J. Wackernagel and E. Löfstedt have both drawn attention to Pindar's ‘Neigung, das Futurum zu setzen bei Verben, die eine jetzt vorhandene, aber auf zukünftiges Tun abzielende Willensrichtung ausdrücken’. But they regarded this as a purely grammatical phenomenon, and did not note that the Pindaric use is practically limited to statements of the type, ‘I shall sing, glorify, testify, etc.’. It was E. Bundy who first drew attention to the conventional nature of these futures and so ended years of misunderstanding. (...) So, for example, Wilamowitz considered that P. 1.75 represented an optative with while Slotty, following Breyer, thought that N. 9. 10 was an aorist subjunctive ‘auf Grund des pindarischen Sprachgebrauches’! Postgate, following Gildersleeve, thought that 0. 8. 57 represented though the contrary would appear to be more true, cf. 0. 13. 11: and also Hoekstra sees in the future ‘den Nebenbegriff des Konnens’. (shrink)

Klaus Alpers has recently recovered from the obscurity of Byzantine lexica the fragments of what appears to be a novel dating from c. A.D. 100, and notable to us, as it was for the Byzantine excerptor, for the elegant verbal borrowings from ancient comedy, always a favourite source of good Attic Greek for the atticists of imperial times. One of these glosses gives occasion to look again at fishing metaphors for erotic business, a subject discussed often enough by scholars, but (...) still perhaps capable of revealing new nuances. These hunting and fishing metaphors are used as one would expect in many non-amatory contexts, but in both love poetry and its allied genres they occur throughout antiquity in such quantity that the metaphorical complexity reaches into very allusive language. Long ago Preston had already pointed out that ‘Figures from hunting, fowling and fishing as parallel to the arts of the meretrix, are very frequent, and are developed at unusual length.’ There was undoubtedly a realistic side to all of this metaphorical hunting. ‘The lover is a fish to be baked, as long he has juice in him’, says the bawd at Plautus, Asinaria 177, and one needs little imagination to realize what plays can be made on such a theme, and indeed were made at all levels throughout antiquity. (shrink)

It is argued that there is no simple or single reason for the riots caused by pantomimes in early imperial Rome, and especially in 14 and 15 A.D. Theatrical passion has been suggested as the main cause, but other factors must be considered: the meaning of the theater as a symbol of order, the peculiar importance of the equestrian order in the architecture of the theater; the position of the main Roman theaters in their relation to the exercise grounds of (...) the iuvenes; the complex relationships of the equestrian iuvenes with the pantomime artists. It is pointed out that it is not always easy to define a pantomime, or to know the nature of the program; but competition was certainly involved. It is argued that the policies of Tiberius toward the theater and the iuvenes were particularly productive of discontent, which led to repeated legislation to control it. The role of Drusus is probably crucial. A central role is also played by the theater claques, and the acclamations of the equestrians, the theater being their principal venue. Various connections between the equestrian iuvenes and the theater are considered. One key is the physical training of Roman youth, which had become affected by Greek concepts of gymnasium dancing, perhaps under the influence of rhetoric. This in turn made it possible for young Romans to develop quasi-pantomime skills, which they could demonstrate in their iuvenalia. Second, it is suggested that the Baths of Agrippa and their decoration can be seen as an indication of such a change in official policy, and their position next to the theaters is stressed. Third, the personal relations between pantomimes and the nobility is documented, and the importance of the private stage in Rome. Finally, the legislation of the Tabula Larinas is considered, as it affected nobles on the stage or in the arena, and other legal implications of this conflict between the senate and the youth are sketched. (shrink)

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

On approach to competitive situations, affective states (emotions and anxiety) occur through the complex interaction of cognitive antecedents. Researchers have intimated that irrational beliefs might play an important role in the relationship between cognitive appraisals and affective states, but has ignored challenge and threat. In the current research, we examine the interaction between cognitive appraisals, irrational beliefs, and challenge and threat to predict golfers’ pre-competitive affective states. We adopted a cross-sectional atemporal design to examine how golfers approached two different competitive (...) situations: imagined imminent golf competition (phase 1), and actual future golf competition (phase 2). Path analysis revealed how cognitive appraisals, irrational beliefs, and challenge and threat interact to predict affective states among golfers. Serial atemporal multiple mediation analysis indicated that the relationships between cognitive appraisals and affective states were mediated by irrational beliefs and challenge and threat. Further, some differences were revealed between phase 1 and phase 2 in the serial multiple atemporal mediation results with regard to challenge. That is, at phase 1 no significant serial mediation was found for any affective outcomes, but at phase 2 significant serial mediation was found for all affective states, showing that irrational beliefs and challenge serial mediated the associations between cognitive appraisals and affective states. The finding that mediation and bivariate associations differed across phase 1 and phase 2 is echoed in the phase 1-phase 2 tests of differences. The current research makes a theoretical advancement by elucidating in more detail the complex interaction between cognitive antecedents and mediators of affective states. Specifically, the inclusion of challenge and threat alongside irrational beliefs and cognitive appraisals is an important theoretical advancement that builds on work inside of sport literature (e.g., Dixon et al., 2016) and outside of sport literature (e.g., David et al., 2002; 2005), as this constellation of theoretically related antecedents of affective states has not been examined together in the extant research. (shrink)

Through clear explanation of its characteristic concepts and doctrines, and paying close attention to the published works of its philosophers, the volume ...

Inleidend studieboek op universitair niveau over de Nederlandse rechtswetenschap.

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)

This is an English translation of Schelling's Ideas for a Philosophy of Nature (first published in 1797 and revised in 1803), one of the most significant works in the German tradition of philosophy of nature and early nineteenth-century philosophy of science. It stands in opposition to the Newtonian picture of matter as constituted by inert, impenetrable particles, and argues instead for matter as an equilibrium of active forces that engage in dynamic polar opposition to one another. In the revisions of (...) 1803 Schelling incorporated this dialectical view into a neo-Platonic conception of an original unity divided upon itself. The text is of more than simply historical interest: its daring and original vision of nature, philosophy, and empirical science will prove absorbing reading for all philosophers concerned with post-Kantian German idealism, for scholars of German Romanticism, and for historians of science. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.

A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈,F〉, whereis an algebra of the appropriate type, andFa subset of the domain of, called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logicE, which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, (...) wherenow is a modal algebra, andFis a filter of. If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jónsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10].The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general. (shrink)

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.

The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...) Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations. (shrink)

W. J. Mander presents the first ever synoptic history of British Idealism, the school of thought which dominated English-language philosophy from the 1860s to the early 20th century. He restores to its proper place this neglected period of philosophy, introducing the exponents of Idealism and explaining its distinctive concepts and doctrines.