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)

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)

Managing ethical behavior is a one of the most pervasive and complex problems facing business organizations today. Employees' decisions to behave ethically or unethically are influenced by a myriad of individual and situational factors. Background, personality, decision history, managerial philosophy, and reinforcement are but a few of the factors which have been identified by researchers as determinants of employees' behavior when faced with ethical dilemmas. The literature related to ethical behavior is reviewed in this article, and a model for understanding (...) ethical behavior in business organizations is proposed. It is concluded that managing ethics in business organizations requires that managers engage in a concentrated effort which involves espousing ethics, behaving ethically, developing screening mechanisms, providing ethical training, creating ethics units and reinforcing ethical behavior. (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.

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)

In this article, I am concerned with the relationship between the visibility of race as color, the memory of injustice, and American identity. The visibility of color would seem to make it a daily reminder of race and its history, and in this way to be intimately a part of American memory and identity. Yet the tie between memory and color is anything but certain or transparent. Rather, as I shall argue, it is a latticework composed of things remembered, forgotten, (...) glossed, or idealized, and the traces they leave in our world, traces that keep that past from falling into the oblivion of forgetfulness. Finally, color, memory, and identity together belong to the struggle over racial justice in this country, a battle in part to recognize the past, of which color is the visible reminder, and to fashion an American identity that does not seek to render it invisible. Ralph Ellison's writings on memory and race, and particularly his defining work, the Invisible Man, map these issues and some of the ways of approaching them. The present essay is an exploration of those issues, conducted through an engagement with his work. (shrink)

In this study of how we know what we know, W. Jay Wood surveys current views of foundationalism, epistemic justification and reliabilism.

I defend an alternative to the two traditional accounts of the relationship between metacognition and social cognition: metacognition as primary versus social cognition as primary. These accounts have complementary explanatory vices and virtues. They also share a natural assumption: that interpretation in terms of mental states is “spectatorial”, aiming exclusively for an objective description of the mental facts about self and others. I argue that if one rejects this assumption in favor of the view that interpretation in terms of mental (...) states also plays important regulative roles with respect to minds and behavior, a new and superior conception of the relationship between metacognition and social cognition comes into view. On this conception, person-level metacognitive concepts are socio-cognitive tools that shape us into better cognitive agents and more predictable cognitive objects, thereby enhancing our abilities at social coordination. Mastery of these metacognitive concepts relies on subpersonal, non-conceptual, procedural metacognition. This reconceptualization of the relationship between metacognition and social cognition combines the complementary explanatory virtues of the two traditional conceptions, while avoiding their complementary explanatory vices. (shrink)

The veiled recession frame has served several times in the literature to provide examples of modal logics failing to have certain desirable properties. Makinson [4] was the first to use it in his presentation of a modal logic without the finite model property. Thomason [5] constructed a (rather complicated) logic whose Kripke frames have an accessibility relation which is reflexive and transitive, but which is satisfied by the (non-transitive) veiled recession frame, and hence incomplete. In Van Benthem [2] the frame (...) was an essential tool to find simple examples of incomplete logics, axiomatized by a formula in two proposition letters of degree 2, or by a formula in one proposition letter of degree 4 (the degree of a modal formula is the maximal number of nested occurrences of the necessity operator in ). In [3] we showed that the modal logic determined by the veiled recession frame is incomplete, and besides that, is an immediate predecessor of classical logic (or, more precisely, the modal logic axiomatized by the formula pp), and hence is a logic, maximal among the incomplete ones. Considering the importance of the modal logic determined by the veiled recession frame, it seems worthwhile to ask for an axiomatization, and in particular, to answer the question if it is finitely axiomatizable. In the present paper we find a finite axiomatization of the logic, and in fact, a rather simple one consisting of formulas in at most two proposition letters and of degree at most three. (shrink)

