Summary of the talk given to the 22nd Conference on the History of Logic, Cracow (Poland), July 5–9, 1976.

Machine ethics and robot rights are quickly becoming hot topics in artificial intelligence and robotics communities. We will argue that attempts to attribute moral agency and assign rights to all intelligent machines are misguided, whether applied to infrahuman or superhuman AIs, as are proposals to limit the negative effects of AIs by constraining their behavior. As an alternative, we propose a new science of safety engineering for intelligent artificial agents based on maximizing for what humans value. In particular, we challenge (...) the scientific community to develop intelligent systems that have human-friendly values that they provably retain, even under recursive self-improvement. (shrink)

The aim of this book is to present and analyze philosophical conceptions concerning mathematics and logic as formulated by Polish logicians, mathematicians and philosophers in the 1920s and 1930s. It was a remarkable period in the history of Polish science, in particular in the history of Polish logic and mathematics. Therefore, it is justified to ask whether and to what extent the development of logic and mathematics was accompanied by a philosophical reflection. We try to answer those questions by analyzing (...) both works of Polish logicians and mathematicians who have a philosophical temperament as well as their research practice. Works and philosophical views of the following Polish scientists will be analyzed: Wacław Sierpiński, Zygmunt Janiszewski, Stefan Mazurkiewicz, Stefan Banach Hugo Steinhaus, Eustachy Żylińsk and Leon Chwistek, Jan Łukasiewicz, Zygmunt Zawirski, Stanisław Leśniewski, Tadeusz Kotarbiński, Kazimierz Ajdukiewicz, Alfred Tarski, Andrzej Mostowski and Henryk Mehlberg, Jan Sleszyński, Stanisław Zaremba and Witold Wilkosz. To indicate the background of scientists being active in the 1920s and 1930s we consider in Chapter 1 some predecessors, in particular: Jan Śniadecki, Józef Maria Hoene-Wroński, Samuel Dickstein and Edward Stamm. (shrink)

In this paper the completeness theorems for the finite-valued ukasiewicz logics are proved with the use of the Lindenbaum algebra.

This volume is written jointly by Witold Marciszewski, who contributed the introductory and the three subsequent chapters, and Roman Murawski who is the author of the next ones - those concerned with the 19th century and the modern inquiries into formalization, algebraization and mechanization of reasonings. Besides the authors there are other persons, as well as institutions, to whom the book owes its coming into being. The study which resulted in this volume was carried out in the Historical Section (...) of the research project _Logical Systems and Algorithms for Automatic Testing of Reasoning,_ 1986-1990, in which participated nine Polish universities; the project was coordinated by the Department of Logic, Methodology and Philosophy of Science of the Bia??l??ystok Branch of the University of Warsaw, and supported by the Ministry of Education 1987). The major part of the project was focussed on the software for computer-aided theorem proving called Mizar MSE ) due to Dr. Andrzej Trybulec. He and other colleagues deserve a grateful mention for a hands-on experience and theoretical stimulants owed to their collaboration. (shrink)

We study a strengthening of the notion of a perfectly meager set. We say that a subset A of a perfect Polish space X is countably perfectly meager in X, if for every sequence of perfect subsets $\{P_n: n \in \mathbb N\}$ of X, there exists an $F_\sigma $ -set F in X such that $A \subseteq F$ and $F\cap P_n$ is meager in $P_n$ for each n. We give various characterizations and examples of countably perfectly meager sets. We prove (...) that not every universally meager set is countably perfectly meager correcting an earlier result of Bartoszyński. (shrink)

It is argued, in this paper, that the core operation underlying any measurement—the inverse modelling under uncertainty—is equivalent to quantitative abductive reasoning which consists in the selection of the best estimate of a measurand in a set of admissible solutions, using a priori information: on the measurand, on the measuring system coupled with an object under measurement, and on the influence of the environment including the user of the measurement results. There are two key premises of this claim: a systematic (...) interpretation of measurement in terms of inverse problems, proposed earlier by the author, and a logical link between inverse problems and abduction, identified by the Finnish philosopher of science Ilkka Niiniluoto. The title claim of this paper is illustrated with an expanded example of measuring optical spectrum by means of a low-resolution spectrometer. (shrink)

