In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with (...) multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives. (shrink)

Einleitung.--Die begriffliche Erkenntniss der Körperwelt.--Natur und Geist.--Natur und Geschichte.--Die historische Begriffsbildung.--Naturphilosophie und Geschichts-Philosophie.

In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.

§ 1. Prolegomena 1. Die Logik, die in diesem Lehrbuch entwickelt wird, ist bestimmt durch die folgenden Kennzeichen: (1) Sie fuBt auf derselben Ontologie wie die von erkennbaren Wider­ sprlichen befreite und in diesem Sinne vertretbare klassische Mathe­ matik. Flir diese Ontologie ist charakteristisch die Grundvoraussetzung, daB die Objekte der Mathematik und mit ihnen die mathematischen Bereiche an sich existieren, wie die platonischen Ideen. Mit Bezug auf diesen An-sich-Charakter sprechen wir von einer platonischen Ontologie. Flir diese Ontologie existieren die unendlichen (...) Bereiche beliebig hoher Machtigkeit als fertig vorliegende Objekte in derselben Art wie die durch Aufzahlung ihrer Elemente erfaBbaren endlichen Mengen und in gleichem Range mit ihnen. Die weittragenden Folgen dieser Auffassung sind in zwei Haupt­ punkten konzentriert. Erster Hauptpunkt: die Beurteilung der Potenz­ mengen. Mit den abzahlbaren Mengen existieren, genauso wie im end­ lichen Falle, auch ihre Potenzmengen, mit dem ihnen zukommenden Charakter der Uberabziihlbarkeit. Das Uberabzahlbare steht also gleich­ berechtigt neben dem Abzahlbaren. Zweiter Hauptpunkt: der flir den Platonismus charakteristische Gehalt des ausgeschlossenen Dritten. Es genligt hier, die mengentheoretische Formulierung dieses Prinzips ins Auge zu fassen. Sie besagt, daB eine flir die Elemente einer beliebigen Menge, also mit EinschlieBung der unendlichen Mengen von einer be­ liebigen Machtigkeit erklarte Eigenschaft allen Elementen der Menge zukommt oder es gibt (wenigstens) ein Mengenelement, dem sie nicht zukommt, unabhangig davon, ob ein solches Element angegeben werden kann oder nicht. Ein Anwendungsfall ist das der elementaren Zahlen­ theorie angeh6rige Prinzip der kleinsten Zahl. (shrink)

In this paper non-normal worlds semantics is presented as a basic, general, and unifying approach to epistemic logic. The semantical framework of non-normal worlds is compared to the model theories of several logics for knowledge and belief that were recently developed in Artificial Intelligence (AI). It is shown that every model for implicit and explicit belief (Levesque), for awareness, general awareness, and local reasoning (Fagin and Halpern), and for awareness and principles (van der Hoek and Meyer) induces a non-normal worlds (...) model validating precisely the same formulas (of the language in question). (shrink)

It is widely accepted that there is a clear sense in which the first-order paraconsistent constructive logic with strong negation of Almukdad and Nelson, QN4, is more constructive than intuitionistic first-order logic, QInt. While QInt and QN4 both possess the disjunction property and the existence property as characteristics of constructiveness (or constructivity), QInt lacks certain features of constructiveness enjoyed by QN4, namely the constructible falsity property and the dual of the existence property. This paper deals with the constructiveness of the (...) contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan’s drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent). (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)

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.

This paper deals with various substructural propositional logics, in particular with substructural subsystems of Nelson's constructive propositional logics N– and N. Doen's groupoid semantics is extended to these constructive systems and is provided with an informational interpretation in terms of information pieces and operations on information pieces.

Many logical systems are such that the addition of Prior's binary connective tonk to them leads to triviality, see [1, 8]. Since tonk is given by some introduction and elimination rules in natural deduction or sequent rules in Gentzen's sequent calculus, the unwanted effects of adding tonk show that some kind of restriction has to be imposed on the acceptable operational inferences rules, in particular if these rules are regarded as definitions of the operations concerned. In this paper, a number (...) of simple observations is made showing that the unwanted phenomenon exemplified by tonk in some logics also occurs in contexts in which tonk is acceptable. In fact, in any non-trivial context, the acceptance of arbitrary introduction rules for logical operations permits operations leading to triviality. Connectives that in all non-trivial contexts lead to triviality will be called non-trivially trivializing connectives. (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)

Das Handlexikon zur KrV gibt verläßliche und unentbehrliche Orientierungshilfen für die systematische Auseinandersetzung mit Kants epochalem Hauptwerk. Es kann für alle Ausgaben, die den Seitenumbruch der ersten und zweiten Auflage (A 1781, B 1787) im Text kennzeichnen, herangezogen werden.

