Given two (positive) equivalence relations ∼ 1 , ∼ 2 on the set ω of natural numbers, we say that ∼ 1 is m-reducible to ∼ 2 if there exists a total recursive function h such that for every x, y ∈ ω, we have $x \sim_1 y \operatorname{iff} hx \sim_2 hy$ . We prove that the equivalence relation induced in ω by a positive precomplete numeration is complete with respect to this reducibility (and, moreover, a "uniformity property" holds). This (...) result allows us to state a classification theorem for positive equivalence relations (Theorem 2). We show that there exist nonisomorphic positive equivalence relations which are complete with respect to the above reducibility; in particular, we discuss the provable equivalence of a strong enough theory: this relation is complete with respect to reducibility but it does not correspond to a precomplete numeration. From this fact we deduce that an equivalence relation on ω can be strongly represented by a formula (see Definition 8) iff it is positive. At last, we interpret the situation from a topological point of view. Among other things, we generalize a result of Visser by showing that the topological space corresponding to a partition in e.i. sets is irreducible and we prove that the set of equivalence classes of true sentences is dense in the Lindenbaum algebra of the theory. (shrink)

It is well known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Theor (˹p˺) ≡ p implies p is a theorem ∼Theor (˹p˺) ≡ p implies p is provably equivalent to Theor (˹0 = 1˺). Therefore, the considered "equations" admit, up to provable equivalence, only one solution. In this paper we prove (Corollary 1) that, in general, if P (x) is an arbitrary formula built (...) from Theor (x), then the fixed-point of P (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction). (shrink)

We generalize a well-knownSmullyan's result, by showing that any two sets of the kindC a = {x/ xa} andC b = {x/ xb} are effectively inseparable (if I b). Then we investigate logical and recursive consequences of this fact (see Introduction).

Some years ago, Yablo gave a paradox concerning an infinite sequence of sentences: if each sentence of the sequence is 'every subsequent sentence in the sequence is false', a contradiction easily follows. In this paper we suggest a formalization of Yablo's paradox in algebraic and topological terms. Our main theorem states that, under a suitable condition, any continuous function from 2N to 2N has a fixed point. This can be translated in the original framework as follows. Consider an infinite sequence (...) of sentences, where any sentence refers to the truth values of the subsequent sentences: if the corresponding function is continuous, no paradox arises. (shrink)

By an unfounded chain for a function f:X→X we mean a sequence nω of elements of X s.t. fxn+1=xn for every n. Unfounded chains can be regarded as a generalization of fixed points, but on the other hand are linked with concepts concerning non-well-founded situations, as ungrounded sentences and the hypergame. In this paper, among other things, we prove a lemma in general topology, we exhibit an extensional recursive function from the set of sentences of PA into itself without an (...) unfounded chain, and we prove that every term in a Magari algebra has an unfounded chain. (shrink)

In Zwicker (1987) the hypergame paradox is introduced and studied. In this paper we continue this investigation, comparing the hypergame argument with the diagonal one, in order to find a proof schema. In particular, in Theorems 9 and 10 we discuss the complexity of the set of founded elements in a recursively enumerable relation on the set N of natural numbers, in the framework of reduction between relations. We also find an application in the theory of diagonalizable algebras and construct (...) an undecidable formula. (shrink)

Extended simple regions have been the focus of recent developments in philosophical logic, metaphysics, and philosophy of physics. However, only a handful of works provides a rigorous characterization of an extended simple region. In particular, a recent paper in this journal defends a definition based on an extrinsic notion of least distance. Call it the Least Distance proposal. This paper provides the first assessment of it. It argues that Least Distance faces difficulties and drawbacks. The paper then goes on to (...) suggest a different proposal, the Diameter proposal that is able to handle such drawbacks and difficulties. (shrink)

Dieser Essay beschreibt die Geburt der faktischen Vernunft und erzahlt vom Ursprung des faktischen Zeitalters bei Parmenides und Wittgenstein bis in unsere Gegenwart hinein. Parmenides und Wittgenstein trennen ganze 2500 Jahre und doch stehen beide fur einen radikalen Realismus und eine zeitlose Ontologie in der Geschichte des Denkens: gemeinsam ist ihnen ein neutraler Blick von oben. Jeder neutrale Realismus ist ein Versuch, gegen die Sinnlosigkeit des Lebens anzugehen. Ob unerschutterliche Seinskugel oder philosophische Leiter, die immer wieder uberwunden werden muss, beides (...) verkorpert den Traum von einer unzerstorbaren, objektiven Welt der Tatsachen. Neutraler Realismus bedeutet daher in der Antike wie im 20. Jahrhundert die Errichtung einer zeitlosen ontologischen Wahrheit, um der unerklarbaren Paradoxie der Welt einen Riegel vorzuschieben. (shrink)

