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.

This book focuses on the development of Platonic philosophy at the hands of Roman writers between the first century BCE and the early fifth century CE. It discusses the interpretation of Plato's Timaeus by Cicero, Apuleius, Calcidius, and Augustine, and examines how these authors created new contexts and settings for the intellectual heritage they received and thereby contributed to the construction of the complex and multifaceted genre of Roman Platonism. It takes advantage of the authors' treatment of Plato's Timaeus as (...) a continuous point of reference to illustrate the individuality and originality of each writer in his engagement with this Greek philosophical text; each chooses a specific vocabulary, methodology, and literary setting for his appropriation of Timaean doctrine. The authors' contributions to the dialogue's history of transmission are shown to have enriched and prolonged the enduring significance of Plato's cosmology. (shrink)

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)

This article presents a cross-contextual examination of St. Augustine's views concerning nonhuman animals. It aligns seemingly disparate conclusions of previous studies by considering both material and metaphorical nonhuman animals across Augustine's writings and by integrating the role he assigns to them into his broader metaphysical framework. While Augustine is found to assign instrumental value to all aspects of material creation, nonhuman animals are shown to carry a particularly complex significance due to their proximity to humans in his hierarchical account of (...) creation. (shrink)

Recent scholarship on Plato'sCratylus has yielded interpretations that assign various functions of philosophical importance to the dialogue's lengthy etymological section. Barney considers the section an ‘agonistic display’ in which Socrates beats contemporary practitioners of etymology at their own game while, at the same time, offering a cosmological theory intended for serious intellectual competition. In this context, Barney emphasizes the importance of Parmenides, a charioteer who journeys towards Truth, as a literary point of reference for Socrates’ own etymological quest after the (...) true meaning of names which, from Cratylus’ naturalist perspective on language, are considered indicative of their referents’ essential nature. The contents of the etymologies may be a ‘rational reconstruction’ of Cratylus’ linguistic naturalism. Sedley stresses the encyclopedic character of Socrates’ lexical interpretations and argues that these are ‘exegetically correct’ in representing the opinions of the name-givers of old who subscribed to a Heraclitean view of a world in flux, as is reflected in the original form of the names they devised. Ademollo stresses that Socrates’ etymologies display the evolution of Greek intellectual thought, shown to be heavily reliant on the assumption of a universe in flux, and serve to exhibit the weaknesses in Cratylus’ naturalist view of language. (shrink)

Cette étude examine le rôle de traduction comme médium dans la tradition des interprétations de Platon. L’examen porte sur une partie du Timée de Platon (29b2-d3), traduite par trois interprètes: un premier échantillon de traduction moderne permet tout d’abord de mettre en lumière certains reflets de la recherche platonicienne contemporaine. Deux spécimens plus détaillés de traductions latines, de Cicéron et de Calcidius, datée du IVe siècle, permettent ensuite d’approfondir l’exégèse ancienne du dialogue. L’article s’attache à démontrer que chacun de ces (...) textes témoigne du platonisme contemporain de son traducteur, de sa mentalité philosophique et intellectuelle. Dans le cas de la version cicéronienne, on rencontre des éléments dialectiques de l’académie philonienne, entremêlés avec des nuances rhétoriques aristotéliciennes. La traduction calcidienne, en revanche, nous invite à réfléchir sur la vie philosophique du moyen platonisme. Loin d’être un instrument neutre et mécanique de dissémination textuelle, la traduction se présente comme une interprétation individuelle et une contribution originale à l’exégèse de l’objet qu’elle transmet. (shrink)

This paper examines Calcidius’ position in the notorious interpretative controversy over Plato’s dialogue Timaeus. Despite Calcidius’ far-reaching influence on the later philosophical and theological tradition, his contribution to the history of this debate has received surprisingly little attention. Against previous studies that have concluded unfavourably with regard to Calcidius’ merits as a commentator, this inquiry shows that his Platonic exegesis, far from being problematic and contradictory, is original in its approach and method. During the course of this paper, moreover, Calcidius’ (...) affiliation with the Christian faith is reevaluated and found to be less extensive than has sometimes been assumed. (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)

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)

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 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.

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.

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)

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)

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.

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)