and about which works to include in that narrative—Gombrich asserts that cubism closes the canon while for Greenberg analytical cubism anticipates Jackson Pollock—but in each case, the art historian aims, as the novelist does, to tell a satisfying story and achieve narrative closure, and so how we think of the artworks the historian discusses depends in part upon the structure of the narrative. In a certain mood, we may find this fact intolerable. Why should a mere text tell us how to see the painting we may stand before?Stokes’ attempt to respond to this mood belongs to a tradition of early twentieth-century antihistorical thinking. For Rainer Maria Rilke, Rodin’s sculpture aimed to “refer to nothing that lay beyond it.” For Ezra Pound, an image “is real because we know it directly”; Henri Gaudier-Brzeska could read Chinese ideograms without knowing that language because those ideograms are transparently meaningful images. For Wyndham Lewis, a musical piece is inferior to a statue, “always there in its entirety before you.”2 Such an artwork need not be interpreted because it contains “within itself all that is relevant to itself.”3 All art is accessible to the gifted observer, and time is, in an interesting double sense, irrelevant. We see directly the meaning of works even from distant cultures; the visual artwork is experienced all at once, outside of time. If these claims are correct, what is the artwriter to do? Speaking of the Tempio Malatestiana, Hugh Kenner points to this issue:There is no description of the Tempio in accordance with good Vorticist logic: one art does not attempt what another can do better, and the meaning of the Tempio has been fully explicated on the spot by Agostino di Duccio with his chisel.4 1. Michael Baxandall, Giotto and the Orators: Humanist Observers of Painting in Italy and the Discovery of Pictorial Composition 1350-1450 , p. 75.2. Rainer Maria Rilke, Rodin, trans. Jessie Lemont and Hans Trausil , p. 19; Ezra Pound, Gaudier-Brzeska: A Memoir , p. 86; Wyndham Lewis, Time and Western Man , p. 174.3. Frank Kermode, Romantic Image , p. 107.4. Hugh Kenner, The Pound Era , p. 428. David Carrier, associate professor of philosophy at Carnegie-Mellon University, is coauthor, with Mark Roskill, of Truth and Falsehood in Visual Images and author of the forthcoming Artwriting, a study of recent American art criticism. He is working on a history of art history. (shrink)

A partir de los conceptos de carácter, virtud y amistad propuestos por la ética de la ficción de Wayne Booth, realizamos un análisis comparativo entre los efectos éticos provocados por el territorio y la música en las novelas Península, Península de Hernán Lara Zavala y en El llamado de los tunk’ules de Marisol Ceh Moo. Sugerimos que, a pesar de estar ante dos novelas que comparten el mismo contexto geo-histórico, los efectos éticos causados por el territorio y la música, bajo (...) la idea de Yucatán, guardan diferencias que ameritan llevar a cabo una co- ducción para dilucidar el tipo de compañía literaria que nos ofrecen. (shrink)