Proof Theory of Modal Logic is devoted to a thorough study of proof systems for modal logics, that is, logics of necessity, possibility, knowledge, belief, time, computations etc. It contains many new technical results and presentations of novel proof procedures. The volume is of immense importance for the interdisciplinary fields of logic, knowledge representation, and automated deduction.

It is shown that every displayable propositional logic enjoys strong cut-elimination. This result strengthens Belnap's general cut-elimination theorem for Display Logic.

Science today is an international business, of course, and there has hardly ever been a partition wall between the logical work in Poland and Germany. However, apart from long lasting personal scientific contacts there are good reasons to further intensify the relations between the German and the Polish Community of Logic and Logical Philosophy. So it was only natural to think about bringing them together at a scientific event in a friendly environment. This idea was carried out as a common (...) initiative of the Polish Association for Logic and Theory of Science (PTL) and of the German based Society for Analytic Philosophy (GAP). The First German-Polish Workshop on Logic and Logical Philosophy was held in Bachotek/Poland from September 10.–13., 1995. It was organized by Kazimierz Świrydowicz (PTL), Heinrich Wansing (GAP) and Max Urchs (both). This part of the present volume of Logic and Logical Philosophy is not the proceedings of the workshop. On one hand, not all the papers presented at the workshop (see previous page for the programme) are attended to this volume. Due to their more technical character, the contributions of Gregory Restall, Tomasz Skura, Heinrich Wansing, Andrzej Wroński and others will appear in the next number of Reports on Mathematical Logic. Some papers included in this issue were changed considerably for publication. On the other hand, colleagues who intended to join the workshop but had to cancel for some reason were invited to submit their material, too. We would like to thank the editors of both journals very kindly for their suggestion to publish the submitted material. (shrink)

A theory of substructural negations as impossibility and as unnecessity based on bi-intuitionistic logic, also known as Heyting-Brouwer logic, has been developed by Takuro Onishi. He notes two problems for that theory and offers the identification of the two negations as a solution to both problems. The first problem is the lack of a structural rule corresponding with double negation elimination for negation as impossibility, DNE, and the second problem is a lack of correspondence between certain sequents and a characterizing (...) frame property. While the identification of negation as impossibility and negation as unnecessity does solve Onishi’s problems, in general it nevertheless seems desirable to keep the two notions separate. The present paper addresses the first problem by introducing a reformulation of Onishi’s display sequent calculus in a language of sequents that incorporates Boolean negation. Instead of identifying negation as impossibility and negation as unnecessity, a notion of weak frame correspondence is defined. It is observed that DNE weakly corresponds with a certain frame property, and two structural sequent rules are presented that together also weakly correspond with that frame property and allow one to derive DNE. Moreover, the reformulated display calculus has an independent motivation by considerations on proof-theoretic semantics. (shrink)

In what was originally a lecture, the well-known German fundamental theologian Heinrich Fries looks at similarities between the general theological characteristics of Karl Rahner (a friend of Fries) and John Henry Newman (the object of Fries’s early books and lasting research). He offers first some contrasts but then notes similarities: theology as an investigation rather than a system, being a theologian concerned with the most basic aspects of faith, faith as a dynamic of subectivity rather than as a collection (...) of beliefs, a primacy of praxis over theory, theological efforts done at the time of an Ecumenical Council. To conclude there are questions addressed to Fries and Rahner (who was present at the original lecture). (shrink)

Hans Drieschs "Wirklichkeitslehre".--Emanuel Laskers "Philosophie des Unvollendbar".--Carl Ludwig Schleich und die "neue Epoche der Weltanschauung".--Fr. J. Kurt Geisslers "System der Seinsgebiete".--Graf Hermann Keyserlings "Gefüge der Welt", "Reisetagebuch eines Philosophen", "Unsterblichkeit", "Prolegomena zur Naturphilosophie".--Henri Bergsons "Schöpferische Entwicklung".--L. William Sterns "Person und Sache".--G. Heymans "psychischer monismus".--Wilhelm Wundts "Sinnliche und übersinnliche Welt".--Emil Boutroux und die "Kontingenz der Naturgesetze".--Rudolf Otto, Christof Schrempf, Romain Rolland und die intuitive Methode des Welterkenens.--Rudolf Steiners "Philosophie der Freiheit".--Erich Becher und die fremddienliche Zweckmässigkeit.--Edmund Husserl, Heinrich Rickert, Emil Lask, (...) Leonard Nelson und der methodologische Gott.--Anhang: Eucken, Dessoir, Scheler, Heiler, James, Bo Yin Ra, Oesterreich, Schneider. (shrink)

