This note presents a point of view upon the notions of programsubstitution which are the tools for proving properties of programs of algorithmic logics [5], [3] being sufficiently strong and universal to comprise almost all previously introduced theories of programming, and the so-called extended algorithmic logic [1], [2] and algorithmic logic with nondeterministic programs [4]. It appears that the mentioned substitution rule allows us to examine more deeply algorithmic properties of terms, formulas and programs. Besides the problem of Post-completeness and (...) structural completeness of algorithmic logics strengthened additionally by the rule of substitution is raised. (shrink)

The famous theory of undecidable sentences created by Kurt Godel in 1931 is presented as clearly and as rigorously as possible. Introductory explanations beginning with the necessary facts of arithmetic of integers and progressing to the theory of representability of arithmetical functions and relations in the system (S) prepare the reader for the systematic exposition of the theory of Godel which is taken up in the final chapter and the appendix.

This review pertains to the book _Evolutionary Theology (Teologia ewolucyjna)_ written by Wojciech P. Grygiel and Damian Wąsek. The book presents a distinct and modern viewpoint on theology by offering a comprehensive analysis of the characteristics of theological language and utilizing it to reevaluate certain theological beliefs, such as the concept of original sin, within the framework of the ever-changing understanding of the Universe. This approach contributes significantly to the restoration of theology’s credibility in modern culture by bridging the gap (...) between science and theology. (shrink)

In this paper, the concept of structural information is presented. The mathematical foundation of the concept is put forward, and the nature of information encoded in a structure is studied. A method for calculating the amount of structural information is introduced. An application to the analysis of cognitive maps is also presented and discussed.

One of the most vigorously debated issues in attention labs concerns the nature of the coupling between the sensory-motor system and covert spatial attention. Proponents of the Premotor Theory of Attention (PToA) claim that attention should be accounted for in terms of motor preparation for goal-directed actions such as eye or hand movements. For others, it is a supramodal psychological entity that is independent of our sensorimotor machinery. Both parties also seek to articulate this controversy in terms of cognitive science (...) as a question of whether attention is embodied or disembodied cognition. The PToA is thought to advocate the embodiment of attention. We, however, are inclined to think that a more nuanced view of this conceptual framework is needed to yield some insights into how radical it actually is in terms of embodied cognition (EC). We argue that PToA still seems to bear some features of weak embodiment. Yet we suggest that it has the potential to build a stronger concept of attention as EC, but somewhat paradoxically this would require giving attention deflationary treatment and reconstructing it in other terms. We propose that the notion of pre-reflective intentionality might serve as an inspiration to this end. (shrink)

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now (...) classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G. (shrink)

Since the very dawn of its history, modern philosophical anthropology has been addressing the issue of the human body. As a result of those efforts, Descartes, de Biran, Husserl, Sartre, Marcel, Merleau-Ponty and others have brought forward a variety of conceptions concerning various aspects of human corporeality. Anthropological explorations concerning the question of the human body, appear in a particularly interesting way, when they are considered in the context of those points of view which, in an essential way, refer to (...) the subjective character of the human being. It is a matter of reconstructing and analyzing how the subject's corporeality is given to the subject, originarily, according to the phenomenological rule zu den Sachen selbst. The aim of this paper is thus to put into some order the concerns of a variety of anthropologists with regard to the question of the human body, as it is given to, or experienced by, the subject. A metatheoretical analysis of this field proves it is possible to do so with the use of a tool, which is called here, a dimension of corporeality. (shrink)

Since the very dawn of its history, modern philosophical anthropology has been addressing the issue of the human body. As a result of those efforts, Descartes, de Biran, Husserl, Sartre, Marcel, Merleau-Ponty and others have brought forward a variety of conceptions concerning various aspects of human corporeality. Anthropological explorations concerning the question of the human body, appear in a particularly interesting way, when they are considered in the context of those points of view which, in an essential way, refer to (...) the subjective character of the human being. It is a matter of reconstructing and analyzing how the subject's corporeality is given to the subject, originarily, according to the phenomenological rule zu den Sachen selbst. The aim of this paper is thus to put into some order the concerns of a variety of anthropologists with regard to the question of the human body, as it is given to, or experienced by, the subject. A metatheoretical analysis of this field proves it is possible to do so with the use of a tool, which is called here, a dimension of corporeality. (shrink)

