Lorenzen, in his book Einführung in die operative Logik und Mathematik has given a relatively precise form of syntactical system which he calls a calculus. The present paper deals with the relationship of Lorenzen's notion of calculus with the notion of formal system . It is shown that the obs of a formal system can be represented as the theses of a calculus of a certain type just when the calculus has a property called the tectonic property, and conditions are (...) given under which one form of system can be transformed into the other.ZusammenfassungLorenzen hat in seinem Buch, Einführung in die operative Logik und Mathematik, eine ziemlich genaue Auffassung eines syntaktischen Systems angegeben, die er Kalkül nennt. Die vorliegende Abhandlung betrifft die Verwandtschaft dieses Lorenzenschen Begriffs mit dem eines formalen Systems . Es wird bewiesen, dass die « Obs » eines formalen Systems sich als die Thesen eines passenden Kalküls genau dann repräsentieren lassen, wenn dieser Kalkül eine gewisse Eigenschaft, die « tectonic property » heisst, besitzt; die Bedingungen für die Überführung einer Art von System in die andere werden aufgezeigt.RésuméLorenzen, dans son livre Einführung in die operative Logik und Mathematik, a exposé une forme assez précise de systéme syntaxique qu'il a appelée un calcul. L'article actuel traite les relations entre cette idée et celle d'un système formel . L'auteur dèmontre que les « obs » d'un système formel peuvent se représenter comme les thèses d'un calcul d'une certaine espèce justement quand le calcul a une propriété que l'on appelle « the tectonic property »; et it énonce des conditions pour qu'un type de système soit transformable en l'autre. (shrink)

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 new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is (...) of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures. (shrink)

[opening paragraph]: Buddhist inquiry into the natural world proceeds from a radically different point of departure than western science, and its methods differ correspondingly. Early pioneers of the scientific revolution, including Copernicus, Kepler, and Galileo, expressed an initial interest in the nature of physical objects most far removed from human subjectivity: such issues as the relative motions of the sun and earth, the surface of the moon, and the revolutions of the planets. And a central principle of scientific naturalism is (...) the pure objectification of the natural world, free of any contamination of subjectivity. This principle of objectivism demands that science deals with empirical facts testable by empirical methods entailing testability by third-person means; and such facts must, therefore, be public rather than private, which is to say, they must be accessible to more than one observer. (shrink)