Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access the field from outside the community of connexive logicians. Along the way, we (...) will make clear the context to which the papers in this special issue on Frontiers of Connexive Logic belong and contribute. (shrink)

Connexive logic has room for two pairs of universal and particular quantifiers: one pair, |$\forall $| and |$\exists $|⁠, are standard quantifiers; the other pair, |$\mathbb{A}$| and |$\mathbb{E}$|⁠, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof-theoretic place, and plausible natural language readings. The results are logics that are negation inconsistent but non-trivial.

The topic of identity of proofs was put on the agenda of general (or structural) proof theory at an early stage. The relevant question is: When are the differences between two distinct proofs (understood as linguistic entities, proof figures) of one and the same formula so inessential that it is justified to identify the two proofs? The paper addresses another question: When are the differences between two distinct formulas so inessential that these formulas admit of identical proofs? The question appears (...) to be especially natural if the idea of working with more than one kind of derivations is taken seriously. If a distinction is drawn between proofs and disproofs (or refutations) as primitive entities, it is quite conceivable that a proof of one formula amounts to a disproof of another formula, and vice versa. A notion of inherited identity of derivations is introduced for derivations in a cut-free sequent system for Almukdad and Nelson’s constructive paraconsistent logic N4 with strong negation. The notion is obtained by identifying sequent rules the application of which has no effect on the identity of derivations. Then the notion of inherited identity is used to define a bilateralist notion of synonymy between formulas, which is a relation drawing more fine-grained distinctions between formulas than strong equivalence. (shrink)

Curry’s paradox is well known. The original version employed a conditional connective, and is not forthcoming if the conditional does not satisfy contraction. A newer version uses a validity predicate, instead of a conditional, and is not forthcoming if validity does not satisfy structural contraction. But there is a variation of the paradox which uses “external validity”. And since external validity contracts, one might expect the appropriate version of the Curry paradox to be inescapable. In this paper we show that (...) this is not the case. We consider two ways of formalising the notion of external validity, and show that in both of these the paradox is not forthcoming without the appropriate forms of contraction. (shrink)

This volume is dedicated to Prof. Dag Prawitz and his outstanding contributions to philosophical and mathematical logic. Prawitz's eminent contributions to structural proof theory, or general proof theory, as he calls it, and inference-based meaning theories have been extremely influential in the development of modern proof theory and anti-realistic semantics. In particular, Prawitz is the main author on natural deduction in addition to Gerhard Gentzen, who defined natural deduction in his PhD thesis published in 1934. The book opens with an (...) introductory paper that surveys Prawitz's numerous contributions to proof theory and proof-theoretic semantics and puts his work into a somewhat broader perspective, both historically and systematically. Chapters include either in-depth studies of certain aspects of Dag Prawitz's work or address open research problems that are concerned with core issues in structural proof theory and range from philosophical essays to papers of a mathematical nature. Investigations into the necessity of thought and the theory of grounds and computational justifications as well as an examination of Prawitz's conception of the validity of inferences in the light of three “dogmas of proof-theoretic semantics” are included. More formal papers deal with the constructive behaviour of fragments of classical logic and fragments of the modal logic S4 among other topics. In addition, there are chapters about inversion principles, normalization of proofs, and the notion of proof-theoretic harmony and other areas of a more mathematical persuasion. Dag Prawitz also writes a chapter in which he explains his current views on the epistemic dimension of proofs and addresses the question why some inferences succeed in conferring evidence on their conclusions when applied to premises for which one already possesses evidence. (shrink)

This conflict can be interpreted in both religious and nonreligious ways. However, some intellectuals have identified a common thread parallel to the theological axis. The research study determines the role of existential philosophy in the contemporary religious beliefs. They have interpreted this contradiction as the conflict between our current selves and aspirations. Recognizing our animality and the role that such creatures play in the world is a requirement of our rational side. You may guarantee a well-attended eulogy by eating well, (...) exercising, not being a burden, helping out where you can, raising the next generation, and leaving the area essentially as you found it when it's time to leave. We must deal with this since it is who we are and what we are at our core. However, to be human means to be unhappy with this chilly, conventional assessment. As human beings, we possess the capacity to make decisions that influence our potential. Our destiny is not predetermined and that we can use our willpower to slightly warm the universe's unbreakable laws so that we can bend and shape them into the things we want. In the end, the cosmos prevails, yet we try to become rather than just exist during our brief existence. In the ongoing struggle against finitude, we strive for transcendence. The general framework has secular and strong religious proponents, and this view has been widely referred to as existentialist. (shrink)

