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.

Text: Reproduktion auf Grundlage der Ausgabe J. C. B. Mohr (Paul Siebeck), Tübingen 1939. - Das Werk, in dem Heinrich Rickert seine Lebensarbeit zusammenfassen wollte, ist sein "System der Philosophie." Der erste Band dieses Werkes enthält die "Allgemeine Grundlegung der Philosophie" (Tübingen, 1921). Der zweite Band sollte die "Philosophie des kontemplativen Lebens," der dritte die des "aktiven Lebens" behandeln. Der Umriß des Systems, der im ersten Bande mitunter vielleicht noch wie ein leeres Rahmen- und Fächerwerk wirken könnte, sollte nun (...) seine Brauchbarkeit zeigen. Er sollte angefüllt und bereichert werden durch sachhaltige Untersuchungen über die einzelnen Teilgebiete des philosophischen Systems. So war für den zweiten Band z. B. eine Wissenschaftslehre (Logik und Methodologie), eine Philosophie der Kunst (Ästhetik) und eine Behandlung der mystischen Religiosität geplant. Der dritte Band sollte vor allem die Sozialphilosophie enthalten; zur Sprache kommen sollte dabei zunächst das sittliche Leben in der "Gemeinschaft freier Personen" (Ethik), dann die über jede sittliche Verpflichtung noch hinausgehende Liebesgemeinschaft, wie sie z.B. in der Freundschaft und in der Ehe erlebt wird (Erotik), schließlich das religiöse Leben auf Grund persönlicher Gottesbegegnung. Druckfertig liegen für die inhaltliche Erfüllung und Ausgestaltung des Systems nur einige Aufsätze vor, die den zweiten Band eröffnen sollten: Rickert selbst hat noch den gesonderten Abdruck dieser Aufsätze geplant und ihre Anordnung genau festgelegt. Sein Plan wird im folgenden ausgeführt. Vorangestellt ist ein Zeitungsaufsatz über die Welt der Erfahrung, der in Kürze das Ziel der folgenden Untersuchungen teilweise sogar schon wörtlich vorwegnimmt. Da die Fehlurteile über Rickerts angeblich wirklichkeitsfremden Formalismus meistens nur darauf beruhen, dass man den Weg der Untersuchung mit ihrem Ziel, die Methode mit der Sache selbst verwechselt, so sei auf diesen kurzen Einleitungsaufsatz und dann namentlich auf den Abschnitt über Sprache und Antlitz der Körperwelt besonders hingewiesen. Die vorliegenden Aufsätze sollten also einen Übergang herstellen von den noch mehr formalen Ausführungen der Allgemeinen Grundlegung zu den dann immer sachhaltiger werdenden Einzeluntersuchungen über den inhaltlichen Reichtum des kontemplativen und des aktiven Lebens.[August Faust; Breslau 1939; Auszug aus dem Vorwort des Herausgebers]. (shrink)

Bd. 1. Stellenindizes, philologischkritischer Apparat.

Imagination has recently attracted considerable attention from epistemologists and is recognized as a source of belief and even knowledge. One remarkable feature of imagination is that it is often and typically agentive: agents decide to imagine. In cases in which imagination results in a belief, the agentiveness of imagination may be taken to give rise to indirect doxastic control and epistemic responsibility. This observation calls for a proper understanding of agentive imagination. In particular, it calls for the development of a (...) semantics of imagination ascriptions. In the present paper an earlier suggestion by Ilkka Niiniluoto for a logic of imagination is considered. This proposal does not capture the agentive nature of imagination, and an alternative semantics is suggested. The new semantics combines the modal logic of agency with the neighbourhood semantics from alethic modal logic. (shrink)

In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther’s claim is not without problems.

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)

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 is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.

The knowability paradox is an instance of a remarkable reasoning pattern (actually, a pair of such patterns), in the course of which an occurrence of the possibility operator, the diamond, disappears. In the present paper, it is pointed out how the unwanted disappearance of the diamond may be escaped. The emphasis is not laid on a discussion of the contentious premise of the knowability paradox, namely that all truths are possibly known, but on how from this assumption the conclusion is (...) derived that all truths are, in fact, known. Nevertheless, the solution offered is in the spirit of the constructivist attitude usually maintained by defenders of the anti-realist premise. In order to avoid the paradoxical reasoning, a paraconsistent constructive relevant modal epistemic logic with strong negation is defined semantically. The system is axiomatized and shown to be complete. (shrink)

According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what it really is. [13, p. 281].

