The paper attempts to answer the questions of what learning from negativity of experience perspective is and if it could become the right way of teaching and learning morality at school. It consists of three sections. The first one explains the fundamental distinction between negative moral experiences and negativity of moral experience. In the second section, the author’s attention focuses on the possibility of didactic application of teaching and learning from negativity of experience. The last section contains J. F. Herbart’s (...) concept of educative guidance as a permanently valid theoretical framework for contemporary moral education at school. -/- . (shrink)

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)

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)

In the chapter, there is an analysis of sharing economy development in Poland. It concerns both the big players on the market like the most known Airbnb and Uber, as well as smaller, local initiatives, flourishing especially in the food sector. Sharing economy is not a normative concept and is defined differently depending on the subject to which it refers. However, the significance of the phenomenon is rising rapidly from year to year. Moreover, sharing economy brings many opportunities but also (...) creates a lot of unsolved issues, such as regulations, tax regulations, labour law, competition, which often can lead to conflicts between diverse groups of actors. The new, unregulated, by law, model of the economy in some sectors has caused a lot of confusion, leading to conflicts, as well as a feeling of inequality. (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)

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)

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) .

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)

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.

Uzasadnienie modelu w kontekście formalnoprawnych aspektów współpracy szkół z otoczeniem .

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 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.

In this paper we consider the logics L(i,n) obtained from the (n+1)-valued Lukasiewicz logics L(n+1) by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong maximality among them are analyzed. We present a very general theorem that provides sufficient conditions for maximality between logics. As a consequence of this theorem, it is shown that L(i,n) is maximal w.r.t. CPL whenever n is prime. Concerning strong maximality (i.e. maximality w.r.t. (...) rules instead of only axioms), we provide algebraic arguments in order to show that the logics L(i,n) are not strongly maximal w.r.t. CPL, even for n prime. Indeed, in such case, we show that there is just one extension between L(i,n) and CPL obtained by adding to L(i,n) a kind of graded explosion rule. Finally, using these results, we show that the logics L(i,n) with n prime and i/n < 1/2 are ideal paraconsistent logics. (shrink)

In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...) not jointly, lack the problematic feature. (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)

JUNE 2015 UPDATE: A BIBLIOGRAPHY: JOHN CORCORAN’S PUBLICATIONS ON ARISTOTLE 1972–2015 By John Corcoran -/- This presentation includes a complete bibliography of John Corcoran’s publications relevant to his research on Aristotle’s logic. Sections I, II, III, and IV list 21 articles, 44 abstracts, 3 books, and 11 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article from Corcoran’s Philadelphia period that antedates his Aristotle studies and the Journal of Symbolic Logic article from his (...) Buffalo period first reporting his original results; it ends with works published in 2015. A few of the 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: 8 items published in the 1970s, 23 in the 1980s, 42 in the 1990s, 56 in the 2000s, and 69 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, of the Lukasiewicz-initiated tradition. As is evident from Section VII, “Acknowledgements”, Corcoran’s publications benefited from consultation with other scholars, most notably 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. -/- REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications. Also, let me know of passages I should comment on. (shrink)

