In this paper we will discuss the active part played by certain diagonal arguments in the genesis of computability theory. 1?In some cases it is enough to assume the enumerability of Y while in others the effective enumerability is a substantial demand. These enigmatical words by Kleene were our point of departure: When Church proposed this thesis, I sat down to disprove it by diagonalizing out of the class of the ??definable functions. But, quickly realizing that the diagonalization cannot be (...) done effectively, I became overnight a supporter of the thesis. (1981, p. 59) The title of our paper alludes to this very work, a task on which Kleene claims to have set out after hearing such a remarkable statement from Church, who was his teacher at the time. There are quite a few points made in this extract that may be surprising. First, it talks about a proof by diagonalization in order to test?in fact to try to falsify?a hypothesis that is not strictly formal. Second, it states that such a proof or diagonal construction fails. Third, it seems to use the failure as a support for the thesis. Finally, the episode we have just described took place at a time, autumn 1933, in which many of the results that characterize Computability Theory had not yet materialized. The aim of this paper is to show that Church and Kleene discovered a way to block a very particular instance of a diagonal construction: one that is closely related to the content of Church's thesis. We will start by analysing the logical structure of a diagonal construction. Then we will introduce the historical context in order to analyse the reasons that might have led Kleene to think that the failure of this very specific diagonal proof could support the thesis. This is a joint paper. We have both attempted to add a small piece to an amazing historical jigsaw puzzle at a juncture we feel to be appropiate. In the paper by Manzano 1997 the aforementioned words by Kleene were quoted, and since then several logicians, Enrique Alonso first and foremost, have questioned her on this issue. Here we both submit our reply. (1999, pp. 249--273). (shrink)
Shared agency is of central importance in our lives in many ways. We enjoy engaging in certain joint activities with others. We also engage in joint activities to achieve complex goals. Current approaches propose that we understand shared agency in terms of the more basic phenomenon of shared intention. However, they have presented two antagonistic views about the nature of this phenomenon. Some have argued that shared intention should be understood as being primarily a structure of attitudes of individual participants (...) and their interrelations (Bratman, Searle, Tuomela and Miller). Others have claimed that shared intention should be regarded as being primarily a normative transaction which gives rise to interpersonal obligations (Gilbert). In contrast to these approaches, I propose a compromise view. I argue that shared intention involves a complex socio-psychological structure which ensures, in the absence of special circumstances, the existence of relevant moral obligations. My argument involves two main steps. First, I show that shared intention includes important relations of mutual reliance between the participants. Then, I argue that the existence of these relations of mutual reliance in shared intention helps us explain why, failing special circumstances, shared intention generates those obligations. This provides, in my view, a solution to the vexed question of the relation between shared intention and interpersonal obligations. (shrink)
This paper focuses on the evolution of the notion of completeness in contemporary logic. We discuss the differences between the notions of completeness of a theory, the completeness of a calculus, and the completeness of a logic in the light of Gödel's and Tarski's crucial contributions.We place special emphasis on understanding the differences in how these concepts were used then and now, as well as on the role they play in logic. Nevertheless, we can still observe a certain ambiguity in (...) the use of the close notions of completeness of a calculus and completeness of a logic. We analyze the state of the art under which Gödel's proof of completeness was developed, particularly when dealing with the decision problem for first-order logic. We believe that Gödel had to face the following dilemma: either semantics is decidable, in which case the completeness of the logic is trivial or, completeness is a critical property but in this case it cannot be obtained as a corollary of a previous decidability result. As far as first-order logic is concerned, our thesis is that the contemporary understanding of completeness of a calculus was born as a generalization of the concept of completeness of a theory. The last part of this study is devoted to Henkin's work concerning the generalization of his completeness proof to any logic from his initial work in type theory. (shrink)
The growth of niche markets in rural industries has been one response to the restructuring of established agricultural industries in developed countries. In some cases entry into niche markets is part of a diversification of activities from other areas of farm-based production or services. In other cases, operators have sought to diversify from niche market production into other areas, such as on-site selling and agritourism. This paper outlines the findings of an exploratory qualitative study of the factors that olive farmers (...) in Western Australia take into account when considering diversification, with a special focus on diversification into servicing visitors in the form of on-site selling and agritourism. Face-to-face and telephone interviews were conducted among 23 small olive growing operations located in the main olive growing region of Western Australia. Decision-making is shown to involve an assessment of risk, which is shaped by their appraisal of economic conditions, market opportunities, access to resources (including labor), and lifestyle factors. The argument is made that a fuller understanding of diversification is gained by studying both those who seek to diversify and those who do not, in contrast to most previous research that has only focussed on those who diversify. Also argued is that diversification is best seen as a continuum of adjustment strategies, which is guided by a combination of economic need, risk assessment (based largely on resource access), market potential, and lifestyle factors. (shrink)
