The paper describes a system for dealing with nestings of belief in terms of the mechanism of computational environment. A method is offered for computing the beliefs of A about B (and so on) in terms of the systems existing knowledge structures about A and B separately. A proposal for belief percolation is put forward: percolation being a side effect of the process of the computation of nested beliefs, but one which could explain the acquisition of unsupported beliefs. It is (...) argued that the mechanism proposed is compatible with a general least effort hypothesis concerning human mental functioning. (shrink)

This book is both suitable for logically and algebraically minded graduate and advanced graduate students of mathematics, computer science and philosophy, and ...

The paper is a response to recent criticisms of agatheism, a new pluralistic interpretation of religious belief put forward by Janusz Salamon with the aim of accommodating the epistemological challenge of religious diversity. Agatheism is an axiologically grounded religious belief which identifies God, the Absolute or the ultimate reality religiously conceived with the ultimate good as the ultimate end of all human agency and thus an explanation of its irreducibly teleological character and a source of its meaning. Janusz (...) Salamon argues that this grounding of religious belief in the human axiological consciousness makes it immune to falsification by any future science. Replying to the concerns of the critics about about irrationality of doxastic commitment to a particular religious tradition, Janusz Salamon argues that to the extent the fundamental agatheistic religious belief is presupposed in such tradition as its doxastic core, its belief system - if internally coherent and aligned with a worldview that is consistent with undisputed scientific findings - may be considered rational, despite there being a plurality of such belief systems. (shrink)

The principle of explosion asserts that any formula can be derived from any pair of other contradictory formulas. Paraconsistent logic is typically regarded as a logic in which the universal validity of this principle is questioned. Therefore, a key point is determining when the validity can be considered universal to classify a logic as paraconsistent. A pertinent example to illustrate this point is the calculus CB1 that admits the principle but only for negated formulas, i.e., from any set {α, ∼α} (...) any other formula follows if and only if α is of the form ∼γ. Another example is Sette’s calculus P1, which is paraconsistent at the level of variables but not complex formulas. Both serve as compelling examples of the so-called borderline cases. In this paper, we examine several calculi expected to be paraconsistent at the level of literals. It means that a pair of formulas, α and ∼α, can yield any β if, and only if α is neither a propositional variable nor is its iterated negation. Furthermore, it is assumed that in some calculi presented here, β must adhere to specific restrictions. Once these conditions are satisfied, we refer to calculus as paraconsistent in a “controllable manner”. (shrink)

The Absolute is a basic and fundamental issue for philosophy as such. I present different concepts of the Absolute (substantialism, energetism, escapism, methodologism). We can say that contemporary European philosophy “orphaned” the neo-Platonic tradition. Thereafter Russian philosophy developed in an intensive and turbulent as well as relatively uniform fashion, in view of the well-established Neo-Platonist context. This makes Russian philosophy not only part of a lasting universally acknowledged tradition; not only has Russian philosophy continued to develop currents of thought abandoned (...) by modern European philosophiers, but it is also heir to a philosophical tradition of particular quality and value in the universal history of thought. (shrink)

We introduce a new cardinal characteristic r*, related to the reaping number r, and show that posets of size $ r* which add reals add unbounded reals; posets of size $ r which add unbounded reals add Cohen reals. We also show that add(M) ≤ min(r, r*). It follows that posets of size < add(M) which add reals add Cohen reals. This improves results of Roslanowski and Shelah [RS] and of Zapletal [Z].

By a sentential logic we understand a pair, where S is a sentential language, i.e. an absolutely free algebra freely generated by an infinite set p, q, r,... of sentential variables and endowed with countably many finitary connectives §1, §2,... and C is a consequence operation on S, the underlying set of S, satisfying the condition of structurality: eC ⊆ C, for every endomorphism e of S and for every X ⊆ S. If no confusion is likely we shall identify (...) a logic with its consequence operation C. A logic C is standard if C = [ {C : Y ⊆ X & Y is finite}, for all X ⊆ S. (shrink)

We propose a new schema for the deduction theorem and prove that the deductive system S of a prepositional logic L fulfills the proposed schema if and only if there exists a finite set A(p, q) of propositional formulae involving only prepositional letters p and q such that A(p, p) L and p, A(p, q) s q.

