The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)

It is often assumed that Aristotle, Boethius, Chrysippus, and other ancient logicians advocated a connexive conception of implication according to which no proposition entails, or is entailed by, its own negation. Thus Aristotle claimed that the proposition ‘if B is not great, B itself is great […] is impossible’. Similarly, Boethius maintained that two implications of the type ‘If p then r’ and ‘If p then not-r’ are incompatible. Furthermore, Chrysippus proclaimed a conditional to be ‘sound when the contradictory of (...) its consequent is incompatible with its antecedent’, a view which, in the opinion of S. McCall, entails the aforementioned theses of Aristotle and Boethius. Now a critical examination of the historical sources shows that the ancient logicians most likely meant their theses as applicable only to ‘normal’ conditionals with antecedents which are not self-contradictory. The corresponding restrictions of Aristotle’s and Boethius’ theses to such self-consistent antecedents, however, turn out to be theorems of ordinary modal logic and thus don’t give rise to any non-classical system of genuinely connexive logic,. (shrink)

The book has a twofold content and aim: on the one hand, it offers a radical critique of the modern world, and on the other, it seeks to expound timeless wisdom. And the second end presupposes the first: for so long as we have not "broken through the barrier of scientistic belief" as the subtitle has it, that timeless wisdom-that veritable sophia perennis-remains inaccessible.

One of the main controversies of the Logic Schools of the 12th century centered on the question: What follows from the impossible? In this paper arguments for two diametrically opposed positions are examined. The author of the ‘Avranches Text’ who probably belonged to the school of the Parvipontani defended the view that from an impossible proposition everything follows (‘Ex impossibili quodlibet’). In particular he developed a proof to show that by means of so-called ‘disjunctive syllogism’ any arbitrary proposition B can (...) be logically derived from a pair of contradictory propositions A and Not-A. The author of the Ars Meliduna instead argued that nothing follows from an impossible proposition (‘ex falso nihil sequitur’). This view is supported by various counterexamples which aimed to show that the admission of impossible premises would give rise to inconsistent conclusions. Upon closer analysis these inconsistencies do not, however, have the formal structure of a real contradiction like A and Not-A, but rather the structure of two rivalling conditionals like ‘If B then A’ and ‘If B then Not-A’. Hence these counterexamples rather have to be considered as refutations of the basic principles of ‘connexive logic’. (shrink)

Gibt es Elemente, Bestandteile, Strukturen, die in allen Wissenschaftsbereichen, Disziplinen und Theorien fast gleich sind? Dieses Buch stellt ein neues und originelles Modell für Theorien, Theoriennetze und dynamische Entwicklungen vor, das für empirische Untersuchungen in den Sozialwissenschaften, für Computersimulationen, aber auch für praktisch-politische Anwendungen geeignet ist. Die Grundelemente in diesem Modell sind Ereignisse, Fakten, Modelle, Netze und Wahrscheinlichkeit.

All statements describing physical reality are derived through interpretation of measurement results that requires a theory of the measuring instruments used to make the measurements. The ultimate measuring instrument is our body which displays its measurement results in our mind. Since a physical theory of our mind-body is unknown, the correct interpretation of its measurement results is unknown. The success of the physical sciences has led to a tendency to treat assumption in physics as indisputable facts. This tendency hampers the (...) development of new theories capable of addressing the foundations of mind. To show the possibility that false interpretations of experimental results have lead to equally false projections onto physical reality may have happened, the double slit experiment and special relativity experiments are examined in detail. I will show that strongly held a-priory beliefs characterizing measurement instruments have lead to unjustified but widely held concepts in physical theories. For example the assumption that material bodies have minds can change the interpretation of experiments to produce alternative physical theories. Since some material bodies have minds this paper calls for a review of the conscious observer’s role in the execution and interpretation of fundamental physics experiments in order to verify or challenge the basic beliefs adopted in standard physical theories. (shrink)

Abelard: Logic This article describes and reconstructs Peter Abelard’s logic of the twelfth century. Much of what he regarded as logic is now classified as ontology or philosophical semantics. The article concentrates on his treatment of the relation of consequence. Abelard’s most important logical innovations consist of two points: The distinction between two kinds of … Continue reading Abelard: Logic →.

