In the article, first I present the atheistic argument from pointless evil and the argument from chance. The essence of the argument from chance consists in the incompatibility of the existence of purposeless events and the existence of a God who planned the universe to the last detail. Second, I would like to show that there is a relation between the evidential argument from evil and the argument from chance. An analysis of the theistic argument from small probabilities is a (...) helpful starting point for the presentation of how the two arguments are related. (shrink)

This article presents Alvin Plantinga’s views on epistemic justification. The first part situates Plantinga’s epistemological views in the context of his epistemology of religion and debates of general epistemology. The second part discusses Plantinga’s argument that the internalism of 20th century epistemology stems from deontologism and that the views on the epistemic justification of analytic philosophers reflect the relationship between classical deontologism and classical internalism. The last part points to the objections with which the Plantinga’s conception met and tries to (...) balance the depth and weakness of its position. (shrink)

Does God suffer? Some critical remarks on Dariusz Łukasiewicz’s paper ‘The suffering of God and the evil’ (Czy Bóg cierpi? Uwagi polemiczne do artykułu Dariusza Łukasiewicza 'Cierpienie Boga za zło') Author of article argues that Dariusz Łukasiewicz's criticism of Thomas G. Weinandy's book Czy Bóg cierpi?, directed towards three arguments for impassibility of God doesn't defeat Weinandy's theses. There are three reasons of that. First, Łukasiewicz criticism doesn't take into account metaphysical nature of Weinandy's arguments concerning nature of (...) suffering and God. Second, some of assumptions are attributed by Łukasiewicz to author of Does God suffer? mistakenly. Third, Łukasiewicz criticism that Weinandy's thought is too optimistic doesn't realize that philosophy cannot justify or disprove all theological theses, because many of them are beyond the reach of human reason. Article ends with some suggestions about proper use of analogy in attribution of properties to God. (shrink)

Łukasiewicz has often been criticized for his motive for inventing his three-valued logic, namely the avoidance of determinism. First of all, I want to show that almost all of the critcism along this line was wrong. Second I will indicate that he made mistakes, however, in constructing his system, because he had other motives at the same time. Finally I will propose some modification of his system and its interpretation which can attain his original purpose in some sense.

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (shrink)

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz [20]. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions [22, 23]. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz (...) and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (shrink)

Dobre praktyki i wyzwania rozwojowe systemu kształcenia zawodowego województwa podlaskiego Andrzej Klimczuk, Dariusz Borowski & Michał Skarzyński In Przyszłość Edukacji Zawodowej. Metody Modernizacji Szkół Zawodowych I Zwiȩkszenia Adaptacyjności Pracowników Oświaty. Izba Rzemieślnicza I Przedsiȩbiorczości W Białymstoku. pp. 177--195 (2015) .

Zygmunt Bauman was one of the leading revisionists in Poland before March 1968. Together with six other academics he was expelled from the University of Warsaw on the basis of the decision of the Minister of Higher Education taken on the 25st March 1968. It should be stressed, however, that at the beginning of his academic career Bauman had been a staunch believer of the Polish United Workers’ Party and an adherent of the Marxist-Leninist ideology. In his first revisionist paper, (...) published soon after the Polish October, he criticized the previous policy of the Party and expressed his hope that significant changes will take place in Poland. As a result of Party withdrawal from the reforms, his attitude towards both the communist rule and Marxism-Leninism had been changing. This paper analyses the evolution of his thought towards revisions. It presents the characteristic features of Bauman’s revisionism as well: an emphasis on human praxis, alternative thinking, and heterogeneity of culture. (shrink)

