In the paper we give a sucient condition of the Interpolation Property in propositional calculi; then we establish the power of the class of the systems with Craig's property. Next we show that there does not exist a minimal R0-system with Craig-Godel-Lindenbaum's property. Finally, we generalize Sobocinski-Tarskis theorem concerning Sobocinski-Tarski's property.

. In this paper we propose a new definition of entailment and construct a system S of predicate calculus based on this entailment. It is also shown that all well-known set theories can be based on the system S.

The present paper is a continuation of [6] and [7]. Thus the content of this paper is the following. At first we establish properties of systems S 2 n and S 2∗ n , where systems S 2 n and S 2∗ n are extensions of Rasiowa-S lupecki’s systems Sn and S ∗ n . Then we shall show that for every cardinal number m there exist a system ST 4 m of propositional calculus and a system SP 4 m (...) of predicate calculus such that the system ST 4 m has exactly m Lindenbaum’s oversystems and the system SP 4 m has exactly m Lindenbaum’s oversystems, where 1 ≤ m ≤ 2 ℵ0. (shrink)

Nagarjuna (c. 150-250), founder of the Madhyamaka or Middle Way school of Buddhist philosophy and the most influential of all Buddhist thinkers aside from the Buddha himself, concludes his masterpiece, Fundamental Verses on the Middle Way, with these baffling verses: -/- For the abandonment of all views He taught the true teaching By means of compassion I salute him, Gautama -/- But how could anyone possibly abandon all views? In Buddhism between Religion and Philosophy, Rafal K. Stepien shows not (...) only how Nagarjuna's radical teaching of no-view or “abelief” makes sense within his Buddhist philosophy, but also how it stands at the summit of his religious mission to care for all living beings. Rather than treating any one aspect of Nagarjuna's ideas in isolation, here his metaphysics, epistemology, and ethics emerge as a single coherent and convincing philosophical-religious system of thought and practice. -/- Grounded in meticulous study of original texts from classical India and China but innovating on the theories and methods underpinning contemporary scholarship East and West, this study shows how profoundly important voices from the diverse religious and philosophical traditions of the world have until now been diminished, distorted, and silenced. In opening up truly global horizons of existing and co-existing in the world, this work challenges the very ways in which we think about religion and philosophy. (shrink)

It is customarily assumed that paracomplete and paraconsistent solutions to liar paradoxes require a logical system weaker than classical logic. That is, if a logic is not fragile to liar paradoxes, it must be logically weaker than classical logic. Defenders of classical logic argue that the losses of weakening it outweigh the gains. Advocates of paracomplete and paraconsistent solutions disagree. We articulate the notion of fragility with respect to the liar paradox and show that it can be disentangled from logical (...) strength. Strength and resilience to paradox do not force a trade-off with respect to liars: there can be logics which are not weaker than classical logic and are solid to the liar. (shrink)

The question that arises in this article is whether we can find elements of phenomenology in Bernard Lonergan’s Trinitarian theology.With help of other Lonergan scholars, I have discovered that modern thinking plays an important role in the theology and philosophy ofthis Jesuit author. Moreover, the terminology of modern philosophy coexists with the terminology of classical and especially Tomisticthought. This article is interested in the elements that Lonergan takes from the modern philosophy and emphasizes the centrality ofHusserlian phenomenology among the other (...) modern authors used by Lonergan. Following the research of the Jesuit thinker, I speakabout two parallel realities coexisting in his Trinitarian theology. Lonergan tries to realize their synthesis, but at the same time healso recognizes their distinctiveness. The most relevant result of this coexistence is obtained through the replacement of the metaphysical differentiation between the level of substance and the level of the three Persons, so that, instead of having the elements of classical theology, Lonergan predicates at the same time that God subsists as well as the Trinitarian Persons subsist. Through this assertion he emphasizes the identity between God’s existence and the existence of the three divine Persons, and eliminates the classical differentiation that might be closer to the danger of subordinating the three Persons to the one God. (shrink)

KNOWN - UNKNOWN GOD. REMARKS ON DEVELOPMENT OF THE DOCTRINE OF UNKNOWABILITY OF GOD IN CHRISTIAN AUTHORS FROM SECOND TO SIXTH CENTURY The Fathers of the Church from the beginning of the Christian thought were under a strong influence of the Greek philosophy which was in this time understood mainly as the path to unity with the Supreme Being. Christian Apologists tried to convince in their apologies that Christianity is the true philosophy because it allows to reach its goal in (...) the best and the most certain way. Apologists commonly claimed that thanks to the biblical revelation Christians have the knowledge of God which is the most perfect and accurate. We can observe such claims also in the writings of Alexandrian Fathers for whom God is somehow known even at the highest mystical experiences. The Christian doctrine of the knowledge of God changed radically in the fourth century AD in the writings of Cappadocian Fathers who defended the orthodox faith against the Arians. The most famous of them - Eunomius claimed that the essence of God is to be unbegotten. Basil the Great and Gregory of Nyssa answered him that we cannot know the essence of God and none of his attributes can be understood as his essence. The Cappadocian Fathers were the founders of the Christian doctrine of unknowability of God, and they formulated it in the precise philosophical language. They also made a great contribution to the further development of this doctrine. Dialectic arguments showed only one aspect of unknowability of God; another one was the darkness in the ultimate mystical experience. Gregory of Nyssa explained it well in his Life of Moses, but this teaching reached its ultimate figure in writings of Pseudo-Dionysius Areopagite - unknown author from the end of the fifth century AD. Pseudo-Dionysius claimed that the best knowledge which we can have of God is ignorance. The man can reach this knowledge only at the highest stage of mystical life at the apophatic way. The conclusion of this brief analysis of unknowability of God in the Patristic tradition is the statement that there were two main stimulants of its evolution: theoretical and mystical. For both of them the key role played the Greek philosophy which was an inspiration in creative explanation of the Holy Scripture made by the Fathers of the Church. (shrink)

