As Classical Propositional Logic finds its algebraic counterpart in Boolean algebras, the logic of Quantum Mechanics, as outlined within G. Birkhoff and J. von Neumann’s approach to Quantum Theory (Birkhoff and von Neumann in Ann Math 37:823–843, 1936) [see also (Husimi in I Proc Phys-Math Soc Japan 19:766–789, 1937)] finds its algebraic alter ego in orthomodular lattices. However, this logic does not incorporate time dimension although it is apparent that the propositions occurring in the logic of Quantum Mechanics are depending (...) on time. The aim of the present paper is to show that tense operators can be introduced in every logic based on a complete lattice, in particular in the logic of quantum mechanics based on a complete orthomodular lattice. If the time set is given together with a preference relation, we introduce tense operators in a purely algebraic way. We derive several important properties of such operators, in particular we show that they form dynamic pairs and, altogether, a dynamic algebra. We investigate connections of these operators with logical connectives conjunction and implication derived from Sasaki projections in an orthomodular lattice. Then we solve the converse problem, namely to find for given time set and given tense operators a time preference relation in order that the resulting time frame induces the given operators. We show that the given operators can be obtained as restrictions of operators induced by a suitable extended time frame. (shrink)

A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were introduced by J. A. Kalman. We extended this concept also for posets with an antitone involution. In our recent paper (Chajda, Länger and Paseka, in: Proceeding of 2022 IEEE 52th International Symposium on Multiple-Valued Logic, Springer, 2022), we showed how to construct such Kleene lattices or Kleene posets from a given distributive lattice or poset and a fixed element of (...) this lattice or poset by using the so-called twist product construction, respectively. We extend this construction of Kleene lattices and Kleene posets by considering a fixed subset instead of a fixed element. Moreover, we show that in some cases, this generating poset can be embedded into the resulting Kleene poset. We investigate the question when a Kleene poset can be represented by a Kleene poset obtained by the mentioned construction. We show that a direct product of representable Kleene posets is again representable and hence a direct product of finite chains is representable. This does not hold in general for subdirect products, but we show some examples where it holds. We present large classes of representable and non-representable Kleene posets. Finally, we investigate two kinds of extensions of a distributive poset $${\textbf{A}}$$ A, namely its Dedekind-MacNeille completion $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) and a completion $$G({\textbf{A}})$$ G ( A ) which coincides with $${{\,\mathrm{\textbf{DM}}\,}}({\textbf{A}})$$ DM ( A ) provided $${\textbf{A}}$$ A is finite. In particular we prove that if $${\textbf{A}}$$ A is a Kleene poset then its extension $$G({\textbf{A}})$$ G ( A ) is also a Kleene lattice. If the subset X of principal order ideals of $${\textbf{A}}$$ A is involution-closed and doubly dense in $$G({\textbf{A}})$$ G ( A ) then it generates $$G({\textbf{A}})$$ G ( A ) and it is isomorphic to $${\textbf{A}}$$ A itself. (shrink)

It is well-known that intuitionistic logics can be formalized by means of Heyting algebras, i.e. relatively pseudocomplemented semilattices. Within such algebras the logical connectives implication and conjunction are formalized as the relative pseudocomplement and the semilattice operation meet, respectively. If the Heyting algebra has a bottom element |$0$|⁠, then the relative pseudocomplement with respect to |$0$| is called the pseudocomplement and it is considered as the connective negation in this logic. Our idea is to consider an arbitrary meet-semilattice with |$0$| (...) satisfying only the Ascending Chain Condition (these assumptions are trivially satisfied in finite meet-semilattices) and introduce the operators formalizing the connectives negation |$x^{0}$| and implication |$x\rightarrow y$| as the set of all maximal elements |$z$| satisfying |$x\wedge z=0$| and as the set of all maximal elements |$z$| satisfying |$x\wedge z\leq y$|⁠, respectively. Such a negation and implication is ‘unsharp’ since it assigns to one entry |$x$| or to two entries |$x$| and |$y$| belonging to the semilattice, respectively, a subset instead of an element of the semilattice. Surprisingly, this kind of negation and implication still shares a number of properties of these connectives in intuitionistic logic, in particular the derivation rule Modus Ponens. Moreover, unsharp negation and unsharp implication can be characterized by means of five, respectively seven simple axioms. We present several examples. The concepts of a deductive system and of a filter are introduced as well as the congruence determined by such a filter. We finally describe certain relationships between these concepts. (shrink)

