Recently discovered correspondence from Oskar Becker to Hermann Weyl sheds new light on Weyl's engagement with Husserlian transcendental phenomenology in 1918-1927. Here the last two of these letters, dated July and August, 1926, dealing with issues in the philosophy of mathematics are presented, together with background and a detailed commentary. The letters provide an instructive context for re-assessing the connection between intuitionism and phenomenology in Weyl's foundational thought, and for understanding Weyl's term ‘symbolic construction’ as marking his own considered position (...) in the foundational controversy of the 1920s. In addition, they reveal Weyl's hitherto unknown objections to Becker's detailed attempt (Mathematische Existenz, 1927) to ground the transfinite phenomenologically. (shrink)

An algebraization of the notion of topology has been proposed more than 70 years ago in a classical paper by McKinsey and Tarski, leading to an area of research still active today, with connections to algebra, geometry, logic and many applications, in particular, to modal logics. In McKinsey and Tarski’s setting the model theoretical notion of homomorphism does not correspond to the notion of continuity. We notice that the two notions correspond if instead we consider a preorder relation \( \sqsubseteq (...) \) defined by \(a \sqsubseteq b\) if _a_ is contained in the topological closure of _b_, for _a_, _b_ subsets of some topological space. A _specialization poset_ is a partially ordered set endowed with a further coarser preorder relation \( \sqsubseteq \). We show that every specialization poset can be embedded in the specialization poset naturally associated to some topological space, where the order relation corresponds to set-theoretical inclusion. Specialization semilattices are defined in an analogous way and the corresponding embedding theorem is proved. Specialization semilattices have the amalgamation property. Some basic topological facts and notions are recovered in this apparently very weak setting. The interest of these structures arises from the fact that they also occur in many rather disparate contexts, even far removed from topology. (shrink)

Two mereological theories are presented based on a primitive apartness relation along with binary relations of mereological excess and weak excess, respectively. It is shown that both theories are acceptable from the standpoint of constructive reasoning while remaining faithful to the spirit of classical mereology. The two theories are then compared and assessed with regard to their extensional import.

In the present paper we discuss a recent suggestion of Schroeder-Heister concerning the possibility of defining an intensional notion of harmony using isomorphism in second-order propositional logic. The latter is not an absolute notion, but its definition is relative to the choice of criteria for identity of proofs. In the paper, it is argued that in order to attain a satisfactory account of harmony, one has to consider a notion of identity stronger than the usual one (based on β- and (...) η-conversions) that the authors have investigated in recent work. (shrink)

In previous work by Baaz and Iemhoff, a Gentzen calculus for intuitionistic logic with existence predicate is presented that satisfies partial cut elimination and Craig's interpolation property; it is also conjectured that interpolation fails for the implication-free fragment. In this paper an equivalent calculus is introduced that satisfies full cut elimination and allows a direct proof of interpolation via Maehara's lemma. In this way, it is possible to obtain much simpler interpolants and to better understand and overcome the failure of (...) interpolation for the implication-free fragment. (shrink)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

In the lively discussions on Galileo's laws of motion after the Pisan's death, we observe what might be called a new “Galilean affair.” That is, a trial brought against his new science of motion mainly by French and Italian Jesuits with the substantial adherence of M. Mersenne. This new trail was originated by Gassendi's presentation of Galileo's de motu not simply as a perfectly coherent doctrine, but also as a convincing argument in favor of the truth of Copernicanism.

This article provides an overview of philosophical interpretations of Dostoevsky, focusing on readings that pay particular attention to his representation of the battle between good and evil, and postulating that said representation constitutes the essence of his works. The analysis maps this history of interpretations as developing within a specific framework: the dispute between interpreters who argue that good triumphs in Dostoevsky’s works and those who maintain that nihilism prevails in the end. In this context, the article submits its own (...) thesis: that a fundamental contradiction haunts the offer, in Dostoevsky’s works, of Christian salvation, and condemns Dostoevsky to defeat at the hands of his nihilists. (shrink)

We present a sequent calculus for extensional mereology. It extends the classical first-order sequent calculus with identity by rules of inference corresponding to well-known mereological axioms. Structural rules, including cut, are admissible.

