ZusammenfassunuIn dem vorliegenden Bericht über einige Arbeiten des Verfassers und eine daran anschliessende Arbeit von G. Emde, Marburg, wird eine Reihe von Ergebnissen behandelt, die die Kombinationen der Grundmodalitäten « Möglichkeit » und « Notwendigkeit » betreffen. Ausgehend von sehr allgemeinen Rahmenkodifikaten wird die durch Basisreduktion zu gewinnende Liste der endlich vielen implikativen Modalitätenlogiken mit idempotenter Möglichkeit erörtert; bei wichtigen Unterklassen der nicht notwendig idempotenten implikativen Modalitätenlogiken treten neben der Basisreduktion vor allem spezielle Entscheidungsprobleme in den Vordergrund.RésuméDans le rapport ci‐dessus (...) concernant quelques travaux de l'auteur et le travail de M. G. Emde qui s'y rapporte, il s'agit d'un ensemble de résultats sur la combinaison des modalités fondamentales de « possibilité» et de « nécessité». Partant de quelques codifications cadres très générales, I'auteur discute la liste en nombre fini des logiques modales implicatives à« possibilité» idempotente, une liste qui est obtenue par une réduction des bases. Quant à certaines sous‐classes importantes des logiques implicatives qui ne sont pas nécessairement idempotentes, outre la réduction des bases, les problèmes de décision qui leur sont spéciaux, se trouvent placés au premier plan.In the present report on some papers of the author and on a sequel to them by G. Emde, Marburg, a series of results concerning the combination of the basic modalities « possibility » and « necessity » are treated. Starting from some very general framing‐codifications, the list of the finitely many implicative modal logics with idempotent « possibility » which is obtainable through basis reduction is discussed. Besides basis reduction, in the case of some important subclasses of the not‐necessarily‐idempotent implicative modal logics, attention is given to the special decision problems. (shrink)

The busy beaver problem of Rado [6] is reexamined for the case of Turing machines given by quadruples rather than quintuples. Moreover several printing symbols are allowed. Some values of the corresponding beaver function are given and it is shown that this function for a fixed number of states and varying number of symbols is nonrecursive for three or more states and recursive for two states. As a byproduct we get that the minimal number of states in a universal Turing (...) machine (quadruples) is three. (shrink)

Context: Although the theory of autopoietic systems was originally formulated to explain the phenomenon of life from an operational and temporal perspective, sociologist Niklas Luhmann incorporated it later within his theory of social systems. Due to this adoption, there have been several discussions regarding the applicability of this concept beyond its biological origins. Problem: This article addresses the conception of Luhman’s autopoietic social systems, and confronts this vision with criticism both of the original authors of the concept of autopoiesis and (...) of other social theorists in order to elucidate the main problems of this debate and its possible solutions. Method: The objectives of the article are reached by means of a theoretical reconstruction of the main issues of the debate on the concept of autopoiesis. The main method used for the research is the use of documentary sources to discuss the arguments. Results: We claim that it is justified to extend the concept of autopoiesis from its biological origin to other disciplines, and to develop its interdisciplinary character, following the spirit of systems theory and constructivism. Implications: Our results are useful for promoting the development of new interdisciplinary research in the field of systems theory and constructivism. Important changes to practice should be made, namely, the development of new research methods, new concepts and perspectives. Constructivist content: The concept of autopoiesis is one of the fundamental concepts of the constructivist epistemology. The discussion proposes a radical understanding of this concept in order to realize all its explanatory potential. (shrink)

Upshot: Firstly, we discuss the main criticisms of our arguments. Secondly, we address the comments and observations on some parts of our article. We conclude with some reflections about the perspectives of the discussion on the autopoiesis concept.