Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.

In this book we study the concepts of Fuzzy Cognitive Maps and their Neutrosophic analogue, the Neutrosophic Cognitive Maps.

In this book the notion of MOD functions are defined on MOD planes. This new concept of MOD functions behaves in a very different way. Even very simple functions like y = nx has several zeros in MOD planes where as they are nice single line graphs with only (0, 0) as the only zero. Further polynomials in MOD planes do not in general follows the usual or classical laws of differentiation or integration.

A new dimension is given to modulo theory by defining MOD planes. In this book, the authors consolidate the entire four quadrant plane into a single quadrant plane defined as the MOD planes. MOD planes can be transformed to infinite plane and vice versa. Several innovative results in this direction are obtained. This paradigm shift will certainly lead to new discoveries.

In this book the notion of semigroups under + is constructed using: the MOD natural neutrosophic integers, or MOD natural neutrosophic-neutrosophic numbers, or MOD natural neutrosophic finite complex modulo integer, or MOD natural neutrosophic dual number integers, or MOD natural neutrosophic special dual like number, or MOD natural neutrosophic special quasi dual numbers.

As I had rejected en bloc references to Bacchanalia as indications of date, it was a mere chance which led me, after the above had left my hands, to look up Cas. 980 ‘ nunc Bacchae nullae ludunt,’ quoted in Schanz, R. Lit.3, p. 78. As this affords an excellent opportunity of testing my conclusions, perhaps a word or two will not be out of place.

Beardsley's exposition of his large subject shows lucidity, objectivity, deftness, and a good sense of proportion; and these virtues become more apparent the closer his history approaches the complex diversity of contemporary aesthetic speculation. Especially skillful are the succinct accounts of those aspects of each philosopher's thought which, though not directly concerned with aesthetics, are necessary for a full understanding of his aesthetic theories. Beardsley himself remains neutral, arguing neither for nor against the theories he analyzes. Some may feel that (...) the visual arts are slighted, but this is a minor criticism of a very informative and illuminating book.—W. B. K. (shrink)

These essays were originally presented at the first of an annual series of seminars in the humanities at John Hopkins. To avoid imposing an artificial unity on the subject, the contributors were deliberately left unguided in their choice of subject and method. The result of this policy is a rich and stimulating collection ranging from gardens to musicology. Reproductions of paintings and copious printings of musical scores show that no expense was spared to make the book as useful as possible. (...) Of greatest interest to philosophers are George Boas's witty demolition of "the age of reason" as a description for the period, J. A. Passmore on "the malleability of man," Isaiah Berlin's long reconsideration of Herder, Alfred Cobban on "the Enlightenment and the French Revolution," and Henry Guerlac on Newton's place in intellectual history.—W. B. K. (shrink)

Designed to complement the editors' earlier selection, The Social and Political Philosophy of Jacques Maritain, this book arranges its material in six sections: theory of knowledge, metaphysics, ethics, esthetics, politics, and philosophy of history, with the editors contributing a one-page or two-page introduction to each section. The texts, taken from some fifteen of Maritain's works and in some cases published for the first time in English, are well chosen and interesting in themselves, but are too brief to present fully developed (...) arguments. This raises the question of the audience being aimed at. The book is not coherent enough to serve as a serious introduction to Maritain or to modern Thomism; it is rather a "sampler," and might be most useful as a kind of bedside book for those already acquainted with Maritain.--W. B. K. (shrink)

Allen begins with a general survey of "atheism and atheists" in the Renaissance, gives brief sketches of six individual "atheists"—Pomponazzi, Cardano, Vanini, Montaigne, Charron, Bodin—devotes chapters to rational theology against atheism and to reason and immorality, and closes with a portrait of the "atheist redeemed" in the person of the Earl of Rochester, the arch-rake of the Restoration who was converted during his final illness. He points out that during this period "atheist" usually meant no more than a person whose (...) theology did not agree fully with that of the name-caller, and that none of the thinkers he mentions merited the term in any strict sense. The book is a wide-ranging, erudite survey without much attempt at either analysis in depth or synthesis, but Allen's somewhat Voltairean point of view helps give it form.—W. B. K. (shrink)