Główną część artykułu stanowi przykładowa analiza ilustrowanego ogłoszenia reklamowego, której celem jest zaprezentowanie sposobów perswazji, jakimi posługują się twórcy takich komunikatów. Na poziomie słowa przedstawiona została przede wszystkim strategia wykorzystywania faktu, że poszczególne wyrazy posiadają określone konotacje. W następnym etapie, analizie składni jednej z części tekstu reklamy, wyjaśniono, jak poprzez odpowiednie konstruowanie zdań udaje się stworzyć wrażenie rzeczowej argumentacji. Kolejny krok stanowi - podobnie jak na poziomie słowa - semantyczna analiza dłuższego fragmentu tekstu, jak również części wizualnej reklamy. Analiza ta (...) ma na celu pokazanie, jak m. in. poprzez budowę tzw. płaszczyzn izotopii semantycznej można przedstawić nic tylko obraz reklamowanego produktu, lecz także obraz adresata komunikatu. Ostatnia część analizy zawiera szczegółową prezentację werbalno-wizualnych figur retorycznych występujących w całym ogłoszeniu. Część właściwą artykułu poprzedzają rozdziały zawierające podstawy' teoretyczne do analizy o naszkicowanych ramach. I tak w pierwszej części publikacji przedstawione zostało rozszerzone pojęcie języka reklamy, cechy odróżniające go od języka standardowego, jak również jego aspekty semiotyczne. Następny rozdział poświęcony jest charakterystyce takich lingwistycznych aspektów reklamy jak leksyka (na przykładzie przymiotników), składnia (na przykładzie zdań eliptycznych) i stylistyka (na przykładzie wartościowania semantycznego) W kolejnym rozdziale omówione zostały problemy semiotycznej analizy komunikatów wizualnych, ze szczególnym uwzględnieniem analizy tych treści obrazu, które nie są wyrażone bezpośrednio, lecz tworzą tzw. implikaty. Ostatnia z części teoretycznych dotyczy werbalno-wizualnych figur retorycznych, których istota została tu krótko wyjaśniona na przykładach wybranych z analizowanego w artykule ogłoszenia reklamowego. (shrink)

Niniejszy artykuł poświęcony jest porównaniu teorii Karla Bühlera i Johna Searle’a w aspekcie pragmalingwistycznym, a konkretnie – w aspekcie działania językowego. Bühler traktuje język jako „organon” (narzędzie), który wykorzystywany jest do uzyskania określonych celów w procesie komunikacji. Jego nauka jest często uważana za fundament zapoczątkowanej przez Johna Austina i rozwiniętej przez Searle’a teorii aktów mowy, ponieważ zgodnie z koncepcją Searle’a formułowanie wypowiedzi językowej jest rodzajem intencjonalnego działania, a więc aktem podporządkowanym uzyskaniu określonego efektu w rzeczywistości pozajęzykowej. W pierwszej części artykułu (...) autor podejmuje próbę nakreślenia różnic i podobieństw pomiędzy stosowanymi przez Bühlera pojęciami Sprechakt i Sprechhandlung a kategorią speech act, zajmującą główne miejsce w modelu Searle’owskim. Drugim polem porównawczym są funkcje języka. Model znaku językowego, zaproponowany przez Bühlera, determinuje istnienie triady: Darstellungsfunktion, Appellfunktion i Ausdrucksfunktion. Funkcje komunikacyjne u Searle’a to funkcje illokucyjne, reprezentowane przez pięć różnych typów aktów mowy, wydzielonych przede wszystkim na podstawie tzw. illocutionary point. Konfrontując obydwa modele, autor wskazuje na heterogenność klasyfikacji funkcji Bühlerowskich i jednorodność taksonomii aktów illokucyjnych Searle’a. (shrink)

The aim of my paper is to clarify the conceptions of epistemic deism and probabilistic theism and to demonstrate that the two doctrines do not finally collapse into one. I would like also to point some reasons for the acceptance of a certain version of probabilistic theism which I will call in the last part of the article “open probabilistic theism”. Open probabilistic theism is not a version of the view called “open theism”. The reasons for the openness of open (...) probabilistic theism are quite different from the reasons supporting open theism. (shrink)

Uzasadnienie modelu w kontekście formalnoprawnych aspektów współpracy szkół z otoczeniem .

A. Klimczuk, D. Borowski, Organizacja i formy świadczenia pracy na styku oświaty, rzemiosła i instytucji rynku pracy – stan prawny, [in:] M. Juchnicka, Formalnoprawne aspekty modernizacji szkolnictwa zawodowego, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2014, pp. 21-76.

