In this paper we present two calculi for intuitionistic logic. The first one, IG, is characterized by the fact that every proof-search terminates and termination is reached without jeopardizing the subformula property. As to the second one, SIC, proof-search terminates, the subformula property is preserved and moreover proof-search is performed without any recourse to metarules, in particular there is no need to back-track. As a consequence, proof-search in the calculus SIC is accomplished by a single tree as in classical logic.

Noetherian type and Noetherian π-type are two cardinal functions which were introduced by Peregudov in 1997, capturing some properties studied earlier by the Russian School. Their behavior has been shown to be akin to that of the cellularity, that is the supremum of the sizes of pairwise disjoint non-empty open sets in a topological space. Building on that analogy, we study the Noetherian π-type of κ-Suslin Lines, and we are able to determine it for every κ up to the first (...) singular cardinal. We then prove a consequence of Changʼs Conjecture for ℵω regarding the Noetherian type of countably supported box products which generalizes a result of Lajos Soukup. We finish with a connection between PCF theory and the Noetherian type of certain Pixley–Roy hyperspaces. (shrink)

This study deals with an exploratory research about understanding of art in students of different age, grades and kind of schools attended. In particular, we analysed how beliefs and reflections about art and aesthetical experiences expressed during a cross-age interview, changed in elementary school children involved for two years in a UE Project titled “Philosophy and European Contemporary Art”. The activities are based on guided philosophical discussions, transforming the classroom in a “community of inquiry”, according to the methodology of “Philosophy (...) for Children” program . The elementary school group was tested pre and post the program activities. A qualitative analysis of the students’ answers was carried out, considering the data with respect to the five stages of art understanding defined by Micheal Parsons which correspond to different beliefs about art in the subjects. (shrink)

