In the year 1714, Johann Christian Lange published a baroque textbook about a logic machine, supposed to simulate human cognitive abilities such as perception, judgement, and reasoning. From today’s perspective, it can be argued that this blueprint is based on an inference engine applied to a strict ontology which serves as a knowledge base. In this paper, I will first introduce Lange’s approach in the period of baroque logic and then present a diagrammatic modernization of Lange’s principles, entitled Calculus (...) CL. Finally, I would like to discuss the possibilities of how to apply CL to modern cases of concern by using an example from epidemiology. (shrink)

In recent years CL diagrams inspired by Lange’s Cubus Logicus have been used in various contexts of diagrammatic reasoning. However, whether CL diagrams can also be used as a formal system seemed questionable. We present a CL diagram as a formal system, which is a fragment of propositional logic. Syntax and semantics are presented separately and a variant of bitstring semantics is applied to prove soundness and completeness of the system.

The paper outlines the advantages and limits of the so-called ‘Calculus CL’ in the field of ontology engineering and automated theorem proving. CL is a diagram type that combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. Due to the simple taxonomical structures and intuitive rules of CL, it is easy to edit ontologies and to prove inferences.

The aim of this chapter is to develop a semantics for Calculus CL. CL is a diagrammatic calculus based on a logic machine presented by Johann Christian Lange in 1714, which combines features of Euler-, Venn-type, tree diagrams, squares of oppositions etc. In this chapter, it is argued that a Boolean account of formal ontology in CL helps to deal with logical oppositions and inferences of extended syllogistics. The result is a combination of Lange’s diagrams with an algebraic (...) semantics of terms: Bit-CL, in which any ordered objects are identified by characteristic bitstrings. Then, a number of objections to Bit-CL are answered to, and the process of inference is explained in this new logical framework. (shrink)

Extensions of traditional syllogistics have been increasingly researched in philosophy, linguistics, and areas such as artificial intelligence and computer science in recent decades. This is mainly due to the fact that syllogistics is seen as a logic that comes very close to natural language abilities. Various forms of extended syllogistics have become established. This paper deals with the question to what extent a syllogistic representation in CL diagrams can be seen as a form of extended syllogistics. It will be shown (...) that the ontology of CL enables numerically exact assertions and inferences. (shrink)

The paper presents the diagrammatic calculus CL, which combines features of tree, Euler-type, Venn-type diagrams and squares of opposition. In its basic form, `CL' (= Cubus Logicus) organizes terms in the form of a square or cube. By applying the arrows of the square of opposition to CL, judgments and inferences can be displayed. Thus CL offers on the one hand an intuitive method to display ontologies and on the other hand a diagrammatic tool to check inferences. The paper (...) focuses mainly on the adaptation of the square of opposition in CL and offers an algebraic notation, which corresponds to the diagrammatic representation. (shrink)

This paper gives the strong reduction of the combinatory calculus SCL, which was introduced as a combinatory calculus corresponding to the untyped Lambda-mu calculus. It proves the confluence of the strong reduction. By the confluence, it also proves the conservativity of the extensional equality of SCL over the combinatory calculus CL, and the consistency of SCL.

The purpose of the paper is to show that by cleaning Classical Logic (CL) from redundancies (irrelevances) and uninformative complexities in the consequence class and from too strong assumptions (of CL) one can avoid most of the paradoxes coming up when CL is applied to empirical sciences including physics. This kind of cleaning of CL has been done successfully by distinguishing two types of theorems of CL by two criteria. One criterion (RC) forbids such theorems in which parts of the (...) consequent (conclusion) can be replaced by arbitrary parts salva validitate of the theorem. The other (RD) reduces the consequences to simplest conjunctive consequence elements. Since the application of RC and RD to CL leads to a logic without the usual closure conditions, an approximation to RC and RD has been constructed by a basic logic with the help of finite (6-valued) matrices. This basic logic called RMQ (relevance, matrix, Quantum Physics) is consistent and decidable. It distinguishes two types of validity (strict validity) and classical or material validity. All theorems of CL (here: classical propositional calculus CPC) are classically or materially valid in RMQ. But those theorems of CPC which obey RC and RD and avoid the difficulties in the application to empirical sciences and to Quantum Physics are separated as strictly valid in RMQ. In the application to empirical sciences in general the proposed logic avoids the well known paradoxes in the area of explanation, confirmation, versimilitude and Deontic Logic. Concerning the application to physics it avoids also the difficulties with distributivity, commensurability and with Bell's inequalities. (shrink)

Le présent défi pour l’Église, c’est à la fois celui de la mondialisation et d’un pluralisme religieux croissant, qu’il s’agisse des grandes religions ou des nouvelles religiosités. Mais elle doit affronter aussi un indifférentisme religieux qui peut être l’envers d’un combat passionné pour l’homme. Face à ces défis, il faut tenir compte d’un nouveau paradigme théologique, celui d’un pluralisme religieux de principe qui s’interroge sur la signification de la pluralité des religions à l’intérieur du dessein de Dieu. Ce nouveau paradigme (...) nous invite à instaurer un nouveau rapport à la vérité en théologie. Et c’est en allant jusqu’au bout du paradoxe christologique que l’on peut désigner le christianisme comme une religion essentiellement dialogale. Comme l’œcuménisme, le dialogue interreligieux doit être une dimension de toute la théologie. La théologie des religions tend alors à devenir une théologie interreligieuse qui manifeste la fécondation mutuelle des religions dans notre discours sur Dieu et sur le salut de l’homme. (shrink)

Aus den Briefen Rainer Maria Rilkes.- Aus den Briefen Hugo von Hofmannsthals.- Gratulationen und Widmungen.- Deutungen und Würdigungen des Werkes und der Persönlichkeit.- Aus den Gesprächen mit Rudolf Kassner, von A. C. Kensik.- Aus den Briefen Rudolf Kassners.- Verzeichnis der Werke Rudolf Kassners (p. 243-248).

The rise in interdisciplinary scholarship between philosophy and theology has produced a number of critiques of historical biblical criticism (HBC) by philosophers of religion. Some dialogue has resulted, but these critiques have gone largely unnoticed by historical critical scholars. This article argues that two such critiques of HBC, offered by Plantinga and Stump, are undermined by faulty presuppositions on the philosophers' part regarding the nature and value of HBC and misunderstandings of the nature of the ancient texts on which the (...) discipline of HBC focuses. (shrink)

La publication du Journal du Concile de l’ambassadeur P. Poswick est l’occasion de rappeler quelques questions majeures de Vatican II dans le traitement desquelles trois évêques belges se sont particulièrement illustrés. Ce rapide parcours permet de dépasser les oppositions émises récemment à propos du Concile entre « l’événement et le texte » de même qu’entre « la discontinuité et la continuité ». On constate en effet que le témoignage des acteurs est indispensable pour la compréhension des textes et que les (...) avancées du Concile permettent une meilleure compréhension de la tradition. (shrink)

La publication du Journal du Concile de l’ambassadeur P. Poswick est l’occasion de rappeler quelques questions majeures de Vatican II dans le traitement desquelles trois évêques belges se sont particulièrement illustrés. Ce rapide parcours permet de dépasser les oppositions émises récemment à propos du Concile entre « l’événement et le texte » de même qu’entre « la discontinuité et la continuité ». On constate en effet que le témoignage des acteurs est indispensable pour la compréhension des textes et que les (...) avancées du Concile permettent une meilleure compréhension de la tradition. (shrink)