To cope with the intersubjective and communicative deficiencies of Heidegger's Analytics of Existence, Hans-Georg Gadamer developed a theory of language whose nature is at one time phenomenological and ontological. Inspired by Plato's dialectics and Aristotle's ethical and rhetorical works, Gadamer sees human linguistic capabilities as the defining trait of all that is human. Language lives in conversation, dialogically structuring all social and cultural relations. Language is the ambit in which human beings and their historical world take place. In Gadamer's thought, (...) logos replaces being as the ontological support. In such a way, Gadamer's hermeneutical philosophy seeks to fill the void opened by the 20th Century deconstruction of Metaphysics. (shrink)

The Modern concept of truth, which subjects truth to certainty, broke the harmonious relation between reality and truth, that prevailed in Ancient and Medieval Philosophy. Hans-Georg Gadamer thinks that the main task of contemporary Philosophy is to recover the original harmony of being and knowledge. To shed light on the nature of this problem, we expound the metaphysical-theological foundation of truth, which is at the roots of Aristotelian and Thomistic Philosophies. Specifically, we analyze here the relation between being, truth and (...) logos in the Aristotelian treatise Perì Hermeneías, and in its Thomistic commentary. (shrink)

Gianni Vattimo's Non-religious Christianity. Weakening of being, secularization and divine kenosis.

After the collapse of the Hegelian philosophy, many thinkers returned to the main principles of Kantian transcendentalism. In this way, they initiated the neo-kantian movement. Wilhelm Dilthey was among them. Nevertheless, only in spirit can his “Critique of the Historical Reason” be called neo-kantian. In fact, the core of Dilthey’s project, the “Categories of Life”, is a completely new gnoseological proposal, that mediates between transcendental philosophy and empiricism.

These pages present the method used by Socrates to teach his disciples to think critically, Leonard Nelson's attempt to apply it in the early 20th century to the teaching of philosophy in schools, and the potential of its use in the contemporary context.

Centrando la mirada en Cristo, las enseñanzas de Benedicto XVI desarrollan la íntima conexión que existe entre las tres virtudes teologales y la Verdad Encarnada, el Hijo de Dios hecho hombre. En efecto, no nos es posible creer en Jesucristo, amarlo y esperar en Él, si no conocemos su verdadero rostro, que se revela al intelecto humano iluminado por la fe. Este hecho pone en evidencia que el hombre necesita su natural capacidad de conocer la verdad para poder descubrir el (...) rostro de Cristo. Si se disocia de la razón, la fe cristiana pierde credibilidad y se convierte en una opción existencial arbitraria, pues resulta imposible argumentar racionalmente sobre ella. Por otra parte, las relaciones sociales y políticas se deshumanizan si se expulsa de la vida pública a las razones de la fe, porque una cultura que cierra sus puertas a Dios deja también afuera al hombre. Podremos alejar estos peligros sólo si la razón y la fe se reencuentran de un modo nuevo. Sin embargo, antes tenemos que recuperar la fe en la razón, es decir, nuestra confianza en su capacidad de conocer la verdad en toda su amplitud. (shrink)

Measurements are shown to be processes designed to return figures: they are effective. This effectivity allows for a formalization as Turing machines, which can be described employing computation theory. Inspired in the halting problem we draw some limitations for measurement procedures: procedures that verify if a quantity is measured cannot work in every case.

This paper investigates the status of the fragments of Peano Arithmetic obtained by restricting induction, collection and least number axiom schemes to formulas which are $${\Delta_1}$$ provably in an arithmetic theory T. In particular, we determine the provably total computable functions of this kind of theories. As an application, we obtain a reduction of the problem whether $${I\Delta_0 + \neg \mathit{exp}}$$ implies $${B\Sigma_1}$$ to a purely recursion-theoretic question.

