Die hier vorliegende rezeptionsgeschichtliche Studie leistet eine systematische Aufarbeitung der in der 'Historik' Johann Gustav Droysens (1808-1884) zu findenden Aristoteles-Bezüge und reiht sich somit in die Gruppe der Arbeiten zu den geistesgeschichtlichen Grundlagen der Geschichtstheorie Droysens ein. Durch die Verortung Droysens im Kontext der Aristoteles-Renaissance im 19. Jahrhundert trägt sie zugleich zu deren weiteren Erforschung bei.

In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally complete. Further, finding axiomatizations (...) of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic. (shrink)

In this paper we define and study a generalized notion of a logical system that covers on an equal formal basis sentential, equational and sequential systems. We develop a general theory of equivalence between generalized logics that provides, first, a conception of algebraizable logic , second, a formal concept of equivalence between sequential systems and, third, a notion of equivalence between sentential and sequential systems. We also use our theory of equivalence for developing a general algebraic approach to conjunctive non-pseudo-axiomatic (...) self-extensional sentential logics. Finally, we consider within the framework of the mentioned approach various sequential formulations for some well-known sentential logics. (shrink)

The aim of this paper is technically to study Belnap's four-valued sentential logic . First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ⌝}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It (...) is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox. (shrink)

The present paper concerns a technical study of PRIEST'S logic of paradox [Pri 79], We prove that this logic has no proper paraconsistent strengthening. It is also proved that the mentioned logic is the largest paraconsistent one satisfaying TARSKI'S conditions for the classical conjunction and disjunction together with DE MORGAN'S laws for negation. Finally, we obtain for the logic of paradox an algebraic completeness result related to Kleene lattices.

The aim of this paper is to study the paraconsistent deductive systemP 1 within the context of Algebraic Logic. It is well known due to Lewin, Mikenberg and Schwarse thatP 1 is algebraizable in the sense of Blok and Pigozzi, the quasivariety generated by Sette's three-element algebraS being the unique quasivariety semantics forP 1. In the present paper we prove that the mentioned quasivariety is not a variety by showing that the variety generated byS is not equivalent to any algebraizable (...) deductive system. We also show thatP 1 has no algebraic semantics in the sense of Czelakowski. Among other results, we study the variety generated by the algebraS. This enables us to prove in a purely algebraic way that the only proper non-trivial axiomatic extension ofP 1 is the classical deductive systemPC. Throughout the paper we also study those abstract logics which are in a way similar toP 1, and are called hereabstract Sette logics. We obtain for them results similar to those obtained for distributive abstract logics by Font, Verdú and the author. (shrink)

The purpose of this article is to describe how expansive learning in organisations can become a resource for learning in a wider community of practice (CoP). The “developmental work research” approach (DWR) based on cultural historical activity theory (CHAT) is beneficial for analysing and interpreting the requirements in a field of action. Engeström’s specific form of “action research” focuses on expansive learning in activity systems. However, complex socio-technical change processes cannot be initiated and managed by the local community of practise (...) alone. In order to establish the use of new tools, new methodologies or organisational solutions in a field of work, a double path of expansive learning is needed: Findings from the participative analysis and interpretation of contradictions in the local activity system have to be transferred to wider communities of practice. This paper illustrates a double path of expansive learning by presenting the experiences of research and development in machine and plant engineering companies in Germany. In the AQUIMO project, a project team has developed an adaptable software tool for multidisciplinary mechatronical engineering and created a related qualification program. The support from external social researchers has helped to initiate, disseminate and establish new ways to organise the division of labour in teams of engineers. (shrink)

