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.

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)

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)

Research collaboration beyond national jurisdiction is one aspect of the globalisation of health research. It has potential to complement researchers in terms of research skills, equipment and lack of adequate numbers of potential research subjects. Collaboration at an equal level of partnership though desirable, may not be practicable. Sometimes, human research specimens must be transported from one country to other. Where this occurs, there should be clear understanding between the collaborating research institutions regarding issues of access and control of the (...) specimens as well as the duration of storage of specimens. The researchers have the duty to inform the research participants about specimen storage and transport across national boundaries. While obtaining informed consent from study subjects if specimens are to be stored beyond the life of the present study could be the ideal, there still remains significant challenges in a multi-cultural world. (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)

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)

Theoretical economics should not be divorced from real life. If theoretical research cannot provide a good explanation for real-world economic phenomena, then we have to question the appropriateness of the paradigm that our theoretical research follows. The battle between neoclassical macroeconomics and Keynesian economics has exposed the inadequacy of the paradigm that modern mainstream economics has followed. Neoclassical macroeconomics and Keynesian economics have the same microeconomic basis. However, the paradigm of the microeconomics on which they are based has serious flaws—the (...) scarcity hypothesis and the economic man hypothesis—do not conform to the facts. These two hypotheses are the basis for other hypotheses and principles, but neither of these two hypotheses holds up to scrutiny. Then the economics edifice built on this foundation is certainly unstable, and the corresponding economic policies are certainly not perfect. (shrink)

The problem of human religious consciousness can be attributed to the category of "eternal" philosophical problems, which have never been removed and cannot be removed from the agenda of humanity. The world outlook of a person is updated throughout history as the person, conditions and content of his life, his goals, ideals and perspectives are constantly changing. In each era, this problem retains its fundamental importance, and, being part of all significant philosophical systems, means not a simple continuation of a (...) particular tradition, but the identification of the changing aspects and historical perspectives of human existence. The question of what consciousness, which is its nature and essence, is of great ideological, ideological and practical importance, since it touches upon the foundations of human existence, content and purpose of life. (shrink)

Christian preaching, the main purpose of which is to educate a person in the spirit of the Christian worldview, should answer the questions of the present, give believers concrete recommendations and patterns of behavior in life situations. At the same time, the sermon is based not on the personal opinion of a priest or pastor, but expresses a confessional point of view on one or another problem of modern life facing believers. This point of view, as a rule, is formulated (...) in special documents of confessions, the totality of which is called "Social doctrine of the church". (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)

In the context of changing paradigms of human thinking, secularization of social consciousness, scientific and technological and information revolution, social and environmental cataclysms, Christian preaching seeks to answer the "challenge of time", seeking and offering man such spiritual foundations of life that will help him to "find himself" in the changing in the modern world.

Decisions concerning children in the health care setting have engendered significant controversy and sparked ethics policies and statements, legal action, and guidelines regarding who ought to make decisions involving children and how such decisions ought to be made. Traditionally, parents have been the default decision-makers for children not only with regard to health care but with regard to other matters, such as religious practice and education. In recent decades, there has been a steady trend away from the view that parents (...) are in authority over their children and toward the view that children are rights-bearers who should be granted greater authority over themselves. The mature minor doctrine refers to the decision to grant mature minors the authority to make decisions traditionally reserved for their parents. This essay (1) documents the trend towards expanding the understanding of some minors as “mature” and hence as having the right and authority to give informed consent, (2) examines the reasons for which some commentators have a special interest in expanding the mature minor doctrine to the research setting and allowing minors to enroll in research without parental permission, and (3) defends the view that the mature minor doctrine, regardless of its application to clinical health care decisions, ought to be set aside in the research setting in favor of greater parental involvement. (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)

Decisions by industry sponsors to end clinical trials early for commercial reasons have been the subject of controversy. I argue that the principal consideration in assessing these decisions ought to be the way in which the termination would affect the trial’s risk–benefit relationship. If there is not yet sufficient benefit to be gained from the study to offset the risks to which participants were exposed and it is expected that important scientific information would be obtained if the trial were continued, (...) early termination constitutes an unethical alteration of the risk−benefit relationship. This violates the grounds on which permission is given to conduct human research, patients consent to participate, and investigators agree to conduct studies. These knowable and avoidable changes in risk–benefit relationship should generally be seen as impermissible. (shrink)

