This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in much (...) more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included. (shrink)

Provability, Computability and Reflection.

Purpose. The paper is aimed at studying the peculiarities of the Oleksandr Kulchytskyi’s doctrine of human, taking into account the context of European philosophy and especially in comparison with the paradigm of philosophizing in the Lviv-Warsaw school. The theoretical basis of the study is determined by Kulchytskyi’s scholarly works in the field of philosophy and philosophical anthropology, as well as the latest researches that reinterpret the influence of Twardowski’s theoretico-methodological ideas on the formation of the philosophical worldview of the Ukrainian (...) thinker. Originality. Based on the appeal to primary sources, Kulchytskyi’s philosophical doctrine of human in the unity of its basic principles and theoretico-practical results is reconstructed. The ways of forming the key ideas of his philosophical anthropology are determined, their originality is substantiated, despite the cooperation with Twardowski’s school, as well as despite numerous discussions and researches of Western European philosophico-anthropological, existentio-ideological and socio-psychological issues. Conclusions. It is found out how the philosophical worldview of Oleksandr Kulchytskyi was formed and how he gradually came from the research of the human psyche within the framework of anthropological structural psychology to the realization of the need to study philosophical anthropology. The personalistic features of his philosophical doctrine of human are characterized; in particular, attention is paid to the distinction between the concepts of person and personality, determining the importance of the social factor for the formation of human worldview, didactic aims of anthropological studies. It is shown how in Kulchytskyi’s philosophical anthropology the analysis of the existentio-worldview dimension of human existence, manifested in different spiritual situations and socio-cultural conditions that influence the specifics of thinking and the nature of the personality mentality, acquires special importance. The originality of Kulchytskyi’s arguments about human in the context of both Ukrainian philosophy and in general European philosophical thought is stated. (shrink)

Purpose. To examine the existential anthropology of G. Marcel and E. Minkowski, in order to demonstrate the necessity of distinguishing the universal-spiritual, as human in human being, apart from the individual-existential in him, and to reveal the hierarchical correlation of biosocial, existential and spiritual spheres in personality. Theoretical basis. Within existential philosophy the author differentiates two separate traditions and proceeds from the insufficiency of the distinction of existential sphere, proposed by phenomenological tradition, showing the necessity of its correlation with the (...) spiritual sphere as a sphere of humanity, proposed by non-phenomenological tradition of G. Marcel and E. Minkowski. Originality. The author presents the anthropological conception of G. Marcel and E. Minkowski, in which human personality is understood as unity of individual-existential and universal-spiritual, which requires a special trans-empirical field of culture, which contains senses, images and symbols of humanity. Also, the author presents the recent developments of existential thinkers in distinguishing existential and spiritual dimensions, both not reducible to the physical and social dimensions. Conclusions. In both existential traditions, the specifically human was founded as a trans-biological and trans-social phenomenon, which appears as indefinable and non-predetermined. But in first tradition, humanity is understood as an existence, as a unique individuality, "project", variant of humanity, equivalent to other variants, and universal is understood as a community of human condition in the world. While in the second tradition, the universal is understood as spiritual. Thus, horizontal level of our private existence, as the process of movement from birth to death, is supplemented by vertical of human, universal ideals and images. Humanity appears as a task, on the way to which human being transcends beyond the limits of his individual "self" to the "super-individual", through inclusion into spiritual community, into universal culture. (shrink)

On fundamentals of Nyaya philosophy with Nūtanāloka autocommentary and Ālokaprakāśa commentary by disciples.

In this paper, I offer an expansionist view of the Frickerian central case of testimonial injustice, citing examples from the South Asian context. To defend this expansionist position, I provide an argument in three parts. First, I argue that credibility deficit and credibility excess are entangled with each other in such a way that often, one produces the other. Secondly, I contend that we should not say that systematic testimonial injustice is a consequence of credibility deficit only because of the (...) entanglement between them. I also contend that for being the central case of testimonial injustice, identity prejudice should not be necessarily negative; it can be positive as well. Propounding a twofold condition of the status of a knower, the last part claims that testimonial injustice occurs when one of the two conditions remains unmet. (shrink)

Spiritual value and business ethics in halal label on Indonesian products.

A lógica não contém teoremas puramente existenciais: as únicas sentenças existenciaisválidas são aquelas com análogas universais válidas. Aqui, mostramos que istorealmente é assim quando corretamente interpretado: toda validade ex- istencial possuiuma análoga universal simples, que também é válida. Também caracterizamos validadesuniversais e existenciais em termos de tautologias.

No part ot Plato's writings has been more debated than the three similes in Books VI.-VII. of the Republic, and still there is a diversity of opinion about their meaning. I believe that most of these difficulties arise from certain assumptions about their purpose which need revision. The current view applies the Cave to the Line, as Plato seems to direct, and this application, which is itself attended by considerable difficulties, leads to an assimilation of the two figures till they (...) seem to have much the same content and purpose. Again, as this makes the lower line appear to be the phenomenal world, it is thought that the simile of the sun foreshadows the theme of the Line by hinting at a connexion between the intelligible and the sensible which is made more explicit in the Line. Thus the group of similes seem mainly intended to show the dependence of Becoming upon Being. This paper will argue that such a view depends upon the misrepresentation of the symbolism adopted by Plato, that two antithetical groups of symbols are confused with one another, and that symbols are even identified with antitypes. Owing to these misinterpretations the Form of the Good has been mistaken for a material cause; both the Line and the Cave have been thought to reveal Plato as embarrassed by a dualism between sense and intellect, and the purpose of the Cave in particular, since the error is cumulative, has been completely obscured. This paper will attempt to substitute for current accounts another interpretation which will relate the three similes closely with the political arguments of Book VI., and with the Platonic education which is set forth in close connexion with them. (shrink)

The first part of this paper argued that the traditional application of the Cave to the Line was not intended by Plato, and led to a misunderstanding of both similes. The Cave, it was said, is attached to the simile of the Sun and the Line by the visible region outside the cave, which is a reintegration of the symbolism of sun, originals and images in the sunlight, and the new system of objects inside the cave is compared and contrasted (...) with the natural objects in the visible outside. As we know that the natural symbolism illustrates the Platonic education, our main task in this paper will be to find the meaning of the cave, untrammelled by the associations of the lower line. (shrink)

The similes of the Sun, Line, and Cave in the Republic remain a reproach to Platonic scholarship because there is no agreement about them, though they are meant to illustrate. I propose to analyse the form of the argument, a clue that has never been properly weighed. The Greek theory and practice of analogia and diairesis give good evidence about the method that Plato adopted; if this usage were respected, the analogical argument would not be so loosely interpreted, and the (...) double diairesis and proportion that the Line actually is could not be mistaken for a classification. I hope also to show that Plato's terminology is definite and consistent; here too ancient usage helps to establish his meaning. (shrink)