The aim of the paper is to analyze the expressive power of the square operator of Łukasiewicz logic: ∗x=x⊙x⁠, where ⊙ is the strong Łukasiewicz conjunction. In particular, we aim at understanding and characterizing those cases in which the square operator is enough to construct a finite MV-chain from a finite totally ordered set endowed with an involutive negation. The first of our main results shows that, indeed, the whole structure of MV-chain can be reconstructed from the involution and the (...) Łukasiewicz square operator if and only if the obtained structure has only trivial subalgebras and, equivalently, if and only if the cardinality of the starting chain is of the form n+1 where n belongs to a class of prime numbers that we fully characterize. Secondly, we axiomatize the algebraizable matrix logic whose semantics is given by the variety generated by a finite totally ordered set endowed with an involutive negation and Łukasiewicz square operator. Finally, we propose an alternative way to account for Łukasiewicz square operator on involutive Gödel chains. In this setting, we show that such an operator can be captured by a rather intuitive set of equations. (shrink)

The need for innovative development of healthcare institutions is determined by the necessity to increase the efficiency of organizational processes based on the formation of new models of cooperation, which will make it possible to get access to new technologies and knowledge. The goal of the study is to determine the parameters of the impact of innovative open cooperation strategy and the strategy of innovative closed cooperation of healthcare institutions on the effectiveness of their organizational structure in the context of (...) dissemination and the use of knowledge. Simulation modeling was applied to generate the most effective organizational management structure in the context of innovative cooperation and knowledge exchange within the organizational processes “Inside-out” and “Inside-in”. It is substantiated that the strategies of innovative cooperation “Open Innovation/Closed Innovation” have a significant impact on the organizational structure of management of healthcare institutions in terms of the “degree of centralization” (Dci), “degree of mediation” (Dii), and “degree of centralization of powers” (Dpi). The values of the selected criteria range from 25,52% to 61,50% in the case of Dii, and from 34,53% to 52,63% in the case of Dci, which indicates a higher efficiency of organizational knowledge exchange processes in healthcare institutions, which adhere to the Open Innovation strategy of innovative cooperation. Therefore, there are significant differences in the effectiveness of the management’s organizational structure depending on the degree of openness of innovative cooperation of healthcare institutions. The strategy of innovative openness allows increasing the number and quality of connections in the context of knowledge exchange between the subjects (actors, agents) of the organizational structure (in a broad sense, considering internal and external levels of externality) of healthcare institutions, regardless of the distance between them and the level of similarity. (shrink)

The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by (...) his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic. (shrink)

The stronger the level of economic integration between countries, the greater the need to study the formation patterns of the stock market reaction to the financial information signals. This concerns the Ukrainian stock market, which is now in its infancy, and which reaction to financial information signals is sometimes ambiguous. The research aims to identify the formation patterns of return and volatility indicators of the Ukrainian stock market reaction to the US financial information signals. To assess the direct nature of (...) US financial information signals effect on the PFTS stock index, the GARCH econometric modeling toolkit was applied. The research information base is the PFTS stock index and the Federal Reserve System financial information signals at the discount rate for 2000–2019. The fetch is divided into intervals corresponded to the ascent and decline phases of the financial cycle. It was found that an unforeseen increase in the discount rate at the financial cycle decline phase by 25 basis points decreases the PFTS stock index return, on average by 2.9%. Besides, the hypothesis about the general change stabilizing effect in the discount rate on the Ukrainian stock market volatility at the financial cycle growth phase was confirmed. Nevertheless, for investors, the most essential is the regulator’s monetary signals in the discount rate at the financial cycle decline phases rather than at the ascent phases because there is a more significant increase in the volatility level. (shrink)

A. Klimczuk, D. Borowski, M. Skarzyński, Wnioski i rekomendacje, [in:] M. Juchnicka, Formalnoprawne aspekty modernizacji szkolnictwa zawodowego, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2014, pp. 161-170.