This paper aims to foster an interdisciplinary dialogue between Ricoeur’s phenomenological- hermeneutical thought and human geography, in particular with respect to the issue of landscape interpretation. The connection draws on the idea that landscapes and lived spaces can be read as texts, not unfamiliar to human geography and semiotics from 1980s onward. In the first part of the paper I will briefly expound some theories of landscape which make use of the metaphors “landscape as cultural image” and “landscape as text” (...) in human and cultural geography. Then, I will discuss the main contribution of Ricoeur to the issue of space. The philosopher already envisioned a possible application of his “threefold mimesis” of Time and Narrative to architectural spaces. In the conclusion, I will propose to rejuvenate the geographical metaphor of “landscape as text” by introducing a possible application of the Ricoeurian notion of “meaningful action as text” to landscape. (shrink)

This paper is the first of a series of three articles that present the syntactic proof of the PA-completeness of the modal system G, by introducing suitable proof-theoretic objects, which also have an independent interest. We start from the syntactic PA-completeness of modal system GL-LIN, previously obtained in [7], [8], and so we assume to be working on modal sequents S which are GL-LIN-theorems. If S is not a G-theorem we define here a notion of syntactic metric d(S, G): we (...) calculate a canonical characteristic fomula H of S (char(S)) so that ⊢G ∼ H → (∼S) and ⊢GL-LIN ∼ H, and the complexity σ of ∼ H gives the distance d(S, G) of S from G. Then, in order to produce the whole completeness proof as an induction on this d(S, G), we introduce the tree-interpretation of a modal sequent Q into PA, that sends the letters of Q into PA-formulas describing the properties of a GL-LIN-proof P of Q: It is also a d(*, G)-metric linked interpretation, since it will be applied to a proof-tree T of ∼ H with H = char(S) and σ(∼ H) = d(S, G). (shrink)

RESUMO O artigo propõe uma releitura cruzada dos conceitos de acidente, desenvolvido por Landowski no âmbito de sua teoria sociossemiótica da interação, e explosão, elaborado por Lotman em seus últimos escritos de semiótica da cultura. Longe de ser um fim em si mesmo, este confronto almeja esboçar uma síntese teórico-epistemológica que possa contribuir à análise dos processos comunicacionais-discursivos que regem o devir dos sistemas socioculturais, bem como ao seu enquadramento conceitual. A minha hipótese é que a cifra desta articulação resida (...) no vínculo entre a indeterminação destacada por ambos os autores e a carga estésica, isto é, o núcleo de tensões sensíveis que, conforme vislumbra Landowski, os acontecimentos acidentais/explosivos são capazes de mobilizar. Para procurar demonstrar sua pertinência e relevância, partirei de um caso concreto: as jornadas de junho de 2013 e seu impacto no processo que levou, em 2016, ao impeachment de Dilma Rousseff e, em 2018, à eleição de Jair Bolsonaro. ABSTRACT The article proposes a comparison between the concepts of accident, developed by Landowski in his sociosemiotic theory of interaction, and explosion, elaborated by Lotman in his last writings on the semiotics of culture. Far from being an end in itself, this confrontation aims to sketch a theoretical-epistemological synthesis that can contribute to the analysis of the communicational-discursive processes that trigger the historical flow of sociocultural systems, as well as to their conceptual categorisation. My hypothesis is that the basis of this articulation lies in the link between the indeterminacy highlighted by both authors, and the aesthesic value, that is, the core of sensible tensions that, as shown by Landowski, the accidental/explosive events could mobilise. In order to demonstrate its pertinence and relevance, I will focus on a specific case study: the 2013 protests in Brazil and their impact on the process that led to the impeachment of Dilma Rousseff in 2016 and the election of Jair Bolsonaro in 2018. (shrink)

Ce texte examine l’affirmation d’Aristote qui se trouve dans les Seconds Analytiques II 19, que la perception porte sur l’universel. L’examen s’effectuera par le biais du De Anima II 6 et III 6-8 où Aristote décrit les objets de la perception et de l’intellect. L’auteur soutient que selon Aristote, la perception humaine porte toujours sur l’universel contenu dans le particulier parce que l’unité de la substance individuelle est garante de l’unité de l’acte de perception. Par conséquent, l’analyse en termes de (...) trois objets de perception n’est que le résultat de la méthode analytique qu’Aristote emploie afin d’étudier l’acte de perception. (shrink)

The question of how, according to Aristotle, the principles of science are acquired remains contested among scholars. An aspect of this broader topic concerns the role of induction, and whether it is able to provide us with knowledge of natural necessity without the assistance of intuition. In a recent publication in this journal, David Botting argues in favour of the enumerative/empiricist interpretation of induction and criticizes the intuitive/rationalist interpretation of it, a version of which was defended in one of my (...) publications. He thinks that Aristotle is like Hume: both understand the cognitive process of induction similarly; and, both are equally skeptical about acquiring knowledge of natural necessity through induction. My reply argues that reading Aristotle’s induction in Humean terms is problematic in several respects. I argue, in addition, that natural necessity can be known through induction if nous is involved. My explanation of how this is possible relies on thinking of the act of noēsis in terms of an act of recognition. Botting claims, furthermore, that Aristotle only differs from Hume in that the former does have a non-inductive and non-intuitive method by which natural necessity may become known, and which Botting calls “the constructive proof of necessity”. My reply examines this method, showing how certain steps in it rely on cognitive acts that are really acts of intuition merely expressed in Humean terms. Despite the criticisms, I end with suggestions for how Botting’s account might offer original paths of research to Aristotle scholars seeking to answer the question of the acquisition of principles of science, particularly in the early stages of this process. (shrink)