We characterize the sets of all Π2 and all equation image theorems of IΠ−1 in terms of restricted exponentiation, and use these characterizations to prove that both sets are not deductively equivalent. We also discuss how these results generalize to n > 0. As an application, we prove that a conservation theorem of Beklemishev stating that IΠ−n + 1 is conservative over IΣ−n with respect to equation image sentences cannot be extended to Πn + 2 sentences. © 2011 WILEY-VCH Verlag (...) GmbH & Co. KGaA, Weinheim. (shrink)

Background and objective: Assuming the hypothesis that the general practitioner can and should be a key player in making end-of-life decisions for hospitalised patients, perceptions of GPs’ role assigned to them by hospital doctors in making withdrawal decisions for such patients were surveyed.Design: Questionnaire survey.Setting: Urban and rural areas.Participants: GPs.Results: The response rate was 32.2% , and it was observed that 70.8% of respondents believed that their participation in withdrawal decisions for their hospitalised patients was essential, whereas 42.1% believed that (...) the hospital doctors were sufficiently skilled to make withdrawal decisions without input from the GPs. Most respondents were found to believe that they had the necessary skills and enough time to participate in withdrawal decisions. The last case of treatment withdrawal in hospital for one of their patients was described by 40% of respondents, of whom only 40.0% believed that they had participated actively in the decision process. The major factors in the multivariate analysis were the GP’s strong belief that his or her participation was essential , information on admission of the patient given to the GP by the hospital department , rural practice , visit to the patient dying in hospital and a request by the family to be kept informed about the patient .Conclusion: Strong interest was evinced among GPs regarding end-of-life issues, as well as considerable experience of patients dying at home. As GPs are more closely corrected to patients’ families, they may be a good choice for third-party intervention in making end-of-life decisions for hospitalised patients. (shrink)

By a theorem of R. Kaye, J. Paris and C. Dimitracopoulos, the class of the Πn+1-sentences true in the standard model is the only consistent Πn+1-theory which extends the scheme of induction for parameter free Πn+1-formulas. Motivated by this result, we present a systematic study of extensions of bounded quantifier complexity of fragments of first-order Peano Arithmetic. Here, we improve that result and show that this property describes a general phenomenon valid for parameter free schemes. As a consequence, we obtain (...) results on the quantifier complexity, finite axiomatizability and relative strength of schemes for Δn+1-formulas. (shrink)

For a theory T, we study relationships among IΔ n +1 (T), LΔ n+1 (T) and B * Δ n+1 (T). These theories are obtained restricting the schemes of induction, minimization and (a version of) collection to Δ n+1 (T) formulas. We obtain conditions on T (T is an extension of B * Δ n+1 (T) or Δ n+1 (T) is closed (in T) under bounded quantification) under which IΔ n+1 (T) and LΔ n+1 (T) are equivalent. These conditions depend (...) on Th Πn +2 (T), the Π n+2 –consequences of T. The first condition is connected with descriptions of Th Πn +2 (T) as IΣ n plus a class of nondecreasing total Π n –functions, and the second one is related with the equivalence between Δ n+1 (T)–formulas and bounded formulas (of a language extending the language of Arithmetic). This last property is closely tied to a general version of a well known theorem of R. Parikh. Using what we call Π n –envelopes we give uniform descriptions of the previous classes of nondecreasing total Π n –functions. Π n –envelopes are a generalization of envelopes (see [10]) and are closely related to indicators (see [12]). Finally, we study the hierarchy of theories IΔ n+1 (IΣ m ), m≥n, and prove a hierarchy theorem. (shrink)

In this paper we continue the study of the theories IΔ n+1 (T), initiated in [7]. We focus on the quantifier complexity of these fragments and theirs (non)finite axiomatization. A characterization is obtained for the class of theories such that IΔ n+1 (T) is Π n+2 –axiomatizable. In particular, IΔ n+1 (IΔ n+1 ) gives an axiomatization of Th Π n+2 (IΔ n+1 ) and is not finitely axiomatizable. This fact relates the fragment IΔ n+1 (IΔ n+1 ) to induction (...) rule for Δ n+1 –formulas. Our arguments, involving a construction due to R. Kaye (see [9]), provide proofs of Parsons’ conservativeness theorem (see [16]) and (a weak version) of a result of L.D. Beklemishev on unnested applications of induction rules for Π n+2 and Δ n+1 formulas (see [2]). (shrink)