English summary: The authors of this conference volume describe and discuss various aspects of Popper's ethics, such as for example his contributions to freedom and responsibility, to objectivity and truth, to humanism and to metaphysics, from a critical-rational point of view. This is the first time that Popper's ethics have been brought face to face with the Christian faith. The lectures and the ensuing discussions between Protestant and Catholic theologians and advocates of critical rationalism deal with the question of whether (...) Popper's critiques of religion can be compatible with modern social ethics based on Christianity or whether theology can be a critical-rational science. One of the special attractions of this volume is the fact that it contains not only the revised talks but also the very animated discussions on the various subjects. German description: Karl Popper war nicht nur ein Mensch und Wissenschaftler mit klaren ethischen Grundsatzen, auch seiner Wissenschafts- und Erkenntnistheorie lagen ethische Pramissen zugrunde. Dieser Sachverhalt ist lange nicht erkannt worden, weil Popper selbst nicht daruber gesprochen hat und weil er diese ethischen Voraussetzungen in seinen Werken nicht systematisch dargelegt hat. Wenn es aber zutrifft, dass dem wissenschaftlichen Lebenswerk Poppers ein ethisches Forschungsprogramm zugrunde lag, dann wird es Zeit, sich damit zu befassen.Die Autoren dieses Bandes stellen verschiedene Aspekte von Poppers Ethik, wie z.B. seine Beitrage zur Freiheit und Verantwortung, zur Objektivitat und Wahrheit, zum Humanismus und zur Metaphysik, von einem kritisch-rationalen Standpunkt aus zur Diskussion. Erstmalig wird die Ethik Poppers mit dem christlichen Glauben konfrontiert. In den Beitragen sowie den anschliessenden Diskussionen zwischen evangelischen und katholischen Theologen mit Vertretern des kritischen Rationalismus geht es darum, ob Poppers religionskritische Darlegungen mit einer modernen Sozialethik auf christlicher Basis vereinbar sind, bzw. ob es eine Theologie als kritisch-rationale Wissenschaft geben kann.Ein besonderer Reiz dieses Bandes liegt darin, dass nicht nur die uberarbeiteten Referate, sondern auch die sehr lebhaften Diskussionen zu den verschiedenen Themen enthalten sind. Hier wird noch deutlicher, dass Poppers Philosophie von starken ethischen Voraussetzungen durchdrungen ist. (shrink)

"Ist der Patient ein Mensch?" is a collection of articles. Its central topic is the question if the object of modern medicine is still the human being or if just organs and tissues are treated by medical doctors? The drawing on the book cover shows a lung instead of a human patient lying in a hospital bed. The approaches to this topic are diverse and surprising. E.g. the surgeon Ankersmit argues that it is impossible for him to see the human (...) being in the body lying on the operation table because then he would be unable to perform his work professionally. Other texts stretch the topic of the book to the questions whether medical doctors are human beings or if the human being of today is a "patient" in the sense of a current crisis of anthropology. Also questions like patient autonomy and communication with patients are tackled. The book is edited by Helmut Hofbauer, Lukas Kaelin, Hendrik Jan Ankersmit & Walter Feigl. Authors are: Lukas Kaelin, Gabriele Baumann, Hendrik Jan Ankersmit, Renate Heinz, Claus G. Krenn, Alexander Lapin, Sigrid Pilz, Margot Ham-Rubisch, Petra Herzeg, Klaus Spiess, Lucie Strecker, Paul Ferstl, Helmut Hofbauer & Peter Kampits. (shrink)