Marxist social scientists have argued that the relationship between social and technical change is one of mutual interaction; innovation in the modes of production affects social organization, and social organization, in turn, has an impact on the development of novel modes of production. This consideration is of fundamental importance for the construction of any economic development policy. However, analyses of this critical relationship have been elaborated within a conceptual framework which most social scientists and policy makers who work within the (...) framework of neoclassical economic thought find difficult to understand. When marxists argue that technical innovations are the product of a class conflict, non-marxist social scientists are left wondering about what the exact meaning of such a statement. Because marxists have been unable to communicate their message, their important insights into the relation between social and technical change have not been incorporated in contemporary development policy; this situation has often resulted in great social costs. In the past fifteen years, however, Yujiro Hayami and Vernon Ruttan have attempted to analyze the critical interaction of social and technical change using neo-classical economic concepts. I argue that their approach can be utilized to express marxist insights in a language accessible to non-marxist social scientists. The careful and critical adoption of this approach could provide the grounds for a more fruitful dialogue about the interaction of social and technical change, and aid the construction of a new development policy. (shrink)

In "The Measure of the Mental" (Davidson 1990), replying to a series of criticisms, that grow out of inadvertence or misunderstanding, Davidson has revisited his thesis concerning the physical and the mental, which he called "anomalous monism" (henceforth, AM). The thesis is subtle and elusive, as it is most often the case with Davidson: there is only one kind of event and state, which has a physical description (i.e., a description in physical terms) and may have a mental description too (...) (i.e., a description in mental terms) -- that shows the monism. But there is no strict law to go from a mental to a physical description of events and states or vice versa -- that shows the anomalousness.This sophisticated third way captures the intuition, generally shared today, that we are physical machines, whereas it acknowledges the mind a peculiarity: the mental is identical with a part of the physical, but no part of the mind is specifically identifiable with any part of the physical; or, more weakly, each mental event or state is identical with a physical one, though there is no systematic way to connect the mental and the physical. (shrink)

Recent crises in Europe and beyond have renewed a longstanding debate on the status and treatment of refugees. Hannah Arendt famously questioned the limits of universalistic human rights discourse based on the widespread phenomena of statelessness and displacement that emerged during and after World War II. In this paper, we analyze recent patterns of inclusion and exclusion of refugees in Italy through the lens of Arendtian narrative and theorizing. We consider three cases of interaction between families, schools, and other public (...) institutions in light of the shifting normative framework before and during the war in Ukraine. Two major insights emerge from this analysis. From a pedagogical point of view, the most promising educational practices with refugees are those centered on enabling their agency and corresponding experiences of "natality". From an ethical-political perspective, these practices highlight a latent tension between the universalistic scope of human rights enshrined in the human rights declarations and their structural dependence on the particular norms and procedures enacted by nation states. The understanding and teaching of human rights within our political communities is inseparable from the practices that engage with refugees. In this sense, our practices of inclusion and exclusion affect the understanding of national borders as a barrier or threshold with other political communities, but also the interpretation of our own ethical-political principles. (shrink)

The purpose of this paper is to contribute to shed some light on the early Stoics' practice of managing platonic suggestions to construct their epistemology. Instances of such a practice, which scholars have recently focussed on, are the Stoic reassessment of the account of phantasia Plato offers in the Sophist and the image of the wax block as discussed in the Theaetetus. In this work I put forward a comparison between the simile of the soul-book, as presented by Socrates in (...) the Philebus (39a1-c2), and the Stoic image of the soul as a sheet in which conceptions are inscribed. I try to show that a far-reaching investigation of the relationship between Plato and early Stoic epistemology should take such a comparison into due account. In section one, I go into the details of the comparison and argue that Plato's perceptual judgment (this is how I translate the term doxa as it is used in the relevant section of the Philebus) is compatible with Stoic phantasia. In section two, I try to show that the theorisation of assent enable the Stoics to reply to an objection Aristotle made to Plato's definition of phantasia as a mixture of perception and judgment. (shrink)

We present a cut-free sequent calculus for a class of first-order theories in negation normal form which include coherent and co-coherent theories alike. All structural rules, including cut, are admissible.