The advent of Generative AI, particularly through Large Language Models (LLMs) like ChatGPT and its successors, marks a paradigm shift in the AI landscape. Advanced LLMs exhibit multimodality, handling diverse data formats, thereby broadening their application scope. However, the complexity and emergent autonomy of these models introduce challenges in predictability and legal compliance. This paper analyses the legal and regulatory implications of Generative AI and LLMs in the European Union context, focusing on liability, privacy, intellectual property, and cybersecurity. It examines (...) the adequacy of the existing and proposed EU legislation, including the Artificial Intelligence Act (AIA), in addressing the challenges posed by Generative AI in general and LLMs in particular. The paper identifies potential gaps and shortcomings in the EU legislative framework and proposes recommendations to ensure the safe and compliant deployment of generative models. (shrink)

This paper examines the associations among social desirability response bias, cultural constructs and gender. The study includes the responses of 1537 students from 12 countries including Australia, Canada, China, Colombia, Ecuador, Hong Kong, Ireland, Japan, Nepal, South Africa, Spain, and the United States. The results of the analysis indicate that, on average, social desirability response bias decreases (increases) as a country’s Individualism (Uncertainty Avoidance) increases. The analysis also indicates that women scored significantly higher on Paulhus’ Image Management Subscale on an (...) overall basis and for seven of the 12 country comparisons. This research serves as a caution when considering the research findings of prior international survey-based ethics research that do not include a direct measure of social desirability response bias. For example, the finding that women score higher on Paulhus’ measure of social desirability response bias calls into question prior research that does not control for social desirability response bias indicating women are more ethically sensitive than men. (shrink)

This paper examines the associations among social desirability response bias, cultural constructs and gender. The study includes the responses of 1537 students from 12 countries including Australia, Canada, China, Colombia, Ecuador, Hong Kong, Ireland, Japan, Nepal, South Africa, Spain, and the United States. The results of the analysis indicate that, on average, social desirability response bias decreases as a country's Individualism increases. The analysis also indicates that women scored significantly higher on Paulhus' Image Management Subscale on an overall basis and (...) for seven of the 12 country comparisons. This research serves as a caution when considering the research findings of prior international survey-based ethics research that do not include a direct measure of social desirability response bias. For example, the finding that women score higher on Paulhus' measure of social desirability response bias calls into question prior research that does not control for social desirability response bias indicating women are more ethically sensitive than men. (shrink)

The landscape of social theory has changed significantly over the three decades since the publication of Anthony Giddens and Jonathan Turner’s seminal Social Theory Today. Sociologists in the twenty-first century desperately need a new agenda centered around central questions of social theory. In Social Theory Now, Claudio E. Benzecry, Monika Krause, and Isaac Ariail Reed set a new course for sociologists, bringing together contributions from the most distinctive sociological traditions in an ambitious survey of where social theory is today (...) and where it might be going. The book provides a strategic window onto social theory based on current research, examining trends in classical traditions and the cutting edge of more recent approaches. From distinctive theoretical positions, contributors address questions about how social order is accomplished; the role of materiality, practice, and meaning; as well as the conditions for the knowledge of the social world. The theoretical traditions presented include cultural sociology, microsociologies, world-system theory and post-colonial theory, gender and feminism, actor network and network theory, systems theory, field theory, rational choice, poststructuralism, pragmatism, and the sociology of conventions. Each chapter introduces a tradition and presents an agenda for further theoretical development. Social Theory Now is an essential tool for sociologists. It will be central to the discussion and teaching of contemporary social theory for years to come. (shrink)

The article argues that AI can enhance the measurement and implementation of democratic processes within political parties, known as Intra-Party Democracy (IPD). It identifies the limitations of traditional methods for measuring IPD, which often rely on formal parameters, self-reported data, and tools like surveys. Such limitations lead to the collection of partial data, rare updates, and significant demands on resources. To address these issues, the article suggests that specific data management and Machine Learning (ML) techniques, such as natural language processing (...) and sentiment analysis, can improve the measurement (ML about) and practice (ML for) of IPD. The article concludes by considering some of the principal risks of ML for IPD, including concerns over data privacy, the potential for manipulation, and the dangers of overreliance on technology. (shrink)

