The aim of this paper is to investigate the variety of symmetric closure algebras, that is, closure algebras endowed with a De Morgan operator. Some general properties are derived. Particularly, the lattice of subvarieties of the subvariety of monadic symmetric algebras is described and an equational basis for each subvariety is given.

In this paper we prove that the free pseudocomplemented residuated lattices are decomposable if and only if they are Stone, i.e., if and only if they satisfy the identity ¬ x ∨ ¬¬ x = 1. Some applications are given.

In this paper we study some questions concerning Łukasiewicz implication algebras. In particular, we show that every subquasivariety of Łukasiewicz implication algebras is, in fact, a variety. We also derive some characterizations of congruence permutable algebras. The starting point for these results is a representation of finite Łukasiewicz implication algebras as upwardly-closed subsets in direct products of MV-chains.

A clearly written book by an accomplished teacher. Though obviously published as a textbook, it contains a kind of learning which can only be possessed by a mature philosopher, and perhaps appreciated in full only by a peer. The book is an introduction to philosophy, philosophy broadly and classically conceived, encompassing metaphysics, a theory of knowledge, and philosophical reflections on science, man, nature, and art. The ten chapters devoted to knowledge present to the beginner, simply and lucidly, a review of (...) some of the best work published in the fields of epistemology and the philosophy of science in recent decades. Abel’s approach is both systematic and historical. He allows philosophers to speak to each other across the ages where they have addressed common problems, but the focus is on the problems. His own viewpoint has obviously been shaped by the naturalism of Dewey and Woodbridge, but the book has the merit of being temperate and fair to other fundamentally different metaphysical positions. Throughout his presentation, the philosophical enterprise is seen, not as a critical one of tearing down, but as a collaborative effort in which the best minds of the past, through their various insights, have contributed to the solution of ancient problems relating to man and knowledge. In effect, the book is a refreshing synthesis, and is apt to be far more valuable as a teaching instrument than the usual heterogeneous anthology published for the same purpose.—J.P.D. (shrink)

Four previously unpublished chapters by Jacob Viner. The first two deal with the economic doctrines of the Christian Fathers and the Scholastics; the last two are each concerned with a particular aspect of the relationship between religious thought, economic ethics, and society. Initially conceived as part of a larger study on "Religion and Society," this volume holds some interest for the philosopher of religion because it examines the treatment by Christian theologians, both Protestant and Catholic, of topics such as private (...) property, riches and poverty, commerce, just price and economic motivation. Viner explores the roles of early Protestant theology in the rise of capitalism, with special reference to the Weber-Tawney thesis which attributes significant responsibility to Calvinist doctrine for the growth and the character of modern capitalism. The chapters on Patristic and Scholastic economic thought are particularly strong. There is a detailed examination of the economic views of Thomas Aquinas, though the author is aware that Aquinas’s influence was not a dominant one before the sixteenth century. In the final chapter Viner amasses considerable historical evidence to construct a case against Weber and his followers. In the first three chapters, Viner appears to have been partly inspired by a desire to correct the false impressions of some earlier and less friendly commentators on Catholic economic thought. Throughout, documentation is extensive. There is a rich bibliography.—J.P.D. (shrink)

This pamphlet contains essays by Will Herberg, C. Herman Pritchett, David Fellman, Valerie Earle and Sidney Hook on the principle of academic freedom, its implications, and its recognition by the courts. Will Herberg in the opening essay argues that the greatest threat to academic freedom is the politicization of the university, the pressure to convert the university into an agency of social and political action. Unless the university is thoroughly depoliticized and rededicated exclusively to the cause of learning and scholarship, (...) warns Herberg, it will be destroyed. C. H. Pritchett provides a useful summary of nearly all the Supreme Court's decisions bearing in some way on the academic freedom of teachers. Sidney Hook maintains that the Supreme Court has failed to make certain basic distinctions in its opinions, i.e., between the obligations of public employees and employees in private institutions; between those in professions of public trust and those who are not; and between membership in highly disciplined organizations with purposes antithetical to democratic values and membership in others which are broad in purpose and loosely bound together. From an analysis of the opinions of the Supreme Court and the nature and defense of academic freedom, Hook concludes that the court is a very uncertain protector and guide. In matters of professional ethics, it is the faculties themselves which must uphold and enforce standards of professional integrity. Their failure to do so has led to unnecessary and unwise legislative intervention. Recent events on many college and university campuses, and in particular the increasing resort to civil courts to adjudicate what are basically professional disputes, have emphasized the need for the type of discussion contained in this brief volume.--J. P. D. (shrink)