According to Roman Ingarden, transcendental idealism prevented Kant from "even undertaking an attempt" at elucidating freedom "in terms of the causal structure of the world." I show that this claim requires qualification. In a remarkable series of Critical-period Reflexionen (5611-4, 5616-9), Kant sketches a defense of the possibility of freedom that differs radically from his published ones by incorporating an indeterministic account of the phenomena. Anticipating Łukasiewicz, he argues that universal causal determination is consistent with an open future: if an (...) action is contingent, there is an infinite regress of determining causes, yet there is a prior time at which this infinite series of causes has not yet commenced. However, he concedes that on this account the unity of experience "cannot fully obtain in the case of free beings." The fact that Kant even contemplated the indeterministic theory may carry implications for interpreting the argument of the Second Analogy. (shrink)

The Introduction outlines, in a concise way, the history of the Lvov-Warsaw School – a most unique Polish school of worldwide renown, which pioneered trends combining philosophy, logic, mathematics and language. The author accepts that the beginnings of the School fall on the year 1895, when its founder Kazimierz Twardowski, a disciple of Franz Brentano, came to Lvov on his mission to organize a scientific circle. Soon, among the characteristic features of the School was its serious approach towards philosophical studies (...) and teaching of philosophy, dealing with philosophy and propagation of it as an intellectual and moral mission, passion for clarity and precision, as well as exchange of thoughts, and cooperation with representatives of other disciplines.The genesis is followed by a chronological presentation of the development of the School in the successive years. The author mentions all the key representatives of the School (among others, Ajdukiewicz, Lesniewski, Łukasiewicz,Tarski), accompanying the names with short descriptions of their achievements. The development of the School after Poland’s regaining independence in 1918 meant part of the members moving from Lvov to Warsaw, thus providing the other segment to the name – Warsaw School of Logic. The author dwells longer on the activity of the School during the Interwar period – the time of its greatest prosperity, which ended along with the outbreak of World War 2. Attempts made after the War to recreate the spirit of the School are also outlined and the names of followers are listed accordingly. The presentation ends with some concluding remarks on the contribution of the School to contemporary developments in the fields of philosophy, mathematical logic or computer science in Poland. (shrink)

Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate truth-value so (...) as to reconstruct Łukasiewicz’s three-valued logic as a kind of extensional modal logic based on partial logic. (shrink)

In this article I try to show that the epistemological component of abductions is creativity and, to do so, I will use an analysis of Thagard's concept of projected-truth as well as reflections on Łukasiewicz's creativity. In the third part I present a real case, using Thagard's theory and introducing Hanson, to make the transition from logical and computational discourse to philosophy of science. At the end I will address one of the current challenges in order to explain creativity namely (...) the necessary and absolute interaction of each thinking subject, and therefore creative in action, with everything around him. To do this, I intend to introduce Feyerabend into the debate, which cleverly analyzes and dismantles the individualist idea of creation. (shrink)

Jan Łukasiewicz, a prominent Polish logician and philosopher, dealt with the scientific analysis of the concept of cause using logic. He wanted first and foremost to construct a definition, which reconciles the irreversibility of causal relationship to the exclusion of time sequence. In this article, I show that his attempts led to many contradictions, paradoxes and inconsistencies between Łukasiewicz’s definitions and commonly recognized examples of causality, even those given by the author himself. First, I present the semantic and formal aspects (...) of the definition proposed by him, and then I analyze examples, most of them proposed by the author. The main charges against his concept of causality are: the ambiguity of the concept of necessity; exclusion “for reasons of terminological” some causal phenomena from the range specified by the definition; paradoxes such as: the existence of the world is the cause of the existence of God; baseless demand, different subjects, and different features for cause and effect; disregard of the defnitive difference between post hoc and propter hoc; unjustified requirement of affirmative statements expressing a possession of attributes. The critique presented in this article is incomplete, but its function is to indicate both the value of logical analysis of philosophical concepts, and the dificulties of which such an analysis can entangle. Such an analysis can sometimes complete the process of defining certain concepts, but more often it provides an opportunity for further discussion and a better overall understanding. (shrink)

