We propose a set theory, called NRFST, in which the Cantorian axiom of infinity is negated, and a new notion of infinity is introduced via non standard methods, i. e. via adequate notions of standard and internal, two unary predicates added to the language of ZF. After some initial results on NRFST, we investigate its relative consistency with respect to ZF and Kawai's WNST.

In this paper we introduce a theory of finite sets FST with a strong negation of the axiom of infinity asserting that every set is provably bijective with a natural number. We study in detail the role of the axioms of Power Set, Choice, Regularity in FST, pointing out the relative dependences or independences among them. FST is shown to be provably equivalent to a fragment of Alternative Set Theory. Furthermore, the introduction of FST is motivated in view of a (...) non-standard development. MSC: 03E30, 03E35. (shrink)

Very often reality is identified with our knowledge of it, and in turn our knowledge of reality is identified with the linguistic manner of describing it. It is claimed that the three moments cannot be identified, by pointing out some crucial differences among them obtained through an analysis of the power and limitations of languages and of the manners of acquisition of knowledge.

Playing fields are “spaces where the communitas suspends its everyday life and structures” and “The internal logic of sporting games is connected to values from the social context”, Playing fields: Power, practice, and passion in sport, 127–144. Reno: University of Nevada Press). But what about the space in between? What kind of semiotics organisation can be detected in the membrane between player and liminal space where spectators are not allowed yet specific characters needed to carry out an event? We can (...) therefore identify a liminality that can be connected either to the controlled or the wild playing field and depending on which of the two is the case can be analysed according to the degree of regulated system of signs which they produce. This implies different pathways and rituals: as matches are played, a variety of bodily activities may be taking place concurrently. Furthermore, it is inevitable that these activities attract the attention of the audience or alternately lead a player to interact with a non-player. In this article, I will first try to identify certain semiotics features, especially connected to Eco’s Peircian concept of Encyclopedia, that characterize the status of liminal space around the playing field. Then I will focus on liminality in soccer, investigating what kinds of interaction exist outside the playing area. (shrink)

No sermão pelo bom sucesso das armas de Portugal contra as da Holanda, Vieira explana todos os seus dotes de prosador invulgar, teólogo eminente, jurista incontornável, humanista convicto e, acima de tudo, patriota assumido. O presente trabalho pretende, sobretudo, relevar o poder argumentative do orador, seguindo de perto as considerações de Chaïm Perelman sobre a Retórica como "discurso que visa convencer ou persuadir". Simultaneamente, desta-cam-se os голоl ou valores universais patenteados no texto de Vieira e que constituem a base da (...) teoria da argumentação de Oswald Ducrot. \\\ In the "Sermon for the good success of the Portuguese army against Holland's", Vieira displays all his gifts as an uncommon writer, an excellent theologian, a non negligeable jurist, a convinced humanist, and, above all, a wholehearted patriot. This essay is an attempt to put in evidence the preacher's argumentative power, on the basis of Chaïm Perelman's considerations on Rethoric as "a speech that aims to convince or persuade". At the same time, we emphasize, as displayed in Vieira's text, the "topoi", or universal values, that are the basis of Oswald Ducrot's argumentation theory. (shrink)

In this paper, a phenomenological perspective on capitalism is given: it is considered as the economic expression of onto-theology. Capitalism is based on egotism, whose principles are private ownership (correlative of intentionality) and free market (correlative of liberty). The current crisis is the symptom of a disease, that is a lack of ethics, an indiscriminate pursuit of egotism. A moral revolution is here proposed as a remedy. The aim is not to destroy capitalism, but to save it with the introduction (...) of an ethical attitude, based on original responsibility and uniqueness (Levinas), as well as on bi-directional respect (Ricoeur). (shrink)

The paper discusses a posthuman reading of Merleau-Ponty’s later works and an application of the concept of flesh to the digital dimension. Whereas, in the Phenomenology of Perception, the world and other beings are seen from an egological and human perspective, in The Visible and the Invisible this perspective is reshaped. Human body is made of the same stuff of other bodies, and they constitute a common being, the flesh of the world. Merleau-Ponty sets out a path through flat ontology (...) and posthumanism, opposing human perspective as a privileged one. His posthuman turn passes through the concepts of reversibility and divergence. Humans are made of the same stuff as non-humans, so they reverse into one another, but, on the other hand, they are not reduced to an undifferentiated entity, because of their divergence. Merleau-Ponty’s problematizing perspective is here actualized and applied to the hybridization between human bodies and digital protheses. (shrink)

A comprehensive and scholarly study Fr. Rosini has, perhaps for the first time, provided a complete, well-balanced exposition of Scotus on Our Lady, with all the many inter-connections between the mystery of Mary and the whole of theology, ...