The paper presents an outline of the general theory of countable arithmetically saturated models of PA and some of its applications. We consider questions concerning the automorphism group of a countable recursively saturated model of PA. We prove new results concerning fixed point sets, open subgroups, and the cofinality of the automorphism group. We also prove that the standard system of a countable arithmetically saturated model of PA is determined by the lattice of its elementary substructures.

This study investigates the negative influence of consumer’s perceptions of online retailer’s deceptive practices on consumer’s relational variables. Also, the moderating role of product type, consumer’s attitude toward the Internet, and consumer’s demographics in the deception-relational outcomes link is considered. Data from 398 online consumers revealed that satisfaction totally mediated the influence of deception on loyalty. Furthermore, the deception-satisfaction link was moderated by all the hypothesized variables. Interestingly, a direct effect of deception on loyalty was found among more educated consumers, (...) consumers who had a more positive attitude toward the Internet and consumers who had purchased a physical product. Implications for theory and management are discussed. (shrink)

In the paper n -valued paraconsistent matrices are defined by an adaptation of the well-known Łukasiewicz’s matrices. An appropriate set of axioms is presented and the 3-valued case is examined.

In the paper the problem of definability and undefinability of the concept of satisfaction and truth is considered. Connections between satisfaction and truth on the one hand and consistency of certain systems of omega-logic and transfinite induction on the other are indicated.

Nicholas of Cusa was first of all a theologian but he was interested also in mathematic and natural sciences. In fact philosophico-theological and mathematical ideas were intertwined by him, theological and philosophical ideas influenced his mathematical considerations, in particular when he considered philosophical problems connected with mathematics and vice versa, mathematical ideas and examples were used by him to explain some ideas from theology. In this paper we attempt to indicate this mutual influence. We shall concentrate on the following problems: (...) the role and place of mathematics and mathematical knowledge in knowledge in general and in particular in theological knowledge, ontology of mathematical objects and their origin, in particular their relations to God and their meaning for the description of the world and physical reality, infinity in mathematics versus infinity in theology and their mutual relations and connections. It will be shown that—according to Nicholas—mathematics and mathematical thinking are tools of rationalization of theology and liberating it in a certain sense from the trap of apophatic theology. (shrink)

La presente investigación consiste en el análisis de la obra del escritor y filósofo Fabrice Hadjadj, desde la perspectiva de uno de los conceptos clave en ella: la «carne». La importancia de la carne para entender al hombre es una intuición desarrollada por Hadjadj en contraposición al espiritualismo dominante de la nueva era tecnológica. Nos encontramos en una era post-ideológica que se caracteriza por el dominio de lo tecnológico. Además, otra de las grandes novedades de nuestro tiempo es la conciencia (...) mayoritaria de la posibilidad de extinción de la especie humana. La crisis actual es profunda, antropológica: se trata de la pérdida de sentido de lo «humano». Esta crisis se ve agravada por una visión cada vez más desencarnada del hombre o espiritualista, lo que supone una ruptura antropológica que es promovida por el impacto de las tecnologías en nuestra lógica. Según Hadjadj, es este espiritualismo lo que contribuye más profundamente a diluir lo humano y acelerar la deriva poshumana de los nuevos tiempos. Nuestro trabajo, además de despejar cuál es el sentido de la carne para Hadjadj, así como el porqué de su particular relevancia para la nueva era, muestra algunas de las principales consecuencias de esa ruptura antropológica que promueve el uso de las tecnologías. La finalidad de esta investigación es mostrar cómo una visión antropológica centrada en la carne como la que propone Hadjadj, constituye una poderosa alternativa (si no la única) para resistir a la tentativa de que el espiritualismo tecnológico acabe devorando lo humano. (shrink)

