This junior/senior level text is devoted to a study of first-order logic and its role in the foundations of mathematics: What is a proof? How can a proof be justified? To what extent can a proof be made a purely mechanical procedure? How much faith can we have in a proof that is so complex that no one can follow it through in a lifetime? The first substantial answers to these questions have only been obtained in this century. The most (...) striking results are contained in Goedel's work: First, it is possible to give a simple set of rules that suffice to carry out all mathematical proofs; but, second, these rules are necessarily incomplete - it is impossible, for example, to prove all true statements of arithmetic. The book begins with an introduction to first-order logic, Goedel's theorem, and model theory. A second part covers extensions of first-order logic and limitations of the formal methods. The book covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem. Fraissé's elementary equivalence, and Lindstroem's theorem on the maximality of first-order logic. (shrink)

This is one of the most important books on quantum mechanics ever written for lay readers, in which an eminent physicist and successful science writer, Heinz Pagels, discusses and explains the core concepts of physics without resorting to complicated mathematics. "Can be read by anyone. I heartily recommend it!" -- New York Times Book Review. 1982 edition.

This contribution to the special issue is an historical account of Paulo Freire’s pedagogical and administrative praxis before his forced exile in 1964. It relies on interviews collected during a field trip in 1976, a conversation with Paulo Freire in Geneva one year later and on the secondary literature up to date. Being the head of the first Extension Service of a major Brazilian university in the early 1960s gave Freire and his collaborators the space and time to experiment with (...) the today world famous literacy method bearing his name. The concept of ‘Field of Cultural Production’ (Bourdieu) is used to elucidate better Freire and his team’s avant-gardist production within the spaces opened up by Brazil’s popular movements in the early sixties. The contribution shows how the ‘Paulo Freire System’ developed in the praxis of a cultural movement and received its academic consecration in an incremental and eclectic style. (shrink)

In Thomas Thomson's System of chemistry of 1802 Bergman and Scheele are actually considered as creators of the analytical concept of an element. With regard to this, a detailed investigation of the work of Bergman and Scheele shows that Thomson's statement contains mistakes as well as inadmissable simplifications and generalizations. It is correct, however, that Bergman in 1774–1777 specifically anticipated in essential aspects the analytical element concept proposed by Lavoisier in 1787–1789.

Alfredo Traps in Durrenmatt’s tale discovers that he has brought off, all by himself, a murder involving considerable ingenuity. The mock prosecutor in the tale demands the death penalty “as reward for a crime that merits admiration, astonishment, and respect.” Traps is deeply moved; indeed, he is exhilarated, and the whole of his life becomes more heroic, and, ironically, more precious. His defense attorney proceeds to argue that Traps was not only innocent but incapable of guilt, “a victim of the (...) age.” This defense Traps disavows with indignation and anger. He makes claim to the murder as his and demands the prescribed punishment—death. (shrink)

Wussten Sie, dass das Schreiben im Mittelalter auch eine körperliche Anstrengung war? Oder dass Frauen einen erheblichen Anteil an der Literaturförderung hatten? Die Beschäftigung mit der deutschsprachigen Literatur des Mittelalters bringt nicht nur die Begegnung mit Figuren wie König Artus, Parzival oder den Nibelungen. Sie öffnet auch den Blick auf einen spannenden Literaturbetrieb – zwischen Analphabetentum und lateinischer Schriftkultur, Mäzenatentum und fahrenden Sängern. Aus dem Inhalt: Diskussion von Epochengrenzen, Sprachstufen und Literaturbegriff; Hintergründe und Entstehungsbedingungen: Mündlichkeit und Schriftlichkeit, Geistlichkeit und Adel, (...) Autor und Publikum; Paläografie und Textkritik: Handschrift und Edition; Dichtung als Formkunst: Reim und Metrum; Literaturperioden im Überblick: Alt-, Mittel- und Frühneuhochdeutsch; Gattungen und Werke des Mittelhochdeutschen: Artusepik, Heldenepik, Grals- und Minneroman, Minnesang; vrouwe und ritter: Geschlechterkonzepte und Genderaspekte. (shrink)

Among the problems raised by admitting statements which are neither true nor false is the problem of how we are to cope with vague concepts. One method of dealing with such concepts has been suggested by Rosser/Turquette (1952), i.e. the employment of a many valued set theory. It is our intention in this paper to discuss the use of many valued logics, especially the set theoretical proposals of Zadeh and Brown, in dealing with this problem. Towards this end, we shall (...) pay close attention to the development of the concepts of fuzzy sets and fuzzy systems. In this regard, it will be argued that Zadeh had in mind a many valued logic where the connectives are interpreted according to Lukasiewicz and Tarski, whereas Brown's version may be based upon a Boolean-valued logic. Furthermore, we shall have occasion to distinguish between two sources of imprecision in specifying the membership of classes, i.e. conceptual vagueness and imprecision due to inexact measurement. Due to Suppes' work in this field, the latter sort of imprecision may be exemplified by providing a theory of the inexact measurement of subjective probability. Finally, we shall discuss some ways in which these two types of imprecision are intertwined. (shrink)

Das Buch ist eine fur den gebildeten Laien verstandliche Einfuhrung in die historische Entwicklung der Grundlagenforschung der Mathematik von der Axiomatik Euklids uber die Prazisierung der Analysis in der Neuzeit und die durch die Entwicklung der Mengenlehre verursachte Grundlagenkrise der Moderne (ausfuhrliche Behandlung der sogenannten Antinomien) bis zu den Godelschen Satzen uber formale Systeme. Da im Gegensatz zu den modernen Umwalzungen in den Grundlagen anderer Wissenschaften (z.B. der Physik) die dazu parallele Erscheinung in der Mathematik immer noch nicht allgemein bekannt (...) ist, wird dabei ein Beitrag geliefert zum Verstandnis des Wesens und der philosophischen Bedeutung der modernen Mathematik.". (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.

Keine ausführliche Beschreibung für "Der Konnossement-Teilschein" verfügbar.

And his writing captures the best of his speaking. In this book we have: . Hippocrates and his Oath validated anew for modern times, . Luke the Physician, .