Fr. Roberto Busa was an Italian Jesuit. In this article his biography will briefly be presented, and some issues raised by his philosophy analyzed. Busa was known as a pioneer of computerized research in the humanities. With the support of IBM he constructed the Index Thomisticus, containing all the works of St. Thomas Aquinas. He believed that expressions of the human can be mathematically modeled. He was the originator of a specific conception of hypertext, in which logically structured programs are (...) able to challenge the general linguistic mode of thinking, in order to make better communication and understanding possible. However, Busa was also con- scious of the general ethical problems involved (Babel), and he hoped that the basic logic of objects could progress towards the truth of being. (shrink)

This volume explores the range of Alfred North Whitehead's philosophy and his relevance to contemporary philosophical traditions.

Paul Edwards' October 1989 essay, ‘Heidegger's Quest for Being’ illustrates the wisdom of the dictum that the only legitimate criticism of a philosopher's position is a constructive criticism. His negative critique amounts to no more than expressions of distaste, dislike, and displeasure, and nothing of philosophical interest follows from his assertions, as the discourse is primarily an argument ad hominem . He grossly misinterprets Heidegger on some elemental and fundamental matters as well. In particular, he sorely misinterprets what he refers (...) to as the ‘Quest for Being’, which only further contributes to the objectionable character of the essay. (shrink)

Any finite support iteration of posets with precalibre ℵ 1 which has the length of cofinality greater than ω 1 yields a model for the dual Borel conjecture in which the real line is covered by ℵ 1 strong measure zero sets.

The European Summer Schools in Logic, Language and Information (ESSLLI) have been organised every year since 1989 under the auspices of the Association for Logic, Language and Information (FoLLI) in different cities around Europe. The 24th European Summer School in Logic, Language and Information (ESSLLI 2012) took place at the University of Opole, Poland, during August 6-17, 2012. The organisation committee was chaired by Janusz Czelakowski and Urszula Wybraniec-Skardowska (Institute of Mathematics and Informatics, University of Opole) and the programme (...) committee was chaired by Andreas Herzig (University of Toulouse and CNRS). During two weeks, over 340 participants from 36 countries were offered a rich academic program of their choice from 9 foundational, 16 introductory and 17 advanced courses and 6 workshops. Just as in the previous years, the 17th conference on Formal Grammar collocated with ESSLLI. Besides the regular courses, a traditional highlight of the summer school were the 4 evening lectures by distinguished academics: - Johan van Benthem (Institute for Logic, Language & Computation (ILLC), Amsterdam and Department of Philosophy, Stanford University), "Computation as Agency''; - Melvin Fitting (Department of Mathematics and Computer Science, City University of New York), "Reasoning About Games''; - Jonathan Ginzburg (UFR Études anglophones, Université Paris-Diderot (Paris 7)), "False starts, jokes, and music:semantics in the 21st century''; - Adam Przepiórkowski (Institute of Computer Science, Polish Academy of Sciences, Warsaw), "Secret life of corpora''. Another traditional event was the student session, organised by a student programme committee chaired by Rasmus K. Rendsvig (University of Copenhagen): master and doctoral students presented 16 papers and 5 posters, and Michał Zawidzki obtained the best paper award and Raul Fervari obtained the best poster award. Moreover, the Beth Dissertation Prizes were announced at the FoLLI General Meeting and went to Andreas Kapsner (University of Barcelona) and Daniel R. Licata (Carnegie Mellon University). Apart from the busy academic programme, participants of the summer school were offered an exciting social program as well. In addition to the traditional ESSLLI Party and the famous Students vs. Lecturers Soccer Match (also called `Johan van Benthem Cup'), kayaking, and excursions to Kraków and Wrocław were offered. -/- . (shrink)

This article attempts to answer the question: what has the current migration crisis revealed in relations between Christianity and Islam, two religions with common Abrahamic roots? What conclusions can be drawn about the state of these relations, particularly with regard to ordinary members of the two religions? How should we assess the reaction of Christians in Europe to the inflow of refugees from Muslim countries in the light of the Gospel, the Second Vatican Council and the teaching of Pope Francis?The (...) article consists of four parts. Part I briefly presents Christian-Muslim relationships over the centuries. Part II focuses on the sense of danger occurring in European societies in connection with the influx of Muslims during the migration crisis. Part III presents the teachings of the Second Vatican Council about Islam and Part IV describes Pope Francis’s attitude towards refugees from Muslim countries. (shrink)