In this essay we discuss Tarski's work on what he calledthe methodology of the deductive sciences, or more briefly, borrowing the terminology of Hilbert,metamathematics, The clearest statement of Tarski's views on this subject can be found in his textbookIntroduction to logic[41m].1Here he describes the tasks of metamathematics as “the detailed analysis and critical evaluation of the fundamental principles that are applied in the construction of logic and mathematics”. He goes on to describe what these fundamental principles are: All the expressions (...) of the discipline under consideration must be defined in terms of a small group of primitive expressions that seem immediately understandable. Furthermore, only those statements of the discipline are accepted as valid that can be deduced by precisely defined and universally accepted means from a small set of axioms whose validity seems evident. The method of constructing a discipline in strict accordance with these principles is known as thedeductive method, and the disciplines constructed in this manner are calleddeductive systems. Since contemporary mathematical logic is one of those disciplines that are subject to these principles, it itself is a deductive science. Tarski then goes on to say:“The view has become more and more common that the deductive method is the only essential feature by means of which the mathematical disciplines can be distinguished from all other sciences; not only is every mathematical discipline a deductive theory, but also, conversely, every deductive theory is a mathematical discipline”.This identification of mathematics with the deductive sciences is in our view one of the distinctive aspects of Tarski's work. Another characteristic feature is his broad view of what constitutes the domain of metamathematical investigations. A clue to this aspect of his work can also be found in Chapter 6 ofIntroduction to logic. After a discussion of the notions of completeness and consistency, he remarks that the investigations concerning these topics were among the most important factors contributing to a considerable extension of the domain of methodological studies, and caused even a fundamental change in the whole character of the methodology of deductive sciences. (shrink)

Early in his career, Karl Marx complained that “Philosophers have hitherto only interpreted the world in various ways; the point is to change it.” Philosophers Robert Frodeman and Adam Briggle have recently issued this same complaint against their contemporaries, arguing that philosophy has become an isolated, “purified” discipline, detached from its historical commitments to virtue and to public engagement. In this paper I argue that they are wrong about contemporary philosophy and about its history. Philosophy hitherto has always been characterized (...) both by a concern with practical engagement and by serious misgivings about such engagement. I show that reluctance to engage with practical affairs was a feature of philosophy long before the advent of the modern university and that a wide range of contemporary philosophers are concerned with virtue and public engagement. Finally, I argue that Frodeman and Briggle’s own account of contemporary philosophy makes it unsuitable both as the subject of their title (“When Philosophy Lost Its Way”) and as the object of their call to action. (shrink)

Although the same environmental regulations apply to all regions in China, legal enforcement can be different due to local economic development priorities. There is still a lack of knowledge about how regional disparities affect the operating performance results of the implementation of corporate environmental management practices, thus providing little information for foreign companies when they invest and develop their production base in China. To fill this research gap, this paper collects data from the Fortune 500 Chinese firms to investigate the (...) moderating role of regional disparities in affecting the performance results of corporate environmental management efforts based on the institutional theory. The disclosed corporate environmental responsibility practices serve as proxy to represent corporate environmental management practices. Content analysis approach was applied to collect and analyze CER practices published in the corporate reports of Chinese manufacturers. The results show that CER has a positive impact on operating income, while regional disparities influence the relationship between CER and corporate operating income. Specifically, CER and operating income are positively related in Eastern China; on the contrary, they are negatively related in Western China. This paper adds to the body of knowledge about environmental discrepancies in the same emerging economy, and provides insights for systematic consideration in terms of the issues of government environmental regulations and corporate environmental strategies. (shrink)

I much appreciate the honour of being invited to deliver the first Manson lecture, which, its founder has laid down, is to be devoted to the consideration of some subject of common interest to philosophy and medicine. I cannot think of anything which better fulfils that condition than the neurological approach to the problem of perception. The neurologist holds the bridge between body and mind. Every day he meets with examples of disordered perception and he learns from observing the effects (...) of lesions produced by disease, or by the physiologist's experiments, something of how the neural basis of perception is organized. It is possible to study perception as though this was largely irrelevant. How far that view is right will be for you to judge when I have finished. (shrink)

This volume of Critical Readings provides an overview of recent scholarship about Japanese thought, as it took shape during the Edo Period. It contains articles about all participants in the intellectual debate: Buddhism, Confucianism, National Studies, and Dutch Learning.

Leonardo Bruni’s well-known oration, the Laudatio Florentinae urbis, has long stood at the center of discussions on the emergence of the modern republican state. Recent historiographical trends have emphasized the degree to which Bruni’s oration represents a propagandistic attempt both to portray Florence as a territorial power of Northern Italy keen to impose its sovereign authority on neighboring polities and as a republic intent on fashioning an image of itself as a popular sovereignty. It is in this second element of (...) Bruni’s oration that we can discover his rhetorical purposes: he needed to give a distorted image of Florence as enjoying “popular” rule precisely because Florence was in fact moving in the opposite direction towards a more oligarchic concentration of political authority. The essay investigates the changes contemplated in revisions to Florence’s juridical codes at precisely the time of the oration’s composition, suggesting that when these two sources are juxtaposed, Bruni’s oration appears as a strongly ideological literary work the rhetorical gestures of which camouflage the actual historical and legal developments of Florence’s political life in the early fifteenth century. (shrink)