This book treats ancient logic: the logic that originated in Greece by Aristotle and the Stoics, mainly in the hundred year period beginning about 350 BCE. Ancient logic was never completely ignored by modern logic from its Boolean origin in the middle 1800s: it was prominent in Boole’s writings and it was mentioned by Frege and by Hilbert. Nevertheless, the first century of mathematical logic did not take it seriously enough to study the ancient logic texts. A renaissance in ancient (...) logic studies occurred in the early 1950s with the publication of the landmark Aristotle’s Syllogistic by Jan Łukasiewicz, Oxford UP 1951, 2nd ed. 1957. Despite its title, it treats the logic of the Stoics as well as that of Aristotle. Łukasiewicz was a distinguished mathematical logician. He had created many-valued logic and the parenthesis-free prefix notation known as Polish notation. He co-authored with Alfred Tarski’s an important paper on metatheory of propositional logic and he was one of Tarski’s the three main teachers at the University of Warsaw. Łukasiewicz’s stature was just short of that of the giants: Aristotle, Boole, Frege, Tarski and Gödel. No mathematical logician of his caliber had ever before quoted the actual teachings of ancient logicians. -/- Not only did Łukasiewicz inject fresh hypotheses, new concepts, and imaginative modern perspectives into the field, his enormous prestige and that of the Warsaw School of Logic reflected on the whole field of ancient logic studies. Suddenly, this previously somewhat dormant and obscure field became active and gained in respectability and importance in the eyes of logicians, mathematicians, linguists, analytic philosophers, and historians. Next to Aristotle himself and perhaps the Stoic logician Chrysippus, Łukasiewicz is the most prominent figure in ancient logic studies. A huge literature traces its origins to Łukasiewicz. -/- This Ancient Logic and Its Modern Interpretations, is based on the 1973 Buffalo Symposium on Modernist Interpretations of Ancient Logic, the first conference devoted entirely to critical assessment of the state of ancient logic studies. (shrink)

A theory of truth is usually demanded to be consistent, but -consistency is less frequently requested. Recently, Yatabe has argued in favour of -inconsistent first-order theories of truth, minimising their odd consequences. In view of this fact, in this paper, we present five arguments against -inconsistent theories of truth. In order to bring out this point, we will focus on two very well-known -inconsistent theories of truth: the classical theory of symmetric truth FS and the non-classical theory of naïve truth (...) based on ᴌukasiewicz infinitely valued logic: PAᴌT. (shrink)

This is the PhD dissertation, written under supervision of Professor Jerzy Słupecki, published in the book: U.Wybraniec-Skardowska i Grzegorz Bryll "Z badań nad teorią zdań odrzuconych" ( "Studies of theory of rejected sentences"), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Seria B: Studia i Monografie nr 22, pp. 5-131. It is the first, original publication on the theory of rejected sentences on which are based, among other, papers: "Theory of rejected propositions. I"and "Theory of rejected propositions II" with Jerzy Słupecki (...) and Grzegorz Bryll. -/- -/- . (shrink)

This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...) natural deduction and prove them to be sound and complete. We conclude with a ‘Theorem of Inversion’. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications relevant on Aristotle’s logic. The Sections I, II, III, and IV list respectively 23 articles, 44 abstracts, 3 books, and 11 reviews. Section I starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article—from Corcoran’s Philadelphia period that antedates his discovery of Aristotle’s natural deduction system—and the Journal of Symbolic Logic article—from his Buffalo period first reporting his original results. It ends with works published in 2015. (...) Some items are annotated as listed or with endnotes connecting them with other work and pointing out passages that, in retrospect, are seen to be misleading and in a few places erroneous. In addition, Section V, “Discussions”, is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 10 items published in the 1970s, 24 in the 1980s, 42 in the 1990s, 60 in the 2000s, and 70 in the current decade. The secondary bibliography is also annotated as listed or with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. Section VI, “Alternatives”, lists recent works on Aristotle’s logic oblivious of Corcoran’s research and, more generally in some cases, even of the Łukasiewicz-initiated tradition. As is evident from Section VII, “Acknowledgements”, Corcoran’s publications benefited from consultation with other scholars, most notably George Boger, Charles Kahn, John Mulhern, Mary Mulhern, Anthony Preus, Timothy Smiley, Michael Scanlan, Roberto Torretti, and Kevin Tracy. All of Corcoran’s Greek translations were done in collaboration with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. (shrink)

