This title from the De Gruyter Book Archive has been digitized in order to make it available for academic research. It was originally published under National Socialism and has to be viewed in this historical context. Learn more. >.

In this paper, we shall consider the so-called cancellation view of negation and the inferential role of contradictions. We will discuss some of the problematic aspects of negation as cancellation, such as its original presentation by Richard and Valery Routley and its role in motivating connexive logic. Furthermore, we will show that the idea of inferential ineffectiveness of contradictions can be conceptually separated from the cancellation model of negation by developing a system we call qLPm, a combination of Graham Priest’s (...) minimally inconsistent Logic of Paradox with q-entailment as introduced by Grzegorz Malinowski. (shrink)

This chapter is concerned with logical aspects of negation, i.e. with the role of negation in valid inferences and hence with the contribution negation makes to the truth and falsity conditions of declarative expressions. Negation is an important philosophical and logical concept. Often differences between logical systems can ‐ at least partially ‐ be described as differences between the notions of negation used in these logics.

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)

A prominent issue in mainstream epistemology is the controversy about doxastic obligations and doxastic voluntarism. In the present paper it is argued that this discussion can benefit from forging links with formal epistemology, namely the combined modal logic of belief, agency, and obligation. A stit-theory-based semantics for deontic doxastic logic is suggested, and it is claimed that this is helpful and illuminating in dealing with the mentioned intricate and important problems from mainstream epistemology. Moreover, it is argued that this linking (...) is of mutual benefit. The discussion of doxastic voluntarism directs the attention of doxastic logicians to the notion of belief formation and thus to dynamic aspects of beliefs that have hitherto been neglected. The development of a formal language and semantics for ascriptions of belief formation may contribute to clarifying the contents and the implications of voluntaristic claims. A simple observation concerning other-agent nestings of stit-operators, for instance, may help illuminating the notions of making belief and responsibility for beliefs of others. In this way, stit-theory may serve as a bridge between mainstream and formal epistemology. (shrink)

The paper provides a uniform Gentzen-style proof-theoretic framework for various subsystems of classical predicate logic. In particular, predicate logics obtained by adopting van Behthem''s modal perspective on first-order logic are considered. The Gentzen systems for these logics augment Belnap''s display logic by introduction rules for the existential and the universal quantifier. These rules for x and x are analogous to the display introduction rules for the modal operators and and do not themselves allow the Barcan formula or its converse to (...) be derived. En route from the minimal modal predicate logic to full first-order logic, axiomatic extensions are captured by purely structural sequent rules. (shrink)

Model-theoretic proofs of functional completenes along the lines of [McCullough 1971, Journal of Symbolic Logic 36, 15–20] are given for various constructive modal propositional logics with strong negation.

Text: Reproduktion nach Scan der Ausgabe von 1934, Verlag von J. C. B. Mohr (Paul Siebeck) in Tübingen. - Von dem kleinen Buch, das ich hier der Öffentlichkeit übergebe, bitte ich den Leser, nichts anderes zu erwarten, als das, was sein Titel ausdrücklich sagt. Es handelt sich in ihm nicht etwa um die Grundlinien eines Systems der Philosophie, sondern ausschließlich um dessen Probleme, und wenn diese sich auch nicht darlegen lassen, ohne die Richtung anzudeuten, in der das System bei der (...) Ausführung sich zu bewegen hätte, so sollen doch in dieser Schrift hauptsächlich Fragen gestellt, nicht Antworten gegeben werden. Oft brechen die Darlegungen dort ab, wo mancher Leser glauben kann, daß die größten Schwierigkeiten noch ungelöst sind. Ja mehr: nur die Grundprobleme der Philosophie werden erörtert, und das Eingehen auf Sonderfragen ist fast überall vermieden. Einzelheiten sind dann allein herangezogen worden, wenn es zur Verdeutlichung der Hauptbegriffe wünschenswert erschien. [Auszug aus dem Vorwort des Buches]. (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)

In this paper functional completeness results are obtained for certain positive and constructive propositional logics associated with a Tarski-type structured consequence relation as defined by Gabbay.

[1. Heft]. Beiträge von Kolloquien des Arbeitskreises Philosophie-Naturwissenschaften, insbesondere vom 31. 5. und 7. 6. 1972.--2. Heft. Beiträge von der wissenschaftlichen Tagung des Arbeitskreises Philosophie-Naturwissenschaften am 9. und 10. April 1974. v.

Band 9 der Schriftenreihe Beitrage zur Angewandten Ethik versammelt Arbeiten zu aktuellen Problemen sowie zu Grundlagenfragen der Medizinischen Ethik. Es handelt sich dabei zum Teil um Beitrage zu wissenschaftlichen Symposien, die das Interuniversitare Institut fur Angewandte Ethik in den Jahren 2008-2011 veranstaltet hat, und zum anderen Teil um Forschungsarbeiten, die im Rahmen von Projekten dieses Instituts entstanden sind. Zu den aktuellen Problemen der Medizinischen Ethik, die in den einzelnen Beitragen angeschnitten werden, gehoren Fragen der Stammzellenforschung und der Praimplantationsdiagnostik ebenso wie (...) Fragen, die sich im Zusammenhang mit den bei der In-Vitro-Fertilisation entstehenden 'uberzahligen' Embryonen ergeben, sowie Fragen bezuglich der neuen Patientenverfugungen - also durchwegs Fragen von hochster Aktualitat und Brisanz. (shrink)