We study arithmetic and hyperarithmetic degrees of categoricity. We extend a result of E. Fokina, I. Kalimullin, and R. Miller to show that for every computable ordinal $\alpha$, $\mathbf{0}^{}$ is the degree of categoricity of some computable structure $\mathcal{A}$. We show additionally that for $\alpha$ a computable successor ordinal, every degree $2$-c.e. in and above $\mathbf{0}^{}$ is a degree of categoricity. We further prove that every degree of categoricity is hyperarithmetic and show that the index set of structures with degrees (...) of categoricity is $\Pi_{1}^{1}$-complete. (shrink)
We give several characterizations of Schnorr trivial sets, including a new lowness notion for Schnorr triviality based on truth-table reducibility. These characterizations allow us to see not only that some natural classes of sets, including maximal sets, are composed entirely of Schnorr trivials, but also that the Schnorr trivial sets form an ideal in the truth-table degrees but not the weak truth-table degrees. This answers a question of Downey, Griffiths and LaForte.
We show that van Lambalgen's Theorem fails with respect to recursive randomness and Schnorr randomness for some real in every high degree and provide a full characterization of the Turing degrees for which van Lambalgen's Theorem can fail with respect to Kurtz randomness. However, we also show that there is a recursively random real that is not Martin-Löf random for which van Lambalgen's Theorem holds with respect to recursive randomness.
We study the connection between Schnorr triviality and genericity. We show that while no 2-generic is Turing equivalent to a Schnorr trivial and no 1-generic is tt-equivalent to a Schnorr trivial, there is a 1-generic that is Turing equivalent to a Schnorr trivial. However, every such 1-generic must be high. As a corollary, we prove that not all K-trivials are Schnorr trivial. We also use these techniques to extend a previous result and show that the bases of cones of Schnorr (...) trivial Turing degrees are precisely those whose jumps are at least 0". (shrink)
A real is Martin-Löf (Schnorr) random if it does not belong to any effectively presented null ${\Sigma^0_1}$ (recursive) class of reals. Although these randomness notions are very closely related, the set of Turing degrees containing reals that are K-trivial has very different properties from the set of Turing degrees that are Schnorr trivial. Nies proved in (Adv Math 197(1):274–305, 2005) that all K-trivial reals are low. In this paper, we prove that if ${{\bf h'} \geq_T {\bf 0''}}$ , then h (...) contains a Schnorr trivial real. Since this concept appears to separate computational complexity from computational strength, it suggests that Schnorr trivial reals should be considered in a structure other than the Turing degrees. (shrink)
We investigate the relationship between lowness for Schnorr randomness and Schnorr triviality. We show that a real is low for Schnorr randomness if and only if it is Schnorr trivial and hyperimmune free.
The weakly random reals contain not only the Schnorr random reals as a subclass but also the weakly 1-generic reals and therefore the n -generic reals for every n . While the class of Schnorr random reals does not overlap with any of these classes of generic reals, their degrees may. In this paper, we describe the extent to which this is possible for the Turing, weak truth-table, and truth-table degrees and then extend our analysis to the Schnorr random and (...) hyperimmune reals. (shrink)
En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)
Es conocido que el método de forcing es una de las técnicas de construcción de modelos más importantes de la Teoría de conjuntos en la actualidad, siendo el mismo muy útil para investigar problemas de matemática y/o de fundamentos de la matemática. El destacado matemático Joan Bagaria afirma lo siguiente sobre el método de forcing en su artículo "Paul Cohen y la técnica del forcing" (Gaceta de la Real Sociedad Matemática Española, Vol. 2, Nº 3, 1999, págs 543-553) : "Aunque (...) Cohen recibió la medalla Fields por su demostración de la independencia de la hipótesis del continuo y del axioma de elección, su contribución va mucho más allá de estos problemas. Su nuevo método, el forcing, no sólo ha permitido resolver un sinfín de problemas importantes en prácticamente todas las áreas de las matemáticas, si no que ha cambiado para siempre nuestra concepción de la matemática como ciencia". El objetivo principal del siguiente trabajo es estudiar el método de forcing describiendo algunas de sus aplicaciones (forcing de Cohen, forcing aleatorio, forcing de Mathias, forcing de Sacks, forcing de Silver, etc.), y ofreciendo una aproximación a sus fundamentos metamatemáticos. Se aspira que estas notas sirvan de apoyo para aprender dicho método. (shrink)
Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...) also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)
The purpose of this study is the reflection on ways of philosophical legitimation for the "Self-made-man" idea in the worldview of the Renaissance and Reformation. Theoretical basis. Historical, comparative, and hermeneutic methods became the basis for this. The study is based on the works of Nicholas of Cusa, G. Pico della Mirandola, N. Machiavelli, M. Montaigne, E. Roterodamus, M. Luther, J. Calvin together with modern researchers of this period. Originality. The analysis allows us to come to the conclusion that casts (...) doubt on the still widespread belief according to which the emergence of the "Self-made-man" idea is localized by the process of forming the American cultural code and the ideological heritage of Benjamin Franklin. It is highlighted that the formation of this idea is the result of a long process that originated in the ancient world and gains a special impetus in the Renaissance and Reformation. Precisely in the cultural context of the latter, the ancient intention to recognize the individual’s right to self-determination and self-government, which in the depths of Christian theology acquires only a potentially universal character, becomes not only acceptable but also, in the context of Protestantism worldview, the only admissible, in fact, individual’s obligatory life guidelines. Conclusions. Humanistic and reformation thoughts quite naturally led to further ideological legitimation of the person’s idea of who is creating oneself. This legitimation was during the complex interaction of numerous factors of culture in the Late Middle Ages, as well as ideas and intentions inherited from Antiquity. Key among them was the gradual formation of a new social order, in essence, indifferent to paternalistic rudiments, together with the ethics of Protestantism corresponding to it. The latter does not only legalize but, de facto, sacralizes the individual’s reorientation from hopes for the synergy of God’s grace and own free will in personal salvation, toward the self-reliance and personal efforts, awareness of personal responsibility for the own fate as key principles of the "Self-made-man" concept. (shrink)