In this paper we deal with infinitary universal Horn logic both with and without equality. First, we obtain a relative Lyndon-style interpolation theorem. Using this result, we prove a non-standard preservation theorem which contains, as a particular case, a Lyndon-style theorem on surjective homomorphisms in its Makkai-style formulation. Another consequence of the preservation theorem is a theorem on bimorphisms, which, in particular, provides a tool for immediate obtaining characterizations of infinitary universal Horn classes without equality from those with equality. From (...) the theorem on surjective homomorphisms we also derive a non-standard Beth-style preservation theorem that yields a non-standard Beth-style definability theorem, according to which implicit definability of a relation symbol in an infinitary universal Horn theory implies its explicit definability by a conjunction of atomic formulas. We also apply our theorem on surjective homomorphisms, theorem on bimorphisms and definability theorem to algebraic logic for general propositional logic. (shrink)

Sartre und Jaspers, in welcher Beziehung stehen sie zueinander, was eint sie, was trennt sie? Jaspers- und Sartre-Forscher zeigen auf, wo das Verbindende, aber auch das Trennende liegt in der Sicht dieser beiden Denker auf zentrale Begriffe wie Existenz, Situation, Freiheit und Verantwortung.

The goal of the paper is to develop a universal semantic approach to derivable rules of propositional multiple-conclusion sequent calculi with structural rules, which explicitly involve not only atomic formulas, treated as metavariables for formulas, but also formula set variables, upon the basis of the conception of model introduced in :27–37, 2001). One of the main results of the paper is that any regular sequent calculus with structural rules has such class of sequent models that a rule is derivable in (...) the calculus iff it is sound with respect to each model of the semantics. We then show how semantics of admissible rules of such calculi can be found with using a method of free models. Next, our universal approach is applied to sequent calculi for many-valued logics with equality determinant. Finally, we exemplify this application by studying sequent calculi for some of such logics. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove that extensions (...) of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)

ABSTRACT A bilattice is said to be regular provided its truth conjunction and disjunction are monotonic with respect to its knowledge ordering. The principal result of this paper is that the following properties of a bilattice B are equivalent: 1. B is regular; 2. the truth conjunction and disjunction of B are definable through the rest of the operations and constants of B; 3. B is isomorphic to a bilattice of the form L 1 · L 2 where L 1 (...) and L 2 are bounded lattices. We also derive from this metaequivalence a number of corollaries concerning distributive bilattices, degenerated bilattices and bilattices with negation. (shrink)

Basic results of the paper are that any four-valued expansion L4 of Dunn-Belnap's logic DB4 is de_ned by a unique conjunctive matrix ℳ4 with exactly two distinguished values over an expansion.

In this paper, we study multiplicative extensions of propositional many-place sequent calculi for finitely-valued logics arising from those introduced in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) through their translation by means of singularity determinants for logics and restriction of the original many-place sequent language. Our generalized approach, first of all, covers, on a uniform formal basis, both the one developed in Sect. 5 of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) for singular finitely-valued logics (...) (when singularity determinants consist of a variable alone) and conventional Gentzen-style (i.e., two-place sequent) calculi suggested in Pynko (Bull Sect Logic 33(1):23–32, 2004) for finitely-valued logics with equality determinant. In addition, it provides a universal method of constructing Tait-style (i.e., one-place sequent) calculi for finitely-valued logics with singularity determinant (in particular, for Łukasiewicz finitely-valued logics) that fits the well-known Tait calculus (Lecture Notes in Mathematics, Springer, Berlin, 1968) for the classical logic. We properly extend main results of Pynko (J Multiple-Valued Logic Soft Comput 10:339–362, 2004) and explore calculi under consideration within the framework of Sect. 7 of Pynko (Arch Math Logic 45:267–305, 2006), generalizing the results obtained in Sect. 7.5 of Pynko (Arch Math Logic 45:267–305 2006) for two-place sequent calculi associated with finitely-valued logics with equality determinant according to Pynko (Bull Sect Logic 33(1):23–32, 2004). We also exemplify our universal elaboration by applying it to some denumerable families of well-known finitely-valued logics. (shrink)