We consider the concept of poverty from the asset-accumulation approach and propose an integrated framework, building upon existing theories, to describe how the interconnected factors of trust (or lack thereof) and social distance can reinforce poverty traps. Social distance is influenced by choice, while trust is the symptom that defines the strength of social ties on a group. We look at how an absence of trust influences how households make decisions about the use and accumulation of assets in ways that (...) could perpetuate poverty. Weak trust also affects how groups interact with each other in a society, creating “trust clusters” within homogeneous groups and antagonism across groups, which in turn affects aspirations and leads to an erosion of the basis of a social contract. For more effective and sustainable poverty reduction, we need to understand these linkages and address them systematically. (shrink)

A well known theorem proved by J. Paris and H. Friedman states that BΣn +1 is a Πn +2-conservative extension of IΣn . In this paper, as a continuation of our previous work on collection schemes for Δn +1-formulas , we study a general version of this theorem and characterize theories T such that T + BΣn +1 is a Πn +2-conservative extension of T . We prove that this conservativeness property is equivalent to a model-theoretic property relating Πn-envelopes and (...) Πn-indicators for T . The analysis of Σn +1-collection we develop here is also applied to Σn +1-induction using Parsons' conservativeness theorem instead of Friedman-Paris' theorem.As a corollary, our work provides new model-theoretic proofs of two theorems of R. Kaye, J. Paris and C. Dimitracopoulos : BΣn +1 and IΣn +1 are Σn +3-conservative extensions of their parameter free versions, BΣ–n +1 and IΣ–n +1. (shrink)

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

We study the quantifier complexity and the relative strength of some fragments of arithmetic axiomatized by induction and minimization schemes for Δn+1 formulas.

El objetivo de esta investigación es poner de manifiesto la importancia de las imágenes de vestir marianas y, también, las joyas y accesorios que presentan. Se plantearán las bases y claves de un lenguaje no verbal que actúa como testimonio de la devoción además de las relaciones sociales y económicas del momento que las marcan. Merced a los casos analizados, se comprobará cómo, con gran frecuencia, se une a la piedad popular de pueblos y de las culturas de determinados acontecimientos (...) de la zona. Los resultados demostrarán la importancia dada y valores atribuidos a este tipo de iconografía. (shrink)

In this paper we study the axiomatic system proposed by Bourbaki for the Theory of Sets in the Éléments de Mathématique. We begin by examining the role played by the sign \(\uptau \) in the framework of its formal logical theory and then we show that the system of axioms for set theory is equivalent to Zermelo–Fraenkel system with the axiom of choice but without the axiom of foundation. Moreover, we study Grothendieck’s proposal of adding to Bourbaki’s system the axiom (...) of universes for the purpose of considering the theory of categories. In this regard, we make some historical and epistemological remarks that could explain the conservative attitude of the Group. (shrink)

The progress of Mathematics during the nineteenth century was characterised both by an enormous acquisition of new knowledge and by the attempts to introduce rigour in reasoning patterns and mathematical writing. Cauchy’s presentation of Mathematical Analysis was not immediately accepted, and many writers, though aware of that new style, did not use it in their own mathematical production. This paper is devoted to an episode of this sort that took place in Spain during the first half of the century: It (...) deals with the presentation of a method for numerically solving algebraic equations by José Mariano Vallejo, a late Spanish follower of the Enlightenment ideas, politician, writer, and mathematician who published it in the fourth (1840) edition of his book Compendio de Matemáticas Puras y Mistas, claiming to have discovered it on his own. Vallejo’s main achievement was to write down the whole procedure in a very careful way taking into account the different types of roots, although he paid little attention to questions such as convergence checks and the fulfilment of the hypotheses of Rolle’s Theorem. For sure this lack of mathematical care prevented Vallejo to occupy a place among the forerunners of Computational Algebra. (shrink)