The law commonly conceived as a norm : deficiency of this conception -- On some general hints of this deficiency, and in particular those evinced by the likely origin of the current definitions of law -- The need to distinguish the distinct legal norms from the legal order considered as a whole. The logical impossibility of defining the legal order as a set of norms -- How the unity of a legal order has been sometimes intuited -- How a legal (...) order is not only a set of norms, as it also encompasses other elements -- How such ements are implicitly postulated by the common inquiry into the distinguishing characteristics of law -- Assessment, from this point of view, of the so-called objectivity of law -- The element of sanction -- The expression "the legal order" -- The essential elements of the concept of law. The law as an institution and the law as a precept -- The preceding doctrine on the concept of institution -- My concept of institution and its fundamental characteristics : 1. The objective existence of the institution; 2. Institution and social body; 3. The institution's selfness; 4. The unity of the institution -- Equivalence of the concept of institution and the concept of a legal order -- Evidence for this equivalence based on the doctrine that the law is only "form" -- Mention of some problems that need solving in the light of this equivalence -- Cases in which the original establishment of a law does not depend on norms, but on the emergence of an institution, and the impossibility of reducing the institution to the norms -- The concept of institution and the international legal order -- The institution and the legal relationship: relationships between more persons -- Relationships between persons and things : examples of some of these relationships that, considered more broadly, cab be portrayed as institutions -- The institution and the legal person -- My conception of the law with respect to certain problems relating to : 1. The legal character of state power; 2. The extension of the state personality; 3. The legal relevance of its territory and citizenry -- Critical assessment of some opinions that attach importance to the legal order only insofar as it reflect relationships between persons. Applications to: 1. The legal sanction; 2. The state territory and citizenship; 3. The state bodies; 4. The limits of the legislative function -- Some consequences of my conception with regard to the subjective aspect of the law: the legal relationship; the status of persons; rights in rem; the correlation between rights and obligations; the equal position of subjects -- Recapitulatory remarks -- The plurality of legal orders and the doctrine that reduces all law to state law -- The untenability of this doctrine from a historical and theoretical point of view -- Its untenability with respect to the existing law -- Non-state legal orders; international law -- Ecclesiastical law -- The order of entities that are considered unlawful or are ignored by the state -- Entities that are regulated by the state, but also have an order of their own which is not recognized by the state (private disciplinary orders; the internal organisation of workplaces; so-called unrecognized associations or institutions, etc.) -- Doctrines that confine the concept of a legal order to the order of communities in general and specifically to necessary communities -- The relations between different legal orders. Principles that have to be taken into account with respect to : 1. Original or derivative institutions; 2. The particular or general ends of institutions; 3. Their diverse basis; 4. Simple or complex institutions; 5. Perfect or imperfect; 6. With or without personality; 7. Independent, coordinated or subordinated -- The concept of relevance of one order to another -- The title for this relevance: a. The relation of superiority and correlative dependence between two orders; b. The relation whereby an order presupposes another; c. The relation whereby reciprocally independent orders depend a further one; d. The relevance unilaterally attributed by an order to another on which it depends; e. The relation of succession between orders -- Diverse aspects (existence, content, effectiveness) expressing the relevance an order to another one. Cases in which the existence of an order depends on another: a. Complete subordination of the former to the latter which directly establishes the former or assigns limited autonomy to it. Independence, as far as its existence is concerned, of an order in case of a less expansive subordination (some spheres of the order of the states of a federal state vis-à-vis the latter; the order of states vis-à-vis international law) and general principles; b. In the hypothesis of an order that represents the presupposition of another (state law vis-à-vis international law) -- The relevance of an order to another with respect to its content. Various cases: a. The superior order as the mediated or unmediated source of an inferior order; the superior order (international law, ecclesiastical concordats) which is not the source, and yet affects the content of inferior orders; b. the Superior order about effects the content of more orders subjected to, which however are independent from each other; c. the order of that itself that determines its own content by considering a subjected or independent order : private international law; ecclesiastical law as it refers to civil laws; the law of the state that refers to ecclesiastical law; d. an order that incorporates another -- The relevance of an order to one another with respect to its effects: external and internal effectiveness of an order. Various cases of external effectiveness: a. The relationships between orders where the one partially or totally depends on the other; b. Relationships between more orders that are independent from each other because of a unilateral disposition of one or each of them. Private international law; civil effectiveness of ecclesiastical law; c. Relationships meeting more orders in which one is of the presupposition of the other; d. Relationships between orders that succeed each other -- Diverse extension of the relevance of an order to another. Applications with regard to the problem of so-called natural obligations -- The irrelevance of an order to another; total or partial, reciprocal or unilateral -- A legal order that as such is irrelevant to another, but it is relevant in other respects (orders that are considered unlawful by the state; corporations, de facto institutions) -- Total developments of an order to another: possibility of such an irrelevance also with respect to the order of the state -- Critical assessment of the opposite doctrine. The limitations of the state order; various figures and consequences; examples of matters that are legally indifferent to the state (private disciplinary orders; particular religious orders; the orders of some non-patrimonial associations; etc.) -- The internal orders of the institutions, especially state ones, vis-à-vis the order of other institutions in which they are included. (shrink)

Social data mining has become an emerging area of research in information and communication technology fields. The scope of social data mining has expanded significantly in the recent years with the advance of telecommunication technologies and the rapidly increasing accessibility of computing resources and mobile devices. People increasingly engage in and rely on phone communications for both personal and business purposes. Hence, mobile phones become an indispensable part of life for many people. In this article, we perform social data mining (...) on mobile social networking by presenting a simple but efficient method to define social closeness and social grouping, which are then used to identify social sizes and scaling ratio of close to “8”. We conclude that social mobile network is a subset of the face-to-face social network, and both groupings are not necessary the same, hence the scaling ratios are distinct. Mobile social data mining. (shrink)

The present essay offers a first, systematic reconstruction of Husserl’s understanding of Socrates’ philosophical position in the Ideengeschichte with a special focus on the Socratic method. Our goal is twofold. On the one hand, we aim to provide a clear presentation of the way in which Husserl himself conceives of the “beginning” of Western philosophy by tackling the specifically Socratic contribution to it. On the other hand, we will clarify in what sense, and to what extent, the assessment of Husserl’s (...) Socrates helps shed some light upon the properly Husserlian conception of philosophy, notably, his twofold notion of “rationality.”. (shrink)

