In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked (...) in Rautenberg [10]. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.2 (2002) 432-442 [Access article in PDF] The Legacy of the Enlightenment James Schmidt What's Left of Enlightenment? A Postmodern Question, edited by Keith Michael Baker and Peter Hanns Reill; ix & 203 pp. Stanford, California: Stanford University Press, $45.00 cloth, $19.95 paper. Postmodernism and the Enlightenment: New Perspectives in Eighteenth-Century French Intellectual History, edited by Daniel Gordon; vi & 227 pp. New York: Routledge, 2001, (...) $80.00 cloth, $22.95 paper. IF THE ENLIGHTENMENT did not exist, postmodernists would have had to invent it. It performs the same function, Daniel Gordon argues in his introduction to Postmodernism and the Enlightenment, that the Ancien Regime did for the French revolutionaries: as the "other of postmodernism," it represents "the modern that postmodernism revolts against" (P&E, p. 1). Indeed, the image of the Enlightenment that emerges from the postmodern critique does seem, in large part, to be an invention. As Keith Michael Baker and Peter Hanns Reill suggest in the introduction to their collection What's Left of Enlightenment? the various strands of thought commonly grouped under the label postmodernism "have at least one thing in common": "they all depend upon a stereotyped, even caricatural, account of the Enlightenment" which sees the Enlightenment as the point of origin for the "rationalism, instrumentalism, scientism, logocentrism, universalism, abstract rights, eurocentrism, individualism, humanism, masculinism, etc." that [End Page 432] defines the modernity which postmodernity hopes to supersede (WLE? p. 1).One consequence of the inclination to trace the origin of the various failings of modernity to the Enlightenment is that arguments about the "legacy of the Enlightenment" tend to get out of hand. In a particularly sharp-sighted contribution to the Baker and Reill collection David Hollinger notes that it is all too easy for a critic of Enlightenment to argue that "I'm hot stuff because I'm not only refuting you, my puny opponent, but... every great thinker from Descartes to Popper," and, conversely, all too enticing for those who have been criticized to counter, "watch out, you think you are arguing only against me, but the implications of your reasoning are to deny the common sense of every humane and rational mind since the seventeenth century" (WLE? p. 9). Historians of the eighteenth century have been curiously reluctant to join this battle and have, for the most part, left the field to philosophers, literary scholars, and political theorists (WLE? pp. 17-18; P&E, p. 3). The intent of the two collections reviewed here is to remedy this situation by setting a group of historians to work scrutinizing differing aspects of the postmodernist critique of the Enlightenment. More often than not, the results are quite rewarding, though the question of the relationship between postmodernism and the Enlightenment remains, in the end, somewhat ambiguous.The scope of these two volumes is quite impressive. Baker and Reill's collection opens with essays by David Hollinger and Richard Rorty (one of the two nonhistorians invited to the festivities) offering contrasting characterizations of the relationship of postmodernism and the Enlightenment. It continues with a discussion of a few important interpretations of the Enlightenment (including articles by Jonathan Knudsen on German historicism, Hans Sluga on Heidegger, Johnson Kent Wright on Cassirer, and Michael Meranze on Foucault) and concludes with essays by Lorraine Daston ("Enlightenment Fears, Fears of Enlightenment"), Dena Goodman (on gender difference in the Enlightenment), and Lawrence Klein (on the idea of "conversation" in the Enlightenment) that seek, in differing ways, to reveal "the existence within the Enlightenment of elements frequently seen as characteristic of Postmodernity itself" (WLE? p. 3).Gordon's volume offers a counterpoint to the final part of Baker and Reill's collection: each of its nine essays is intended as confrontation between a postmodernist characterization of a particular aspect of the Enlightenment and an account of "how the theme really operates in [End Page 433] Enlightenment thought" (P&E, p. 5). Thus Malick W. Ghachem examines how Montesquieu's account of law was applied to French colonies in the Caribbean, Arthur Goldhammer discusses Diderot's view of language, Daniel Rosenberg... (shrink)