Logos – serie

The essays collected in this volume focus on the role of formalist aspects in mathematical theorizing and practice, examining issues such as infinity, finiteness, and proof procedures, as well as central historical figures in the field, including Frege, Russell, Hilbert and Wittgenstein. Using modern logico-philosophical tools and systematic conceptual and logical analyses, the volume provides a thorough, up-to-date account of the subject.

Philosophy took a "linguistic turn" 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 "contextualism" and "anti-realism." 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.

Conditional structures lie at the heart of the sciences, humanities, and everyday reasoning. This is why conditional logics – logics specifically designed to account for natural language conditionals – are an active, interdisciplinary area. Discussing a wide range of topics, this book gives a formal and a philosophical account of indicative and counterfactual conditionals in terms of Chellas-Segerberg semantics.

One main interest of philosophy is to become clear about the assumptions, premisses and inconsistencies of our thoughts and theories. And even for a formal language like mathematics it is controversial if consistency is acheivable or necessary like the articles in the firt part of the publication show. Also the role of formal derivations, the role of the concept of apriority, and the intuitions of mathematical principles and properties need to be discussed. The second part is a contribution on nominalistic and platonistic views in mathematics, like the "indispensability argument" of W. v. O. Quine H. Putnam and the "makes no difference argument" of A. Baker. Not only in retrospect, the third part shows the problems of Mill, Frege's and the unity of mathematics and Descartes's contradictional conception of mathematical essences. Together, these articles give us a hint into the relationship between mathematics and world, that is, one of the central problems in philosophy of mathematics and philosophy of science.

The book discusses contemporary metaphysics of science and deals with the central question which ontology fits best with our knowledge of the world. Two competing positions in today's metaphysics of science are analysed: Humeanism and dispositionalism. There are physical and metaphysical arguments to show that orthodox Humeanism is in trouble. The unorthodox metaphysical turn consists in taking the fundamental properties to be relations rather than intrinsic properties. The book spells out in detail what an unorthodox version of Humeanism amounts to and shows that in turning unorthodox Humeanism offers a competitive metaphysical framework for science without commitment to irreducible causation.

Die Philosophie wurde von so unterschiedlichen Philosophen wie Wolff und Russell als Moglichkeitswissenschaft bezeichnet. Doch erwiesen sich die modalen Konzepte von Moglichkeit und Notwendigkeit als sperrig und vieldeutig, und ihr Verhaltnis zum Wirklichkeitsbegriff bleibt problematisch. Die vorliegende Sammlung beleuchtet die Metaphysik und Logik von Moglichkeit und Wirklichkeit aufs Neue und betrachtet sie aus unterschiedlichsten Perspektiven jenseits der Dichotomie von analytischer und kontinentaler Philosophie. Die Philosophiegeschichte (von der griechischen Antike bis zu David Lewis) kommt ebenso zu Wort wie die Semantik moglicher Welten; Logik, Mathematik und Computerwissenschaft ebenso wie Literatur und Neue Medien; Formen des wissenschaftlichen ebenso wie des fiktionalen Diskurses. Philosophy has been called the science of the possible by philosophers as diverse as Christian Wolff and Bertrand Russell. The modal concepts of possibility and necessity, however, have proved to be ambiguous and recalcitrant to analysis, and their relation to the concept of reality have remained problematic up to the present day.Transcending the worn-out dichotomy between analytic and continental philosophy, this collection of papers takes a fresh look at the metaphysics and logic of possibility and reality, and illuminates them from a great variety of perspectives. Topics include the history of philosophy (from Greek antiquity to David Lewis) as well as the semantics of possible worlds; logic, mathematics and computer science as well as literature and the new media; forms of scientific as well as fictional discourse.

In this book, Andrea Clausen intends to reconcile Kripke's point according to which conceptual content has to be considered as being constituted by social, normative practice - by a process of mutual assessments - with the view that the content of empirical assertions has to be conceived as objective. She criticizes approaches that explicate content-constitutive practice in non-normative terms, namely in terms of sanctioning behavior (Haugeland, Pettit, Esfeld). She also rejects a pragmatist reading of Heidegger that proceeds from thoroughly normative but pre-conceptual practice. She develops and defends a particular reading of an approach that conceives normative, conceptually articulated practice - giving and asking for reasons - as primitive (Brandom, McDowell).

The book aims at a comprehensive account of the relationship between Wittgenstein’s Tractatus Logico-Philosophicus and Russell’s philosophy as it developed between 1903 and 1918. The focus is on the central nucleus of the Tractatus, i.e., on its ontology and the picture theory of language. On Russell’s side, the multiple-relation theory of judgment has been chosen as the leading theme around which the presentation of several other issues is organized. Whereas the similarity between Russell’s and Wittgenstein’s problems is pointed out, the deep difference between their solutions is acknowledged, in particular with reference to the opposition between objects and names on the one hand, and facts and propositions on the other.

The problem of truth and the liar paradox is one of the most extensive problems of philosophy. The liar paradox can be avoided by assuming a so-called theory of partial truth instead of a classical theory of truth. Theories of partial truth, however, cannot solve the so-called strengthened liar paradox, which is the problem that many semantic statements about the so-called strengthened liar cannot be true in a theory of partial truth. If such semantic statements were true in the theory, another paradox would emerge. To proponents of contextual accounts, which assume that the concept of truth is context-dependent, the strengthened liar paradox is the core of the liar problem. This book provides an overview of current contextual approaches to the strengthened liar paradox. For this purpose, the author investigates formal theories of truth that result from formal reconstructions of such contextual approaches.

This series provides a forum for cutting-edge studies in logic and the modern philosophy of language as well as for publications in the field of analytical metaphysics.

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.