First published in 1938. The aim of this book is to expound Kant’s _Critique of Judgement _by interpreting all the details in the light of what Kant himself declares to be his fundamental problem. _A Commentary on Kant’s Critique of Judgement _provides an excellent introduction to Kant’s third critique, and will be of interest to students of philosophy.

The present monograph is a slightly revised version of my Habilitations schrift Proof-theoretic Aspects of Intensional and Non-Classical Logics, successfully defended at Leipzig University, November 1997. It collects work on proof systems for modal and constructive logics I have done over the last few years. The main concern is display logic, a certain refinement of Gentzen's sequent calculus developed by Nuel D. Belnap. This book is far from offering a comprehensive presentation of generalized sequent systems for modal logics broadly conceived. (...) The proof-theory of non-classical logics is a rapidly developing field, and even the generalizations of the ordinary notion of sequent listed in Chapter 1 can hardly be presented in great detail within a single volume. In addition to further investigating the various approaches toward generalized Gentzen systems, it is important to compare them and to discuss their relative advantages and disadvantages. An initial attempt at bringing together work on different kinds of proof systems for modal logics has been made in [188]. Another step in the same direction is [196]. Since Chapter 1 contains introductory considerations and, moreover, every remaining chapter begins with some surveying or summarizing remarks, in this preface I shall only emphasize a relation to philosophy that is important to me, register the sources of papers that have entered this book in some form or another, and acknowledge advice and support. (shrink)

A version of strong negation is introduced into Categorial Grammar. The resulting syntactic calculi turn out to be systems of connexive logic.

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.

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)

Recovering Reason: Essays in Honor of Thomas L. Pangle is a collection of essays composed by students and friends of Thomas L. Pangle to honor his seminal work and outstanding guidance in the study of political philosophy. These essays examine both Socrates' and modern political philosophers' attempts to answer the question of the right life for human beings, as those attempts are introduced and elaborated in the work of thinkers from Homer and Thucydides to Nietzsche and Charles Taylor.

Originally published in 1973. The volume is divided into four sections: The introduction places the position of the Buddhist Tantras within Mahayana Buddhism and recalls their early literary history, especially the Guhyasamahatantra; the section also covers Buddhist Genesis and the Tantric tradition. The foundations of the Buddhist Tantras are discussed and the Tantric presentation of divinity; the preparation of disciples and the meaning of initiation; symbolism of the mandala-palace Tantric ritual and the twilight language. This section explores the Tantric teachings (...) of the inner Zodiac and the fivefold ritual symbolism of passion. The bibliographical research contains an analysis of the Tantric section of the Kanjur exegesis and a selected Western Bibliography of the Buddhist Tantras with comments. (shrink)

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)

In this paper, a family of paraconsistent propositional logics with constructive negation, constructive implication, and constructive co-implication is introduced. Although some fragments of these logics are known from the literature and although these logics emerge quite naturally, it seems that none of them has been considered so far. A relational possible worlds semantics as well as sound and complete display sequent calculi for the logics under consideration are presented.

Modal logic is one of the most widely applied logical formalisms. Systems of modal logic are being used in many disciplines, ranging from artificial intelligence, computer science, mathematics, formal grammar and semantics to philosophy. This volume presents substantial recent advances in the relational and the algorithmic treatment of modal logics. It contains papers from the fifth conference on "Advances in Modal logic," held in Manchester (UK) in September 2004. Written by leading experts in the field, the present book is indispensable (...) for any advanced student and researcher in pure and applied modal logic. (shrink)

In Phenomena of Power, one of the leading figures of postwar German sociology reflects on the nature, and many forms of, power. For Heinrich Popitz, power is rooted in the human condition and is therefore part of all social relations. Drawing on philosophical anthropology, he identifies the elementary forms of power to provide detailed insight into how individuals gain and perpetuate control over others. Instead of striving for a power-free society, Popitz argues, humanity should try to impose limits on (...) power where possible and establish counterpower where necessary. Phenomena of Power delves into the sociohistorical manifestations of power and breaks through to its general structures. Popitz distinguishes the forms of the enforcement of power as well as of its stabilization and institutionalization, clearly articulating how the mechanisms of power work and how to track them in the social world. Philosophically trained, historically informed, and endowed with keen observation, Popitz uses examples ranging from the way passengers on a ship organize deck chairs to how prisoners of war share property to illustrate his theory. Long influential in German sociology, Phenomena of Power offers a challenging reworking of one of the essential concepts of the social sciences. (shrink)