"First published by Oxford University Press, 1916."--Title page verso.

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers.

"Bibliographical notes": pages [243]-244.

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)

It is often said to-day that mathematics is nothing but an extension or development of logic; indeed, the identity of logic and pure mathematics is alleged so confidently by persons whose mathematical attainments entitle them to consideration when they talk about the subject-matter of mathematics, as to be in danger of being ranked with the truths that an educated man should accept on the authority of the specialist. Yet a little reflection might at least make one hesitate. For whatever else (...) may be said about logic, it is generally allowed to study thinking. Some would say merely that it studies inference; but inference is thinking. Now the mathematician thinks and infers, but he does not study the activity of thinking and inferring; and a study of that activity would never make the discoveries credited to the mathematicians. (shrink)

(1983). The illustrations of birds in the Vatican manuscript of De arte venandi cum avibus of Frederick II. Annals of Science: Vol. 40, No. 6, pp. 597-634.

Principled discussions of civil rights became inherently less likely as a direct result of the observation by Earl Warren, in Brown v. Board of Education, that, respecting freedmen, “Education of Negroes was almost non-existent, and practically all of the race were illiterate,” and in proportion as that observation increasingly became the foundation of common opinion on the subject. Warren's observation was not true in any meaningful or non-trivial sense. Nevertheless, it served to perpetuate the myth of a backward people needing (...) help to catch up instead of the truth of a people being held back. That is the perspective – the disadvantaged group perspective – that ultimately infected all discussion of civil rights, even after the designation of so-called “disadvantaged groups” had been extended beyond American blacks. To define civil rights, we may well begin with what all mankind would likely recognize. Thus the dictionary definition of “civil rights” stands: “the rights that belong to all individuals in a nation or community touching property, marriage, and the like.” In that definition the term “rights” may be further expanded to mean “legitimate claims,” following the definition of right as law – as “a claim or title or interest in anything whatever that is enforceable by law.” This definition applies with minimal distinction of regimes intruding and, therefore, without the host of recent complications in the United States that create the impression that civil rights have something to do with pluralism. Previously, the generic definition was thought to exhaust the meaning of the term in the United States. (shrink)

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. This book introduces the concept of fuzzy super matrices and operations on them. The author has provided only those operations on fuzzy supermatrices that are essential for developing super fuzzy multi expert models. This book will be highly useful to social scientists who wish to (...) work with multi expert models. (shrink)