The primary objective of this paper, which is an addendum to the author’s [8], is to apply the general study of the latter to Łukasiewicz’s n-valued logics [4]. The paper provides an analytical expression of a 2(n−1)-place sequent calculus (in the sense of [10, 9]) with the cut-elimination property and a strong completeness with respect to the logic involved which is most compact among similar calculi in the sense of a complexity of systems of premises of introduction rules. This together (...) with a quite effective procedure of construction of an equality determinant (in the sense of [5]) for the logics involved to be extracted from the constructive proof of Proposition 6.10 of [6] yields an equally effective procedure of construction of both Gentzen-style [2] (i.e., 2-place) and Tait-style [11] (i.e., 1-place) minimal sequent calculi following the method of translations described in Subsection 4.2 of [7]. (shrink)

Die Frage, ob sich auf existenzphilosophischer Grundlage eine Ethik entwickeln lässt, ist seit jeher umstritten. Die Autoren dieses Bandes widmen sich dem Widerspruch, dass der Existenzphilosophie entweder eine starke Ethikverbundenheit oder eine große Ethikferne zugeschrieben wird. Befragt wurden hierzu die Ansätze Sören Kierkegaards, Heideggers, Karl Jaspers', Jean-Paul Sartres und anderer Autoren der Existenzphilosophie.

Lee and Schwarz suggest that separation is the grounded procedure underlying cleansing effects in different psychological domains. Here, we interpret L&S's account from a hierarchical view of cognition that considers the influence of physical properties and sensorimotor constraints on mental representations. This approach allows theoretical integration and generalization of L&S's account to the domain of formal quantitative reasoning.

Immunity has established itself as one of the most exciting and productive conceptual lenses being used in contemporary social theory. Ulbricht’s first book demonstrates why this is the case, through using the imaginary of immunity to explicate a selection of the features of liberal multicultural theory. Influenced by the work of Italian philosopher Robert Esposito, the book traces ideas of tolerance, consensus and rights as they appear across a selection of liberal theoretical interventions. After engaging with an impressive swathe of (...) literature throughout his book, Ulbricht’s critical arrival point is an exciting use of Lefebvrian rhythmanalysis in a bid to supplant universal theories of multiculturalism with a recognition of multiculturalism as an intensely local and ad hoc human experience. (shrink)

Alexej Remizov is usually regarded by literary critics as a Symbolist rather than a Futurist writer. However, I would posit that Remizov similarly to the Futurists viewed language as “logos,” bozhestvennii glagol. According to the mystical interpretation of the famous words “At the beginning there was Word and the Word was with God and the Word was God”, when God was creating the world he named the objects, and these abstract names became a force for the appearance of an (...) object in physical reality. In the light of these words, The Medieval mystical and magical philosophers claimed that one could restore the divine language of Creation, possess the ability to create objects anew, and thereby become Creator himself. One can argue that a major goal of Remizov was similar to that of hisMedieval predecessors: to reveal the mystical power of language in order to create, not to describe reality. The paper analyzes three chapters from Alexej Remizov’s Rossiya v pis’menah, a book which can be read as a manifesto of Remizov’s attitude toward language and reality, and discuss possible sourcesthat might have influenced Remizov in his attitude towards language. (shrink)

Alexej Remizov is usually regarded by literary critics as a Symbolist rather than a Futurist writer. However, I would posit that Remizov similarly to the Futurists viewed language as “logos,” bozhestvennii glagol. According to the mystical interpretation of the famous words “At the beginning there was Word and the Word was with God and the Word was God”, when God was creating the world he named the objects, and these abstract names became a force for the appearance of an (...) object in physical reality. In the light of these words, The Medieval mystical and magical philosophers claimed that one could restore the divine language of Creation, possess the ability to create objects anew, and thereby become Creator himself. One can argue that a major goal of Remizov was similar to that of hisMedieval predecessors: to reveal the mystical power of language in order to create, not to describe reality. The paper analyzes three chapters from Alexej Remizov’s Rossiya v pis’menah, a book which can be read as a manifesto of Remizov’s attitude toward language and reality, and discuss possible sourcesthat might have influenced Remizov in his attitude towards language. (shrink)