Primitive awareness leading to consciousness can be explained as a manifestation of internal forces between charge and mass. These internal forces, related to the weak and strong forces, balance the external forces of gravity-inertia and electricity-magnetism and thereby accommodate outside influences by adjusting the internal structure of material from which we are composed. Such accommodation is the physical implementation of a model of the external physical world and qualifies as Vitiello's double held inside ourselves. We experience this accommodation as the (...) conscious experience in front of our noses. Neural pulse traffic is interpreted as unconscious signal processing activity happening between this internal accommodation and our external interface of sensors and actuators. Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;} Normal 0 false false false EN-US X-NONE X-NONE /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-qformat:yes; mso-style-parent:""; mso-padding-alt:0in 5.4pt 0in 5.4pt; mso-para-margin:0in; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:11.0pt; font-family:"Calibri","sans-serif"; mso-ascii-font-family:Calibri; mso-ascii-theme-font:minor-latin; mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast; mso-hansi-font-family:Calibri; mso-hansi-theme-font:minor-latin; mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:minor-bidi;}. (shrink)

It is well known that in his logical writings Leibniz typically disregarded the operation of disjunction, confining himself to the theory of conjunction ajid negation. Now, while this fact has been interpreted by Couturat and others as indicating a serious incompleteness of the Leibnizian calculus, it is shown in this paper that actually Leibniz's conjunction-negation logic, with 'est Ens', i. e. 'is possible' as an additional logical operator, is provably equivalent to Boolean algebra. Moreover, already in the Generales Inquisitiones of (...) 1686 Leibniz had established all basic principles that are necessary for a complete axiomatization of "Boolean" algebra. In this sense Leibniz should be acknowledged as the true inventor of the algebra of sets. (shrink)

Indikatoren sind Anzeiger, die zur Steuerung verwendet werden. Als Anzeiger dienen sie dazu, Auskunft über Gegenstände oder Sachverhalte zu geben, die nicht, schwer oder nur unter großem Aufwand messbar sind. In der Regel werden quantitative Maßzahlen erstellt, die entsprechend dem eigentlich interessierenden Objekt interpretiert werden (Kenngrößen).

Indikatoren sind in erster Linie Messinstrumente und somit gelten hier auch dieselben Qualitätsanforderungen. Die Besonderheit besteht allerdings in der Anzeigefunktion, d. h. im Unterschied zu anderen Messinstrumenten bilden Indikatoren nicht nur direkt ein Messobjekt ab, sondern sollen indirekt auch noch Aufschluss über andere, nicht direkt gemessene Konstrukte geben.

Indikatoren sind wesentliche Teile des Monitorings und dienen in diesem Zusammenhang der politischen Steuerung auf verschiedenen Ebenen – vom lokalen Kleinprojekt bis zur globalen Governance. Sie sind ein Instrument zur Produktion von Daten als Grundlage für rationale Entscheidungen und ermöglichen so eine „evidence-based policy“. Die grundlegende Idee eines solchen Konzepts rationaler Politik besteht darin, dass politische Entscheidungsträger Indikatoren als Erhebungsinstrumente im Rahmen eines Monitoring- und Evaluationssystems einsetzen und so auf diese Weise ihre Instrumente in Richtung besserer positiver Wirksamkeit und Verringerung (...) schädlicher Nebenwirkungen lenken können. (shrink)

Reconstruimos la teoría central de las redes bayesianas n-dimensionales de forma clara y completa en el marco estructuralista. Nuestra formulación también incluye los n espacios de probabilidad unidimensionales y un espacio de probabilidad n-dimensional. Explicamos los sistemas previstos y la afirmación empírica de la teoría de las redes bayesianas n-dimensionales. En nuestra formulación, se destaca el concepto de dimensión, y discutimos si los eventos o las oraciones (enunciados, proposiciones) podrían usarse como bloques de construcción básicos.