Von den Sachen und vom Widerspruch. Der eigene Gegenstand der Geisteswissenschaften -- Steinzeit. Das Erwachen der Vernunft. Judaismus -- Ockhams Willkürgott in der Schleuse des Widerspruchsprinzips. Miniaturen -- Ockham in der Geschichte. Wissenschaftstheorie und Bewusstsein -- Mythos und Evidenz. Ockhams Rekalzitranz -- Kausalität und Affektbezug. Die Annäherung an Gott -- Die Subtilität in den Materien der Philosophie. Gott, wir und die Welt -- Die Brücke vom Diesseits zum Jenseits, oder, Der Abstand der Neuzeit zum Mittelalter -- Der Sinn bei Begriffen (...) und Schlüssen. Der Scharfsinnige und der mehr als Scharfsinnige -- Satz und Satzgefüge. Der Beweis ohne Gegenständlichkeit -- Am Torweg. Der nicht unabänderliche Wille Gottes. (shrink)

Das Verhältnis der Begriffe bei Ockham -- Suppositionslogische Identität und Kontingenz -- Zum Verhältnis der Satzformen -- Fides et scientia -- Aus dem innern Gottes -- Theologie und Logikbegriff -- Formbegriff und reale Wahrheit -- Glaube und Welt. Im Vorhof der Naturphilosophie -- Ontologie und Induktion -- Beweis, Satz, Akt -- Abstraktion und scholastischer Beweiszweck -- Verflechtung und Abgrenzung der Akte -- Naturgrund und Realerkenntnis -- Widerspruch und Accidens.

Als in der spätscholastischen Epoche der philosophische Ausdruck sich von der streng theologischen und religiösen Exegese entfernt und einer genuin humanen Selbstvertretung annähert, ist Ockham am ehesten und im Grunde allein erfolgreich in der Formulierung eines rationalen Formativs, worin der Mensch zur Gegenstellung gegen die göttliche Person, ihre Intellektion und Willenshaltung und die offenbarte Wahrheit gelangt. Er erweist sich als brillant und virtuos in der Handhabung von Induktion, persuasio und Reprobation, d.h. im Prinzip: der Widerlegung fremder Meinungen. Er ist weniger (...) erfolgreich bei der direkten Fixierung der Fehlgriffe anderer Scholastiker, wenn sie methodisch nicht ausgewiesenen Lösungen zuneigen, worin jede Problematik unterlaufen wird. Ockham hat da, ausser bei Duns Scotus, auch keine aristotelische Expertise mehr zur Verfügung. Das verweist darauf, dass neuzeitliche wissenschaftliche Antworten gefordert waren, die mit der scholastischen Einstellung nichts mehr gemein hatten. Das war in der mittelalterlichen Epoche aber nicht verhandelbar. Ebenso konnten Ockhams Abgrenzungsversuche nicht verstanden werden. Schon die Bestrebungen, Scholastiker umstandslos vor kirchliche Strafgerichte zu ziehen, offenbaren die Erschöpfung des Zeitalters"-- Back cover. (shrink)

On February 24-25, 1956, in a closed session of the 20th Congress of the Communist Party of the Soviet Union, Nikita S. Khrushchev made his now famous speech on the crimes of the Stalin era. That speech marked a break with the past and it marked the end of what J.M. Bochenski dubbed the "dead period" of Soviet philosophy. Soviet philosophy changed abruptly after 1956, especially in the area of dialectical materialism. Yet most philosophers in the West neither noticed nor (...) cared. For them, the resurrection of Soviet philosophy, even if believable, was of little interest. The reasons for the lack of belief and interest were multiple. Soviet philosophy had been dull for so long that subtle differences made little difference. The Cold War was in a frigid period and reinforced the attitude of avoiding anything Soviet. Phenomenology and exis tentialism were booming in Europe and analytic philosophy was king on the Anglo-American philosophical scene. Moreover, not many philosophers in the West knew or could read Russian or were motivated to learn it to be able to read Soviet philosophical works. The launching of Sputnik awakened the West from its self complacent slumbers. Academic interest in the Soviet Union grew. (shrink)

The question is whether the message of early Christianity was revolutionary and aimed at a revolutionary change in history? Had this change already begun in the life of primitive Christianity in a way that is exemplary to all later life based on the message?

1. Bd. Dogmatische, philosophische und kontroverstheologische Grundlegung.--2. Bd. Entfaltung. 2. T. Ethik des Politischen.