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)

Dieses Werk ist Teil der Buchreihe TREDITION CLASSICS. Der Verlag tredition aus Hamburg veroffentlicht in der Buchreihe TREDITION CLASSICS Werke aus mehr als zwei Jahrtausenden. Diese waren zu einem Grossteil vergriffen oder nur noch antiquarisch erhaltlich. Mit der Buchreihe TREDITION CLASSICS verfolgt tredition das Ziel, tausende Klassiker der Weltliteratur verschiedener Sprachen wieder als gedruckte Bucher zu verlegen - und das weltweit! Die Buchreihe dient zur Bewahrung der Literatur und Forderung der Kultur. Sie tragt so dazu bei, dass viele tausend Werke (...) nicht in Vergessenheit geraten. (shrink)

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)

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.

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)

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain (...) in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (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)

Neinsagen ist die Formel des Protestes. In einer Welt, die zu Protesten Anlaß bietet, scheint es nicht überflüssig, diese Formel zu untersuchen.

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.

In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...) information carried by sentences of a given language and to present a formalized version of the Ackermann principle as an inclusion relationship between the informational contents of the conclusions and the premises of a valid entailment. Being so interpreted, the entailment relation exhibits certain properties, including the property of transitivity. Whereas properties such as Anderson and Belnap’s variable sharing property or Parry’s proscriptive principle are normally presented as imposing a relevance requirement on valid entailment, the suggested formalization of the Ackermann principle supports all of Gentzen’s structural rules, including weakening, a rule that is normally given up in sequent-style proof systems for relevance logics. In this way we propose an Ackermann-inspired explication of the nature of entailment as a relation between the informational contents of sentences. (shrink)

Excerpt from Die Religionsphilosophie des als-Ob: Eine Nachprufung Kants und des Idealistischen Positivismus Der theologischen Fakultat der Berliner Universitat uberreiche ich diese Blatter als Ausdruck des ehrerbietigsten Dankes fur die mir am 15. Dezember 1917 verliehene theologische Doktorwurde. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst (...) repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. (shrink)

Leibniz hat sein Projekt einer Scientia generalis, die das gesamte Wissen seiner Zeit in einer Enzyklopädie komprimieren sollte, vor seinen Zeitgenossen geheim gehalten. Bei einzelnen Briefpartnern versuchte er, Verständnis für Thesen seiner Metaphysik zu finden, ohne zu viel davon preiszugeben. Heinrich Schepers will in seinen Beiträgen dem nahe kommen, was Leibniz' wahre Metaphysik ausmacht. Die Perzeption und der Appetitus sind die spontanen Handlungen, mit denen sich die Individuen selbst konstituieren. Die Kompatibilität ist die Relation, die sie auf die vielen (...) möglichen Welten verteilt. Die sich dabei herausstellenden Grade der Perfektion machen die Wahl der besten unter ihnen möglich. Aus den spontanen Handlungen der einfachen Substanzen leitet Leibniz seine Begriffe von Raum und Zeit ab. Tragend für diese Theorie ist sein konzeptualistischer Gottesbegriff, demzufolge nicht allein die Essenzen, sondern alles Denkbare in Form vollausgebildeter Subjekte materiell Gottes Verstand ausmachen. (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)

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)

Zahl. Ding.--Über die Anfänge der Vernunft beim Beginn der Dinge.--Der Makrokosmos.--Die Vernunft und ihr Object.--Die Schwingung und Kreisung der Gestirne.--Das Wesen der Liebe.--Heimsuchung und Auferstehung. Die Art und Weise der Himmelfahrt.--Die Gattungen der Bewegung.--Ursache und Wirkung.--Definitionen und Grundzüge.

The article presents the catechumenal theology of St. Ambrose and St. Augustine, highlighting in the former, four elements proper to the baptismal itinerary of Milan, such as the agonistic character of the baptismal preparation, the biblical catechesis related to the biblical characters of the Old Testament, the virtues and the rite of the Effetá. Thirdly, the importance of the Traditio Symboli in Milan with its theology is highlighted, and finally the secret that St. Ambrose kept on the rites of Christian (...) initiation, in order to arise curiosity in those who were going to receive them. Subsequently, the theology of two rites belonging to the Easter Vigil, namely, the washing of the feet and the post-baptismal anointing with myrum, is discussed. The second part of the article, presents the Augustinian theology of the catechumenate, stressing three elements of the catechumenal process, namely, the fasting and other ascetic practices, the traditio symboli and the traditio orationis. On the post-baptismal rites the article emphasises the Eucharistic catechesis preached on Easter Sunday with its special characteristics and the final procession that was done on the last day of the Easter Week to a memoria martyrum. (shrink)

An extension L + of the non-associative Lambek calculus Lis defined. In L + the restriction to formula-conclusion sequents is given up, and additional left introduction rules for the directional implications are introduced. The system L + is sound and complete with respect to a modification of the ternary frame semantics for L.

Volume 12 in the edition of the complete Jerusalem Talmud. Tractates Sanhedrin and Makkot belong together as one tractate, covering procedural law for panels of arbitration, communal rabbinic courts and an elaborate construction of hypothetical criminal courts supposedly independent of the king's administration. Tractate Horaiot, an elaboration of Lev. 4:1-26, defines the roles of High Priest, rabbinate, and prince in a Commonwealth strictly following biblical rules.