Turing and Church formulated two different formal accounts of computability that turned out to be extensionally equivalent. Since the accounts refer to different properties they cannot both be adequate conceptual analyses of the concept of computability. This insight has led to a discussion concerning which account is adequate. Some authors have suggested that this philosophical debate—which shows few signs of converging on one view—can be circumvented by regarding Church’s and Turing’s theses as explications. This move opens up the possibility that (...) both accounts could be adequate, albeit in their own different ways. In this paper, I focus on the question of whether Church’s thesis can be seen as an explication in the precise Carnapian sense. Most importantly, I address an additional constraint that Carnap puts on the explicative power of axiomatic systems—an axiomatisation explicates when it is clear which mathematical entities form the theory’s intended model—and that implicitly applies to axiomatisations of recursion theory used in Church’s account of computability. To overcome this difficulty, I propose two possible clarifications of the pre-systematic concept of “computability” that can both be captured in recursion theory, and I show how both clarifications avoid an objection arising from Carnap’s constraint. (shrink)

ABSTRACTEmotion regulation substantially develops during the childhood years. This growth includes an increasing awareness that certain ER strategies are more appropriate in some contexts than...

According to one of the most powerful paradigms explaining the meaning of the concept of natural number, natural numbers get a large part of their conceptual content from core cognitive abilities. Carey’s bootstrapping provides a model of the role of core cognition in the creation of mature mathematical concepts. In this paper, I conduct conceptual analyses of various theories within this paradigm, concluding that the theories based on the ability to subitize (i.e., to assess anexactquantity of the elements in a (...) collection without counting them), or on the ability to approximate quantities (i.e., to assess anapproximatequantity of the elements in a collection without counting them), or both, fail to provide a conceptual basis for bootstrapping the concept of an exact natural number. In particular, I argue that none of the existing theories explains one of the key characteristics of the natural number structure: the equidistances between successive elements of the natural numbers progression. I suggest that this regularity could be based on another innate cognitive ability, namely sensitivity to the regularity of rhythm. In the final section, I propose a new position within the core cognition paradigm, inspired by structuralist positions in philosophy of mathematics. (shrink)

This paper aims to explore and offer different hypotheses that could account for an adequate understanding of the duty to die and its relation to biopolitics from two neglected approaches. First, death will be analysed from a biopolitical perspective to understand the crucial role it has in biopower. Second, the focus lies on the two-folded implication that death has in biopower, for it could be either a defiance of it or the final sublimation of its control. Similarly, the next section (...) addresses the relations between death and neoliberalism from a biopolitical perspective, exploring the possibility of understanding the duty to die as resistance to economic mandates or, on the contrary, as the fulfilment of neoliberal interests. Finally, as a continuation of the relations between the duty to die and neo-liberalism, the paper analyses a similar two-folded view of the former from a psychopolitical perspective. (shrink)

This paper straightforwardly addresses one of the strongest, from an ethical perspective, objections presented to the duty to die, the one concerned with the lack of a normative theory to support it, offered by Seay in his paper Can there be a “duty to die” without a normative theory? The aim of the paper is to provide strong metaethical grounds to support the duty to die without the need of a moral normative theory. First, the definition and main argument for (...) the duty to die will be presented. Second, Seay’s objection will be described and clearly explained. Third, our metaphysical assumptions and a preliminary metaethical discussion will be offered to situate and understand the context. Finally, we will show how the duty to die can be integrated within the metaethical approach previously presented, defending that there is no need of a normative theory to provide good justification and strong ethical grounds for the duty to die, because they will have already been provided by our metaethical argument. (shrink)

When considering our own death, we normally weigh its impact on the people we love and care about, as well as worrying about the way in which our life might end, hoping that not too much suffering precedes it. However, such view, despite necessary, is a passive understanding of death, interpreted as something that merely happens to us, where we would have some control over timing if physician-assisted dying were legal in our countries. But what if our relation to death (...) would not end there? What if special medical needs, such as the emergency situation resulting from the Covid-19 pandemic, could have a direct impact on us creating a moral duty to end our lives? That is the thesis that will be advocated for in this paper: a moral duty to die will arise in some people to save resources that will help others get through Covid-19. It is important to indicate that the duty to die is personally acknowledged and self-imposed, thus nobody can be coerced to carry it out; for autonomy would be lost and such action should be considered an instance of incitement to die, therefore being morally blameworthy. (shrink)