John Corcoran and George Boger. Aristotelian logic and Euclidean geometry. Bulletin of Symbolic Logic. 20 (2014) 131. -/- By an Aristotelian logic we mean any system of direct and indirect deductions, chains of reasoning linking conclusions to premises—complete syllogisms, to use Aristotle’s phrase—1) intended to show that their conclusions follow logically from their respective premises and 2) resembling those in Aristotle’s Prior Analytics. Such systems presuppose existence of cases where it is not obvious that the conclusion follows from the premises: (...) there must be something deductions can show. Corcoran calls a proposition that follows from given premises a hidden consequence of those premises if it is not obvious that the proposition follows from those premises. By a Euclidean geometry we mean an extended discourse beginning with basic premises—axioms, postulates, definitions—1) treating a universe of geometrical figures and 2) resembling Euclid’s Elements. There were Euclidean geometries before Euclid (fl. 300 BCE), even before Aristotle (384–322 BCE). Bochenski, Lukasiewicz, Patzig and others never new this or if they did they found it inconvenient to mention. Euclid shows no awareness of Aristotle. It is obvious today—as it should have been obvious in Euclid’s time, if anyone knew both—that Aristotle’s logic was insufficient for Euclid’s geometry: few if any geometrical theorems can be deduced from Euclid’s premises by means of Aristotle’s deductions. Aristotle’s writings don’t say whether his logic is sufficient for Euclidean geometry. But, there is not even one fully-presented example. However, Aristotle’s writings do make clear that he endorsed the goal of a sufficient system. Nevertheless, incredible as this is today, many logicians after Aristotle claimed that Aristotelian logics are sufficient for Euclidean geometries. This paper reviews and analyses such claims by Mill, Boole, De Morgan, Russell, Poincaré, and others. It also examines early contrary statements by Hintikka, Mueller, Smith, and others. Special attention is given to the argumentations pro or con and especially to their logical, epistemic, and ontological presuppositions. What methodology is necessary or sufficient to show that a given logic is adequate or inadequate to serve as the underlying logi of a given science. (shrink)

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)

Growing-Block theorists hold that past and present things are real, while future things do not yet exist. This generates a puzzle: how can Growing-Block theorists explain the fact that some sentences about the future appear to be true? Briggs and Forbes develop a modal ersatzist framework, on which the concrete actual world is associated with a branching-time structure of ersatz possible worlds. They then show how this branching structure might be used to determine the truth values of future contingents. They (...) point out three different ways of interpreting the logical connectives, which give rise to three different logics of the open future: one supervaluationist, one corresponding to Lukasiewicz's strong Kleene logic, and one intuitionist. (shrink)

The book titled The Collaborative Economy in Action: European Perspectives is one of the important outcomes of the COST Action CA16121, From Sharing to Caring: Examining the Socio-Technical Aspects of the Collaborative Economy that was active between March 2017 and September 2021. The Action was funded by the European Cooperation in Science and Technology - COST. The main objective of the COST Action Sharing and Caring is the development of a European network of researchers and practitioners interested in investigating the (...) collaborative economy models, platforms, and their socio-technological implications. The network involves scholars, practitioners, communities, and policymakers. The COST Action Sharing and Caring helped to connect research initiatives across Europe and enabled scientists to develop their ideas by collaborating with peers. This collaboration opportunity represented a boost for the participants’ research, careers, and innovation potential. The main aim of this book is to provide a comprehensive overview of the collaborative economy in European countries with a variety of its aspects for a deeper understanding of the phenomenon as a whole. For this reason, in July 2017, an open call for country reports was distributed among the members of the COST Action Sharing and Caring. Representatives of the member countries were invited to produce short country reports covering: definition of the CE; types and models of the CE; key stakeholders involved; as well as legislation and technological tools relevant for the CE. Submitted reports varied in length and regarding the level of detail included, in accordance with how much information was available in each respective country at the time of writing. Editors of the book have compiled these early reports into a summary report, which was intended as a first step in mapping the state of the CE in Europe. The Member Countries Report on the Collaborative Economy, edited by Gaia Mosconi, Agnieszka Lukasiewicz, and Gabriela Avram that was published on the Sharing and Caring website, represented its first synergetic outcome and provided an overview of the CE phenomenon as interpreted and manifested in each of the countries part of the network. Additionally, Sergio Nassare-Aznar, Kosjenka Dumančić, and Giulia Priora compiled a Preliminary Legal Analysis of Country Reports on Cases of Collaborative Economy. In 2018, after undertaking an analysis of the previous reports’ strengths and weaknesses, the book editors issued a call for an updated version of these country reports. Prof. Ann Light advised the editorial team, proposing a new format for country reports and 4000 words limit. The template included: Introduction, Definition, Key Questions, Examples, Illustration, Context, Developments, Issues, Other Major Players, and Relevant Literature. The new template was approved by the Management Committee in October 2018. The task force that had supported the production of the first series of country reports acted as mentors for the team of authors in each country. The final reports arrived at the end of 2018, bringing the total number of submissions to 30. A call for book editors was issued, and a new editorial team was formed by volunteers from the participants of the COST Action: Andrzej Klimczuk, Vida Česnuityte, Cristina Miguel, Santa Mijalche, Gabriela Avram, Bori Simonovits, Bálint Balázs, Kostas Stefanidis, and Rafael Laurenti. The editorial team organized the double-blind reviews of reports and communicated to the authors the requirements for improving their texts. After reviews, the authors submitted updated versions of their country reports providing up-to-date interdisciplinary analysis on the state of the CE in 2019, when the reports were collected. During the final phase, the chapters were again reviewed by the lead editors together with all editorial team members. At the time, the intention was to update these reports again just before the end of the COST Action Sharing and Caring in 2021 and to produce a third edition. However, the COVID-19 pandemic changed these plans. Thus, this final volume was created by 82 scholars-editors and contributors-and consists of reports on 27 countries participating in the COST Action. M4 - Citavi. (shrink)