The aim of this paper is to say something significant about Stanley Cavell's style. To accomplish this task, we adopt a distant reading approach, quantifying what seems to be an idiosyncratic use of parentheses. After outlining our methodological approach and the choices of texts from Cavell's corpus, we will present the results of our quantitative analysis. Two kinds of results will be presented and interpreted: the result of a comparison between Cavell and other authors (i.e. why Cavell's use of parentheses (...) is exceptional) and the result of a quantitative analysis of Cavell's texts (i.e. how Cavell uses parentheses throughout his books). For both results, we will provide our own interpretation. In the conclusion, we will draw the moral of this parenthetical story, hoping to open future parentheses. (shrink)

The specific complexity of the question of genres depends on the plurality of the problems to which genre is pertinent and relevant. When Croce proclaimed, at the beginning of the century, the non-existence of the genre, he reduced the entire range of problems to the sole question relative to a work's belonging to a genre. In more recent times, there has been an attempt to reduce genre to the property of the linguistic act, in a methodological framework that understands poetics (...) exclusively as the science of literature. Against such reductionism, it is important to keep in mind a wider, more articulated idea of poetics as a pragmatic meditation, to investigate genres according to the multiple lines of systematization that are pertinent to them. (shrink)

Towards the end of The Coming Community (1993) [La comunità che viene, 1990], Giorgio Agamben writes something that may be interpreted as a paraphrase of Franz Kafka's famous statement that while t...

This paper explores the death of God narrative through the lens of kenosis, drawing insights from thinkers such as Marcel, Heidegger, Vattimo, and Girard. It investigates the implications of kenotic thought for contemporary religious and philosophical discourse, exploring various interpretations of kenosis, ranging from Altizer and Žižek’s apocalyptic views to Vattimo’s more hopeful perspective. Through critical engagement with these viewpoints, this paper advocates for a nuanced understanding of kenosis inspired by Hegel, one that bypasses both radical theology and excessive optimism. (...) Methodologically, this study adopts a hermeneutic approach, analyzing key texts and engaging in philosophical dialogue. This paper concludes that rethinking kenotic thought could provide a robust framework for grappling with the death of God in the contemporary context, offering avenues for ethical reflection, social critique, and speculative renewal. (shrink)

[ES] El artículo es una introducción a un nuevo enfoque para la filosofía de las matemáticas, conocido con el nombre de «la filosofía de la práctica matemática». El nuevo enfoque encontró su expresión en la colección La Filosofía de la Práctica Matemática editada por el autor. El artículo sitúa la «filosofía de la práctica matemática» dentro del contexto de otras tradiciones en la filosofía de las matemáticas y traza las similitudes y diferencias con estas tradiciones. [EN] The article is an (...) introduction to a new approach to the philosophy of mathematics that goes under the name of «the philosophy of mathematical practice». The new approach found its expression in the collection The Philosophy of Mathematical Practice edited by the author. The article situates the «philosophy of mathematical practice» within the context of other traditions in the philosophy of mathematics and outlines the similarities and differences with those traditions. (shrink)

A default theory can be seen as a way for representing a set of formulae, i.e., its extensions. In this paper, we characterize the sets of formulae that can be expressed by a default theory according to various semantics: justified, constrained, rational, cumulative, QDL, CADL, and two semantics with priorities. These characterizations imply some non-translatability results between semantics.

The purpose of this paper is 1) to focus on the last section of the In Parmenidem, analyzing Proclus’ reflection on the relationship between the First God and what he calls the “axioms of contradiction”, accompanied by an attempt to harmonize in a subordinate sense the Aristotelian perspective with the Platonic one; 2) to analyze the reception of this idea in Nicholas of Cusa, the first Latin author to be systematically influenced by the In Parmenidem. It will be possible to (...) show how Cusanus develops a perspective that, on the one hand, finds its explicit antecedent in Proclus and, on the other, how he radicalizes Proclus’ perspective, developing theoretical tensions that we can find unsystematically in Proclus’ own thought. Proclus is aware that the Principle of all reality—and of science itself—must be conceived as in itself unknowable. At the same time, he seeks to save the ability of human knowledge to describe reality. Starting from an idea of the relationship between God and the laws of contradiction close to that of Proclus, Cusanus develops an epistemology that, on the one hand, recognizes the principle of contradiction as the ultimate principle of reason and, on the other hand, comes to the conclusion of a separation between thought and reality outside thought. (shrink)

This issue of Itinera aims to address the connections between architecture and the performing arts in its various aspects and from multiple points of view. The growing emphasis on the performative character of artistic practices, namely, their ability to involve spectators directly and pervasively (Dixon 2007), imbues the relationship between architecture, the performing arts, and the spectator’s experience. The sharing of the scenic space by spectators and performers is essential for the co-production of a common energy which operates as a (...) “transforming force” and thereby opens up the shared experience of discovering oneself and the other as a union of the body and the mind (Fischer-Lichte 2004). (shrink)