Resumen En este artículo de reflexión se plantea que el concepto de ‘pensamiento crítico’ formulado por los pensadores del Movimiento de Pensamiento Crítico contiene un presupuesto que mina en gran medida su empresa: el movimiento asume que el pensador crítico desarrolla un autoconocimiento directo y transparente, lo que implicaría cuasi-infalibilidad. En la historia de la filosofía algunos pensadores han defendido esta posibilidad de un autoconocimiento directo e infalible, por ejemplo René Descartes y más recientemente Donald Davidson. Sin embargo, tal conocimiento (...) parece tener unos límites más o menos claros que no son tenidos en cuenta por los pensadores del MPC al formular su noción de pensamiento crítico, y debido a este presupuesto su proyecto filosófico e incluso pedagógico podría quedar sin fundamento.Palabras clave: pensamiento crítico; autoconocimiento; autoatribuciones infalibles; habilidades del pensamiento; disposiciones; estados mentales. (shrink)

History and Philosophy of Logic, Volume 32, Issue 2, Page 191-193, May 2011.

According to Perfect Being Theism, God is the absolutely perfect (i.e., greatest possible) being. The notion of absolute perfection can be analyzed in different ways. On one interpretation, to be absolutely perfect requires the exemplification of all absolute perfections. On another interpretation, to be perfect requires the exemplification of the best possible combination of perfections. It seems that the latter analysis is better than the former, because it does not fall prey to the problem of incompatible perfections, viz., that there (...) (probably) are perfections that cannot be coexemplified. Here I argue that even if perfect being theists accept the latter analysis, the problem of incompatibility does not go away. I argue that perfections are (probably) incomparable: it is false that some perfection is better than, worse than, or equally good to another perfection. If so, then it is impossible or at least extremely difficult to say that among the combination of perfections there are, there is one that is best among them. I also argue that adopting the former analysis with some restrictions (as Mark Murphy does) leads to the same incompatibility and incomparability problems. (shrink)

The main objective of this paper is to design a common background for various philosophical discussions about adequate conceptual analysis of “computation”.

The core of the problem discussed in this paper is the following: the Church-Turing Thesis states that Turing Machines formally explicate the intuitive concept of computability. The description of Turing Machines requires description of the notation used for the input and for the output. Providing a general definition of notations acceptable in the process of computations causes problems. This is because a notation, or an encoding suitable for a computation, has to be computable. Yet, using the concept of computation, in (...) a definition of a notation, which will be further used in a definition of the concept of computation yields an obvious vicious circle. The circularity of this definition causes trouble in distinguishing on the theoretical level, what is an acceptable notation from what is not an acceptable notation, or as it is usually referred to in the literature, “deviant encodings”. Deviant encodings appear explicitly in discussions about what is an adequate or correct conceptual analysis of the concept of computation. In this paper, I focus on philosophical examples where the phenomenon appears implicitly, in a “disguised” version. In particular, I present its use in the analysis of the concept of natural number. I also point at additional phenomena related to deviant encodings: conceptual fixed points and apparent “computability” of uncomputable functions. In parallel, I develop the idea that Carnapian explications provide a much more adequate framework for understanding the concept of computation, than the classical philosophical analysis. (shrink)

Euthanasia and the duty to die have both been thoroughly discussed in the field of bioethics as morally justifiable practices within medical healthcare contexts. The existence of a narrow connection between both could also be established, for people having a duty to die should be allowed to actively hasten their death by the active means offered by euthanasia. Choosing the right time to end one’s own life is a decisive factor to retain autonomy at the end of our lives. However, (...) there is no definitive consensus on why physicians should be the ones performing the medical procedure to end a person’s life. The moral problems arising from such assertion are not to be taken lightly, for medical tradition has long regarded the duty not to kill, not to actively end a patient’s life, as the core moral obligation that gives meaning to the medical profession. Our concern is to question the moral justifiability of the arguments offered by physicians not to actively help patients die. (shrink)

The use of artificial intelligence in healthcare contexts is highly controversial for the (bio)ethical conundrums it creates. One of the main problems arising from its implementation is the lack of transparency of machine learning algorithms, which is thought to impede the patient’s autonomous choice regarding their medical decisions. If the patient is unable to clearly understand why and how an AI algorithm reached certain medical decision, their autonomy is being hovered. However, there are alternatives to prevent the negative impact of (...) AI opacity in shared (healthcare professional–patient) decision-making processes, and benefit from the high accuracy of such systems. Despite these ethical issues, this paper advocates for its usage and also defends the positive role that it could have in enhancing patients’ autonomy. I advocate for a system where the implementation of AI is only partial, and humans will remain in control of oversighting algorithm interpretation of medical images and patients’ data. (shrink)

Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...) áreas fundamentales de la matemática, su aplicación en la lógica de primer orden, así como una breve descripción de las pruebas de consistencia relativa debidas a Gödel y Cohen, las cuales establecieron su independencia del sistema axiomático Zermelo-Fraenkel (ZF). Con todo lo anterior mostraremos cómo el quehacer matemático contemporáneo se adscribe al platonismo matemático en los términos de Bernays y Ferreirós. Revisaremos también los argumentos de Zermelo y Cantor para permitir el uso de asunciones en la matemática, los cuales se acercan a los planteamientos de la investigación científica y esbozan relaciones con la filosofía de la práctica matemática. Finalmente, justificamos el uso del axioma de elección en la contemporaneidad, abogando por unas relaciones de equidad entre la matemática y la filosofía, presentando además su plena vigencia, a través de la referencia a algunos problemas abiertos en la actualidad que vinculan el axioma de elección con la teoría de Ramsey. (shrink)

This paper reassesses the criticism of the Lucas-Penrose anti-mechanist argument, based on Gödel’s incompleteness theorems, as formulated by Krajewski : this argument only works with the additional extra-formal assumption that “the human mind is consistent”. Krajewski argues that this assumption cannot be formalized, and therefore that the anti-mechanist argument – which requires the formalization of the whole reasoning process – fails to establish that the human mind is not mechanistic. A similar situation occurs with a corollary to the argument, that (...) the human mind allegedly outperforms machines, because although there is no exhaustive formal definition of natural numbers, mathematicians can successfully work with natural numbers. Again, the corollary requires an extra-formal assumption: “PA is complete” or “the set of all natural numbers exists”. I agree that extra-formal assumptions are necessary in order to validate the anti-mechanist argument and its corollary, and that those assumptions are problematic. However, I argue that formalization is possible and the problem is instead the circularity of reasoning that they cause. The human mind does not prove its own consistency, and outperforms the machine, simply by making the assumption “I am consistent”. Starting from the analysis of circularity, I propose a way of thinking about the interplay between informal and formal in mathematics. (shrink)

This is a descriptive and detailed revision of qualitative investigations of coping styles and strategies; academic performance of adolescent students. It considered both, independent and correlational studies among the two variables. Different data bases were revised like Dialnet, Redalyc, Scielo y Science Direct. 479 articles were obtained from these, 46 of these responded to the selection criteria that entailed (research article, indexed journal, adolescents). Alongside this search there was a prevalence of the studies related to different variables and their relationship (...) with coping styles and strategies. The studies present common results in terms of positive correlations between active coping styles and well being. (shrink)

En su artículo, Leonardo Ruíz Gómez busca dilucidar la articulación leibniciana entre fuerza primitiva y fuerza derivativa, de modo que se tengan luces sobre uno de los asuntos problemáticos de la propuesta de Leibniz, a la vez que se aporten elementos de comprensión para una posible articulación entre la dinámica y la metafísica leibnicianas. Mi texto breve es un comentario del artículo de Ruíz Gómez en el que reconstruyo de manera general la estructura de su texto y señalo algunas inquietudes (...) y reparos frente al análisis que Ruíz Gómez hace de tres caraterizaciones de la fuerza derivativa y de la articulación de esta con la fuerza primitiva. (shrink)

El presente ensayo quiere profundizar en el alcance de la metáfora “el amigo es otro yo” contenida en la Ética a Nicómaco 1166a, 31-32. En términos epistemológicos, evaluaremos cómo esta metáfora tiene relación con (i) el tipo de entidad que es el amigo y (ii) el tipo de relación que es la amistad. En cuanto al ámbito psicológico, se someterá a examen el grado de identidad implícito en la metáfora. Es decir, mediante un examen de diversos pasajes del libro IX (...) de la Ética a Nicómaco, argumentaremos que el grado de identidad implícito en la metáfora “el amigo es otro yo” admite ciertas diferencias de carácter y de opinión, pues esto también es propio del tipo específico de relación que es la amistad virtuosa. (shrink)

This paper discusses the introduction of fraudulent “molecular detector” technology into Mexico. The case is used to argue that contemporary science and technology studies’ approaches to scientific policy-making make basic assumptions about the societies they operate in that are inconsistent with the Mexican context. This paper also argues that contrary to what happens in the so-called Global North, the relative power of Mexican science in government and policy circles is as much limited by its relatively weak position as much as (...) it is by self-censorship and unrealized impact in the country’s fragile democracy. The case is also used to highlight the necessity for more politically involved scientific institutions in Mexico, as these become critical safeguards against incoming destabilizing technologies from more powerful nations into the local “peripheral” context. (shrink)

Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...) de forma estándar, lo único que hemos leído es su motivación como condición necesaria. El objetivo de este trabajo es ofrecer una fundamentación de las mismas usando la noción de conjunto (o clase) y la técnica de diagramas de Venn, un concepto y una técnica que están expuestos en los principales textos de lógica elemental, incluyendo el referido anteriormente. -/- Abstract: Currently, one of the most widely used textbooks in elementary logic is the one by Irving Copi and Carl Cohen (Introduction to Logic, 2001). They offer rules for deciding the validity of standard categorical syllogisms. But neither that textbook, nor any other we know of, provides the foundations of these rules; that is to say, the demonstration that they are a necessary and sufficient condition for the validity of a standard categorical syllogism. We have only found motivations for the necessary condition. The main goal of this work is to provide a foundation of these rules using the notion of set as well as Venn diagrams, a concept and a technique exposed in the main textbooks of logic, including the aforementioned. (shrink)

ObjectiveTo determine the factors associated with quality of life and depressive symptoms in Peruvian university students during the COVID-19 pandemic.MethodsMulticentre study in 1,634 students recruited by convenience sampling. The quality of life was assessed with the European Quality of Life-5 Dimensions at three levels and depressive symptoms with the Patient Health Questionnaire-9. To assess factors associated with QoL and depressive symptoms, linear regressions and fitted regressions were used, with robust coefficients of variance information.ResultsA 345 reported problems in performing daily activities, (...) 544 reported pain and discomfort, 772 were moderately/very anxious or depressed. Furthermore, 207 had moderate-severe and severe depressive symptoms. Men reported better QoL than women and fewer depressive symptoms. Ayacucho’s residents had more depressive symptoms than Ancash’s residents and Piura’s residents had fewer depressive symptoms than Ancash’s residents. Students who left home during quarantine reported more depressive symptoms.ConclusionProblems performing daily activities, pain and discomfort, as well as mild to severe depressive symptoms were found in more than three-quarters of the sample. Authorities could consider depression care to improve quality of life in regions where high rates of infection occurred during the pandemic. (shrink)

The aim of this paper is to point out significant and meaningful overlapping between several styles of scientific thinking, as they were proposed by Crombie (1981) and discussed by Hacking (1985; 2009). This paper is divided in four sections. First, I examine an interpretation made by Barnes (2004) about the incompatibility among scientific styles. As explained by its author, this interpretation denies any possibility of similarities between styles of scientific reasoning. In opposition, the following sections of this paper include explanations (...) of relevant characteristics of Geometry, as stated in Euclid's Elements, which are also present in other three scientific styles: modeling, experimental exploration and taxonomic style (and some of the shared characteristics are even used to define such styles). By stressing out these characteristics I argue that these four styles discussed by Hacking are not so different from each other, in fact, they overlap and may even be abridged into one foundational style: geometric. El objetivo de este artículo consiste en explicar traslapes importantes y significativos entre varios estilos de pensamiento científico, tal como fueron propuestos por Crombie (1981) y discutidos por Hacking (1985; 2009). El presente artículo está dividido en cuatro secciones. Primero, se examina la interpretación de Barnes (2004) sobre la incompatibilidad entre diversos estilos. Según este autor, no existe posibilidad alguna de encontrar similitudes en los estilos de razonamiento científico. En oposición a esta interpretación, las siguientes secciones explican características relevantes de la Geometría, tal como fueron plasmadas en Los Elementos de Euclides, y que están presentes en otros tres estilos: de modelación, de experimentación y taxonómico (las características compartidas incluso definen algunos de estos estilos). Destacar estas características me permite argumentar que estos cuatro estilos discutidos por Hacking no son tan diferentes entre sí, de hecho, se traslapan e incluso pueden ser condensados en un estilo fundacional: el geométrico. (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

Mounting evidence suggests that participation in clinical trials confers neither advantage nor disadvantage on those enrolled. Narrow focus on the question of a “trial effect,” however, distracts from a broader mechanism by which patients may benefit from ongoing clinical research. We hypothesize that the existence of clinical trials infrastructure—the organizational culture, systems, and expertise that develop as a product of sustained participation in cooperative clinical trials research—may function as a quality improvement lever, improving the quality of care and outcomes of (...) all patients within an institution or region independent of their individual participation in trials. We further contend that this “infrastructure effect” can yield particular benefits for patients in low- and middle-income countries. The hypothesis of an infrastructure effect as a quality improvement intervention, if correct, justifies enhanced research capacity in LMIC as a pillar of health system development. (shrink)