Complete deductive systems are constructed for the non-valid (refutable) formulae and sequents of some propositional modal logics. Thus, complete syntactic characterizations in the sense of Lukasiewicz are established for these logics and, in particular, purely syntactic decision procedures for them are obtained. The paper also contains some historical remarks and a general discussion on refutation systems.

I apply Kooi and Tamminga's (2012) idea of correspondence analysis for many-valued logics to strong three-valued logic (K3). First, I characterize each possible single entry in the truth-table of a unary or a binary truth-functional operator that could be added to K3 by a basic inference scheme. Second, I define a class of natural deduction systems on the basis of these characterizing basic inference schemes and a natural deduction system for K3. Third, I show that each of the resulting natural (...) deduction systems is sound and complete with respect to its particular semantics. Among other things, I thus obtain a new proof system for Lukasiewicz's three-valued logic. (shrink)

Contents: Danuta Ługowska, Incommensurability of Paradigms Exemplified by the Differences Between the Western and Eastern European Image of the Human Person ; Maria-Magdalena Weker, Light, Body and Soul – the Issues Fundamental for Theories of Vision. A Historical Survey ; Dariusz Kucharski, The Conception of Sensory Perception and Scientific Research. (The Theory of Sign within Philosophy of G. Berkeley and T. Reid) ; Grzegorz Bugajak, Causality and Determinism in Physics ; Anna Lemańska, Truth in Mathematics ; Anna Latawiec, Troubles (...) with the Philosophy of Medicine ; Adam Świeżyński, Values, Axiological Experience, and Scientific Research ; Grzegorz Bugajak, Fears of Science. Nature and Human Actions ; Adam Świeżyński, Some Remarks on the Human Search for Sense in the Context of Human Actions. (shrink)

This note considers deductive systems for the operator a of unprovability in some particular propositional normal modal logics. We give thus complete syntactic characterization of these logics in the sense of Lukasiewicz: for every formula  either `  or a  (but not both) is derivable. In particular, purely syntactic decision procedure is provided for the logics under considerations.

