In this paper we generalize the pigeonhole principle by using isols as our fundamental counting tool.

In this paper we discuss the following contributions to recursion theory made by John Myhill: two sets are recursively isomorphic iff they are one-one equivalent; two sets are recursively isomorphic iff they are recursively equivalent and their complements are also recursively equivalent; every two creative sets are recursively isomorphic; the recursive analogue of the Cantor–Bernstein theorem; the notion of a combinatorial function and its use in the theory of recursive equivalence types.

In this paper we present a contribution to a classical result of E. Ellentuck in the theory of regressive isols. E. Ellentuck introduced the concept of a hyper-torre isol, established their existence for regressive isols, and then proved that associated with these isols a special kind of semi-ring of isols is a model of the true universal-recursive statements of arithmetic. This result took on an added significance when it was later shown that for regressive isols, the property of (...) being hyper-torre is equivalent to being hereditarily odd-even. In this paper we present a simplification to the original proof for establishing that equivalence. (shrink)

In this paper we present an equivalence between the category of commutative regular rings and the category of Boolean-valued fields, i.e., Boolean-valued sets for which the field axioms are true. The author used this equivalence in [12] to develop a Galois theory for commutative regular rings. Here we apply the equivalence to give an alternative construction of an algebraic closure for any commutative regular ring.Boolean-valued sets were developed in 1965 by Scott and Solovay [10] to simplify independence proofs in set (...) theory. They later were applied by Takeuti [13] to obtain results on Hilbert and Banach spaces. Ellentuck [3] and Weispfenning [14] considered Boolean-valued rings which consisted of rings and associated Boolean-valued relations. To the author's knowledge, the present work is the first to employ the Boolean-valued sets of Scott and Solovay to obtain results in algebra.The idea that commutative regular rings can be studied by examining the properties of related fields is not new. For several years algebraists and logicians have investigated commutative regular rings by representing a commutative regular ring as a subdirect product of fields or as the ring of global sections of a sheaf of fields over a Boolean space. These representations depend, as does the work presented here, on the fact that the set of central idempotents of any ring with identity forms a Boolean algebra. The advantage of the Boolean-valued set approach is that the axioms of classical logic and set theory are true in the Boolean universe. Therefore, if the axioms for a field are true for a Boolean-valued set, then other properties of the set can be deduced immediately from field theory. (shrink)

Presentación del Dossier 'Perspectivas aristotélicas contemporáneas'.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:WisCon 46Laurie Fuller, Jenna N. Hanchey, and E. OrnelasExistence as Resistance, WisCon 46, May 26–29, 2023, Madison, Wisconsin, United StatesIn a world that seems structured to kill most of its occupants, there is a utopian impulse in the act of existence itself. WisCon 46 represented a prefigurative utopian impulse through centering continued marginalized existence as resistance.1 Leah Lakshmi Piepzna-Samarasinha calls “prefigurative politics” the “fancy term for the idea (...) of imagining and building the world we want to see now,” particularly in terms of access needs.2 The structure as well as the content of the convention itself created a space in which to set the groundwork for utopia: the ways that we live and act to resist structures of oppression in order to prefigure a better world.Since WisCon’s founding in 1977, its intended audience has been fans, authors, and academics interested in the intersection between feminism and “science fiction, fantasy, and speculative literature of all sorts.”3 While neither feminism nor speculative fiction could be solely defined as utopian, both do explore utopian impulses that inspire change for the better. Therein lies the hope of Alessa Johns’s proposal that “the utopian imagination has been crucial for feminists.”4 Lisa Yaszek agrees: “for nearly 200 years writers have used speculative fiction consciously and collectively to dramatize the political issues most central to women living in a technocultural world and to create a sense of wonder about the interrelated possibilities of social and scientific change.”5 Envisioning a liberatory world is a feminist imperative, and speculative fiction offers a unique venue to do so. This imperative informed WisCon this year, as participants collectively worked to imagine and enact a better future for marginalized folks, in and beyond the space of the conference. [End Page 618]Enabling Existence through Con StructuresWisCon is unique in attuning its organizational structure to the creation of liberatory futures in the here and now. WisCon is strongly attentive to disability access of all kinds, COVID safety, antiracist/anti-oppression principles, and safety and anti-abuse support for all these areas. In the contemporary US context—where COVID-19 remains a major barrier to disabled people wishing to participate in conventions, where racist violence continues to threaten BIPOC (Black, Indigenous, and People of Color) life, where queer and trans folks are under exacerbated legal attacks—creating a convention space that protects and enables marginalized participation becomes a means of prefiguring utopian potential through embodied praxis. As mask, capacity, and vaccination mandates disappear (despite these ongoing pandemic times), and as bigotry of all forms continues relatively unabated, WisCon 46 remains steadfast in its commitment to safety. In short, the conference itself aims to become a utopian space.WisCon organizers are also keenly aware of the challenges that many different bodyminds might encounter in large group settings.6 Trained monitors oversee in-person and online programming in an effort to discourage harmful words and actions as well as ensure the fullest participation for those most impacted. Hence, disability justice lies at the center of the Con’s policies and practices. The event is made as accessible as possible through careful attention to venue selection, including the availability of gender-neutral bathrooms, scent-free spaces, and quiet rooms, as well as the use of color communication badges.This year’s event followed strict masking and testing protocols: individually packaged rapid COVID-19 tests were available without cost at registration, as were KN95 masks. The Con kept an anonymized record of self-reported positive COVID-19 tests, in case of possible exposure. This mutual responsibility reflects the kind of utopianism inherent to disability politics; that is, disability “allows for reformulation of in/dependence and community,” a way of rethinking how we share space and produce knowledge together.7The conference’s decidedly feminist approach “to creating a space for feminism and its consideration within the science fiction community” is applied at every level. The Con’s general organization and procedures are structured as nonhierarchically as possible. There is a board of directors as well as co-chairs, but these are rotating positions. This “commitment to feminism” is [End Page 619] reflected... (shrink)