ABSTRACTIn this paper, I discuss my personal experience of the issues that can arise when adopting critical realism in academic contexts dominated by irrealist methodological approaches. I draw inspiration for my analysis from the concept of Gramscian hegemony and the concept of ‘authenticity’. These concepts are related because hegemonic processes prevent individuals from freely expressing themselves. In my case, academic hegemony has resulted in social pressure to sacrifice my authentic critical realist self in order to achieve academic success. I also (...) discuss groupthink dynamics, suggesting that they are a mechanism by which hegemony – and denial of individual authenticity – can be achieved. This paper is meant to be a theoretical and reflexive discussion, which could be the starting point for empirical studies investigating the situation of a critical realist in a hegemonic academic context. (shrink)

The present article is framed within the biosemiotic glossary project as a way to address common terminology within biosemiotic research. The glossary integrates the view of the members of the biosemiotic community through a standard survey and a literature review. The concept of ‘semiotic threshold’ was first introduced by Umberto Eco, defining it as a boundary between semiotic and non-semiotic areas. We review here the concept of ‘semiotic threshold’, first describing its denotation within semiotics via an examination on the history (...) of the concept, its synonyms, antonyms, etymology, usage in other languages and context in which it is used. Then we present a general overview of the survey among researchers, analyzing the difference in responses for the concept of ‘lower semiotic threshold’ and related concepts. From the answers we also review the difference between the general usage of ‘semiotic threshold’ versus its specific use within biosemiotics, and attempt to make a general synthesis of the concept taking into account what we have learned from the survey and the literature review. (shrink)

Die Bibliotheca Teubneriana, established in 1849, has evolved into the world's most venerable and extensive series of editions of Greek and Latin literature, ranging from classical to Neo-Latin texts. Some 4-5 new editions are published every year. A team of renowned scholars in the field of Classical Philology acts as advisory board: Gian Biagio Conte (Scuola Normale Superiore di Pisa) James Diggle (University of Cambridge) Donald J. Mastronarde (University of California, Berkeley) Franco Montanari (Università di Genova) Heinz-Günther Nesselrath (Georg-August-Universität Göttingen) (...) Dirk Obbink (University of Oxford) Oliver Primavesi (Ludwig-Maximilians Universität München) Michael D. Reeve (University of Cambridge) Richard J. Tarrant (Harvard University) Formerly out-of-print editions are offered as print-on-demand reprints. Furthermore, all new books in the Bibliotheca Teubneriana series are published as eBooks. The older volumes of the series are being successively digitized and made available as eBooks. If you are interested in ordering an out-of-print edition, which hasn't been yet made available as print-on-demand reprint, please contact us:[email protected] All editions of Latin texts published in the Bibliotheca Teubneriana are collected in the online database BTL Online. (shrink)

This volume serves as a reference on the field of cognitive semantics. It offers a systematic and original discussion of the issues at the core of the debate in semiotics and the cognitive sciences. It takes into account the problems of representation, the nature of mind, the structure of perception, beliefs associated with habits, social cognition, autism, intersubjectivity and subjectivity. The chapters in this volume present the foundation of semiotics as a theory of cognition, offer a semiotic model of cognitive (...) integration that combines Enactivism and the Extended Mind Theory, and investigate the role of imagination as the origin of perception. The author develops an account of beliefs that are associated with habits and meaning, grounded in Pragmatism, testing his Narrative Practice Semiotic Hypothesis on persons with autism spectrum disorders. He also integrates his ideas about the formation of the theory of mind with a theory of subjectivity, understood as self-consciousness which derives from semiotic cognitive abilities. This text appeals to students, professors and researchers in the field. (shrink)

Accountability is a cornerstone of the governance of artificial intelligence (AI). However, it is often defined too imprecisely because its multifaceted nature and the sociotechnical structure of AI systems imply a variety of values, practices, and measures to which accountability in AI can refer. We address this lack of clarity by defining accountability in terms of answerability, identifying three conditions of possibility (authority recognition, interrogation, and limitation of power), and an architecture of seven features (context, range, agent, forum, standards, process, (...) and implications). We analyse this architecture through four accountability goals (compliance, report, oversight, and enforcement). We argue that these goals are often complementary and that policy-makers emphasise or prioritise some over others depending on the proactive or reactive use of accountability and the missions of AI governance. (shrink)

Much has been written about recidivist punishments, particularly within the area of criminology. However there is a notorious lack of penal philosophical reflection on this issue. This book attempts to fill that gap by presenting the philosopher’s view on this matter as a way of furthering the debate on recidivist punishments.

