Bücher der Reihe Logos

Diese Reihe bietet ein Forum fur innovative Beitrage zur Logik und zur modernen Sprachphilosophie ebenso wie fur Studien zur analytischen Metaphysik.

In contrast to the importance of real numbers for mathematical sciences a metamathematical approach to real numbers has never been developed systematically, a gap this book undertakes to fill. The investigated formal theories of real numbers are based on the theory of real closed fields, due to Tarski known as a complete theory. Theory extensions are considered by adding different set-theoretical or arithmetical concepts, like a pairing function, a predicate for natural numbers or second-order logic. To capture the special features of the metamathematics of real numbers the intertheoretical relation of interpretability is presented and examined, particularly slight variations on the common definition that allow a more accurate classification of the theories of real numbers. Thus the main theorems proven in this book are positive and negative propositions about the interpretability of and in theories of real numbers, constituting a hierarchy among them and comparing them with other canonical mathematical theories. Philosophically the results determine the resources that are employed in these theories and establish a reducibility approach to real numbers inspired by Hilbert's philosophy of mathematics.

Diese Reihe bietet ein Forum fur innovative Beitrage zur Logik und zur modernen Sprachphilosophie ebenso wie fur Studien zur analytischen Metaphysik.

Diese Reihe bietet ein Forum fur innovative Beitrage zur Logik und zur modernen Sprachphilosophie ebenso wie fur Studien zur analytischen Metaphysik.

Diese Reihe bietet ein Forum fur innovative Beitrage zur Logik und zur modernen Sprachphilosophie ebenso wie fur Studien zur analytischen Metaphysik.

Logik ist nach dem traditionellen Verstandnis eine ars iudicandi, eine Kunst, die Gultigkeit von Schlussen zu prufen. Da mit die normalen Mittel der modernen Logik zu diesem Zweck eingesetzt werden konnen, mussen erst Formeln an die Stelle von Satzen treten: umgangssprachliche Schlusse mussen adaquat formalisiert werden. Die richtige Formel entwickelt ein theoretisches Konzept des Formalisierens und praktisch anwendbare Adaquatheitskriterien fur Formalisierungen. Dabei werden zentrale Fragen der Philosophie der Logik unter dem Gesichtspunkt des Zusammenspiels von Umgangssprache und Formalismus untersucht. Die ausfuhrliche und systematische Diskussion von Formalisierungstests bietet eine wichtige Erganzung zu den traditionellen Logiklehrbuchern.

Philosophy took a "e;linguistic turn"e; in the twentieth century that was marked by the focus on theories of meaning, reference, description, predication and truth. Starting with the roots of the analytic tradition in Frege, Meinong and Bradley, this book follows its development in Russell and Wittgenstein and the writings of major philosophers of the analytic tradition and of various lesser, but well known and widely discussed, contemporary figures. In dealing with basic issues that have preoccupied analytic philosophers in the past century, the author notes how analytic philosophy is sometimes transformed from its original concern with careful and precise formulations of classical issues into the dismissal of such issues and the resultant spinning of intricate verbal webs, often signaling the rebirth of idealism in the guises of "e;contextualism"e; and "e;anti-realism."e; The book thus examines the change that came to dominate the analytic tradition by a shift of focus from the world, as what words are about, to a preoccupation with language itself.

Possibility and Reality