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Jan Woleński, Urszula Wybraniec-Skardowska, Andrzej Pietruszczak, Yaroslav Shramko, Andrew Schumann, Piotr Łukowski, Matheus Gabriel Barbosa, Fabien Schang, Vadim Verenich, Jaap Hage, Roman Murawski, Arkady Zakrevsky, Andrea Reichenberger, Marina F. Bykova, Robert W. McGee, Mustafa Khuramy, Erik Schulz,


No Perils of Rejecting the Parity Argument

Many moral realists have employed a strategy for arguing for moral realism by claiming that if epistemic normativity is categorical and that if this epistemic normativity exists, then categorical normativity exists. In this paper, we will discuss that argument, examine a way out, and respond to the objections people have recently raised in the literature. In the end, we conclude that the objections to our way out will do little in the way of motivating those who already do not believe in categorical normativity, thereby severing the power the aforementioned parity argument is designed to possess.

Book review: Libertarian Autobiographies: Moving Toward Freedom in Today’s World. Edited by Jo Ann Cavallo and Walter E. Block. Palgrave Macmillan, 2023

The Author: Robert W. McGee,
Book review

Living in Illusion is Dangerous

The Author: Marina F. Bykova,
The interview given by Marina F. Bykova, Professor of Philosophy at the Department of Philosophy and Religious Studies at North Carolina State University (USA), and the Editor-in-Chief of the journal Studies in East European Thought. She earned her PhD and Dr. Habil in Philosophy from the Institute of Philosophy, Russian Academy of Sciences (Moscow, Russia), where she worked until relocating to the USA in 2000. Bykova specializes in the history of nineteenth century continental philosophy, with a particular focus on German idealism. She has also written extensively on Russian philosophy and intellectual tradition. She has published 11 books and over 250 scholarly articles. Her forthcoming book, Hegel’s Philosophy of Nature: A Critical Guide, is set to be released by Cambridge University Press in 2024.

Logic Matters – Gender and Diversity, Too

This interview features Andrea Reichenberger. Currently she holds a substitute professorship for history of technology at TUM Technical University of Munich. She is junior research group leader at the Department of Mathematics, University of Siegen, Germany, and leads the research project “Rethinking the History of Mathematics and Physics: Women in Focus.” Reichenberger has held several postdoctoral positions, e.g., at the Center for the History of Women Philosophers and Scientists (HWPS) at Paderborn University (Germany) and in the DFG research project “Thought Experiment, Metaphor, Model” at the Institute for Philosophy I at the Ruhr University Bochum. Between 2019 and 2021, she was a fellow at the University of Paderborn and principal investigator of the research project “Foundational research in mathematical logic – relativity – quantum physics. Case studies on the integration of women philosophers.” Reichenberger has written a book on Émilie du Châtelet (Springer, 2016) and has published many articles in journals, collected editions, and encyclopedias.

The Past and Future of High Technology

The Author: Arkady Zakrevsky,
The interview given in 2008 by Arkady Zakrevsky (1928–2014), Corresponding Member of the National Academy of Sciences of Belarus (1972), Doctor of Technical Sciences (1967), Professor (1969). He stood at the origins of the birth of cybernetics in the Soviet Union. He proposed the programming language for logical tasks LYaPAS, on the basis of which a series of computer-aided design systems for discrete devices were created, and methods for implementing parallel algorithms for the logical control of interacting processes. Some monographs: LYaPAS: A Programming Language for Logic and Coding Algorithms (N.-Y., L.: Academic Press, 1969; with M. A. Gavrilov); Boolesche Gleichungen: Theorie, Anwendung, Algorithmen (Berlin: VEB Verlag Technik, 1984; mit Dieter Bochmann und Christian Posthoff); Combinatorial Algorithms of Discrete Mathematics (Tallinn: TUT Press, 2008; with Yu. Pottosin, L. Cheremisinova); Optimization in Boolean Space (Tallinn: TUT Press, 2009; with Yu. Pottosin, L. Cheremisinova); Design of Logical Control Devices (Tallinn: TUT Press, 2009; with Yu. Pottosin, L. Cheremisinova); Combinatorial Calculations in Many-Dimensional Boolean Space (Tallinn: TUT Press, 2012); Solving Large Systems Logical Equations (Tallinn: TUT Press, 2013).

100 Years of Logical Investigations at University of Poznań

The Author: Roman Murawski,
The aim of the paper is to describe the history of logical investigations at the University of Poznań. The organizational structures within the discipline as well as the outstanding logicians and their achievements are presented. Connections with the Lvov-Warsaw School are indicated.

How Law’s Nature Influences Law’s Logic

The Author: Jaap Hage,
Classical logic is based on an underlying view of the world, according to which
there are elementary facts and compound facts, which are logical combinations
of these elementary facts. Sentences are true if they correspond to, in last
instance, the elementary facts in the world. This world view has no place for
rules, which exist as individuals in the world, and which create relations between
the most elementary facts. As a result, classical logic is not suitable to deal with
rules, and is therefore unsuitable to deal with legal reasoning. A logic that is
more suitable should take into account that law is a part of social reality, in
particular a part that consists of constructivist facts, and that rules play a central
role in law. This article gives a superficial description of how social reality exists
and of the place of law and legal rules in it. It uses this description to argue that
traditional techniques to reason with and about legal rules provide a better logic
for law than classical logic. These techniques can be accommodated in a logic
that treats rules as logical individuals.