Aristotle in Analytica Posteriora presented a notion of proof as a special case of syllogism. In the present paper the remarks of Aristotle on the subject are used as an inspiration for developing formal systems of demonstrative syllogistic, which are supposed to formalize syllogisms that are proofs. We build our systems in the style of J. Łukasiewicz as theories based on classical propositional logic. The difference between our systems and systems of syllogistic known from the literature lays in the interpretation (...) of general positive sentences in which the same name occurs twice (of the form SaS). As a basic assumption of demonstrative syllogistic we accept a negation of such a sentence. We present three systems which differ in the interpretation of specific positive sentences in which the same name occurs twice (of the form SiS). The theories are defined as axiomatic systems. For all of them rejected axiomatizations are also supplied. For two of them a set theoretical model is also defined. (shrink)

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized (...) logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness. (shrink)

El objetivo principal de este trabajo es presentar el sistema lógico que resulta de extender, de una manera natural, a la Silogística con la Lógica proposicional, y demostrar que tal extensión se puede caracterizar como un sistema axiomático. Los axiomas que se utilizan son los de Jan Łukasiewicz , y la completitud de tal sistema de axiomas se prueba utilizando un método análogo al método del conjunto maximal consistente con testigos de Henkin, siguiendo algunas ideas que utiliza John Corcoran para (...) probar que su sistema de reglas de inferencia para la Silogística es completo. (shrink)

Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I compare that way with (...) other two ways based on Łukasiewicz’s three-valued logic and branching temporal logic. (shrink)

The purpose of this essay is to study the extent in which the semantics for different logical systems can be represented game theoretically. I will begin by considering different definitions of what it means to gamify a semantics, and show completeness and limitative results. In particular, I will argue that under a proper definition of gamification, all finitely algebraizable logics can be gamified, as well as some infinitely algebraizable ones (like Łukasiewicz) and some non-algebraizable (like intuitionistic and van Fraassen supervaluation (...) logic). (shrink)

In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one of Gödel (...) 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)

In the contemporary philosophical debate about probability, one of the main problems con‐ cerns the relation between objective probability and determinism. Is it possible for objective probability and determinism to co‐exist? this is one of the questions this dispute tries to answer. the scope of discussion is conducted between advocates of a positive answer (com‐ patibilist) and co‐existence opponents (incompatibilist). In the early twentieth century, many logicians also developed topics regarding probability and determinism. One of them was the outstanding Polish (...) logician and philosopher — Jan Łukasiewicz. the general purpose of this paper is to analyse and implement Łukasiewicz’s views regarding determinism and probability in the contemporary eld of this problem. I will try to show the relation between his interpre‐ tations of these concepts and in consequence his attempt to con ont them. As a result of the above analysis, I present some di erent positions (located in the elds of logic and semantics) in the contemporary discourse about the relation between objective probability and determi‐ nism. moreover, I will present Łukasiewicz’s views about this relation and the consequence of these solutions in the eld of logic. (shrink)

This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.