Between 1873 and 1876, Felix Klein published a series of papers that he later placed under the rubric anschauliche Geometrie in the second volume of his collected works (1922). The present study attempts not only to follow the course of this work, but also to place it in a larger historical context. Methodologically, Klein’s approach had roots in Poncelet’s principle of continuity, though the more immediate influences on him came from his teachers, Plücker and Clebsch. In the 1860s, Clebsch reworked (...) some of the central ideas in Riemann’s theory of Abelian functions to obtain complicated results for systems of algebraic curves, most published earlier by Hesse and Steiner. These findings played a major role in enumerative geometry, whereas Plücker’s work had a strongly qualitative character that imbued Klein’s early studies. A leitmotif in these works can be seen in the interplay between real curves and surfaces as reflected by their transformational properties. During the early 1870s, Klein and Zeuthen began to explore the possibility of deriving all possible forms for real cubic surfaces as well as quartic curves. They did so using continuity methods reminiscent of Poncelet’s earlier approach. Both authors also relied on visual arguments, which Klein would later advance under the banner of intuitive geometry (anschauliche Geometrie). (shrink)

Background Integrating artificial intelligence (AI) into healthcare has raised significant ethical concerns. In pharmacy practice, AI offers promising advances but also poses ethical challenges. Methods A cross-sectional study was conducted in countries from the Middle East and North Africa (MENA) region on 501 pharmacy professionals. A 12-item online questionnaire assessed ethical concerns related to the adoption of AI in pharmacy practice. Demographic factors associated with ethical concerns were analyzed via SPSS v.27 software using appropriate statistical tests. Results Participants expressed concerns (...) about patient data privacy (58.9%), cybersecurity threats (58.9%), potential job displacement (62.9%), and lack of legal regulation (67.0%). Tech-savviness and basic AI understanding were correlated with higher concern scores (p < 0.001). Ethical implications include the need for informed consent, beneficence, justice, and transparency in the use of AI. Conclusion The findings emphasize the importance of ethical guidelines, education, and patient autonomy in adopting AI. Collaboration, data privacy, and equitable access are crucial to the responsible use of AI in pharmacy practice. (shrink)

In one of his last texts, Foucault defined his philosophical enterprise as an?analysis of the conditions in which certain relations between subject and object are formed or modified, insofar as they are constitutive of a possible knowledge,? or again as?the manner in which the emergence of games of truth constituted, for a particular time and place and certain individuals, the historical a priori of a possible experience.? Despite its eclipse during the genealogical period, the notion of the historical a priori (...) is thus reaffirmed as central by later Foucault. There is, however, an essential modification with respect to its archaeological problematisation: In The Order of Things, the various historical a priori were characterized by specific relations between being and language, relations in which the subject of knowledge did not always or necessarily have a place. The Renaissance episteme was defined by the homogeneity of words and things, and its Classical counterpart by the transparent distance between being and representation, which excluded any positioning for the subject (the missing?place of the king?). Within the archaeological configuration, only the contemporary historical a priori was characterized by the invention of a new position for the subject of knowledge, that of Man, which according to Foucault generated the Analytic of Finitude and ultimately resulted in the?anthropological sleep? criticised at the end of The Order of Things. So although later Foucault refocuses his work around the notion of the historical a priori, he gives the notion a considerable twist whereby the conditions of truth saying are no longer referred back to an implicit connection between being and language, but to the various relations historically established between?modes of subjectivation? and?modes of objectification.? (shrink)

O objetivo deste texto é explorar aproximações e divergências no pensamento de Paulo Freire e Ivan Illich na forma como eles vêem a relação entre educação e transformação social. Acredita-se que a retomada da polêmica Freire e Illich sobre o problema educação e transformação social pode contribuir para melhor compreender e esclarecer a verdadeira natureza desse problema, já clássico na história da educação moderna.

Monograph in six chapters, plus introductory essay, conclusions, two appendixes, notes, and bibliography.

Il libro, diviso in quattro sezioni, mette in luce un'indagine storica del tutto originale di documenti noti e meno noti sulla figura di Gesù in fonti non cristiane del I secolo; su come il cristianesimo fu conosciuto a Roma già nel I secolo; sulle allusioni al cristianesimo nei romanzi e nelle satire pagane del I-II secolo; su alcuni esempi della prima diffusione del cristianesimo dal Vicino Oriente all'India.