AI can identify images, but cannot understand them as man does. The problem of understanding the iconic signs is the analogy, which cannot be clearly operationalized. Nothing guarantees signification by analogy, because it is neither the necessary effect of a cause, as in the indicative signs, nor the obligatory consequence of a rule, as of symbols. But the analogy is also fundamental to the human condition because our Ego implies the presence of Other. Or, just as the images, the understanding (...) of Other implies the analogy: he is a self like me, but another self than myself, that is, an analogous self. That is, you can understand the behavior of the other's activities and actions, even what he communicates as messages because you interpret them as if it were about yourself. Different from the human being who is an existent, in AI the essence precedes existence. Even if the algorithms of the analogy process will be infinitely perfected, that analogy will miss the interpretation that comes from the life of the existing one. AI knows digital, man understands analog; AI understands from knowledge, man knows from understanding. (shrink)

This paper’s aim is to promote greater interest in courtroom practices of minute-taking—the preparation of written documents that constitute a record of what was said and done in the courtroom during a case hearing, very often based on a judge’s dictation of rephrased questioned person’s statements to a clerk who records them. This aim is achieved through discussion ultimately focused on the distinguishable aspects of minute-taking, its possible underlying mechanisms, and further consequences, followed by some remarks concerning the judge–clerk relationship (...) outside the scope of minute-taking and more direct discussion of clerks themselves. The discussions and analyses presented here are empirically-grounded, forming a side result of a larger research project conducted in a Polish lower court that combined observations of case hearings with witness interviews. Despite their inadvertent origin, the investigations presented here demonstrate the complexity and multifaceted nature of minute-taking to a greater extent than previous relevant studies have revealed. While minute-taking has not been neglected entirely in legal research, there remain many questions to be addressed. This paper suggests some of these questions as well as potential directions for future research on minute-taking through discussion of how the identified aspects of minute-taking can be utilized and which theoretical frameworks may be applicable. Although the paper is a result of empirical research conducted in Poland, its aims are relevant outside the Polish context, particularly in other continental European countries where minutes are also taken from case hearings. (shrink)

To facilitate recruitment of conscript cyber soldiers in Sweden, the Cyber Test for Future Soldiers was developed as a complement to the existing generic enrolment test. Consisting of several parts, CTFS measures different aspects of computer-related knowledge and cognitive abilities that we believe are of particular relevance to cyber security. This article describes the evaluation regarding CTFS’s validity and reliability based on data from 62 conscripts that took the test and the 27 selected conscripts finishing the training 1 year later. (...) Reliability was predicted through internal consistency and test–retest measures. Cronbach’s alpha for CTFS ranges from 0.79 to 0.86 whereas the test–retest reliability is 0.60. Evidence regarding validity was collected based on test content and internal structure. Convergent, discriminant, and predictive evidence are also presented. Perhaps most importantly, CTFS could predict the cyber soldiers’ performance during their training and added incremental validity to I-prov 2000. When adjusted for range restriction, I-prov 2000 predicted 20% of the variation in course score, while 34% of the variance was explained when CTFS was used in conjunction with I-prov 2000. The results show that CTFS already in its first version is adding value for the Swedish Armed Forces. (shrink)

The high prevalence of brain injury incidents in adolescence and adulthood demands effective models for re-learning lost cognitive abilities. Impairment in brain injury survivors’ higher-level cognitive functions is common and a negative predictor for long-term outcome. We conducted two small-scale interventions (N = 12; 33.33% female) with persons with acquired brain injuries in two municipalities in Sweden. Age ranged from 17 to 65 years (M = 51.17, SD = 14.53). The interventions were dialogic, inquiry-based, and inspired by the Philosophy for (...) Children Programme, a participatory thinking skills approach with documented higher-order cognitive outcomes, such as developed argumentation skills, in other target groups. Philosophical dialogues were conducted once a week in the two groups, totalling 12 dialogues per group. Group argumentation development was measured through compared scores from structured observations of filmed dialogues early and late in the intervention. Large positive changes in mean scores from early to late in the intervention, together with constantly high facilitator quality, suggest argumentation development in the sample due to the intervention. (shrink)

In this study we present some contributions of the logician and philosopher Petre Botezatu (27.02.1911-01.12.1981), who turned the idea of complementarity,formulated by Niels Bohr for the interpretation of the wave-particle structure of the quantum world, into an ordering principle of his work. Thus, he understood general logic as a synthesis in which the style of classical logic is complementary to the style of the 20th century logic. He didn’t give up either the mathematical modelling of logical language or the conceptual (...) description through natural language. Thus, natural operational logic was created. Then Petre Botezatu assessed the achievements and failures of deduction in order to build the notion of methodological antinomy, and formulated five antinomies of axiomatization and five antinomies of formalization. The main purpose of this study is to present and interpret them. (shrink)