Alexej Remizov is usually regarded by literary critics as a Symbolist rather than a Futurist writer. However, I would posit that Remizov similarly to the Futurists viewed language as “logos,” bozhestvennii glagol. According to the mystical interpretation of the famous words “At the beginning there was Word and the Word was with God and the Word was God”, when God was creating the world he named the objects, and these abstract names became a force for the appearance of an (...) object in physical reality. In the light of these words, The Medieval mystical and magical philosophers claimed that one could restore the divine language of Creation, possess the ability to create objects anew, and thereby become Creator himself. One can argue that a major goal of Remizov was similar to that of hisMedieval predecessors: to reveal the mystical power of language in order to create, not to describe reality. The paper analyzes three chapters from Alexej Remizov’s Rossiya v pis’menah, a book which can be read as a manifesto of Remizov’s attitude toward language and reality, and discuss possible sourcesthat might have influenced Remizov in his attitude towards language. (shrink)

Alexej Remizov is usually regarded by literary critics as a Symbolist rather than a Futurist writer. However, I would posit that Remizov similarly to the Futurists viewed language as “logos,” bozhestvennii glagol. According to the mystical interpretation of the famous words “At the beginning there was Word and the Word was with God and the Word was God”, when God was creating the world he named the objects, and these abstract names became a force for the appearance of an (...) object in physical reality. In the light of these words, The Medieval mystical and magical philosophers claimed that one could restore the divine language of Creation, possess the ability to create objects anew, and thereby become Creator himself. One can argue that a major goal of Remizov was similar to that of hisMedieval predecessors: to reveal the mystical power of language in order to create, not to describe reality. The paper analyzes three chapters from Alexej Remizov’s Rossiya v pis’menah, a book which can be read as a manifesto of Remizov’s attitude toward language and reality, and discuss possible sourcesthat might have influenced Remizov in his attitude towards language. (shrink)

Paraconsistent weak Kleene logic is the $3$-valued logic based on the weak Kleene matrices and with two designated values. In this paper, we investigate the poset of prevarieties of generalized involutive bisemilattices, focussing in particular on the order ideal generated by Α$\textrm{lg} $. Applying to this poset a general result by Alexej Pynko, we prove that, exactly like Priest’s logic of paradox, $\textrm{PWK}$ has only one proper nontrivial extension apart from classical logic: $\textrm{PWK}_{\textrm{E}}\textrm{,}$ PWK logic plus explosion. This $6$-valued (...) logic, unlike $\textrm{PWK} $, fails to be paraconsistent. We describe its consequence relation via a variable inclusion criterion and identify its Suszko-reduced models. (shrink)

With Carl Gegenbaur and Ernst Haeckel, inspiredby Darwin and the cell theory, comparativeanatomy and embryology became established andflourished in Jena. This tradition wascontinued and developed further with new ideasand methods devised by some of Haeckelsstudents. This first period of innovative workin evolutionary morphology was followed byperiods of crisis and even a disintegration ofthe discipline in the early twentieth century.This stagnation was caused by a lack ofinterest among morphologists in Mendeliangenetics, and uncertainty about the mechanismsof evolution. Idealistic morphology was stillinfluental in (...) Germany, which prevented a fullappreciation of the importance of Darwinstheory of natural selection for comparativemorphology. Evolutionary morphology andembryology failed to contribute significantlyto the modern synthesis of evolutionarybiology, thereby probably delaying theintegration of developmental biology intomodern evolutionary biology. However, Haeckelsstudent Oscar Hertwig, as well as Victor Franzand Alexej N. Sewertzoff from a youngergeneration, all tried to forge their ownsynthetic approaches in which (inspired byHaeckels work) embryology played an importantrole. Important for all three researchers wereattempts to refine, and sometimes redefine, thebiogenetic law, and to find new scientificexplanations for it (and for the manyexceptions to it). Their research was latermore or less forgotten, and had littleinfluence on the architects of the modernsynthesis. As the relationship betweenevolutionary and developmental biology is nowagain rising in importance in the form ofEvo-Devo, we would like to draw attention tohow this earlier research tradition grappledwith similar questions to those now on theagenda, albeit from sometimes quite differentperspectives. (shrink)