A hundred years ago Frege had published most of his arguments against psychologism and Husserl was busy writing his Logical Investigations, which was to appear at the turn of the century and open with a long onslaught on psychologism. The arguments of these two logicians against the psychologistic view - of Mill, Erdmann and many others - that the discipline of logic, its sentences, or its "laws", deal with psychological phenomena met with widespread approval from those best qualified to judge (...) (for example Lukasiewicz). They set the agenda for most twentieth century work in exact, "scientific", or analytic philosophy. As the century draws to its close, many of the arguments of Frege and Husserl have been found wanting by analytic philosophers and cognitive scientists who are prepared to argue that the laws of logic are just laws of human thought. (shrink)

Why does Aristotle not use the copulative wording for categorical propositions, but instead the clumsier terminological formulations (e. g. the B belongs to every A) in his syllogistic? The proposed explanations by Alexander, Lukasiewicz and Patzig: Aristotle wants to make clear the difference between subject and predicate, seems to be insufficient. In quantified categorical propositions, this difference is always sufficiently clear by the use of the pronouns going with the subject expressions. Aristotle opts for the terminological wording because in premiss (...) pairs of figures two and three he can thus suppress the middle term in one of the premisses and connect the major and minor term, using connecting particles. This renders the syllogisms more transparent. Had he used the copulative wording instead, he would have run into difficulties, in particular with o-propositions among the premisses (i. e. in Baroco and Bocardo) because in these cases the pronoun expressing the quantification would have to go with the subject term, the negation with the predicate. (shrink)

Etude de l'extension par la negation semi-intuitionniste de la logique positive des propositions appelee logique C, developpee par A. Urquhart afin de definir une semantique relationnelle valable pour la logique des valeurs infinies de Lukasiewicz (Lw). Evitant les axiomes de contraction et de reduction propres a la logique classique de Dummett, l'A. propose une semantique de type Routley-Meyer pour le systeme d'Urquhart (CI) en tant que celle-la ne fournit que des theories consistantes pour la completude de celui-ci.

This work studies some problems connected to the role of negation in logic, treating the positive fragments of propositional calculus in order to deal with two main questions: the proof of the completeness theorems in systems lacking negation, and the puzzle raised by positive paradoxes like the well-known argument of Haskel Curry. We study the constructive com- pleteness method proposed by Leon Henkin for classical fragments endowed with implication, and advance some reasons explaining what makes difficult to extend this constructive (...) method to non-classical fragments equipped with weaker implications (that avoid Curry's objection). This is the case, for example, of Jan Lukasiewicz's n-valued logics and Wilhelm Ackermann's logic of restricted implication. Besides such problems, both Henkin's method and the triviality phenomenon enable us to propose a new positive tableau proof system which uses only positive meta-linguistic resources, and to mo- tivate a new discussion concerning the role of negation in logic proposing the concept of paratriviality. In this way, some relations between positive reasoning and infinity, the possibilities to obtain a ¯first-order positive logic as well as the philosophical connection between truth and meaning are dis- cussed from a conceptual point of view. (shrink)

In the present article we attempt to show that Aristotle's syllogistic is an underlying logiC which includes a natural deductive system and that it isn't an axiomatic theory as had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic. We examine the relation of the model to the system of logic envisaged in scattered parts of Prior and Posterior Analytics. Our interpretation restores Aristotle's reputation as a logician of consummate imagination and skill. Several (...) attributions of shortcomings and logical errors to Aristotle are shown to be without merit. Aristotle's logic is found to be self-sufficient in several senses: his theory of deduction is logically sound in every detail. (His indirect deductions have been criticized, but incorrectly on our account.) Aristotle's logic presupposes no other logical concepts, not even those of propositional logic. The Aristotelian system is seen to be complete in the sense that every valid argument expressible in his system admits of a deduction within his deductive system: every semantically valid argument is deducible. (shrink)

This presentation of Aristotle's natural deduction system supplements earlier presentations and gives more historical evidence. Some fine-tunings resulted from conversations with Timothy Smiley, Charles Kahn, Josiah Gould, John Kearns,John Glanvillle, and William Parry.The criticism of Aristotle's theory of propositions found at the end of this 1974 presentation was retracted in Corcoran's 2009 HPL article "Aristotle's demonstrative logic".

