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.

In this article, we present results from a literature review of intrinsic, instrumental, and relational values of nature conducted for the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services, as part of the Methodological Assessment of the Diverse Values and Valuations of Nature. We identify the most frequently recurring meanings in the heterogeneous use of different value types and their association with worldviews and other key concepts. From frequent uses, we determine a core meaning for each value type, which is (...) sufficiently inclusive to serve as an umbrella over different understandings in the literature and specific enough to help highlight its difference from the other types of values. Finally, we discuss convergences, overlapping areas, and fuzzy boundaries between different value types to facilitate dialogue, reduce misunderstandings, and improve the methods for valuation of nature's contributions to people, including ecosystem services, to inform policy and direct future research. © 2023 The Author(s). Published by Oxford University Press on behalf of the American Institute of Biological Sciences. (shrink)

Open theists argue that God's relationship to time, as conceived in classical theism, is erroneous. They explain that it is contradictory for an atemporal being to act in a temporal universe, including experiencing its temporal successions. Contrary to the atemporalists, redemptive history has shown that God interacts with humans in time. This relational nature of God nullifies the classical notion of God as timelessly eternal. Therefore, it lacks a philosophical and theological basis. Because God is in time, He does not (...) know all future contingencies and, therefore, changes. This study examines open theism's appropriation of the A and B theories of time to the divine-human relationship. The study argues that divine temporality does not solve the tension of divine-human relationships, especially in relation to the future. Further, historical divine temporality does not negate the fact of divine atemporality. It mainly stems from God's choice to create temporal creatures and His relationship with them. Furthermore, if it is not logically and metaphysically contradictory for an omnipresent being to act in space, then it follows that an atemporal being can act in time. Whether time is understood from the metric or psychological point of view, it does not transcend God, and therefore, the limitation it places on human creatures with respect to the future does not apply to God. Lastly, although a few philosophers reject the notion of eternity as timelessly eternal, the doctrine has a philosophical and theological basis in the Scripture. (shrink)

The fundamental ideas concerning computation and recursion naturally find their place at the interface between logic and theoretical computer science. The contributions in this book, by leaders in the field, provide a picture of current ideas and methods in the ongoing investigations into the pure mathematical foundations of computability theory. The topics range over computable functions, enumerable sets, degree structures, complexity, subrecursiveness, domains and inductive inference. A number of the articles contain introductory and background material which it is hoped will (...) make this volume an invaluable resource for specialists and non-specialists alike. (shrink)

t. 1. Obshchai︠a︡ teorii︠a︡ prava. Ugolovnoe pravo -- t. 2. Kriminologii︠a︡, sot︠s︡iologii︠a︡, konfliktologii︠a︡ -- t. 3. Politologii︠a︡, ideologii︠a︡, ėtika.

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)