The purpose of this study is to analyse the structure of written argumentative texts produced by pupils in grades 3, 5, 7 and 11 in relation to three different tasks: Group A — subjects are assigned a topic question consisting of a single statement ; Group B — subjects are given a topic question consisting of both a statement and its opposite ; Group C — subjects are given an initial and a final sentence of a text, which they have (...) to complete, and which refers to opposite opinions . Six different types of text organization were evidenced on the basis of the argumentative moves presented in the texts, the linguistic indexes used to express the relationships between the moves, the presence or absence of counter-arguments and the type of argumentation or reasoning used. The organization of the texts range from a simple affirmation of a position to a use of data or reasons to support a position, to others still in which two positions are presented in the body of a unitary structure, developed ‘in parallel’ and interconnected regularly. Our analysis found a well-defined tendency corresponding to the age levels in the types of texts produced by the subjects. The texts produced by the younger group, the pupils in elementary school, contained a fairly simple structural organization, characterized by very few argumentations or a lack of explicitness of the essential moves and a juxtaposing of arguments. The older subjects, in particular those attending secondary school, were able to produce texts which were more complex with regard to the presence and the organization of the argumentative moves, and more coherent and cohesive with respect to their articulation of opinions and use of adequate linguistic indices to analyze t topic. As regards the different types of tasks, when the subjects were presented explicitly with two opposite opinions , they developed both positions in their responses, contrary to the situation in which they produced one position when only one of two opinions was presented. (shrink)

Studying the origin of semiosis is a task obscured by terminological and metaphysical issues which create an ambiguous set of definitions for biosemiotics when referring to the concept of emergence. The question is, how emergent can semiosis be? And what are the conditions for semiosis to be an emergent of a certain type? This paper will attempt to briefly deal with the general terminology of emergence from a philosophical point of view and will discuss the characterization of semiosis as an (...) emergent phenomenon based on the distinctions made by Bedau, Kim and Chalmers. Accordingly, we will consider the possibility of strong and weak emergence in an attempt to bring some clarity to what it means for something in biosemiotics to be an emergent and how the philosophical concepts play out when applied to biosemiotic research. In inquiring into the metaphysical status of semiosis, we change our semiotic theories to correspond to the assumptions contained in the elementary objects of our theories. This being the case, the way semiosis–the constitutive element that it is for semiotics–is taken to be with regards to its possible ontology, will conduct to different research objects for the long-term investigation of its origins and necessary conditions. (shrink)

In responding to a question posed by Professor Vincent Carraud regarding a passage in a letter by Etienne Pascal in which he mentions an author who speaks of the mysteries of Pythagorean numbers we have resumed our dossiers on number theory in Mersenne. We have pointed to texts from Mersenne’s correspondence, printed books, and unpublished theological manuscripts between 1638 and 1648 in which the mysteries of the Pythagorean numbers are mentioned with reference to the theory of perfect numbers and with (...) reference to Peter Bongo’s work, which was widespread throughout Europe and particularly in France, De numerorum mysteria (1599 ed. aucta). This has allowed us to provide some indications taken from Mersenne’s unpublished manuscripts in which he addresses the mathematical problem of perfect numbers in exegesis, according to the new dating of his unpublished theological manuscripts that we have established. (shrink)

This commentary draws upon the author's experience in bioethics and as a physician, ordained Rabbi, and certified Mohel (a Jewish professional qualified to perform infant male circumcisions (MC)). People's identity and adherence to a religious belief are frequently cited reasons for deciding whether to circumcise their male children. For Jewish and Muslim males, circumcision is considered essential. In this commentary, the author uses his medical, religious, and bioethical knowledge, expertise, and experience to address common arguments used in opposing nontherapeutic male (...) circumcision of minors. In these narratives, half of the parents agreed with circumcision, and half did not. The parents against circumcision cite human rights violations, security, privacy, and bodily integrity issues and refer to circumcision as genital mutilation, while those who agree argue that circumcision should be done for religious reasons to prevent health issues, promote hygiene and cleanness, avoid cancer, or for later sexual enjoyment. After evaluating the evidence, the author states that parents should be free to either consent or decline MC for a son. Though a reoccurring theme in these narratives was for mothers to leave the circumcision decision up to their male partners, the author concludes that women have considerable power regarding the decision. (shrink)