Suszko’s Thesis is a philosophical claim regarding the nature of many-valuedness. It was formulated by the Polish logician Roman Suszko during the middle 70s and states the existence of “only but two truth values”. The thesis is a reaction against the notion of many-valuedness conceived by Jan Łukasiewicz. Reputed as one of the modern founders of many-valued logics, Łukasiewicz considered a third undeter- mined value in addition to the traditional Fregean values of Truth and Falsehood. For Łukasiewicz, his third value (...) could be seen as a step beyond the Aristotelian dichotomy of Being and non-Being. According to Suszko, Łukasiewicz’s ideas rested on a confusion between algebraic values (what sentences describe/denote) and log- ical values (truth and falsity). Thus, Łukasiewicz’s third undetermined value is no more than an algebraic value, a possible denotation for a sentence, but not a genuine logical value. Suszko’s Thesis is endorsed by a formal result baptized as Suszko’s Reduction, a theorem that states every Tarskian logic may be characterized by a two-valued semantics. The present study is intended as a thorough investigation of Suszko’s thesis and its implications. The first part is devoted to the historical roots of many-valuedness and introduce Suszko’s main motivations in formulating the double character of truth-values by drawing the distinction in between algebraic and logical values. The second part explores Suszko’s Reduction and presents the developments achieved from it; the properties of two-valued semantics in comparison to many-valued semantics are also explored and discussed. Last but not least, the third part investigates the notion of logical values in the context of non-Tarskian notions of entailment; the meaning of Suszko’s thesis within such frameworks is also discussed. Moreover, the philosophical foundations for non-Tarskian notions of entailment are explored in the light of recent debates concerning logical pluralism. (shrink)

In La Silogística de Aristóteles, Antonio Benítez (i) offers a critical analysis of two contemporary interpretations of Aristotle's syllogistic of assertoric propositions (Corcoran and Łukasiewicz), and (ii) proposes to demonstrate the benefits of a mereological interpretation of the non-modal Aristotelian syllogistic.

In this article I define a strong conditional for classical sentential logic, and then extend it to three non-classical sentential logics. It is stronger than the material conditional and is not subject to the standard paradoxes of material implication, nor is it subject to some of the standard paradoxes of C. I. Lewis’s strict implication. My conditional has some counterintuitive consequences of its own, but I think its pros outweigh its cons. In any case, one can always augment one’s language (...) with more than one conditional, and it may be that no single conditional will satisfy all of our intuitions about how a conditional should behave. Finally, I suspect the strong conditional will be of more use for logic rather than the philosophy of language, and I will make no claim that the strong conditional is a good model for any particular use of the indicative conditional in English or other natural languages. Still, it would certainly be a nice bonus if some modified version of the strong conditional could serve as one. -/- I begin by exploring some of the disadvantages of the material conditional, the strict conditional, and some relevant conditionals. I proceed to define a strong conditional for classical sentential logic. I go on to adapt this account to Graham Priest’s Logic of Paradox, to S. C. Kleene’s logic K3, and then to J. Łukasiewicz’s logic Ł, a standard version of fuzzy logic. (shrink)

In the article I deal with some paradoxes and errors caused by improper usage of logical and philosophical terms appearing in the arguments for existence of god and other philosophical issues. I point at rst some paradoxes coming om improper usage of propositional calculus as an instrument for analysis of a natural language. this language is actually not using simple sentences but rather propositional functions, their logical connections, and some replacements for variables in them. We still have to deal with (...) so called paradox of material implication. the second paragraph provides formal and metatheoretical critics of Charles Sanders Peirce’s theory of deduction, induction and abduction. I argue that what Peirce and his followers call abduction is actually deduction or some reasoning unable to describe in terms of the logic used by them. Both syllogistic and inferential theory of abduction generate some paradoxes and contradictions. In the last paragraph also some paradoxes and contradictions resulting om the theory of causation by Jan Łukasiewicz are presented. the central issue of the article is erroneous usage of the implication: in logical paraphrases of a natural language, in description of the scienti c reasoning, and in description of causality. However, my objective is not to solve all problems mentioned above but rather to open a discussion over them. (shrink)