Abstract Internet communication technology has been said to affect our sense of self by altering the way we construct “personal identity,” understood as identificatory valuative narratives about the self; in addition, some authors have warned that internet communication creates special conditions for moral agency that might gradually change our moral intuitions. Both of these effects are attributed to the fact that internet communication is “disembodied.” Our aim in this paper is to establish a link between this complex of claims and (...) past and ongoing research in phenomenology, empirical psychology and cognitive science, in order to formulate an empirical hypothesis that can assist development and evaluation of recent technology for embodied telecommunication. We first suggest that for the purposes of interdisciplinary exchange, personal identity is formally best represented by a selection function that (for temporal intervals of variable length) “bundles” capacity ascriptions into identificatory narratives. Based on this model, we discuss which cultural changes engendered by the internet affect the construction of personal identity in ways that diminish our ethical sensitivies. In a second step, working from phenomenological claims by Martin Buber, we argue that disembodied communication severs two modes of cognitive function, preconceptual and conceptual, which tie together moral motivation, self-experience, and identity construction. We translate Buber’s claims into the theoretical idiom of the “theory of cognitive orientation,” a psychological theory of motivation that links up with recent research in embodied cognition. In a third step, we investigate whether the embodiment of the internet with communication robots (e.g., telenoids) holds out the prospect of reverting this structural change at least partially. We conclude by formulating an empirical hypothesis (for researchers in cognitive science) that has direct import, we submit, on the question whether embodied telecommunication promises a new form of ethically sensitive self-constituting encounter. Content Type Journal Article Category Special Issue Pages 1-23 DOI 10.1007/s13347-012-0064-9 Authors Johanna Seibt, Department for Philosophy and the History of Ideas, Aarhus University, Aarhus, Denmark Marco Nørskov, Department for Philosophy and the History of Ideas, Aarhus University, Aarhus, Denmark Journal Philosophy & Technology Online ISSN 2210-5441 Print ISSN 2210-5433. (shrink)
L'État actionnaire de la télévision publique est soucieux du rendement social de son investissement. Les programmes des chaînes publiques doivent être globalement vus par le plus grand nombre. Mais en même temps, chaque entité du service public doit respecter un cahier des charges et ne peut être une simple addition de «pièges à audience». Au programmateur de gérer ces paradoxes en forgeant une grille qui s'appuie sur ces contraintes et affirme la relation particulière de chaque chaîne avec le public. L'audience (...) est la récompense d'une programmation généreuse, qui prend des risques et produit du sens. La grille de France 3 s'est construite autour des concepts de proximité et de curiosité; France 2 doit être une grande chaîne de divertissement, d'information et de création; France 5 est une chaîne pédagogique qui tente d'apporter à certains publics qui en ont besoin , des clés pour mieux comprendre la réalité de tous les jours.As the main shareholder in public television, the State is of course concerned by the level of social profit in return for its investment. Overall, public channels' programme schedules should be seen by the largest audience possible. But at the same time, each public channel has to respect certain obligations and cannot be a simple accumulation of "audience traps". It is the programmer’s responsibility to manage these paradoxes when constructing a schedule which should be based on these very constraints while affirming each channel's particular relationship with its audience. High audience ratings are the reward for generous scheduling in which risks are taken and a certain meaning is produced. France 3's programming was built around the concepts of proximity and curiosity; France 2 is intended to be a major entertainment, information and creation channel; France 5 is an educational channel aiming to bring keys to better understand everyday reality to certain audiences who need it, particularly young people. (shrink)
Sudoku puzzles, which are popular worldwide, require individuals to infer the missing digits in a 9 9 array according to the general rule that every digit from 1 to 9 must occur once in each row, in each column, and in each of the 3-by-3 boxes in the array. We present a theory of how individuals solve these puzzles. It postulates that they rely solely on pure deductions, and that they spontaneously acquire various deductive tactics, which differ in their difficulty (...) depending on their “relational complexity”, i.e., the number of constraints on which they depend. A major strategic shift is necessary to acquire tactics for more difficult puzzles: solvers have to keep track of possible digits in a cell. We report three experiments corroborating this theory. We also discuss their implications for theories of reasoning that downplay the role of deduction in everyday reasoning. (shrink)
Here presented are three singular, philosophical perspectives on the Delhi student protests which took place in 2019 and 2020, before the coronavirus pandemic. The writers hail from India, England...