Este artículo trata de contextualizar la dificultad de entender el término innovación y por ello el conocimiento de los valores encerrados en ella. Se apuesta entonces por definir innovación como producto de la actividad humana en campos diferentes. Asimismo se toma como marco de referencia la axiología de los valores tecnocientíficos de J. Echeverría. A partir de ahí se examinan diferentes valores como el de libertad, convivencialidad y comunidad propios del movimiento “open”. Se concluye que en este movimiento existe una (...) apuesta decisiva de una innovación basada en valores. (shrink)
Explicit and implicit learning have been attributed to different learning processes that create different types of knowledge structures. Consistent with that claim, our study provides evidence that people integrate stimulus events differently when consciously aware versus unaware of the relationship between the events. In a first, acquisition phase participants sorted words into two categories , which were fully predicted by task-irrelevant primes—the labels of two other, semantically unrelated categories . In a second, test phase participants performed a lexical decision task, (...) in which all word stimuli stemmed from the previous prime categories and the primes were the labels of the previous target categories . Reliable priming effects in the second phase demonstrated that bidirectional associations between the respective categories had been formed in the acquisition phase , but these effects were found only in participants that were unaware of the relationship between the categories! We suggest that unconscious, implicit learning of event relationships results in the rather unsophisticated integration of the underlying event representations, whereas explicit learning takes the meaning of the order of the events into account, and thus creates unidirectional associations. (shrink)
The importance that banks have in our lives goes beyond the simple fact of being guardians of our money. The close relationship they have with political leaders affects us in every facet of life, including work, health, pensions, and social benefits in general. Being aware of this relationship warns us against the interested abuses by those who claim to represent us. Political leaders actually represent big capital. The most palpable evidence is the international refusal to ban tax havens that hide (...) great fortunes and escape the control of states. If we want global justice, few things are as unfair as the economic inequality that is encouraged by our leaders. It is us citizens who must clearly state what kind of society we want and what kinds of banks we want. Redistribution of wealth has become a social categorical imperative. There is no justice without economic equality. (shrink)
this article, I discuss the Protestant contribution to the modern concept of autonomy on the basis of an analysis of John Calvin's moral theology. I show that Calvin affirms our incapacity to know and want what is morally good, as expressed by natural law. Such incapacity is compensated for by the biblical mandates that, according to Calvin, should be incorporated into the positive legislation of Christian republics. In view of all this, I conclude that Calvin is far from the Kantian (...) idea of autonomy which defines our Modernity. (shrink)
El concepto de clases sociales pese a los cambios que ha sufrido está lejos de ser obsoleto, como algunos han llegado a afirmar. Las contradicciones sociales y la lucha clasista propiciada por las tensiones que generaban, hacen surgir una elite crítica que una vez instalada en el poder influye en lo..
Este trabajo constituye una revisión de los contenidos, orientación y objetivos de una parte significativa de los manuales de lógica elemental de las décadas de 1960 y 1970 redactados por autores españoles. En concreto, analizamos los prólogos, los rudimentos prerios, y la presentación de los distintos cálculos gue aparecen en tales obras. EI estudio de la semántica, los contenidos metatcóricos o las extensiones de Ia lógica elemental quedan para una segunda etapa de esta investigacion.This work is a critical examination of (...) contents, orientation, and goals of a significative portion of elementary spanish logic textbooks in the 60’s and 70’s. It is centered on an analysis ofprefaces, preliminaries and the different kinds of calculi appearing in these books. Topics, like semantics, metatheory or extensiones of elementary logic, are left for futrher analysis. (shrink)
La Teoría de la Computación es un campo especialmente rico para la indagación filosófica. EI debate sobre el mecanicismo y la discusión en torno a los fundamentos de la matemática son tópicos que estan directamente asociados a la Teoria de la Computación desde su misma creación como disciplina independiente. La Tesis de Turing-Church constituye uno de los resultados mas característicos en este campo estando, además, lleno de consecuencias filosóficas. En este ensayo se ofrece una guía de referencia útil a aquellos (...) que desean prestar alguna atención a estos asuntos y carecen de la base técnica o histórica que se precisa. En primer lugar se ofrece un resurnen de los principales problemas relacionados con la Tesis de Turing-Church para ofrecer a continuación información sobre sus aspectos más controvertidos. Se proponen algunos problemas no resueltos y se analiza su relevancia filosófica.Computer Science is a field specially rich for philosophical inquiry. Mechanism and the discussion around foundations of mathematics are topics directly asociated to Computer Science for its very constitution as an independent discipline. Church-Turing Thesis is one of the most characteristic results in this field and is plenty of philosophical consequences. In this article I offer a referenee guide useful for those who are willing to pay some attention to these matters and ignore the technical and historical basis needed for this task. I resume the main topics related to Church-Turing Thesis and give some informationabout the most controversial aspects of this subject. Some open questions are settled for further investigation paying special attention to their philosophical importance. (shrink)
Para abordar el miedo desde el Coaching, hay primero que definir qué es el Coaching. Según la Internacional Coach Federation (ICF), e Coaching profesional consiste en una relación profesional continuada que ayuda a obtener resultados extraordinarios en la vida, profesión, empresa o negocios de las personas. Mediante el proceso de Coaching, el cliente (coachee) profundiza en su conocimiento, aumenta su rendimiento y mejora su calidad de vida.