This paper aims at offering a concise, yet systematic, presentation of the Husserlian method of “self-variation” in connection to eidetic variation sic et simpliciter. After a brief review of the different meanings of this method in Husserl’s writings, I will focus on the way in which Husserl employs it to bring the eidos “ego” to the fore. To this end, I will take into account the specific subject matter of self-variation by resorting to a twofold concept of essence as well (...) as to the formal-ontological notion of τóδε τι. The present investigation will have an almost exclusively methodological character, its purpose being to clarify a specific, yet still quite unexplored, tool of Husserl’s phenomenology. (shrink)

This book presents a systematic discussion of the development of Husserl’s concept of the a priori from his early and through his later writings. The chapters contained herein analyze the different phases and aspects of Husserl’s phenomenology of the a priori in light of his twofold notion of reason, construed as both ontological and transcendental. Starting from the assessment of the introduction of the notion of a priori knowledge in the context of the Logical Investigations, this text uniquely explores its (...) development during the Göttingen years. It is at this time during his work on The Crisis of European Sciences, that Husserl comes to see the a priori as a criterion to interpret the history of philosophy, notably, modern philosophy. This book sheds light upon such concepts as: essence and eidos; ideation, eidetic attitude and eidetic reduction; as well as formal and material, innate and contingent a priori. The author argues that the a priori becomes for Husserl the expression of an ontological form of rationality, i.e., the rationality immanent to being. This book appeals to students and researchers working on Husserl and phenomenology. (shrink)

El ordenamiento jurídico de Santi Romano es, sin duda alguna, una obra fundamental. Y no es la circunstancia concreta de presentar ahora la obra al lector español la que dicta estas palabras, sino que las recojo conociendo plenamente el valor objetivo que ellas tienen; sobradamente tendremos ocasión de ver la consideración que la obra de Romano recibe por parte de la doctrina, como de un auténtico y verdadero hito en el desarrollo del pensamiento jurídico contemporáneo. De ahí precisamente que (...) no trate de llevar a cabo ni un análisis crítico de la misma, ni menos aún de la obra de Romano en general; tal pretensión de enjuiciamiento limitaría casi con lo grotesco, por carecer de toda autoridad en el campo de la dogmática general del Derecho, que es en el que, en concreto, se mueve Santi Romano en la obra que presentamos. Estas páginas, por el contrario, pretenden tener una finalidad mucho más modesta: simplemente presentar la obra al lector español, formulando al mismo tiempo algunas aplicaciones concretas de la tesis ordinamental en el campo específico del Derecho administrativo. Sebastián Martín Retortillo. (shrink)

"Phenomenology was one of the twentieth century's major philosophical movements, and it continues to be a vibrant and widely studied subject today with relevance beyond philosophy in areas such as medicine and cognitive sciences. The Routledge Handbook of Phenomenology and Phenomenological Philosophy is an outstanding guide and reference source to this important and fascinating topic. Comprising seventy-five chapters by a team of international contributors, the Handbook offers unparalleled coverage of the subject, and is divided into five clear parts: Phenomenology and (...) the History of Philosophy Issues and Concepts in phnomenology Major Figures in Phenomenology Intersections Phenomenology in the World. Essential reading for students and researchers in philosophy studying phenomenology, The Routledge Handbook of Phenomenology and Phenomenological Philosophy is also suitable for those in related disciplines such as psychology, religion, literature, sociology and anthropology"--. (shrink)

