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)

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.

Abstract:This article is concerned with the role of Buddhist philosophy, and more broadly of non-Western philosophies, within the discipline of philosophy as this is professed and practiced today. I begin by deliberately engaging in a game of definitions to demonstrate that, whichever of the definitions standardly employed to deny non-Western philosophy the prestigious moniker, Buddhism nevertheless wins: it does count as philosophy. Having made that point, however, I go on to effectively undermine it by pointing out that anyone can win (...) the game if they get to make up the rules. Given that the score is arbitrary, then, I show up the game itself as absurd. On this basis, I ultimately cry foul at the perpetuation of a game still so plainly played on fields far from level, and therefore argue against excusing philosophers engaged in it of the charge of racism. (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)

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)

This article considers the issue of changes in the understanding of symbols as an integral part of spiritual life in Neoplatonic philosophy. It seems that ancient Neoplatonic philosophers were the first who clearly realized the importance of symbols to spiritual life. However, it happened due to the influence of the mystical Chaldean and Egyptian thought transferred to philosophical investigation by the Chaldean oracles and Corpus hermeticum. The late Neoplatonic thought of Iamblichus and Eastern Neoplatonic schools used symbols and rituals as (...) integral parts of philosophical investigation, understood as having a mystical goal. Especially mathematical symbols played a significant role, because they were used in the most advanced theurgical rituals. This analysis of the pagan Neoplatonic philosophy permits us to show properly the thought of Pseudo- Dionysius the Areopagite, who creatively transformed the teaching of his pagan predecessors, by incorporating ancient Neoplatonic tradition into Christian theology. Pseudo-Dionysius excludes liturgical symbols from the order of the cosmos and transfers them to the plane of Salvation grounded in Biblical Revelation. Only true symbols are used in the liturgy of the Church, and thus mathematical symbols are no longer needed in the ascent of the soul to unity with God. The third part analyzes the meaning of symbolism in the thought of Nicolas of Cusa. Thanks to the rediscovery of ancient pagan Neoplatonism and Pythagorean thought, Cusanus also brings new life to the mystical meaning of mathematics. Mathematical symbols once again become an im- portant part of the mystical ascent of the soul, but this time without their ritual context. (shrink)

This article seeks to introduce a greater degree of precision into our understanding of Madhyamaka Buddhist ontological non-foundationalism, focussing specifically on the Madhyamaka founder Nāgārjuna (c. 150–250 CE). It distinguishes four senses of what the ‘foundation’ whose existence Mādhyamikas deny means; that is, (1) as ‘something that stands under or grounds things’ (a position known as generic substantialism); (2) as ‘a particular kind of basic entity’ (specific substantialism); (3) as ‘an individual essence (a haecceity or thisness of that object) by (...) means of which it is identical to that very object, to itself’ (modal essentialism); and (4) as ‘an essence in the absence of which an object could be of a radically different kind or sort of object than it in fact is’ (sortal essentialism). It then proceeds to delineate the Madhyamaka refutation of the specific substantialist position in terms of its argued denial of dharma as basic entity; of generic substantialism and modal essentialism in terms of its argued denial of svabhāva as both foundation for and essence of putative entities; and of sortal essentialism in terms of its argued denial of essentialist conceptions of conceptual thought (vikalpa), mental construction (prapañca), and in short the entire domain of ratiocination (kalpanā), by means of its notion of conceptual imputation (prajñaptir upādāya)—a denial strictly speaking ontological, but of what are putative epistemic entities. The final portion of the article explains the relationship of ontological to other forms of non-foundationalism according to Madhyamaka. (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)

Buddhist Philosophy of Consciousness: Tradition and Dialogue, edited by Mark Siderits, Ching Keng and John Spackman. Brill, 2021. 356pp., €135/$162. Hb ISBN-13: 9789004440890; e-PDF ISBN-13: 9789004440913.

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)

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)

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)

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)