Examines the diverse cultural influences which have shaped the basic philosophical traditions of India "Indian philosophy was at the heart of Zimmer's interest..

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.

Pars 1. Contemplativa -- Pars 2. Activa.

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)

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)

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, 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)

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 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, 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.

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)

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.

Heinrich Rickert (1863-1936) war einer der bedeutendsten deutschen Philosophen vor dem Zweiten Weltkrieg und gilt neben Wilhelm Windelband als einer der Hauptvertreter der südwestdeutschen Schule des Neukantianismus. Seine auch heute noch anregende Philosophie hatte großen, interdisziplinären wie internationalen Einfluss. Die philologisch-kritische Ausgabe macht die Schriften endlich wieder verfügbar.

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)

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)

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.

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].

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)

Bd. 1. Die Geschichte der Rechtsphilosophie und die allgemeinen Lehren.--Bd. 2. Das System des Privatrechts, die Staatslehre und die Prinzipien des Völkerrechts.

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

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.

This book is the culmination of Heinrich Meier's acclaimed analyses of the controversial thought of Carl Schmitt. Meier identifies the core of Schmitt's thought as political theology--that is, political theorizing that claims to have its ultimate ground in the revelation of a mysterious or supra-rational God. This radical, but half-hidden, theological foundation unifies the whole of Schmitt's often difficult and complex oeuvre, cutting through the intentional deceptions and unintentional obfuscations that have eluded previous commentators. Relating this religious dimension to (...) Schmitt's support for National Socialism and his continuing anti-Semitism, Meier compels the reader to come to terms with the irreconcilable differences between political theology and political philosophy. His book will give pause to those who have tended to gloss over the troubling aspects of some of Schmitt's ideas. With editions in German, French, Italian, and now English, Meier's two books on Schmitt have dramatically reoriented the international debate about Carl Schmitt and his significance for twentieth-century political thought. "Standing far above the rest . . . is Heinrich Meier's new study, Die Lehre Carl Schmitts , which covers all of Schmitt's writings. . . . Meier's work has forced everyone to take a second look at the assumptions underlying Schmitt's better-known writings and reconsider some that have been ignored."--Mark Lilla, reviewing the German edition in The New York Review of Books. (shrink)

This book, by one of the most prominent interpreters of Leo Strauss's thought, was the first to address the problem that Leo Strauss himself said was the theme of his studies: the theologico-political problem or the confrontation with the theological and the political alternative to philosophy as a way of life. In his theologico-political treatise, which comprises four parts and an appendix, Heinrich Meier clarifies the distinction between political theology and political philosophy and reappraises the unifying center of Strauss's (...) philosophical enterprise. The book is the culmination of Meier's work on the theologico-political problem. It will interest anyone who seeks to understand both the problem caused by revelation for philosophy and the challenge posed by political-religious radicalism. The appendix makes available for the first time two lectures by Strauss that are immediately relevant to the subject of this book and that will open the way for future research and debate on the legacy of Strauss. (shrink)

Graham Priest takes the relation of identity to be non-transitive. In this paper, we are going to discuss several consequences of identity as a non-transitive relation. We will consider the Henkin-style completeness proof for classical first-order logic with a non-transitive “identity” predicate, Leibniz-identity in Priest’s second-order minimal logic of paradox, and the question whether or not identity of individuals should be defined as Leibniz-identity.

Justification stit logic is a logic for reasoning about proving as a certain kind of activity, namely seeing to it that a proof is publicly available. It merges the semantical analysis of deliberatively seeing-to-it-that from stit theory and the semantics of the epistemic logic with justification from. In this paper, after recalling its language and basic semantical definitions, various ramifications and refinements of justification stit logic are presented and discussed: imposing natural restrictions upon the class of models under consideration, making (...) use of modalities that assert the existence of a proof, introducing a variant of justification stit logic based on a semantics introduced by M. Fitting, and adding variable-binding operators and extending the set of proof polynomials. (shrink)

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.

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)