The work of this dissertation, in a broad sense, seeks to rescue what may be in the original project or nucleus of philosophy, from its Socratic arising: the idea of elucidative rationality. This rationality is aimed at expressing our practices in a way that can be confronted with objections and alternatives. The notion of expression is central to this rationality. This centrality is elucidated by the contemporary philosopher Brandom (1994, 2000, 2008a, 2013), from his view of the semantic inferentialism. With (...) this view, this dissertation, in a strict sense, investigates evidences that leads to the distinction of the inferentially expressivist tradition of syllogistic. In this semantic inferentialism, logic is the “organ of semantic self-consciousness”. In this sense, logic does not define the rational, in the most basic sense, but allows us to be aware, through inferential articulation, of the conceptual contents, which govern all our thoughts. Evidences presented in the work of this dissertation seek to show that the syllogism is marked by the logical-elucidative character of this semantic self-consciousness, because of its expressive role as inseparable from the notion of inference. In the first part of this dissertation, then, the tradition of syllogistics is examined, in which the expression is the main notion. This study is based on the tradition of syllogistics, composed of the Aristotelian school of Campinas, organized by Angioni (2014a), the logical economist Keynes (1906), and the “formalist” schools, represented mainly by the logician Łukasiewicz (1957, 1929/1963) and by Corcoran (1972, 1974, 2009, 2015). The main claims of the Campinas school are analyzed: the non-epistemological, but explanatory, exposition of (scientific) knowledge, in the syllogism, the secondary role of the notion of truth, the priority of the predicative structure, and the suggestion of approaching of the syllogistic to the relevant system of logic. In this analysis, we add the discussion about the reasoning of the epagogic type, important to the practical understanding of the “first principles”. The key points of Keynes are also discussed: the semantic priority of propositional judgment and the explanatory role of deductive inference. The second part of this dissertation discusses the relation between expression, inference and the expressive role of logic, based on the semantic inferentialism of Brandom. In order to discuss this relationship, propaedeutic questions are raised, related to the semantic role of sentences and subsentences (terms and predicates) in language, to different conceptions of logical validity, beyond the truth-functional aspect, to the logical demarcation of symbolic rules, to demarcation of logic, the idea of “formal logic”, and the removal of formal semantics from natural language concern. Next, the theoretical framework of Brandom's semantic inferentialism is presented. In this framework, the idea of philosophical semantics, pragmatisms of the semantic and conceptual type, expressivisms of the rationalist, logical and propositional conceptual type, and the semantically primitive notion of incompatibility come into play. Thus, to those who are interested in the correspondence between ancient logic and modern logic, the work of this dissertation offers a useful contribution, especially to projects of formalization of the syllogistics, which need not appeal against or in favor of a strictly formal approach to logic. (shrink)

In previous work, I introduced a complete axiomatization of classical non-tautologies based essentially on Łukasiewicz’s rejection method. The present paper provides a new, Hilbert-type axiomatization (along with related systems to axiomatize classical contradictions, non-contradictions, contingencies and non-contingencies respectively). This new system is mathematically less elegant, but the format of the inferential rules and the structure of the completeness proof possess some intrinsic interest and suggests instructive comparisons with the logic of tautologies.

The aim of this paper is to show how the invention of imaginary logic by Nikolaj A. Vasil’ev, forerunner of various logical and metaphysical theories appeared in the 20th century, is grounded on a revaluation of Aristotelian ontology. I shall introduce the reason why Aristotle believes that the study of the principle of contradiction is part of ontology (§ 2); I shall explain why Vasil’ev considers the law of contradiction an empirical law, and not a logical one (§ 3.1). I (...) will show his conception of contradiction (§ 3.2) and I will discuss how he believes that it’s possible to renounce this law; (§ 3.3). I shall then explain the fundamental features of imaginary logic (§ 4.1 and § 4.2); and, finally I shall claim how, in spite of a convergence from the logical point of view (§ 5.1), the incompatibility of the two authors takes place on an ontological level (§ 5.2). In order to do so, I shall implement the analysis of the Aristotelian syllogistic conducted by the Polish logician and philosopher Jan Łukasiewicz, together with a crucial distinction between two concepts: the one of ‘law’ and the one of ‘principle’. -/- . (shrink)

In 1942 Haskell B. Curry presented what is now called Curry's paradox which can be found in a logic independently of its stand on negation. In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this article the non-classical resolution of Curry’s Paradox and Shaw-Kwei' sparadox without rejection any contraction postulate is proposed. In additional relevant paraconsistent logic C ̌_n^#,1≤n<ω, in fact,provide an effective way of circumventing triviality of da Costa’s paraconsistent Set Theories〖NF〗n^C.