This paper studies, by way of an example, the intuitionistic propositional connective * defined in the language of second order propositional logic by. In full topological models * is not generally definable, but over Cantor-space and the reals it can be classically shown that; on the other hand, this is false constructively, i.e. a contradiction with Church's thesis is obtained. This is comparable with some well-known results on the completeness of intuitionistic first-order predicate logic.Over [0, 1], the operator * is (...) (constructively and classically) undefinable. We show how to recast this argument in terms of intuitive intuitionistic validity in some parameter. The undefinability argument essentially uses the connectedness of [0, 1]; most of the work of recasting consists in the choice of a suitable intuitionistically meaningful parameter, so as to imitate the effect of connectedness. (shrink)

The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator of intuitionistic linear logic. The first version, ILL, appears in a paper by Benton, Bierman, Hyland and de Paiva; the second one, ILL+, is described in this paper. ILL has a contraction rule and an introduction rule !I for the exponential; in ILL+, instead of a contraction rule, multiple occurrences of labels for assumptions are permitted under certain conditions; moreover, there is a different (...) introduction rule for the exponential, !I+, which is closer in spirit to the necessitation rule for the normalizable version of S4 discussed by Prawitz in his monograph “Natural Deduction”.It is relatively easy to adapt Prawitz's treatment of natural deduction for intuitionistic logic to ILL+; in particular one can formulate a notion of strong validity permitting a proof of strong normalization.The conversion rules for ILL explicitly mentioned in the paper by Benton et al. do not suffice for normal forms with subformula property, but we can show that this can be remedied by addition of a special permutation conversion plus some “satellite” permutation conversions.Some discussion of the categorical models which might correspond to ILL+ is given. (shrink)

Traditionally, people were recognized as being dead using cardio-respiratory criteria: individuals who had permanently stopped breathing and whose heart had permanently stopped beating were dead. Technological developments in the middle of the twentieth century and the advent of the intensive care unit made it possible to sustain cardio-respiratory and other functions in patients with severe brain injury who previously would have lost such functions permanently shortly after sustaining a brain injury. What could and should physicians caring for such patients do? (...) Significant advances in human organ transplantation also played direct and indirect roles in discussions regarding the care of such patients. Because successful transplantation requires that organs be removed from cadavers shortly after death to avoid organ damage due to loss of oxygen, there has been keen interest in knowing precisely when people are dead so that organs could be removed. Criteria for declaring death using neurological criteria developed, and today a whole brain definition of death is widely used and recognized by all 50 states in the United States as an acceptable way to determine death. We explore the ongoing debate over definitions of death, particularly over brain death or death determined using neurological criteria, and the relationship between definitions of death and organ transplantation. (shrink)

Is there any link between the doctrine of logical fatalism and prime numbers? What do logic and prime numbers have in common? The book adopts truth-functional approach to examine functional properties of finite-valued Łukasiewicz logics Łn+1. Prime numbers are defined in algebraic-logical terms and represented as rooted trees. The author designs an algorithm which for every prime number n constructs a rooted tree where nodes are natural numbers and n is a root. Finite-valued logics Kn+1 are specified that they have (...) tautologies if and only if n is a prime number. It is discovered that Kn+1 have the same functional properties as Łn+1 whenever n is a prime number. Thus, Kn+1 are 'logics' of prime numbers. Amazingly, combination of logics of prime numbers led to uncovering a law of generation of classes of prime numbers. Along with characterization of prime numbers author also gives characterization, in terms of Łukasiewicz logical matrices, of powers of primes, odd numbers, and even numbers. (shrink)

Silence has gained a prominent role in the field of psychotherapy because of its potential to facilitate a plethora of therapeutically beneficial processes within patients’ inner dynamics. This study examined the phenomenon from a conversation analytical perspective in order to investigate how silence emerges as an interactional accomplishment and how it attains interactional meaning by the speakers’ adjacent turns. We restricted our attention to one particular sequential context in which a patient’s turn comes to a point of possible completion and (...) receives a continuer by the therapist upon which a substantial silence follows. The data collection consisted of 74 instances of such post-continuer silences. The analysis revealed that silence can retroactively become part of a topic closure sequence, can become shaped as an intra-topic silence, and can be explicitly characterized as an activity in itself that is relevant for the therapy in process. Only in this last case, the absence of talk is actually treated as disruptive to the ongoing talk. Although silence is often seen as a therapeutic instrument that can be implemented intentionally and purposefully, our analysis demonstrated how it is co-constructed by speakers and indexically obtains meaning by adjacent turns of talk. In the ensuing turns, silence indeed shows to facilitate access to the patient’s subjective experience at unconscious levels. (shrink)