A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.

Climate change, rising energy costs, and other dilemmas raise the prospect for major change in energy-ecology-society relations. Two prominent proposals for change include: a nuclear power renaissance; and mega-scale renewable energy development. Both suggest that modern society will receive a rising stream of less CO2-rich kilowatt-hours, so that increased energy consumption and economic growth can continue. The article doubts these CO2 claims and finds both options lead to deepening unsustainability and environmental injustice. A third approach is proposed. A new institutional (...) and community strategy called a Sustainability Energy Utility. The SEU looks to reduce energy use and seeks to support remaining energy needs by community-scale renewables. To accomplish deep energy change, the authors show how an SEU can move society from an energy commodity to energy commons regime. Commonwealth economy and community trusts are key means to significant change: a future commons is offered as the more appropriate strategy. (shrink)

We present a reading of the traditional syllogistics in a fragment of the propositional intuitionistic multiplicative linear logic and prove that with respect to a diagrammatic logical calculus that we introduced in a previous paper, a syllogism is provable in such a fragment if and only if it is diagrammatically provable. We extend this result to syllogistics with complemented terms à la De Morgan, with respect to a suitable extension of the diagrammatic reasoning system for the traditional case and a (...) corresponding reading of such De Morgan style syllogistics in the previously referred to fragment of linear logic. (shrink)

This paper focuses on Levinas’ concept of ipseity and on its change between the 1960’s and the 1970’s, arguing that this change implies the undoing of the subject. In Totality and Infinity (1961), ipseity is considered as the deep core of the I, whereas, in Otherwise Than Being (1974), it is the other person inside the self. Levinas also theorizes another kind of other-in-the-same, which is illeity, the trace of God inside the human soul. It is shown that illeity is (...) not problematic for the subject, since it does not cause its undoing. Furthermore, it is argued that ipseity, in Otherwise Than Being, is not a mere opening to alterity, but a source of alienation. Finally, it is shown that Levinas starts to change his mind on ipseity in 1968 (“Substitution”), however this modification becomes clear only in 1970 (“No Identity”). (shrink)

From the Introduction: "William James and Gilles Deleuze gave two specific definitions of their own ways of thinking: James used the expression “radical empiricism”, whereas Deleuze wrote about “transcendental empiricism”. In both cases, empiricism is brought out as the main feature of their perspective on reality. I will show that both authors share an empiricist background, regarding especially the concept of “pure experience”. [...] Furthermore, I will bring out that Deleuze, even if he shares the same starting point of James’s (...) philosophy, shifts the axis of repetition according to difference: he develops his perspective on pure experience through a redefinition of the transcendental.". (shrink)

Doors play a complex role in architecture. The very word, at least in Italian and French, illuminates the marking of the deliberate interruption of the act of foundation during the ceremony of the wall's enceinte tracing. The word porta indicates the action of portare. During the tracing of the furrow into the ground, the blade is lifted out of the ground in order to mark the place of the future entrance to the city. Another significant role is the marking of (...) the “exit” from this world and it is loaded with intense significance in funereal architecture. But if we look at the semantic “Mirror, mirror on the wall,” it will be easy to discover the other, complementary, and necessary role of the porta. The reading of Aristophanes' Lysistrata shows the explicit “hidden” metaphor of the door, which has been very well christened as the “Origin of the World” in the famous Courbet painting. (shrink)