In “Lectio 55” of his Notule libri Priorum, Robert Kilwardby discussed various objections that had been raised against Aristotle’s Theses. The first thesis, AT1, says that no proposition q is implied both by a proposition p and by its negation, ∼p. AT2 says that no proposition p is implied by its own negation. In Prior Analytics, Aristotle had shown that AT2 entails AT1, and he argued that the assumption of a proposition p such that (∼p → p) would be “absurd”. (...) The unrestricted validity of AT1, AT2, however, is at odds with other principles which were widely accepted by medieval logicians, namely the law Ex Impossibili Quodlibet, EIQ, and the rules of disjunction introduction. Since, according to EIQ, the impossible proposition (p ∧ ∼p) implies every proposition, it also implies ∼(p∧∼p), in contradiction to AT2. Furthermore, by way of disjunction introduction, the proposition (p∨∼p) is implied both by p and by ∼p, in contradiction to AT1. Kilwardby tried to defend AT1, AT2 against these objections by claiming that EIQ holds only for accidental but not for natural implications. The second argument, however, cannot be refuted in this way because Kilwardby had to admit that every disjunction (p ∨ q) is naturally implied by its disjuncts. He therefore introduced the further requirement that, in order to constitute a genuine counterexample to AT1, (p → q) and (∼p → q) have to hold “by virtue of the same thing”. In a recently published paper, Spencer Johnston accepted this futile defence of AT1 and developed a formal semantics that would fit Kilwardby’s presumably connexive implication. This procedure, however, is misguided because the remaining considerations of Lesson 55  which were entirely ignored by Johnston  show that Kilwardby eventually recognized that AT2 is bound to fail. After all he concluded: “So it should be granted that from the impossible its opposite follows, and that the necessary follows from its opposite”. (shrink)

Leibniz's development of a "calculus universalis" stands and falls with his theory of negation. During the entire period of the elaboration of the algebra of concepts, L1, Leibniz had to struggle hard to grasp the difference between propositional and conceptual negation. Within the framework of syllogistic, this difference seems to disappear because 'Omne A non B' may be taken to be equivalent to ‘Omne A est non-B’. Within the "universal calculus", however, the informal quantifier expression 'omne' is to be dropped. (...) Accordingly, ‘A non est B' expresses only the propositional negation of ‘A est B' and is hence logically weaker than ‘A est non-B'. Besides Leibniz's cardinal error of confusing propositional and conceptual negation the following issues are dealt with in this paper: -"Aristotelian" vs. "Scholastic" Syllogistic; – Metalinguistic theory of the truth-predicate; -Individual-concepts vs. concepts in general. (shrink)

After giving a short summary of the traditional theory of the syllogism, it is shown how the square of opposition reappears in the much more powerful concept logic of Leibniz. Within Leibniz’s algebra of concepts, the categorical forms are formalized straightforwardly by means of the relation of concept-containment plus the operator of concept-negation as ‘S contains P’ and ‘S contains Not-P’, ‘S doesn’t contain P’ and ‘S doesn’t contain Not-P’, respectively. Next we consider Leibniz’s version of the so-called Quantification of (...) the Predicate which consists in the introduction of four additional forms ‘Every S is every P’, ‘Some S is every P’, ‘Every S isn’t some P’, and ‘Some S isn’t some P’. Given the logical interpretation suggested by Leibniz, these unorthodox propositions also form a Square of Opposition which, when added to the traditional Square, yields a “Cube of Opposition”. Finally it is shown that besides the categorical forms, also the non-categorical forms can be formalized within an extension of Leibniz’s logic where “indefinite concepts” X, Y, Z\ function as quantifiers and where individual concepts are introduced as maximally consistent concepts. (shrink)

This article argues that current civilizational analysis as exemplified by the work of Shmuel N. Eisenstadt still shares the strengths and weaknesses of the original approach as developed by Marcel Mauss (and Émile Durkheim) a century ago. Eisenstadt’s approach basically relies on a particular understanding of path dependency which immediately raises the question how civilizational patterns are reproduced after the crucial turning point of the Axial Age. This problem of civilizational persistence, however, remains largely unresolved and will not even be (...) resolved in the future as long as civilizational analysis relies on mostly culturalist premises. Only a combination of arguments from the field of political sociology and the sociology of religion — as suggested by Johann P. Arnason — promises to explain how civilizations are able to reproduce their patterns over and over again. (shrink)

In order to raise awareness of the ambiguous nature of scientific-technological progress, and of the challenging problems it raises, problems which are not easily addressed by courses in a single discipline and cannot be projected onto disciplinary curricula, Technical University of Darmstadt has established three interdisciplinary study concentrations: “Technology and International Development”, “Environmental Sciences”, and “Sustainable Shaping of Technology and Science”. These three programmes seek to overcome the limitations of strictly disciplinary research and teaching by developing an integrated, problem-oriented approach. (...) For example, one course considers fundamental nuclear dilemmas and uses role-playing techniques to address a controversy in the area of nuclear security. At the same time, incorporating interdisciplinary teaching into a university that is organized around mono- or multi-disciplinary faculties also poses a number of challenges. Recognition in disciplinary curricula, and appropriate organizational support and funding are examples of those challenges. It is expected that science and engineering students, empowered by such interdisciplinary study programmes, will be better prepared to act responsibly with regard to scientific and technological challenges. (shrink)