The present essay, here published for the first time, is part of a group of four texts on the history of the early phenomenological movement that Theodor Conrad wrote right after World War II. One of these texts known as “Conrads Bericht” was edited by Eberhard Avé-Lallemant and Karl Schuhmann and published in Husserl Studies in 1992. The four original typescripts are preserved in the archive of the Munich Circle of phenomenology at the Bavarian State Library. As the reader will (...) immediately realize, at the center of the present text is a peculiar account of the beginning of the phenomenological tradition, namely, of its first schism. Contrary to the usual thesis according to which the first schism revolved mainly, if not exclusively around the so-called “idealism-realism controversy,” Conrad points out that this was only part of it, and that the first controversy between Husserl and some of his early disciples or students bore on the nature of phenomenology itself. (shrink)

The present research contributes to the elucidation of an important aspect of Husserl’s interpretation of the history of philosophy, that is, his reading of the beginning of Western thought. In par...

The paper presents an epistemic logic with quantification over agents of knowledge and with a syntactical distinction between de re and de dicto occurrences of terms. Knowledge de dicto is characterized as ‘knowledge that’, and knowlegde de re as ‘knowledge of’. Transition semantics turns out to be an adequate tool to account for the distinctions introduced.

Proprioception has a crucial role in promoting or hindering motor learning. In particular, an intact position sense strongly correlates with the chances of recovery after stroke. A great majority of neurological patients present both motor dysfunctions and impairments in kinesthesia, but traditional robot and virtual reality training techniques focus either in recovering motor functions or in assessing proprioceptive deficits. An open challenge is to implement effective and reliable tests and training protocols for proprioception that go beyond the mere position sense (...) evaluation and exploit the intrinsic bidirectionality of the kinesthetic sense, which refers to both sense of position and sense of movement. Modulated haptic interaction has a leading role in promoting sensorimotor integration and it is a natural way to enhance volitional effort. Therefore, we designed a preliminary clinical study to test a new proprioception-based motor training technique for augmenting kinesthetic awareness via haptic feedback. The feedback was provided by a robotic manipulandum and the test involved 7 chronic hemiparetic subjects over three weeks. The protocol included evaluation sessions, that consisted of a psychometric estimate of the subject’s kinesthetic sensation, and training sessions, in which the subject executed planar reaching movements in the absence of vision and under a minimally assistive haptic guidance made by sequences of graded force pulses. The bidirectional haptic interaction between the subject and the robot was optimally adapted to each participant in order to achieve a uniform task difficulty over the workspace. All the subjects consistently improved in the perceptual scores as a consequence of training. Moreover, they could minimize the level of haptic guidance in time. Results suggest that the proposed method is effective in enhancing kinesthetic acuity, but the level of impairment may affect the ability of subjects to retain their improvement in time. (shrink)

The main goal of this article is to examine Edmund Husserl’s method of “eidetic variation”—that is, to examine the way this method is supposed to work in connection with the notion of “similarity” (Ähnlichkeit). Unlike most interpretations, it will be suggested that similarity represents the leading methodologicalprinciple of eidetic variation. We will argue, therefore, that, on the one hand, this method is rooted in the sphere of association and passivity while, on the otherhand, it is constituted by the transposition of (...) a passive synthesis into an active operation. After having introduced and discussed a twofold notion of phantasy(as “localized phantasy” and as “pure phantasy”) as well as a twofold concept of eidos (as “hen epi pollon” and as “pure eidos”), the extent to which for Husserl there cannot be any eidetic variation without a monadology will be shown. (shrink)

The main goal of this article is to examine Edmund Husserl’s method of “eidetic variation”—that is, to examine the way this method is supposed to work in connection with the notion of “similarity” (Ähnlichkeit). Unlike most interpretations, it will be suggested that similarity represents the leading methodologicalprinciple of eidetic variation. We will argue, therefore, that, on the one hand, this method is rooted in the sphere of association and passivity while, on the otherhand, it is constituted by the transposition of (...) a passive synthesis into an active operation. After having introduced and discussed a twofold notion of phantasy(as “localized phantasy” and as “pure phantasy”) as well as a twofold concept of eidos (as “hen epi pollon” and as “pure eidos”), the extent to which for Husserl there cannot be any eidetic variation without a monadology will be shown. (shrink)

Dummett's logic LC quantified, Q-LC, is shown to be characterized by the extended frame Q+, ,D, where Q+ is the set of non-negative rational numbers, is the numerical relation less or equal then and D is the domain function such that for all v, w Q+, Dv and if v w, then D v . D v D w . Moreover, simple completeness proofs of extensions of Q-LC are given.