Should we in the moral community accept the modern business corporation as one of us? French answers 'yes'. In this book, French investigates the metaphysical foundations of the application of our established moral principles to corporations as moral persons.
Spivak translates Derrida’s “il n’y a pas de hors-texte” as “there is nothing outside the text.” By considering how the aphorism works within his study of Rousseau on sexual and textual supplements, and by reviewing related expressions in French, a mistranslation is revealed. This is not a simple error, however. The distortion is generated by Derrida’s own broader context. We must not only distinguish signification from reference but also place the aphorism within Derrida’s allusion, in the first part of Of (...) Grammatology, to an all-embracing arche-writing. The paper ends in thus opening out the discussion of a textual “inside” or “outside.”. (shrink)
« En vertu de quoi la catégorie de l’Utopique possède donc à côté de son sens habituel et justement dépréciatif, cet autre sens qui, loin d’être nécessairement abstrait et détourné du monde, est au contraire centralement préoccupé du monde : celui du dépassement de la marche naturelle des événements »« Il n’y a guère, même parmi les économistes bourgeois, un savant..
A highly idiosyncratic search for universal laws governing the development of a feeling of well-being and creative involvement in life. Numerous, somewhat mystical, experiences are described with enthusiasm and candor, but, perhaps, uncertain significance for those less inclined toward mysticism.—N. Y.
La formule de Ga 3,28 « ...Il y a ni esclave ni libre, il n’y a pas l’homme et la femme... » est souvent citée pour justifier une vision égalitaire de la communauté chrétienne, notamment par des théologien(ne)s féministes. La majorité des exégètes limite pourtant l’effet de ces paroles de Paul au domaine spirituel ou eschatologique ; s’agirait-il, au fond, d’une simple utopie ? Pour tenter de répondre à cette interrogation, Ga 3,28 est resitué dans le contexte de l’épître, puis (...) dans celui d’une éventuelle formule de foi pré-paulinienne. Les résultats sont ensuite comparés au texte de Mc 10,6-8 qui comporte lui aussi l’expression « l’homme et la femme », dans le contexte du divorce. L’ensemble de ce dossier permettra d’esquisser quelques modestes repères pour une interprétation de Ga 3,28, qui ne se cantonne pas uniquement au constat de l’utopie. (shrink)
The medical ethics of a physician’s relationship with a prisoner who is participating in a collective hunger strike has become a major public, professional, and governmental concern in The Republic of Turkey. This article examines the Turkish experience and debate about physician ethics during prison hunger strikes. It is hoped that this analysis will be of use to those formulating policy in similar situations.