The crux of the dispute on the mutual relations between attention and consciousness, and to which I have referred in this paper, lies in the question of what can be attended in spatial attention that obviously resonates with the phenomenological issue of intentionality. The discussion has been initiated by Christopher Mole. He began by calling for a commonsense psychology, according to which one is conscious of everything that one pays attention to, but one does not pay attention to all the (...) things that one is conscious of. In other words, attention is supposed to be a condition which is sufficient but not necessary for consciousness, i.e., consciousness is a necessary concomitant of attention, but attention is not a necessary concomitant of consciousness. Mole seeks to validate his stance with data from psychology labs. His view is, however, partly confronted, for instance, by Robert Kentridge, Lee de-Wit and Charles Heywood, who used their experimental research on a neurological condition called blindsight as evidence of a dissociation between attention and consciousness, i.e., that visual attention is not a sufficient precondition for visual awareness. In this meta-theoretical state of affairs, I would like to focus on the cognitive phenomenon most often referred to as Inhibition of Return and suggest that, following its micro dynamics from the perspective of micro-phenomenology, it can be used to actually showcase all of the options on both sides of the argument. One of my leading goals would be also to follow Mole’s attempt to link attention with agency but where we differ is that I wish to heuristically articulate the matter in terms of Merleau-Ponty’s phenomenological notion of embodied pre-reflective intentionality. (shrink)

The purpose of this paper is to show the methodological power and potentiality of the concept paradigm of unity introduced originally in the ceremony on the occasion of honoring Chiara Lubich with the doctor honoris causa title by the Catholic University of Lublin in 1996. Originally this conception was used to suggest the societal activity of Chiara Lubich in building, via the Focolari movement, psychosocial infrastructures for unity in various social domains,, in public media, in ecumenism and inter-religious contacts This (...) conception is a kind of a great inspiration which would motivate the social sciences to build their own research paradigm of a type of mental and methodological power and potentiality which could give a new vision of social world ). Thomas Kuhn regarded the Copernician revolution as the one which, in the history of science, best illustrates the nature of scientific revolution. The essence of paradigm in a Kuhnian sense is a mentality change in its nature. Copernicus had to change the well-established geocentric system which functioned not only in the science of his day but also in culture, tradition, social perception, and even in the mentality of religious and political authorities. And he did it in a well prepared empirical, methodological and psychological way. In a similar way Chiara Lubich created by her social acting a revolutionary inspiration for building paradigm in social science She decided in an extremely difficult and risky situation in 1944 in Trento not only to escape from her own life emergency but she with her friends made a decision to help other people who were in a much more difficult situation to survive. She decided to take a war bombing risk to be with lost children and older people who were in need. It was a practical building of the unity with the real people who were in need. This kind of experience rediscovered the community as a model for the real life and made a concretization and clarification of the charisma of the unity. However, the development of this charisma shows that it is simply a concrete and practical actualization of the new vision of social, economic, political and religious relationships which advises, recommends, suggests, and promotes the unity with others persons. (shrink)

During the global financial crisis of 2007–2009 and the currentCovid-19 debacle, central banks acted quickly, boldly, and effectively. The paper argues that they did so thanks to the lessons learned from the past financial crises, which provided them with opportunities to reconsider their previous beliefs. A case in point is the banking crisis in the United States during the Great Depression of the 1930s that taught central banks to act rapidly and decisively in order to prevent an initial liquidity crisis (...) from escalating into a solvency crisis leading to bankruptcies of banks with potentially disastrous consequences for the entire economy. The paper revisits the consequences of the currency crises of the 1990s, which transformed exchange rate regimes across the world: the EMS one of 1992–1993 that accelerated the launch of the euro, and the Asian one of 1997–1998 resulted in the proliferation of floating exchange rates in emerging economies. (shrink)

The main aim of the present paper is to explain a nature of relationships exist between Nelson and Heyting algebras. In the realization, a topological duality theory of Heyting and Nelson algebras based on the topological duality theory of Priestley for bounded distributive lattices are applied. The general method of construction of spaces dual to Nelson algebras from a given dual space to Heyting algebra is described. The algebraic counterpart of this construction being a generalization of the Fidel-Vakarelov construction is (...) also given. These results are applied to compare the equational category N of Nelson algebras and some its subcategories with the equational category H of Heyting algebras. It is proved that the category N is topological over the category H. (shrink)

In this article, the author notes that Thomas Aquinas, in his brief work entitled De Ente et Essentia, proved that at the base of understanding the world, the human being, and God in particular, there is our understanding of being and its essence. When we make a small mistake at the beginning in our understanding of being and its essence, it will turn to be a big one in the end. And what is “at the end” of our knowledge is (...) the discovery of the First and Ultimate Cause of all things, known as: Ipsum Esse, God, the Absolute, The Most Perfect Substance, on whom everything depends, and who depends not on anything else. These present inquiries about the proper understanding of being and its essence are aimed at formulating proof of the necessity of existence of a Being that is the First Cause, and which, existing as Ipsum Esse, is the source and reason of existence of all beings. Without these inquiries, the proof itself would be incomprehensible, and more importantly it would be a purely a priori one. Furthermore, without the existential conception of being, which Thomas first formulated, one could not discover the First Cause which, as Ipsum Esse, is the source of the existence of every being. This issue seems to have escaped the attention of the author of the book Aquinas’s Way to God. The Proof in “De Ente et Essentia.”. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

We examine some extensions of the constructive propositional logic with strong negation in the setting of varieties of $\mathcal{N}$ -lattices. The main aim of the paper is to give a description of all pretabular, primitive and preprimitive varieties of $\mathcal{N}$ -lattices.

Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.

Jean Vanier is the founder of two major international community-based organizations for people with intellectual disabilities: the L’Arche Communities and the “Faith & Light” movement. He is a great Catholic and a teacher of merciful love. His life is a message to the world that each person is an infinite value for who they are, not for what they can do, and that each person is unique and sacred, no matter of their health condition, disability or fragility. Each person is (...) created in God’s image and each one has an inner beauty, a capacity to love and to be loved, and possesses inherent qualities of belonging, bonding, friendship and spirituality. Persons with intellectual disabilities are a gift for the society. Thanks to the testimony of his life, Jean Vanier has developed the international network of L’Arche Communities all over the world. The communities are based on family-like residential communities, where people with and without intellectual disabilities share life together in the spirit of faith, dignity of every human being, understanding, love and joy. The L’Arche homes and communities are rooted in the ideas of “living with,” and not just “doing for” those with mental disabilities. Weakness carries a secret power within, it can open up the hearts to God’s grace. Our contemporary world strongly needs the weak, as they evangelize us, transform us and help us to be more human. They help us discover that the good news of Jesus is announced not to those who serve the poor, but to those who are themselves poor and need God’s merciful love and forgiveness. (shrink)

The traditional approach to the relation between parents and their prenatal child presents the child as a fetus, a mainly passive recipient of the mother’s vital biological resources. Contemporary prenatal psychology and pedagogy recognizes this relationship in a quite different perspective: the prenatal child is a member of the family and may be seen as an active member of the wider family as a community, extended to grandparents and other relatives. Between parents and their child in the womb exists a (...) reciprocal relationship at a physiological, psychological and spiritual level. The prenatal child communicates with the parents in different ways and reacts to their stimulation. This dialogue of the parents and their prenatal child enriches each member of the family community. In this sense, the prenatal child is a gift and a challenge for the parents to develop their personality, social competences and spiritual life. The reflections presented in this paper fit the conception of the paradigm of unity applied into the area of prenatal education and prenatal pedagogy as a new pedagogical subdisciline. The concept of paradigm in the philosophy of science was introduced by T. Kuhn. In his understanding, paradigm means a mental breakthrough in the way of ujmowaniu/describing/approaching the subject of study, and/or in the research methods used, but above all in the theoretical and systemic vision of reality, which is the basis for formulating research questions and hypotheses, operationalising the research procedure, analyzing the obtained research results and a theoretical interpretation of these results. To Kuhn, a paradigm may be understood in such way only in the natural sciences, when new visions of the studied natural reality appear. This is accompanied by a mental change in the cognitive schema itself of understanding reality not only for the creator of this vision, but also in its/his/her broader scientific environment. Kuhn considered the most eminent example of such appearing paradigm in the history of science to be the Copernican revolution, thanks to which the view on the world of nature surrounding the human being has completely changed and there was a mental breakthrough in the 15th and 16th century not only in the area of science, but also in the worldview of people of those times, for whom the world has become more open and broad. Kuhn, however, did not consider a paradigm to be a methodological concept in the humanities or social sciences. He was of the opinion that they must first mature more and make their methodological status more precise if one wishes to talk about a paradigm in these sciences. A scientific event that gave an occasion to reflect on the possibility of introducing the concept of paradigm into social sciences was the occasion of granting the title of doctor honoris causa in the field of social sciences by the Catholic University of Lublin to Chiara Lubich. The Focolare movement, also called The Movement of Unity, founded and led by her, introduced, a new approach to the area of human relations at every level. The arguments for granting the title included the fact that the practical activity of Ch. Lubich in various areas of social integration may be described as a Copernican revolution in the cultural-religious relations, and even in social-economical ones, according to the new paradigm, understood practically, which may be called a paradigm of unity. It was stressed that these activities may play a serious/significant inspiring role in the methodological reflections on the paradigm of unity in the social sciences. Such reflections were actually brought up first generally in the social sciences, and then within the methodology of psychology and education. At present, one may consider introducing this paradigm into prenatal education and pedagogy. (shrink)

This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. (...) Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)