Die vorliegende Arbeit fragt nach Formen autonomer Individualität, welche zugleich nicht hinter die postmoderne 'Auflösung des Subjekts' zurückgehen. Diese Problematik wird zunächst vor dem Hintergrund der Analyse von Friedrich Nietzsches Begriff des souveränen Individuums diskutiert. Hierbei werden neben der begrifflichen Analyse auch die Ergebnisse der Nietzscheforschung zum Thema behandelt. Um das Konzept souveräner Individualität aber auch weiter zu entwickeln, wird darüber hinaus ein Vergleich zu Foucaults Analyse der antiken Selbstsorge vorgenommen. Die Ergebnisse dieser Analyse werden daraufhin auf Probleme der aktuellen (...) Subjektphilosophie übertragen. Hierbei steht die Frage im Mittelpunkt, wie die Depotenzierung des Subjekts durch die Idee einer autonomen Individualität ergänzt werden kann. Neben dem erstmals vorgenommenen Vergleich zwischen Nietzsches und Foucaults Konzepten der Selbstsorge entwickelt Johannes Heinrich also auch den Begriff einer autonomen Identität, der bereits durch die dekonstruierende Kritik jüngster Subjekttheorien hindurchgegangen ist. (shrink)

Bücher zählen bis heute zu den wichtigsten kulturellen Errungenschaften der Menschheit. Ihre Erfindung war mit der Einführung des Buchdrucks ähnlich bedeutsam wie des Internets: Erstmals wurde eine massenweise Weitergabe von Informationen möglich. Bildung, Wissenschaft, Forschung, aber auch die Unterhaltung wurde auf neuartige, technisch wie inhaltlich revolutionäre Basis gestellt. Bücher verändern die Gesellschaft bei heute. Die technischen Möglichkeiten des Massen-Buchdrucks führten zu einem radikalen Zuwachs an Titeln im 18. Und 19 Jahrhundert. Dennoch waren die Rahmenbedingungen immer noch ganz andere als heute: (...) Wer damals ein Buch schrieb, verfasste oftmals ein Lebenswerk. Dies spiegelt sich in der hohen Qualität alter Bücher wider. Leider altern Bücher. Papier ist nicht für die Ewigkeit gemacht. Daher haben wir es uns zur Aufgabe gemacht, das zu Buch gebrachte Wissen der Menschheit zu konservieren und alte Bücher in möglichst hoher Qualität zu niedrigen Preisen verfügbar zu machen. (shrink)

If one compares Hans Blumenberg with the dominant contemporary German-speaking characters of philosophy and heads of their own schools, Husserl, Heidegger and Adorno, then one sees that Blumenberg’s understanding of philosophy proves tobe emphatically unemphatic, withdrawn, and deeply stacked. He exchanges the big bills of those philosophies for small coins: Philosophy is attention first, thoughtfulness second, consolation third, and memory fourth. – An introduction is evidence of the reorientation that Blumenberg undertook in the 1950s with regard to his Catholic-theological and (...) Heideggerian philosophical beginnings. This led him to redefine the modern age from one of crisis to one of overcoming the crisis. (shrink)

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.

Des choses divines et de leur revelation est le testament philosophique de son auteur, Friedrich Heinrich Jacobi. La premiere evaluation d'ensemble du postkantisme et des grands systemes idealistes qu'il y propose determine encore l'image que nous pouvons nous faire de la philosophie classique allemande. La querelle qu'elle a declenchee et la reponse outranciere que lui a apportee Schelling, blesse par la critique du naturalisme que developpe la deuxieme partie de l'ouvrage, en font le document le plus precieux dont nous (...) disposions pour interpreter les debats qui, durant les premieres decennies du XIXe siecle, ont mis aux prises la philosophie de la religion et la theologie speculative. La discussion des rapports du realisme et de l'idealisme religieux, de la revelation de la raison et de la doctrine positive que Jacobi developpe d'abord en reponse a Matthias Claudius, puis lors d'un dialogue avec Friedrich Schlegel, non seulement eclaire cette lecture de l'histoire de la philosophie a l'heure de l'avenement du nihilisme, mais permet aussi de comprendre ce que l'auteur entend par ce vrai rationalisme qu'il oppose aux philosophes de son temps. Elle donne ainsi a celui qui fut l'un des peres de l'idealisme allemand en meme temps que son critique le plus acerbe l'occasion de preciser une derniere fois les rapports de la raison et de l'entendement, question qu'avec Kant, il fut l'un des premiers a poser a la pensee moderne. (shrink)

Johann-Heinrich Königshausen. D. Zur Differenz zwischen der transzendentalen Deduktion der Ausgabe A und der Ausgabe B unter der Rücksicht der Problematik der subjektiven Deduktion Wir zitierten bereits jene Mitteilung Kants aus der ...