Action theory may be regarded as a theoretical foundation of AI, because it provides in a logically coherent way the principles of performing actions by agents. But, more importantly, action theory offers a formal ontology mainly based on set-theoretic constructs. This ontology isolates various types of actions as structured entities: atomic, sequential, compound, ordered, situational actions etc., and it is a solid and non-removable foundation of any rational activity. The paper is mainly concerned with a bunch of issues centered around (...) the notion of performability of actions. It seems that the problem of performability of actions, though of basic importance for purely practical applications, has not been investigated in the literature in a systematic way thus far. This work, being a companion to the book as reported, elaborates the theory of performability of actions based on relational models and formal constructs borrowed from formal lingusistics. The discussion of performability of actions is encapsulated in the form of a strict logical system. This system is semantically defined in terms of its intended models in which the role of actions of various types is accentuated. Since due to the nature of compound actions the system is not finitary, other semantic variants of are defined. The focus in on the system of performability of finite compound actions. An adequate axiom system for is defined. The strong completeness theorem is the central result. The role of the canonical model in the proof of the completeness theorem is highlighted. The relationship between performability of actions and dynamic logic is also discussed. (shrink)

In the domain of astronomy the object oriented paradigm of informatics needs to construct an ontology to be able to reason about concepts and to construct queries in a computerized knowledge system. The article presents approaches to ontology in philosophy, the natural sciences and informatics and shows their limits and reciprocity.

This text offers the report on the activities of The Centre for Interdisciplinary Studies in Cracow—a research and educational institution at the Department of Philosophy of the Pontifical Academy of Philosophy in the Cracow. The main areas of its research are the philosophy of science, the history of science, and problems connected with the interrelations between philosophy, theology and the sciences.

In this article I want to continue the characteristics of philosophical methods specific to analytical philosophy, which were and are important for Professor Jan Woleński. So I refer to his work on the methods of analytical philosophy, but I also point out a few new methods that have grown up in the climate of studies of philosophers, especially analytical ontologists. I will therefore describe the following methods: generalization, specialization, formalization, de-formalization and topological hermeneutics. Instead of the term “method” I use (...) interchangeably the terms “operation” or “procedure”. I will show that each of these operations makes an important contribution to ontological investigations, and, in particular, to formal ontology. (shrink)

Endowed with all the traits of an outstanding monarch and creator of his state, King Kazimierz III (also known as the Great) appears one of the greatest figures in the history of Poland. It was him who laid out the legal and political foundation of the modern state. He initiated legislative, administrative, economic, military and cultural reforms which became the source of the power of the Jagiellonian dynasty. However, apart from the above mentioned virtues, Kazimierz Wielki had a number of (...) vices and weaknesses. He tended to be irritable and bad-tempered. He overly appreciated jewels and luxury. What is more, he was promiscuous and overindulged in drinking and eating. (shrink)

Those who have written on Paweł Brzostowski have lacked to pay much attention to his patriotism and his activities as a priest. Some have disapproved the fact that in hard times he left his peasants and sought peace abroad. It is obvious that he lacked the courage of priest Stanisław Brzóska or one of priest Ignacy Skorupka to take the leadership of his own army of peasants to defend Poland. Yet he showed through his life much commitment to strengthen Poland (...) in order to avoid its defeat. He never stooped to the role of tsar’s confidant like other magnates and priests. His peasant army participated in the Kościuszko Insurrection and the November Insurrection. In 1798, after Napoleon’s army had entered Italy, he returned to Poland and gave away 3 000 Zlotys aid to peasants. He also made sure that the fund for the teacher, the doctor and the chemist’s always served the local community. J. Bartyś states that Paweł Brzostowski was a priest by choice: “he always strived to put into practice the Church’s teaching on neighbour-love, honesty and equality of all people regardless their social status”. (shrink)

We are facing a crisis of trust in expertise today. Fewer and fewer people trust experts, and more and more politicians openly ignore expert consensus. 'Democracy in the Post-Truth Era' asks what might happen to democracy if we reject the fundamental liberal assumption that people are capable of making informed choices. The book explores the potential impact on society if people, including politicians, never appreciate the relevance of expert opinions. What if people cannot choose between supporters and opponents of key (...) issues such as the causes of climate change, effectiveness of vaccines and ways of combating economic and social crises? Applying social epistemology to these questions, the book considers whether democracy can be defended in the post-truth era. (shrink)

In this paper, we present a calculus of paraconsistent logic. We propose an axiomatisation and a semantics for the calculus, and prove several important meta-theorems. The calculus, denoted as CB1, is an extension of systems PI, C min and B1, and a proper subsystem of Sette’s calculus P1. We also investigate the generalization of CB1 to the hierarchy of related calculi.

Autor przedstawia krytykę praw metafizyki przedstawionych przez Immanuela Kanta w tzw. przedkrytycznym okresie jego twórczości. Zdaniem Kanta, prawa te składają się na tzw. Boży układ świata.