The volume contains twenty essays devoted to the philosophy of mathematics and the history of logic. They have been divided into four parts: general philosophical problems of mathematics, Hilbert's program vs. the incompleteness phenomenon, philosophy of mathematics in Poland, mathematical logic in Poland. Among considered problems are: epistemology of mathematics, the meaning of the axiomatic method, existence of mathematical objects, distinction between proof and truth, undefinability of truth, Goedel's theorems and computer science, philosophy of mathematics in Polish mathematical and logical (...) schools, beginnings of mathematical logic in Poland, contribution of Polish logicians to recursion theory. (shrink)

This article examines Aristotle’s use of the term philia. As a basis for the analysis, the author employs the communicative component of this notion. This allows us to consider friendship as a process, distinguishing it from everything else that cannot be identified as such. This “residue” is something that comes from nature, common to all living creatures, and is at the root of all types of positive communication. The goal of this article is to show that the content identified as (...) such can be understood as a separate concept. (shrink)

The study analyzes the theory presented in the book Critical Theory and Social Media: Between Emancipation and Commodification by Thomas Allmer. The primary goal of the study is to place this work in the broader context of the critical theory of technology. The first part analyzes the context and the requirement for the philosophy of technology in the current digital age. Subsequently, Allmer’s methodology is described as an offshoot of critical theory. This theory is set in the context of the (...) book’s primary sources of thought, especially the critical theory of technology and Andrew Feenberg’s theory. Based on this theoretical understanding, research areas in critical media and technology theory are defined. The critical theory of technology shows that in the society of big data, there are similar contradictions of capitalism as we can find in the material world. Finally, there requirement for a political theory of technology is theorized, contrary to the widespread view that the current contradictions of digital capitalism can be solved by the ethics (design) of new technologies. In this context, critical theory is compared with the – so-called – ethics of new technologies. (shrink)

Recently, reliable interindividual differences were found for the way how individuals process multiple tasks and how they organize their responses. Previous studies have shown mixed results with respect to the flexibility of these preferences. On the one hand, individuals tend to adjust their preferred task processing mode to varying degrees of risk of crosstalk between tasks. On the other, response strategies were observed to be highly stable under varying between-resource competition. In the present study, we investigated whether the stability of (...) response strategies also persists with increased risk of crosstalk or whether individuals adjust their choice of response strategy, similar to what has been found at the level of task processing modes. Besides, related differences in multitasking efficiency were assessed. For this purpose, 53 participants performed the Free Concurrent Dual-Tasking paradigm, which allows them to control their task scheduling and response organization. The participants completed the FCDT paradigm under two conditions including task pairs characterized by either low or high levels of risk of crosstalk. The free choice of task scheduling resulted in the previously found distinct response patterns, best described as blocking, switching or response grouping. Remarkably, we did not find any notable adjustments of strategies of response organization to the extent of crosstalk. However, we observed suspected performance decrements of a switching strategy in the condition of high risk of crosstalk. The results suggest that individual strategies of response organization are stable habits. Further, they illustrate disadvantages of switching vs. blocking strategies of response organization in case of high task similarity. (shrink)

Among the main theorems obtained in mathematical logic in this century are the so called limitation theorems, i.e., the Löwenheim-Skolem theorem on the cardinality of models of first-order theories, Gödel’s incompleteness theorems and Tarski’s theorem on the undefinability of truth. Problems connected with the latter are the subject of this paper. In Section 1 we shall consider Tarski’s theorem. In particular the original formulation of it as well as some specifications will be provided. Next various meanings of the notion of (...) a satisfaction predicate will be studied. In Section 2 the problem of definability of the notion of truth, in particular of the notion of truth for the language of Peano arithmetic PA, will be discussed. It will be explicitly shown that the notion of satisfaction for the language of PA can be defined in a certain weak fragment of the second order arithmetic. Finally the axiomatic characterization of satisfaction and truth as well and its mathematical and philosophical meaning will be discussed. (shrink)