Neural Networks in Legal Theory

The Author: Vadim Verenich,
This article explores the domain of legal analysis and its methodologies, emphasizing the significance of generalization in legal systems. It discusses the process of generalization in relation to legal concepts and the development of ideal concepts that form the foundation of law. The article examines the role of logical induction and its similarities with semantic generalization, highlighting their importance in legal decision-making. It also critiques the formal-deductive approach in legal practice and advocates for more adaptable models, incorporating fuzzy logic, non-monotonic defeasible reasoning, and artificial intelligence. The potential application of neural networks, specifically deep learning algorithms, in legal theory is also discussed. The article discusses how neural networks encode legal knowledge in their synaptic connections, while the syllogistic model condenses legal information into axioms. The article also highlights how neural networks assimilate novel experiences and exhibit evolutionary progression, unlike the deductive model of law. Additionally, the article examines the historical and theoretical foundations of jurisprudence that align with the basic principles of neural networks. It delves into the statistical analysis of legal phenomena and theories that view legal development as an evolutionary process. The article then explores Friedrich Hayek’s theory of law as an autonomous self-organizing system and its compatibility with neural network models. It concludes by discussing the implications of Hayek’s theory on the role of a lawyer and the precision of neural networks.

Legal Gaps and their Logical Forms

The concept of legal gap is tackled from a number of logical perspectives and semantic methods. After presenting our own goal (Section 1), a first introduction into legal logic refers to Bobbio’s works and his formalization of legal statements (Sections 2 and 3). Then Woleński’s contribution to the area is taken into account through his reference to the distinction between two juridical systems (viz. Common Law vs Civil Law) and the notion of conditional norms (Section 4). The notion of reason is also highlighted in the case of Raz’s legal logic, thereby leading to a future connection with von Wright’s logic of truth and an analogy made with an anti-realist reading of truth-values and norms (Section 5). Our personal contribution is introduced through a reflection on how logic should deal with the logical form of norms (Section 6), before entering a number of crucial definitions and distinctions for the concepts of norm, legal statement, and promulgation (Section 7). The final point is a proposed semantics for legal statements, which is both many-valued and gap-friendly (Section 8). A distinction between a number of requirements for permission and forbiddance leads to a set of non-classical juridical systems in which non-permission and forbiddance are not equivalent with each other any more; this does justice to Woleński’s former distinction between Common Law and Civil Law, also leading ultimately to a non-classical square of legal oppositions in which several legal operators may collapse into other ones (Section 9).

Proof of the Existence of Hell: An Extension of the Stone Paradox

The Author: Piotr Łukowski,
As shown in [24], the paradox of the stone is a failed attempt to show that “omnipotence” is a contradictory concept. An element of the argument presented there is that God, while unable to lift the stone, can nevertheless annihilate it. This work considers the amplification of the paradox of the stone to the form generated by the question: can God create a stone which He will not be able to lift, nor, once created, will He be able to destroy.

Philosophy and Logic in Time of War

The interview given by Yaroslav Shramko (b. 1963), professor of the Department of Philosophy, rector of the Kryvyi Rih State Pedagogical University (Ukraine). His main research interests lie in the fields of logic and analytical philosophy. He has carried out several projects on modern non-classical logic: 1996-1998, within the Alexander von Humboldt Foundation Fellowship at Humboldt University in Berlin (Germany); 1999-2000, within the Fulbright Program at Indiana University in Bloomington (USA); 2003-2004, as a Wilhelm Bessel Awardee at Dresden University of Technology (Germany) among them. He has been a frequent invited speaker at international conferences and congresses. He is a member of the editorial boards of several international logic journals, such as Logic and Logical Philosophy (Torun, Poland), Bulletin of the Section of Logic (Łódź, Poland), European Journal of Mathematics (Springer), Studia Logica (Springer). Prof. Shramko is the author of “Truth and Falsehood. An Inquiry into Generalized Logical Values” (Springer, 2011, joint work with Heinrich Wansing) and of a number of articles on logic and analytic philosophy in peer-reviewed international journals.

From the History of Lesniewski’s Mereology

In this paper, we want to present the genesis of Stanisław Lesniewski’s mereology. Although ‘mereology’ comes from the word ‘part’, mereology arose as a theory of collective classes. That is why we present the differences between the concepts of being a distributive class and being a collective class. Next, we present Lesniewski’s original mereology from 1927, but with a modern approach. Lesniewski was inspired to create his concept of classes and their elements by Russell’s antinomy. To face it, Lesniewski had to define the concept of being an element of based on the concept of being part of. Lesniewski showed that in his theory, there is no equivalent to Russell’s antinomy. We will show that his solution has nothing to do with the original approach because, in both cases, we are talking about objects of a different kind. Russell’s original antinomy concerned distributive classes, and Lesniewski’s considerations concerned collective classes.

The Warsaw School of Logic: Main Pillars, Ideas, Significance

The Warsaw School of Logic (WSL) was the famous branch of the Lvov-Warsaw School (LWS) – the most important movement in the history of Polish philosophy. Logic made the most important field in the activities of the WSL. The aim of this work is to highlight the role and significance of the WSL in the history of logic in the 20th century.

Logic and Metalogic: a Historical Sketch

The Author: Jan Woleński,
This paper briefly discusses the relations between logic and metalogic in history. Metalogic is understood as a reflection on logic in its various senses, particularly sensu stricto (formal, mathematical) and sensu largo (formal logic plus semantic plus methodology of science). It is shown that metalogic in its contemporary understanding arose after mathematical logic had become a mature discipline. Special passage is devoted to metalogic in Poland. The last part of the paper discussed so-called logocentric predicament.