Herophilus, a contemporary of Euclid, practiced medicine in Alexandria in the third century B.C., and seems to have been the first Western scientist to dissect the human body. He made especially impressive contributions to many branches of anatomy and also developed influential views on many other aspects of medicine. Von Staden assembles the fragmentary evidence concerning one of the more important scientists of ancient Greece. Part 1 of the book presents the Greek and Latin texts accompanied by English translation and (...) interpretative commentary. Significant background information is given in the introductory essay preceding each chapter. Part 2 briefly sketches the major developments within the Herophilean school after Herophilus, and discusses the individual members within it. Anyone interested in the history of science, the history of medicine, or intellectual history will find this book a rich source of information about an unusual and important aspect of Greek culture. (shrink)

References to God. Some Remarks by Wittgenstein on Religion in the Years 1949 – 51. After a brief overview of Wittgenstein's stock of remarks on the subject of religion from 1949 – 1951, this article will focus on two particular points: (1) supposedly nonsensical conceptions of God, for instance in the context of proofs of God, (2) definitions of the term ”God” by hinting at something. Connections between (1) and (2) both systematically and exegetically within the framework of Wittgenstein's remarks (...) are made. Ich danke Anja Weiberg für sehr hilfreiche Kommentare. (shrink)

Einführende Bemerkungen zu einem umstrittenen Begriff.

Ein Buch nicht der Re-Mythisierung, sondern der Mythoskritik, allerdings einer Kritik, die den Mythos ernst nimmt. Daher: »Mein Thema lautet: die Funktion der Genealogie im Mythos. So formuliert, setzt es eine rationale Vorstellung vom Funktionieren des Mythos voraus – es fordert zu einer systematischen Erörtertung auf. Wir brauchen nicht zu befürchten, daß eine systematische Erörterung das Mystische des Mythos verfehlt, weil sie archaische Verhältnisse dem Zwang der Rationalität unterwirft. Eher wird sie die Verbindung deutlich machen, die zwischen Mythos, Rationalität und (...) Zwang besteht.«. (shrink)

Bei Gilles Deleuze findet man einen der seltenen Ansätze zu einem genuin philosophischen Verständnis der Linie. Er versucht eine Emanzipation der Linie nicht nur aus der Geometrie, sondern auch aus der Dominanz des Raumes. Die wichtigsten Motive, die ihn dabei leiten, hat er in dem Konzept der Fluchtlinie gebündelt. Dessen potentiell metaphorischer Status wird ebenso befragt wie seine Aussagekraft für das deleuzianische Verständnis von Philosophie überhaupt. The work of Gilles Deleuze is one of the rare cases in which a genuinely (...) philosophical understanding of the line is attempted. He not only tries to dissociate the line from geometry, but also to free it from the dominance of space. The most important motives behind his thinking about the line converge in the concept of the ›ligne de fuite‹. The text examines the potentially metaphorical status of this notion, as well as its significance for Deleuze’s view of philosophy in general. (shrink)

Alexandre Kojève had traveled via Peking. The high official of the French Ministry of the Economy stopped off in Berlin in order to speak to the heads of the German Socialist Student Association. In the Hotel Berliner Hof on Lake Diana, the Parisian guest advised Dutschke & Co. that the most important thing they could do would be to learn Greek. Such an answer to the question “What is to be done?” was not expected from this famous man, whose legendary (...) seminars on Hegel's Phenomenology of Spirit in the Thirties had inspired an entire generation of French scholars and intellectuals. Kojève's long-standing acquaintance, who looked after his guest during his stay in Berlin, was no less baffled to hear from the Hegelian that his next stop was Plettenberg. “Where else should one travel to in Germany? Carl Schmitt is after all the only one with whom it is worthwhile to talk.”. (shrink)

Dieser Buchtitel ist Teil des Digitalisierungsprojekts Springer Book Archives mit Publikationen, die seit den Anfängen des Verlags von 1842 erschienen sind. Der Verlag stellt mit diesem Archiv Quellen für die historische wie auch die disziplingeschichtliche Forschung zur Verfügung, die jeweils im historischen Kontext betrachtet werden müssen. Dieser Titel erschien in der Zeit vor 1945 und wird daher in seiner zeittypischen politisch-ideologischen Ausrichtung vom Verlag nicht beworben.

Le mot rythme est entré dans le vocabulaire esthétique allemand au milieu des années 1760. Son emploi est alors devenu nettement plus fréquent et a cessé d'apparaître comme un emprunt au grec. Une fois acclimaté dans la théorie allemande des arts du déroulement dans le temps ou arts diachroniques, il a assumé la fonction de terme technique plus ou moins pointu — quelquefois très pointu —, auquel ont été attribués trois types de sens. En premier lieu, il pouvait - XVIIIe (...) siècle – Nouvel article. (shrink)

Betr. u.a. die letzten Briefe Friedrich Nietzsches an Jacob Burckhardt.