Als sozial und kulturell verfasstes Subjekt steht der Mensch in einem inneren Spannungsfeld zwischen Begehren und Gesetz. Seinen Wunschregungen sind Begrenzungen auferlegt, die stets Fragen der Ethik aufrufen. Die Beitrage dieses Buches untersuchen das Verhaltnis von Gesetz und Begehren in einer Reihe von Diskursfeldern, die untereinander in enger Beruhrung stehen: dem theologischen judischer und christlicher Pragung, dem (moral-)philosophischen und literarischen, schliesslich dem psychoanalytischen mit besonderer Gewichtung der Psychoanalyse Jacques Lacans.

Among the most interesting ideas of New Left in the US is a search for authenticity in human personality, or investigation of the place and role of the contemporary man when he is found in the setting: man-group-society-state. Finding such authenticity non-existent on the American scene the ideologists of New Left trace back the causes of this situation, characterized by deformation of personality deprived of the ego, and depict an authentic man who accepts himself both with respect to his ego (...) and as a part of a social group in which he lives. Surreptitious emphasis of the value of the individual and of his unique personality points to the individuality of man as a central category of this line of thought. In the consequence of coexistence of various personalities, variety is the main feature of the new American society postulated by New Left. Individuality and variety imply freedom as a key concept of that thought. Variety of human individualities enjoying freedom will enable the quest for the authentic ego and abolish the manifestations of alienation which do not exist within the real interpersonal community. Community as a structural form of social coexistence is based on close, often intimate, interpersonal relations and allegedly enables unconstrained search for individuality, showing a new way from the present atomization of the American society. The key values of that thought are potentially conflicting: on the one hand there is a set of ideas: individuality, variety, freedom; on the other, there is the concept of community. The two counterparts may easily stand in conflict or mutually limit their application. In such cases it is postulated to detect the causes of conflict and eliminate them. (shrink)

L. L. Fuller offers definitions of the essence of morals and the essence of law, taking them as the starting point for his theory which describes the relationships between these two normative spheres. Both law and morality are studied from the perspective of the natural law.

Joseph E. Brenner, "Logic in Reality", Springer, 2008, ISBN 978-1-4020-8374-7.

In the paper I ask the question about the relation between formal logic and the natural logic of human mind. By a natural logic I mean the ways of thinking of a person that is intelligent but untrained in formal logic. As it turns out that the laws, rules or properties of formal logic in some cases diverge from the natural ways of reasoning, I explain the causes of this divergence. Since the majority of research in this area has been (...) carried out from the standpoint of psychology, as a logician I suggest a slight change of the angle from which we look at the problem. I argue that certain narrowing of an interdisciplinary research would be helpful in getting a better picture of natural logic, and might provide a new stimulus for formal investigations. (shrink)

The aim of this paper is to describe the history of logical investigations at the University of Poznań. The organisational structures within the discipline as well as the outstanding logicians and their achievements are presented. Connections with the Lviv–Warsaw School are indicated.

Goncharov and Peretyat'kin independently gave necessary and sufficient conditions for when a set of types of a complete theory is the type spectrum of some homogeneous model of. Their result can be stated as a principle of second order arithmetic, which is called the Homogeneous Model Theorem (HMT), and analyzed from the points of view of computability theory and reverse mathematics. Previous computability theoretic results by Lange suggested a close connection between HMT and the Atomic Model Theorem (AMT), which states (...) that every complete atomic theory has an atomic model. The authors show that HMT and AMT are indeed equivalent in the sense of reverse mathematics, as well as in a strong computability theoretic sense and do the same for an analogous result of Peretyat'kin giving necessary and sufficient conditions for when a set of types is the type spectrum of some model. (shrink)

An adequate conjunction-implication pair is given for complete orthomodular lattices. The resulting conjunction is noncommutative in nature. We use the well-known lattice of closed subspaces of a Hilbert space, to give physical meaning to the given lattice operation.