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)

What have the following in common: Epimetheus, Paris, Anchises, and the suitors of Penelope? The ready answer might be that it must have something to do with women, for it requires no great thought to see that the attractions of femininity proved the undoing of three of them, while for Anchises life was never to be the same again after his encounter with Aphrodite. But suppose we add to our first group such figures as Zeus, Priam, Polynices, and Eumaeus? The (...) fates of all these characters as they, appear at certain points in the poetry of Homer, Hesiod, and others give expression i to a network of interrelated sexual and economic anxieties that seem to underlie a { great deal of what the Archaic poets say about the female sex. In this article I 1 propose to explore a particular part of that network, which I have called the ? ‘Pandora complex’, since it is Hesiod′s version of the Pandora myth which provides the classic statement of the male dilemma over women, poised between the conflicting desires for sexual gratification and domestic stability.1. (shrink)

HSÜN Tzu's essay on "Rectifying Terms" is justly considered a work of "great logical interest." For in this essay, one finds a remarkably modern concern with such topics as the rationale for having terms; the empirical and pragmatic bases for the classification of terms; the formation of generic and specific terms; the importance of observing established linguistic practices; the necessity of complying with proper standards for the institution, ratification, and regulation of the uses of language ; the nature of argumentative (...) discourse ; and the problems inherent in successful linguistic communication. A careful examination of some passages in other essays also suggests an awareness of the distinction between deductive, inductive, and analogical inferences, though Hsün Tzu provides us no explicit discussion of the nature of reasoning and its validating rules. (shrink)

UNTIL RECENT YEARS moral traditions have not been an important topic for moral philosophy. With few exceptions, attention has been directed to the problem of moral justification, to the search for universal criteria for the assessment of moral beliefs or judgments regardless of their traditional provenance. Generally, philosophers aspire to formulate "the view from nowhere." Since the publication of Alasdair MacIntyre's After Virtue there has been a revival of interest in the concept of a living, moral tradition, especially among moral (...) philosophers concerned with the possibility of an ethics of virtue or character as a viable alternative to the ethics of principle or, say, to deontological, utilitarian, or contractarian ethics. We must observe here that in the three decades prior to 1981, some moral philosophers displayed similar concern with tradition, although terms other than "tradition" were used, for example, "forms of life," "ways of life," "moral practices," and "moral community." Rawls's conception of reflective equilibrium is also developed with an eye on the notion of tradition. Indeed, Rawls has been quite explicit about his tradition-oriented approach to moral theory: "What justifies a conception of justice is not its being true to an order antecedent to and given to us, but its congruence with our deeper understanding of ourselves and our aspirations, and our realization that, given our history and the traditions embedded in our public life, it is the most reasonable doctrine.". (shrink)

THIS ESSAY PRESENTS A CONFUCIAN PERSPECTIVE ON LI. My main concern is the question, “How can a Confucian moral philosopher move from the ethical to the religious dimension of li?” Section 1 provides an analysis of the scope, evolution, functions, and a brief discussion of the question of justification of li. Section 2 deals with the inner aspect of the foundation of conduct, the motivational aspect of li-performance. Section 3 discusses the outer aspect of the foundation of li, focusing on (...) Hsün Tzu’s vision of the triad of t’ien, earth, and humanity, an interpretation of his use of t’ien, shen and shen-ming as expressing a respect for established linguistic, religious practice without an endorsement of associated popular religious beliefs. This interpretation leaves open the question of the validity of reasoned religious beliefs, while presuming the religious dimension of li as extension of Confucian ethics. Section 4 centers on the ethical significance of the li of mourning and sacrifice and the more general question on the efficacy of li, and concludes with some remarks on the transformative significance of the religious dimension of li. (shrink)