"Mit den digitalen Medien haben sich neue Formen der Warenzirkulation auf der Grundlage sozialer Netzwerke etabliert, die unter dem Begriff Sharing Economy zusammen- gefasst werden. Die Durchsetzung dieser onlinebasierten Transaktionen ist von einem euphorischen Diskurs begleitet, der der Sharing Economy utopische Potenziale einer gemeinschaftlichen Mehrwerterzeugung zuschreibt. Wolfgang Sützls Beitrag betont, dass die rhetorische Wirkung des Teilens und dessen Idealisierung über den Tausch als eigentliche ökomische Form hinwegtäusche. Anhand von Gabentheorien zeigt er auf, wie das Teilen (durch die Leugnung der (...) Äquivalenzerwartungen) an seine Grenzen komme, indem es mit dem Geben verwechselt werde, und außerdem Wertschöpfungsprozesse von Unternehmen sowie die Verwertung von Ressourcen verschleiere. Den Gedanken, dass diese zur ›Ökonomisierbarkeit von allem‹ neige, greift auch Tomasz Konicz auf, der in der Ökonomie des Teilens einen ›anomalen‹ Wunsch nach alternativen Wirtschaftsformen angesichts der ›Krise des Kapitals‹ erkennt. Dafür bringt Konicz aus einer marxistischen Perspektive den ›prozessierenden Widerspruch‹ der Technologieentwicklung und ihre verheerenden Implikationen in Anschlag, die auch die Grundlage der Sharing Economy darstellen. Insofern sei die Suche nach Alternativen noch offen. With the digital media, new forms of the circulation of goods have been established on the basis of social networks, summarily addressed under the term ‘sharing economy.’ The enforcement of these online transactions is accompanied by a euphoric discourse, ascribing to the sharing economy utopian potentials to commonly generate added value. Wolfgang Sützl’s contribution emphasizes that the rhetorical effect of sharing and its idealization distract from exchange as basic economic form. With reference to theories of gift exchange, he shows how sharing (by denying the expectation of equivalence) reaches its limits by being confused with giving, and how it also conceals the value-creation processes of companies as well as the exploitation of resources. Tomasz Konicz also picks up on the idea that the sharing economy tends to an ‘economization of everything,’ seeing in it an ‘anomalous’ desire for alternative forms of economy in the face of the ‘crisis of capital.’ On the other hand, from a Marxist perspective, Konicz points to the ‘processing contradiction’ of technology development and its devastating implications, which also form the basis of the sharing economy. In this respect, the search for alternatives still goes on. ". (shrink)

Der Fortschritt der Aussagenlogik in jungster Zeit HiBt es sinnvoll erscheinen, einen breiteren Leserkreis mit dieser Entwicklung bekannt zu machen. Obwohl vorliegendes Buch als Lehrbuch, nicht als Monographie fUr einen engeren Spezialistenkreis konzipiert wurde, soli es in einigen Themen einen tieferen Einblick in den aktuellen Stand der Dinge vermitteln. Kap. lund ein Tei! von Kap. II befassen sich mit der zweiwertigen Aussagenlogik und sind fUr Leser gedacht, die an Logik interessiert sind, doch noch nicht niiher mit ihr befaBt waren. Die (...) etwas breitere Darstellung in diesen Teilen sollte allerdings kein falsches Bild von den wahren Proportionen entstehen lassen. Denn danach nimmt die zweiwertige Aussagenlogik nicht nur innerhalb der Logik insgesamt, sondern schon innerhalb der Aussagenlogik einen Platz ein, der vergleichbar ist mit dem der euklidischen Planimetrie im Rahmen der neueren Geometrie. Lesern mit ausreichenden Vorkennt­ nissen wird es nichts ausmachen, die anfanglichen Teile zu ubergehen und dort zu be­ ginnen, wo Aussagenlogik erst interessant zu werden beginnt, niimlich wo sie den Rahmen zweiwertiger Logik verliiBt. (shrink)