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.

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent (...) computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate. (shrink)

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)