The Enlightenment was the age in which the world became modern, challenging tradition in favor of reason, freedom, and critical inquiry. While many aspects of the Enlightenment have been rigorously scrutinized—its origins and motivations, its principal characters and defining features, its legacy and modern relevance—the geographical dimensions of the era have until now largely been ignored. Placing the Enlightenment contends that the Age of Reason was not only a period of pioneering geographical investigation but also an age with spatial dimensions (...) to its content and concerns. Investigating the role space and location played in the creation and reception of Enlightenment ideas, Charles W. J. Withers draws from the fields of art, science, history, geography, politics, and religion to explore the legacies of Enlightenment national identity, navigation, discovery, and knowledge. Ultimately, geography is revealed to be the source of much of the raw material from which philosophers fashioned theories of the human condition. Lavishly illustrated and engagingly written, Placing the Enlightenment will interest Enlightenment specialists from across the disciplines as well as any scholar curious about the role geography has played in the making of the modern world. (shrink)

F. H. Bradley did not write extensively or systematically on the philosophy of religion, and much of what he did write has the character of either tentative speculation or the pre-emptive rebuttal of potential misinterpretations that might threaten his general philosophical position. ‘I admit that on this subject I never had much to say’ he warns. But such a remark should not discourage us from considering his views on this topic, since the disclaimer is typically Bradleian, and more reflective of (...) his high standards for what is required in order to claim to have something to say about some matter than of any genuine lack of opinion. On closer inspection we find that he has, scattered throughout his work, a great many important things to say about this subject. (shrink)

W. J. Mander presents a history of metaphysics in nineteenth-century Britain. He traces the story of the development and interplay of three great schools of thought, the agnostics, the empiricists, and the idealists, and their different responses to the idea of an ultimate but unknowable way that things really are in themselves.

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.

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)

What precisely, W. J. T. Mitchell asks, are pictures (and theories of pictures) doing now, in the late twentieth century, when the power of the visual is said to be greater than ever before, and the "pictorial turn" supplants the "linguistic turn" in the study of culture? This book by one of America's leading theorists of visual representation offers a rich account of the interplay between the visible and the readable across culture, from literature to visual art to the mass (...) media. (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)

"[Mitchell] undertakes to explore the nature of images by comparing them with words, or, more precisely, by looking at them from the viewpoint of verbal language.... The most lucid exposition of the subject I have ever read."—Rudolf Arnheim, _Times Literary Supplement_.

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)

Although the notion of spatiality has always lurked in the background of discussions of literary form, the self-conscious use of the term as a critical concept is generally traced to Joseph Frank's seminal essay of 1945, "Spatial Form in Modern Literature."1 Frank's basic argument is that modernist literary works are "spatial" insofar as they replace history and narrative sequence with a sense of mythic simultaneity and disrupt the normal continuities of English prose with disjunctive syntactic arrangements. This argument has been (...) attacked on several fronts. An almost universal objection is that spatial form is a "mere metaphor" which has been given misplaced concreteness and that it denies the essentially temporal nature of literature. Some critics will concede that the metaphor contains a half-truth, but one which is likely to distract attention from more important features of the reading experience. The most polemical attacks have come from those who regard spatial form as an actual, but highly regrettable, characteristic of modern literature and who have linked it with antihistorical and even fascist ideologies.2 Advocates of Frank's position, on the other hand, have generally been content to extrapolate his premises rather than criticize them, and have compiled an ever-mounting list of modernist texts which can be seen, in some sense, as "antitemporal." The whole debate can best be advanced, in my view, not by some patchwork compromise among the conflicting claims but by a radical, even outrageous statement of the basic hypothesis in its most general form. I propose, therefore, that far from being a unique phenomenon of some modern literature, and far from being restricted to the features which Frank identifies in those works , spatial form is a crucial aspect of the experience and interpretation of literature in all ages and cultures. The burden of proof, in other words, is not on Frank to show that some works have spatial form but on his critics to provide an example of any work that does not. · 1. Frank's essay first appeared in Sewanee Review 53 and was revised in his The Widening Gyre . Frank's basic argument has not changed essentially even in his most avante-garde statements; he still regards spatial form "as a particular phenomenon of modern avante-garde writing." See "Spatial Form: An Answer to Critics," Critical Inquiry 4 : 231-52. A useful bibliography, "Space and Spatial Form in Narrative," is being complied by Jeffrey Smitten .· 2. This charge generally links the notion of spatial form with Wyndham Lewis and Ezra Pound, the imagist movement, the "irrationality" and pessimistic antihistoricism of modernism, and the conservative Romantic tradition. Frank discusses the complex motives behind these associations in the work of Robert Weimann and Frank Kermode in his "Answer to Critics," pp. 238-48. W. J. T. Mitchell, editor of Critical Inquiry, is the author of Blake's Composite Art, and The Last Dinosaur Book: The Life and Times of a Cultural Icon. The present essay is part of Iconology: The Image in Literature and the Visual Arts. "Diagrammatology" appeared in the Spring 1981 issue of Critical Inquiry. Leon Surette responds to the current essay in "‘Rational Form in Literature’". (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.