One does not need to read many pages of this very rich book to realize that it is the fruit of a lifetime of study and that it is both speculatively wise and prudent. Though it may not receive the same degree of attention as other well publicized studies it clearly ranks with studies such as Hart's The Concept of Law and Erlich's The Sociology of Law. The author intends to develop a systematic theory of positive law, with close attention (...) to the circumstances that bring law into being, the purposes that law is designed to serve, and the structure of the legal system itself. He also proposes to apply this theory to an examination of the problems that law faces and the conditions that it must satisfy if it is to be an effective force in society. Nineteen chapters follow. Jenkins is aware that the study of law is but part of the larger study of society from which law receives its tasks and form. To determine the origin, end and functions of law is to search for those objective principles that define the conditions of man's well-being. While the first part of the book is concerned with the formulation of a general theory of law, the second explores the role of law in the social order and the conditions of legal effectiveness. Jenkins provides dramatic evidence that in our day, particularly in the United States, law is being employed for purposes that are unprecedented. "The legal apparatus," he writes, "is being asked to intervene in areas of social and personal life that have hitherto been handled by other agencies in other ways." It is the author's judgment that these nontraditional uses of law have for the most part been disappointing in their results. "We abuse the legal apparatus," writes Jenkins "because we have inadequate notions both of what the law is and how it works." Jenkins is convinced that law supplies the compelling social need for a force that is at once sovereign and principled. As sovereign it is entitled to habitual obedience and to the use of force when necessary. As sovereign, subject to no external control, it must be principled. It must govern itself by self-imposed provisions and mechanisms that determine the use of this power and prevent it from becoming autocratic and arbitrary. (shrink)

The Indiana Court of Appeals, in JKB, Sr. v. Armour Pharmaceutical Co. ), held that the state's Blood Shield Act does not protect pharmaceutical companies that produce blood-derived products from product liability suits based on injuries attributable to tainted blood supplies. Blood shield statutes help to guarantee adequate blood supplies by limiting the liability of blood banks. This holding limits the defenses available to pharmaceutical companies sued under product liability theory.The defendant, Armour Pharmaceutical, produces and sells clotting factor agents, which (...) are derived through plasmapheresis. Plasmapheresis is a costly and complex donation process through which the plasma and red blood cells of a donor's blood are separated. After separation, the process returns the red blood cells to the donor but retains the plasma. (shrink)

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (...) (Q 3 ) of the variety Q 3. (shrink)

This paper is devoted to the study of some subvarieties of the variety Q of Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q subscript 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Q is far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q subscript 3 and we construct (...) the lattice of subvarieties lambda (Q subscript 3) of the variety Q subscript 3. (shrink)

Onderwerp en gezegde, door D. M. Bakker.--Enkele opmerkingen over het Godsbegrip van Justinus Martyr, door J. den Boeft.--Heidegger, Descartes, Luther, door J. van der Hoeven.--"Geschichtlichkeit" bij Carl Friedrich von Weizsäcker, door G. Horsman.--Menselijke ontmaskering en Bijbels démasqué , door R. Huson.--Kleine geschiedenis van het begrip "niets" in de antieke wijsbegeerte (tot e met de Sofisten en Plato), door P. A. Meijer.--De structuur van opvoeden en opvoedkunde, door J. W. Mojet.--Individualiteit in de fysica, door M. D. (...) Stafleu. (shrink)

Here is a deft and new introduction to Gentzen proof techniques in axiom systems and to the analysis of formal axiom systems; in short, axiomatics inside and out. Treating of deduction in propositional and predicate logic, metatheoretical problems about both set theory and its paradoxes, the book is flexibly structured for selective use as a text. Yet the discussion is unified and motivated by the concept of the axiomatic system--the history of its use and analysis, and its present practical and (...) theoretical status. Well-chosen illustrations convey an historical overview of Euclid, non-Euclidean geometers, Peano, Boole, Hilbert and Gödel.--P. D. J. (shrink)

An exposition of the views of literary critics of present day influence, presented to illustrate the thesis that the study of the humanities guided by a traditional mode of analysis, fails to encourage and produce the methodological habits and styles of thought needed by the citizen to understand social and political problems. Lane--a political scientist--proposes that the teaching of the humanities would contribute to the development of democratic citizenship if it were recognized that there is no logical or methodological difference (...) between the sciences and the humanities.--P. D. J. (shrink)

In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic ℓ -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ℓ -groups with strong unit. Some applications are given thereof.

There is a constructive method to define a structure of simple k -cyclic Post algebra of order p , L p , k , on a given finite field F ( p k ), and conversely. There exists an interpretation Φ 1 of the variety $${\mathcal{V}(L_{p,k})}$$ generated by L p , k into the variety $${\mathcal{V}(F(p^k))}$$ generated by F ( p k ) and an interpretation Φ 2 of $${\mathcal{V}(F(p^k))}$$ into $${\mathcal{V}(L_{p,k})}$$ such that Φ 2 Φ 1 ( B ) (...) = B for every $${B \in \mathcal{V}(L_{p,k})}$$ and Φ 1 Φ 2 ( R ) = R for every $${R \in \mathcal{V}(F(p^k))}$$. In this paper we show how we can solve an algebraic system of equations over an arbitrary cyclic Post algebra of order p, p prime, using the above interpretation, Gröbner bases and algorithms programmed in Maple. (shrink)