Although the essays in this book vary a good deal in quality, they all distort the eighteenth century to some extent by concentrating on its "modernity," about the scope of which, to increase the confusion, none of the authors is very explicit. One essay treats the emergence of scientific thought quite superficially; another presents Jacobi as an anti-type of Goethe and a fore-runner of existentialism. Herbert Dieckmann argues against the common "from classic to romantic" view of eighteenth-century aesthetic history. Ernest (...) Mossner characterizes "the enlightenment of David Hume," seeing him as a liberator of the mind from its various idols and reiterating his view that Hume was only a "mitigated sceptic." Dietrich Ritschl emphasizes Semler's contribution to the historical study of the Bible; his essay also contains, but only implicitly, some warnings for today's aggiornamento theologians.—W. B. K. (shrink)

Father Etcheverry examines four varieties of humanism: rationalist-idealist, existentialist, Marxist, and Christian. For each of the first three varieties he centers his analysis on one or two individuals: Leon Brunschvicg, Sartre and Camus, and Marx and Engels respectively. He writes as a committed Christian humanist, arguing that only a relationship with God enables man to become truly man. All other varieties of humanism prevent this full development by raising to absolute status one or another of man's essential properties—reason, liberty, matter, (...) sociability, etc.—and subordinating him too exclusively to that property alone.—W. B. K. (shrink)

"The drama Nietzsche has written is for the future Greeks." This somber note is the tonic both for the major and minor elements of Alderman’s Nietzsche’s Gift. The "drama" refers to Also Sprach Zarathustra, the central text in Alderman’s interpretation. The intention of placing Nietzsche centrally in the stream of philosophic creation is the minor theme.

The late Jacob Klein’s important book is, remarkably, a lucid presentation of esoteric argument. Dealing with the famed Platonic triad, Theaetetus, Sophist, and Statesman, Klein settles the dispute about the missing dialogue, "The Philosopher," by first denying that it is missing and second showing that it is unnecessary. He argues, in short, that the triad is a dyad. That argument is reinforced by the distinction Klein strongly implies between the Socratic Theaetetus and the Eleatic Sophist and Statesman. "We can now (...) understand why the conversations of the ‘trilogy’ occur in two, not three, days and why the Sophist, the Statesman, and the Philosopher are dealt with in two, not three, dialogues". (shrink)

This historical study of the responses that man has tried to give to the problem of death-"If I must some day die, what can I do to satisfy my desire to live?" as defined by Fr. Dunne—is occasionally turgid but more often provocative and enlightening. From the dawn of history in Mesopotamia to the present, the book investigates the political and literary consequences of different answers to this question and of different attitudes toward death in general. Although the book's organization (...) is chronological, it is explicitly oriented to contemporary concerns, with Nietzsche's statement that "God is dead" serving as a unifying leit-motif. The most rewarding sections are the discussions of Homer's epics and the analysis of the confusions between the right to life and the right over life that are traced from Calvin, Luther, Hobbes, and Rousseau to modern totalitarianism.—W. B. K. (shrink)

Margolis's main concern is to clarify aesthetic terminology, and especially to distinguish between normative and descriptive uses of such terms as "taste" and "aesthetic." His own definition of a work of art, however, "an artifact considered with respect to its design," hardly improves on the definitions he criticizes. Some of the problems he discusses can be seen as versions of the One and the Many: e.g., the relation between a symphony and its different performances or between a poem and the (...) different interpretations it gives rise to. Among the more interesting chapters are those on figurative language and on "truth and reference in fiction."—W. B. K. (shrink)

West takes his title from Camus, and quotes Camus' definition of absurdity: "the division between the mind that desires and the world that disappoints." The essays, which originally appeared in periodicals, discuss Yeats, Lawrence, Sartre, Camus, Simon Weil, Graham Greene, Santayana, and other modern writers. There is no analysis, either philosophical or literary; West attempts overall estimates of each writer's contribution to the problem of absurdity, but succeeds in providing neither insights for those already familiar with the problem nor useful (...) introductions for the uninitiated. Nor, despite the expectations aroused by the preface, do we get a very strong impression of an individual's encounter with the thinkers from whom he has learned most. In vino vacuitas.—W. B. K. (shrink)