The tensorial relativistic quantum mechanics in (1+1) dimensions is considered. Its kinematical and dynamical features are reviewed as well as the problem of finding the Dirac spinor for given finite multivectors. For stationary states, the dynamical tensorial equations, equivalent to the Dirac equation, are solved for a free particle, for a particle inside a box, and for a particle in a step potential.
Después de ofrecer una definición tipológica de profesión, se presenta desde diversas perspectivas (la de los sociólogos, la de los historiadores y la de los mismos profesionales) la problemática actual de la ética de las profesiones. Se parte de la tesis de que, hoy por hoy, en este campo, todo planteamiento es deudor de la deontología médica. Se concluye afirmando que la ética profesional no puede ser patrimonio exclusivo de los profesionales, pero tampoco puede ser hecha sin ellos.
Leon Henkin (1921–2006) was not only an extraordinary logician, but also an excellent teacher, a dedicated professor and an exceptional person. The first two sections of this paper are biographical, discussing both his personal and academic life. In the last section we present three aspects of Henkin’s work. First we comment part of his work fruit of his emphasis on teaching. In a personal communication he affirms that On mathematical induction, published in 1969, was the favourite among his articles with (...) a somewhat panoramic nature and not meant exclusively to specialists. This subject is covered in the first subsection. Needless to say that we also analyse Henkin’s better known contribution: his completeness method. His renowned results on completeness for both type theory and first order logic were part of his thesis, The Completeness of Formal Systems, presented at Princeton in 1947 under the advise of Alonzo Church. It is interesting to note that he obtained the proof of completeness for first order logic readapting the argument for the theory of types. The last subsection is devoted to philosophy. The work most directly related to philosophy is an article entitled: Some Notes on Nominalism which appeared in the Journal of Symbolic Logic in 1953. Unfortunately, we are not covering his contribution to the field of cylindric algebras. As a matter of fact, Henkin spent many years investigating algebraic structures with Alfred Tarski and Donald Monk, among others. (shrink)
In this work we study the behavior of a time discrete multiregional stochastic model for a population structured in age classes and spread out in different spatial patches between which individuals can migrate. The dynamics of the population is controlled both by reproduction-survival and by migration. These processes take place at different time scales in the sense of the latter being much faster than the former. We incorporate the effect of demographic stochasticity into the population, which results in both dynamics (...) being modelled by multitype Bienaymé–Galton–Watson branching processes. We present a multitype global model that incorporates the effect of both processes and, making use of the existence of different time scales for demography and migration, build a reduced model in which the variables correspond to the total population in each age class. We extend previous results that relate the behavior of the original and the reduced model showing that, given a large enough separation of time scales between demography and migration, we can obtain information about the behavior of the multitype global model through the study of the simpler reduced model. We concentrate on the case where the two systems are supercritical and therefore the expected number of individuals grows to infinity, and show that we can approximate the asymptotic structure of the population vector and the asymptotic population size of the original system through the study of the reduced model. (shrink)
In this article I defend that Floridi’s Theory of Strongly Semantic Information – TSSI – is correct while encompassing the Veracity Thesis, which guides the semantic information definition as “p is information if and only if p is constituted by meaningful, truth well-formed data”. I argue that the theory is not arbitrary because it deals with important philosophical conundrums, mainly by avoiding the Bar-Hillel and Carnap paradox (1953) generated from the classical theory of semantic information. First, one of the classic (...) theory’s main result is discussed: the production of “too much informative sentences to be true”. Then the motivations to elaborate a “logic of being informed” are summarized and it is shown how the KTB-IL system is built and modelled keeping the veracity axiom among its axioms – K or A4. Finally the TSSI is examined and defended by showing that it aletically restricts the extension of the classic concept of information, avoiding problems with tautologies and contradictions. The TSSI offers an original solution by capturing our modal intuitions concerning informativeness as a basic notion. (shrink)