This interesting and imaginative monograph is based on the author’s PhD dissertation supervised by Saul Kripke. It is dedicated to Timothy Smiley, whose interpretation of PRIOR ANALYTICS informs its approach. As suggested by its title, this short work demonstrates conclusively that Aristotle’s syllogistic is a suitable vehicle for fruitful discussion of contemporary issues in logical theory. Aristotle’s syllogistic is represented by Corcoran’s 1972 reconstruction. The review studies Lear’s treatment of Aristotle’s logic, his appreciation of the Corcoran-Smiley paradigm, and his understanding (...) of modern logical theory. In the process Corcoran and Scanlan present new, previously unpublished results. Corcoran regards this review as an important contribution to contemporary study of PRIOR ANALYTICS: both the book and the review deserve to be better known. (shrink)

This presentation includes a complete bibliography of John Corcoran’s publications devoted at least in part to Aristotle’s logic. Sections I–IV list 20 articles, 43 abstracts, 3 books, and 10 reviews. It starts with two watershed articles published in 1972: the Philosophy & Phenomenological Research article that antedates Corcoran’s Aristotle’s studies and the Journal of Symbolic Logic article first reporting his original results; it ends with works published in 2015. A few of the items are annotated with endnotes connecting them with (...) other work. In addition, Section V “Discussions” is a nearly complete secondary bibliography of works describing, interpreting, extending, improving, supporting, and criticizing Corcoran’s work: 8 items published in the 1970s, 22 in the 1980s, 39 in the 1990s, 56 in the 2000s, and 65 in the current decade. The secondary bibliography is annotated with endnotes: some simply quoting from the cited item, but several answering criticisms and identifying errors. As is evident from the Acknowledgements sections, all of Corcoran’s publications benefited from correspondence with other scholars, most notably Timothy Smiley, Michael Scanlan, and Kevin Tracy. All of Corcoran’s Greek translations were done in consultation with two or more classicists. Corcoran never published a sentence without discussing it with his colleagues and students. REQUEST: Please send errors, omissions, and suggestions. I am especially interested in citations made in non-English publications. (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)

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)

This review places this translation and commentary on Book A of Prior Analytics in historical, logical, and philosophical perspective. In particular, it details the author’s positions on current controversies. The author of this translation and commentary is a prolific and respected scholar, a leading figure in a large and still rapidly growing area of scholarship: Prior Analytics studies PAS. PAS treats many aspects of Aristotle’s Prior Analytics: historical context, previous writings that influenced it, preservation and transmission of its manuscripts, editions (...) of its manuscripts, interpretations, commentaries, translations, and its influence on subsequent logic, philosophy, and mathematics. All this attention is warranted because Prior Analytics marks the origin of logic: the field that, among other things, asks of a given proposition whether it follows from a given set of propositions; and, if it follows, how we determine that it follows; and, if it does not follow, how we determine that it does not follow. This translation and commentary is not suitable for use in an undergraduate course. It has too many quirks that the teacher would want to warn against. A copy editor should have dealt with these things and with other matters such as incorrect punctuation and improper end-of-line divisions. The prose is heavily laden with glaring clichés. The one-page preface contains “longer than I care to remember”, “more than I can possibly list here”, “first and foremost”, and “last and by no means least”—a sentence later is devoted to thanking the “incredibly meticulous and helpful copy-editor”. A few pages later the translator reveals the need “to find a path between the Scylla … and the Charybdis …”. Moreover, the index is far from meeting the needs of undergraduate students. The attention to scholarly detail is not what one hoped for from Oxford University Press. At 26b10-15, this translation reads “let swan and white be chosen as white things” for what Smith correctly translates “let swan and snow be selected from among those white things”. At 41b16, “angles AB and CD” should read “angles AC and BD”. Despite this book’s flaws, it will be found useful if not indispensable for those currently engaged in Prior Analytics studies. The alternatives suggested to Robin Smith’s translation choices are often worth consideration. It is to be emphasized, however, that this book is unsuitable for those entering Prior Analytics studies. (shrink)