Si on cherche une définition minimale de la phénoménologie, on trouvera l'idée de philosophie descriptive. En ce sens, on peut imputer quelque chose de phénoménologique á de nombreuses philosophies contemporaines, audelà des limites de la phénoménologie au sens étroit et historique du terme. Néanmoins, il faut alors prendre en compte la question de savoir ce qui est à décrire. La réponse phénoménologique est: ce qui est vu. Qu'est-ce qui est donc vu ? Cette question est inséparable de celle de la (...) grammaire du voir. L'auteur soutient que c'est ce qui doit être retenu de la critique wittgensteinienne de la phénoménologie. Mais, si ce qui doit être dit est le vu en tant qu'il est dit, il n'en reste pas moins qu'il doit être dit en tant que vu. Que faire de cette dimension qui est celle de l'« être-vu » ? En ce point, la phénoménologie est inévitable, non plus comme discipline, mais au moins comme problème. If one requires a minimal definition for phenomenology, one may settle for the idea of a descriptive philosophy. In that sense, something phenomenological can be ascribed to many contemporary species of philosophiy, beyond the limits of « phenomenology » taken in a narrow, historical sense. However, the question arises : what is to be described? Phenomenology's answer is: what is seen. What, then, is seen ? This question is inseparable from the question of the grammar of seeing, as the author holds to be drawn from the wittgensteinian criticism of phenomenology. But if what is to be said is what is seen, as said, yet it remains that it is to be said as seen. What can be done with this « being-seen-ness » ? Here, phenomenology is unavoidable, not as a discipline anymore, but at least as a problem. (shrink)
En su encierro durante la II Guerra Mundial, Althusser, según declaró, solamente tuvo al alcance un libro: los Pensées de Pascal, un clásico que, tras la reflexión religiosa, también planteó problemas epistemológicos, históricos y sociológicos de tal manera que en él se pueden encontrar rasgos “profundamente materialistas”. [1] La influencia de Pascal es expresa, cuando Althusser recoge la parábola de la conversión religiosa para explicar (insuficientemente) el fenómeno de la interpelación ideológica. Pero los textos de Pascal contienen intuiciones que sobrepasan (...) los límites de la teoría althusseriana y que se pueden rastrear a la luz de la teoría psicoanalítica de la ideología tal como ésta es elaborada por los autores de la escuela eslovena. [1] L. Althusser: Filosofía y marxismo. Entrevista por Fernanda Navarro , Madrid, Siglo XXI, 1988, pp. 46-47. (shrink)
In an excerpt preserved by John Stobaeus in the chapter of the Anthologion entitled Peri tôn eph’hêmin, Porphyry addresses the issue of the origin of evil within the context of a broader investigation of individual autonomy : is it enough to envisage man as a subject with the freedom to act in order to make him responsible for evil and thus to free God of any responsibility with regard to the ills besetting individuals? An answer to this question is provided (...) on the basis of a comparative reading of the Myth of Er and of Homer. The conclusion reached is that evil is not intrinsic to human nature, but rather concerns certain forms of existence which individuals opt for when they disregard the divine and forego rationality. Consequently, God is not responsible for evil.The exegetical and argumentative strategy adopted by Porphyry in order to support this answer suggests that his stance is a polemical one, targeting Stoics in particular. Against Chrysippus’ reading of the same verses from Homer, which leads to a deterministic perspective, or at any rate one likely to prove inconsistent, Porphyry offers an interpretation of Homer as a coherent thinker and a forerunner of Plato : Homer is seen to have proposed a kind of dichotomy between the self-determination and the necessity that characterise the life of the soul, and as having assigned individuals the faculty of choosing between virtue and vice, thus making them ultimately responsible with regard to evil. (shrink)
En la sección titulada Irreversibilidad y el Poder de Perdonar en La Condición Humana, Arendt afirma que “el descubridor del papel del perdón en la esfera de los asuntos humanos fue Jesús de Nazaret”. En lo que sigue, quisiéramos aproximarnos al uso antiguo del verbo griego sungignôskô que a nuestro entender cumple el mismo papel que Arendt advierte en esta supuesta novedad cristiana —la “mutua exoneración de lo que se ha hecho”—, no sólo para entender en qué consistiría el descubrimiento (...) que Arendt atribuye a Jesús, sino porque creemos que la idea de que los griegos desconocían la facultad de perdonar es, si no falsa, al menos imprecisa. In the section titled Irreversibility and the Power to Forgive in the Human Condition, Arendt claims that “the discoverer of the role of forgiveness in the sphere of human affairs was Jesus of Nazareth”. In what follows, we would like to approach the ancient use of the Greek verb sungignôskô which, in our opinion, fulfills the same role that Arendt finds in this alleged Christian novelty —the “mutual exoneration of what has been done”— not only to understand what would the actual discovery Arendt attributes to Jesus imply, but because we believe claiming the Greeks were unaware of the faculty of forgiveness is, if not false, at least inaccurate. (shrink)
The Court of Appeals of New York held, in Council of the City of New York u. Giuliani, slip op. 02634, 1999 WL 179257, that New York City may not privatize a public city hospital without state statutory authorization. The court found invalid a sublease of a municipal hospital operated by a public benefit corporation to a private, for-profit entity. The court reasoned that the controlling statute prescribed the operation of a municipal hospital as a government function that must be (...) fulfilled by the public benefit corporation as long as it exists, and nothing short of legislative action could put an end to the corporation's existence.In 1969, the New York State legislature enacted the Health and Hospitals Corporation Act, establishing the New York City Health and Hospitals Corporation as an attempt to improve the New York City public health system. Thirty years later, on a renewed perception that the public health system was once again lacking, the city administration approved a sublease of Coney Island Hospital from HHC to PHS New York, Inc., a private, for-profit entity. (shrink)