Von der Mehrzahl der Dimensionen kollektiver Identität erkundet diese Arbeit die Identität als rhetorisches Werkzeug. Die Identitätsmarke steht für einen für die pragmatische Effektivität relevanten Fall. Um eine solche Macht zu erläutern, wird ein hypothetisches Modell der Identitätskategorien dargeboten. Dessen Bestandsmodule formen vier Basisdimensionen: Position, Entindividualisierung, Ausschließung sowie kognitive Abschirmung. Eine so deskribierte narrative Identität wird zum Äquivalent der informellen Ideologie . Als konstitutive Rhetorik überführt die narrative Identitätskonstruktion die selbstreferenzielle Tautologie in die Strategien der Diskriminierung, Säuberung und Ausrottung der (...) Anderheitsvertreter. Die Massenvernichtungen des zurückliegenden Jahrhunderts – Totalitarismus, Kolonialismus, Ethnonationalismus – sind Fabrikate des Identitätsparadigmas. (shrink)
This is both an illuminating and penetrating study of the history of casuistry, and a persuasive argument for its relevance in contemporary ethics. The authors seek to revitalize "case argument as a fruitful method of practical moral reasoning". In so doing, they hope to steer safely between a rigid morality which holds to certain eternal and invariable principles, and a relativistic morality which repudiates the notion of an inflexible body of dogmatic principles. To support their contention, they provide a historical (...) account of the practice of casuistry, identify its shortcomings and past abuses, and try to reconstruct it to make it appetizing to a modern audience. (shrink)
Este ensayo ofrece un análisis crítico del último argumento que el matemático y filósofo Roger Penrose ofrece a favor de la tesis según la cual hay habilidades de la mente humana que nunca podrán ser igualadas por ingenio mecánico alguno. Al mismo tiempo se ofrece una descripción general de los últimos episodios del eterno enfrentamiento entre mentalismo y mecanicismo y se concluye con una sugerencia acerca de los puntos en los que cabe esperar nuevas situaciones de tensión entre estos dos (...) grandes paradigmas. Este trabajo pretende, además, mostrar la vigencia de un tipo de filosofía elaborada a partir de las herramientas de la ciencia moderna cuyos problemas son, no obstante, los del pensamiento filosófico tradicional. (shrink)
Parmi les nombreuses dimensions de l’identité collective, cet article examine celle de l’identité en tant qu’instrument rhétorique. Le repère identitaire est précisément un exemple d’efficacité pragmatique. Afin d’expliquer un tel pouvoir, un modèle hypothétique des catégories d’identité sera présenté. Ses éléments constitutifs forment quatre dimensions principales : position, désindividuation, exclusion et protection cognitive. L’identité narrative ainsi définie devient équivalente à une idéologie informelle . En tant que rhétorique constitutive , la construction narrative de l’identité transforme la tautologie autoréférentielle en stratégies (...) de discrimination, d’épuration et d’extermination du porteur d’altérité. Les violences massives du siècle passé – totalitarisme, colonialisme, ethno-nationalisme – sont tributaires du paradigme identitaire. (shrink)
En el presente artículo, el autor pretende hacer una reivindicación del proyecto humanista-cosmopolita de Immanuel Kant como un sistema adecuado para la integración de los intereses o fines individuales con los valores particulares y universales, aparentemente tan irreconciliables entre sí. En esta especie de "aldea global" que es nuestro mundo, no cabe obstaculizar la difusión general de los derechos humanos, y menos aún si esa limitación se lleva a cabo en aras de cualquier relativismo ético-cultural o soberanismo de estricta observancia. (...) Como contrapunto al concepto romántico de "comunidad nacional" -orgánica, monolítica, y estructurada jerárquicamente- que algunos intentan recuperar desde planteamientos localistas y excluyentes, reivindicamos los valores humanistas y universales de la Ilustración, en clara consonancia con las aspiraciones de un modelo de sociedad civil, abierto y plural como el que impera en el mundo occidental. Este hecho constituye también un motivo adecuado para evocar la modernidad del pensamiento político kantiano, en el cual se asientan las bases de una futura constitución cosmopolita que garantice a la humanidad una convivencia pacífica, racional y democrática. (shrink)