ResumoO argumento do milagre afirma que o realismo científico é a melhor explicação para o sucesso da ciência:teorias científicas são bem-sucedidas porque são verdadeiras, e cientistas são bem-sucedidos em encontrarteorias verdadeiras porque se baseiam em normas metodológicas confiáveis. A tese da incomensurabilidademetodológica afirma que teorias científicas não são escolhidas através de um algoritmo neutro de normas epistêmicas. Isso revela uma lacuna na explicação realista: normas epistêmicas confiáveis não são suficientes para conduzir a escolhas de teorias verdadeiras, pois tais escolhas também (...) são determinadas por outros fatores além de normas epistêmicas. A introdução de fatores adicionais como subdeterminando a escolha de teorias engendrou argumentos relativistas e antirrealistas contra o realismo. A explicação realista pode ser reabilitada se postular que os cientistas possuem autoridade epistêmica para aprimorar as normas metodológicas da ciência, sendo aptos a tomar decisões autônomas em vez de regidas por regras.AbstractThe no miracles argument claims that scientific realism is the best explanation to science’s success: scientifictheories are empirically successful because they are truthlike, and scientists are successful in theory-choices because they rely on reliable methodological norms. The methodological incommensurability thesis claims that there is no neutral algorithm for theory-choice. It reveals a gap in the realist explanation: reliable epistemic norms are not sufficient to guarantee successful theory-choices, because theory- choices are also determined by other factors besides epistemic norms. The introduction of additional factors as underdetermining theory-choices motivates relativist and antirealist positions. But the realist explanation can be rehabilitated if it postulates that scientists have epistemic authority to develop methodological norms, being apt to take decisions which are autonomous rather than rule-driven. (shrink)

In The Form of Truth: Hegel’s Philosophical Logic, Elena Ficara offers a reappraisal of G.W.F. Hegel’s logic within the history of logic and in relation to the logics of today. She brings together...

A renowned scholar investigates the "human crisis" that Albert Camus confronted in his world and in ours, producing a brilliant study of Camus's life and influence for those readers who, in Camus's words, "cannot live without dialogue and friendship. As France--and all of the world--was emerging from the depths of World War II, Camus summed up what he saw as 'the human crisis'. 'We gasp for air among people who believe they are absolutely right, whether it be in their machines (...) or their ideas. And for all who cannot live without dialogue and the friendship of other human beings, this silence is the end of the world.' In the years after he wrote these words, until his death fourteen years later, Camus labored to address this crisis, arguing for dialogue, understanding, clarity, and truth. When he sailed to New York, in March 1946--for his first and only visit to the United States--he found an ebullient nation celebrating victory. Camus warned against the common postwar complacency that took false comfort in the fact that Hitler was dead and the Third Reich had fallen. Yes, the serpentine beast was dead, but "we know perfectly well," he argued, "that the venom is not gone, that each of us carries it in our own hearts." All around him in the postwar world, Camus saw disheartening evidence of a global community revealing a heightened indifference to a number of societal ills. It is the same indifference to human suffering that we see all around, and within ourselves, today. (shrink)

What do we do when we say ‘We’? This paper pursues a response from analytic pragmatism. The guiding idea of analytic pragmatism is to look to what one must implicitly know how do to be able to use expressions to say something, including how to make that implicit know-how explicit. Accordingly, the question we are tasked to answer is what one must know how to do to say ‘We’ – that is, what practical know-how saying ‘We’ requires and can be (...) employed to make explicit. The concept normative ascent is introduced in developing an answer. On this approach, the know-how in question turns out to be a distinctively normative capacity. Both being and saying ‘We’ turns out to involve being able to do and say something normative. (shrink)

En este artículo exploraremos un dilema surgido del progresivo asentamiento de una disciplina reciente en el ámbito de la teoría moral, comprendida como una rama de los enfoques naturalistas de la ética, a saber, la ‘ética evolutiva’. Esta disciplina incluye en sus investigaciones de orden ético conocimientos de tipo biológico y, particularmente, estudios en clave de las teorías posdarwinianas de la evolución. En pocas palabras, el dilema surgido de la articulación entre ética y naturalismo evolutivo consiste en lo siguiente: (i) (...) o bien las propiedades morales son naturales y explican nuestro comportamiento como resultado de procesos evolutivos, pero no alcanzan para justificar el comportamiento moral; (ii) o bien lo justifican, pues tales propiedades retienen su autonomía respecto de las propiedades naturales, pero dejan de explicar o anclar la moral en bases ‘reales’ (naturales, fácticas) objetivas de la moralidad como tal. Nuestra propuesta en este artículo busca, si no solucionar dicho dilema, al menos ‘relajar’ la tensión que contiene. Para ello realizaremos una exploración del debate en torno al realismo moral que subyace al dilema en cuestión, así como también, y particularmente, a los posibles aportes que algunas perspectivas neoaristotélicas contemporáneas podrían ofrecer para la elucidación de una vía intermedia, que evite caer en ambos extremos. (shrink)