Segundo o autor do artigo, o estudo do tédio na obra de Kierkegaard tem sido objecto de relativamente pouco interesse, sobretudo quando comparado com a angústia, a melancolia, a ironia ou o desespero. A verdade, porém, é que o tédio constitui uma disposição fundamental, um limite extremo de uma forma da existência. Neste sentido, o artigo pretende fazer uma análise das principais formas que a disposição do tédio assume, e da sua particular relevância no interior do que, na obra de (...) Kierkegaard, se chama "estádio estético". Em ordem a esse fim, o autor analisa a relação que o tédio mantém com as possibilidades que a vida disponibiliza e, sobretudo, a sua peculiar relação com o nada. Mostra-se sobretudo que tipo de lucidez se pode considerar como efeito do tédio, qual o aspecto da vida que nele se torna patente e de que forma, por ele, o sujeito acaba por reconhecer estar constituído numa superioridade relativamente a tudo o que é finito. Assim, no centro deste estudo estão as determinações fundamentais de disposição e de finito, bem como, num segundo momento, o esboço de uma "anatomia comparada" das disposições fundamentais do sujeito humano, a saber, do tédio, da melancolia e da angústia. \\\ The study of boredom in Kierkegaard's work has attracted relatively little interest compared to the more visited themes of anxiety, melancholy, irony and despair. For Kierkegaard, boredom is a fundamental mood. And only when we are in this mood can we experience one of the extreme states of existence. For Kierkegaard, boredom manifests itself in what he terms the "aesthetic stage". With this premise in mind, the article explains the relationship boredom has with the possibilities life puts before us, but more importantly its peculiar relationship with nothingness. The article explores in particular the effect boredom has on lucidity and, more specifically, attempts to answer the question about the aspect of life that is better perceived when the subject is in a state of boredom. A crucial question, for example, is this: how does being in a state of boredom reveal to the human subject the fact that he/she is superior to everything that is finite? At the centre of the article are the notions of mood and finiteness, in accordance to which the author delivers what might be called a "comparative anatomy" of fundamental states of human existence such as boredom, melancholy and anxiety. (shrink)

De spatio, ac tempore -- De spatio, et tempore, ut a nobis cognoscuntur -- De motu absoluto, an possit a relativo distingui -- De vi inertiae.

As far as we know, no notion of concrete fibration is available. We provide one such notion in adherence to the foundational attitude that characterizes the adoption of the fibrational perspective in approaching fundamental subjects in category theory and discuss it in connection with the notion of concrete category and the notions of locally small and small fibrations. We also discuss the appropriateness of our notion of concrete fibration for fibrations of small maps, which is relevant to algebraic set theory.

By splitting idempotent morphisms in the total and base categories of fibrations we provide an explicit elementary description of the Cauchy completion of objects in the categories Fib) of fibrations with a fixed base category \ and Fib of fibrations with any base category. Two universal constructions are at issue, corresponding to two fibered reflections involving the fibration of fibrations \.

A growing body of evidence in cognitive psychology and neuroscience suggests a deep interconnection between sensory-motor and language systems in the brain. Based on recent neurophysiological findings on the anatomo-functional organization of the fronto-parietal network, we present a computational model showing that language processing may have reused or co-developed organizing principles, functionality, and learning mechanisms typical of premotor circuit. The proposed model combines principles of Hebbian topological self-organization and prediction learning. Trained on sequences of either motor or linguistic units, the (...) network develops independent neuronal chains, formed by dedicated nodes encoding only context-specific stimuli. Moreover, neurons responding to the same stimulus or class of stimuli tend to cluster together to form topologically connected areas similar to those observed in the brain cortex. Simulations support a unitary explanatory framework reconciling neurophysiological motor data with established behavioral evidence on lexical acquisition, access, and recall. (shrink)

Pre-existing mathematical formulations are generally used for the treatment of new scientific problems. In this note we show that the construction of mathematical structures from open physical, chemical, and biological problems leads to new intriguing mathematics of increasing complexity called iso-, geno-, and hyper-mathematics for the treatment of matter in reversible, irreversible, and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter. These novel mathematics are based on the lifting of the multiplicative unit of ordinary (...) fields (with characteristic zero) from its traditional value +1 into: (1) invertible, Hermitean, and single-valued units for isomathematics; (2) invertible, non-Hermitean, and single-valued units for genomathematics; and (3) invertible, non-Hermitean, and multi-valued units for hypermathematics; with corresponding liftings of the conventional associative product and consequential lifting of all branches of mathematics admitting a (left and right) multiplicative unit. An anti-Hermitean conjugation applied to the totality of quantities and their operation of the preceding mathematics characterizes the isodual mathematics. Intriguingly, the emerging formulations preserve the abstract axioms of conventional mathematics (that based on the unit +1). As such, the new formulations result to be new realizations of existing abstract mathematical axioms. We then show that the above mathematical advances permit corresponding liftings of conventional classical and quantum theories with a resolution of basic open problems in physics, chemistry, and biology, numerous experimental verifications, as well as new industrial applications. (shrink)