In times of crisis, connections among people, cultures, and societies seem to be the main antidotes available against the risks of individualism, auto-referentiality, and a revenge culture. Connectivity offers opportunities to nurture human generativity (Santi, 2021) in the service of better futures and cosmopolitan scenarios, contrasting the delusion of autarchical economies, the rhetoric of political nationalism, and the reinforcement of social polarization by way of competition/marginalization, which applies to education as well. The pandemia that occurred in 2020 brought both (...) risks of isolation and opportunities for connection: it has been a paradoxical and even paroxysmal situation that has challenged us to think about forms of dependence, especially in instructional contexts. The stimulus for an inquiry that was carried out with 817 students at the University of Padova was the provocative title of an album by well-known musicians: “Declaration of Dependence.” The aim was to think about dependencies in the form of regular roles such as “study/student” that are important for our human existence, and which were profoundly upset by the “sindemia” (Singer, 2009). Our aspiration was to explore what it means to belong to a thriving university whose over-arching goal is to serve the dependencies of people in a generative community of future horizons. Our efforts led to the drafting of the “Declaration of Dependence,” a shared manifesto by the research group that enumerated a thorough list of the students' self-declared dependencies, and which was later shared with the university community in multiple languages. This led, in turn, to the use of the Declaration to launch multiple focus groups, which discussed these dependencies in a setting devoted to dialogue and the practice of complex thinking. Subsequently, in a workshop carried out in 2020 at the 20th Biennial Conference of the International Council of Philosophical Inquiry with Children (ICPIC) in Tokyo, we opened an international dimension on the reflections that had preoccupied us in the Padova University context. Here, the aim was to reflect on the personal, collective and educational dependencies of the present historical moment through the practice of community of philosophical inquiry, which offers a paradigmatic time and space for sharing, listening, questioning, and gaining perspective. The conference workshop offered an international group of scholars and practitioners from various socio-political contexts the opportunity to deliberate on how the pandemic has impacted both their local and the global community. Considering the new educational and philosophical challenges presented by the pandemic, the group expressed an urgent need to deconstruct established boundaries and return to “origins.” Invoking metaphors taken from the natural world (Roversi et al, 2022), an inquiry into the nature and scope of our fundamental dependencies reminds us that we are part of a socio-cultural ecology that is grounded and nurtured in our relationship with others. A community that understands its dependencies as gifts that call us to the design of a better future could in fact represent a foreshadowing of a better tomorrow. (shrink)

Predicate extensions of the intermediate logic of the weak excluded middle and of the modal logic S4.2 are introduced and investigated. In particular it is shown that some of them are characterized by subclasses of the class of directed frames with either constant or nested domains.

A general strategy for proving completeness theorems for quantified modal logics is provided. Starting from free quantified modal logic K, with or without identity, extensions obtained either by adding the principle of universal instantiation or the converse of the Barcan formula or the Barcan formula are considered and proved complete in a uniform way. Completeness theorems are also shown for systems with the extended Barcan rule as well as for some quantified extensions of the modal logic B. The incompleteness of (...) Q°.B + BF is also proved. (shrink)

The present paper provides the first reconstruction of the discussion between Martin Heidegger and Maximilian Beck, a former member of the Munich Circle of Phenomenology—a discussion that revolved around Beck’s interpretation of the “fundamental ontology” of Being and Time. Based upon the still unpublished correspondence between Heidegger and Beck, the essay first reconstructs their relation and then offers a meticulous discussion of Beck’s major criticism of Heidegger, i.e., “correlativism,” and the latter’s response to it in his courses of 1928.