Philosophy of Mathematics


Book Description

One of the most striking features of mathematics is the fact that we are much more certain about the mathematical knowledge we have than about what mathematical knowledge is knowledge of. Are numbers, sets, functions and groups physical entities of some kind? Are they objectively existing objects in some non-physical, mathematical realm? Are they ideas that are present only in the mind? Or do mathematical truths not involve referents of any kind? It is these kinds of questions that have encouraged philosophers and mathematicians alike to focus their attention on issues in the philosophy of mathematics. Over the centuries a number of reasonably well-defined positions about the nature of mathematics have been developed and it is these positions (both historical and current) that are surveyed in the current volume. Traditional theories (Platonism, Aristotelianism, Kantianism), as well as dominant modern theories (logicism, formalism, constructivism, fictionalism, etc.), are all analyzed and evaluated. Leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) is also discussed. The result is a handbook that not only provides a comprehensive overview of recent developments but that also serves as an indispensable resource for anyone wanting to learn about current developments in the philosophy of mathematics.-Comprehensive coverage of all main theories in the philosophy of mathematics-Clearly written expositions of fundamental ideas and concepts-Definitive discussions by leading researchers in the field-Summaries of leading-edge research in related fields (set theory, computability theory, probability theory, paraconsistency) are also included




Geometry in History


Book Description

This is a collection of surveys on important mathematical ideas, their origin, their evolution and their impact in current research. The authors are mathematicians who are leading experts in their fields. The book is addressed to all mathematicians, from undergraduate students to senior researchers, regardless of the specialty.




Analytic Methods in Applied Probability


Book Description

This volume is dedicated to F. I. Karpelevich, an outstanding Russian mathematician who made important contributions to applied probability theory. The book contains original papers focusing on several areas of applied probability and its uses in modern industrial processes, telecommunications, computing, mathematical economics, and finance. It opens with a review of Karpelevich's contributions to applied probability theory and includes a bibliography of his works. Other articles discuss queueing network theory, in particular, in heavy traffic approximation (fluid models). The book is suitable for graduate students, theoretical and applied probabilists, computer scientists, and engineers.




Seven papers translated from the Russian


Book Description

Papers focus on topics in matrix theory and generalized complex function theory.




Logic from Russell to Church


Book Description

This volume is number five in the 11-volume Handbook of the History of Logic. It covers the first 50 years of the development of mathematical logic in the 20th century, and concentrates on the achievements of the great names of the period--Russell, Post, Gödel, Tarski, Church, and the like. This was the period in which mathematical logic gave mature expression to its four main parts: set theory, model theory, proof theory and recursion theory. Collectively, this work ranks as one of the greatest achievements of our intellectual history. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in the history of logic, the history of philosophy, and any discipline, such as mathematics, computer science, and artificial intelligence, for whom the historical background of his or her work is a salient consideration.• The entire range of modal logic is covered• Serves as a singular contribution to the intellectual history of the 20th century• Contains the latest scholarly discoveries and interpretative insights







1-2 Kings, 1-2 Chronicles, Ezra, Nehemiah, Esther


Book Description

The church fathers, as they did in earlier books dealing with Israel's history from the time of Joshua to the united monarchy, found ample material for typological and moral interpretation in 1-2 Kings, 1-2 Chronicles, Ezra, Nehemiah and Esther. This ACCS volume includes comment from Greek, Latin, and Syriac theologians, some of which is available in English for the first time.




Tales and Translation


Book Description

Dealing with the most translated work of German literature, the Tales of the brothers Grimm (1812-1815), this book discusses their history, notably in relation to Denmark and subsequently other nations from 1816 to 1986. The Danish intelligentsia responded enthusiastically to the tales and some were immediately translated into Danish by a nobleman and by the foremost Romantic poet. Their renditions remained in print for a century and embued the tales with high prestige. This book discusses translators, approaches, and other parameters such as copyright, and changes in target audiences. The tales’ social acceptability inspired Hans Christian Andersen to write his celebrated fairytales. Combined, the Grimm and Andersen tales came to constitute the ‘international fairytale’.This genre was born in processes of translation and, today, it is rooted more firmly in the world of translation than in national literatures. This book thus addresses issues of interest to literary, cross-cultural studies and translation.




Reconsidering Creation Ex Nihilo in Genesis 1


Book Description

There is a broad consensus among biblical scholars that creation ex nihilo (from nothing) is a late Hellenistic concept with little inherent connection to Genesis 1 and other biblical creation texts. In this book, Nathan J. Chambers forces us to reconsider the question, arguing in favor of reading this chapter of the Bible in terms of ex nihilo creation and demonstrating that there is a sound basis for the early Christian development of the doctrine. Drawing on the theology of Augustine of Hippo and Thomas Aquinas, Chambers considers what the ex nihilo doctrine means and does in classical Christian dogma. He examines ancient Near Eastern cosmological texts that provide a potential context for reading Genesis 1. Recognizing the distance between the possible historical and theological frameworks for interpreting the text, he illuminates how this doctrine developed within early Christian thought as a consequence of the church’s commitment to reading Genesis 1 as part of Christian Scripture. Through original close readings of the chapter that engage critically with the work of Jon Levenson, Hermann Gunkel, and Brevard Childs, Chambers demonstrates that, far from precluding interpretive possibilities, reading Genesis 1 in terms of creation from nothing opens up a variety of interpretive avenues that have largely been overlooked in contemporary biblical scholarship. Timely and innovative, this book makes the case for a new (or recovered) framework for reading Genesis 1 that will appeal to biblical studies scholars and seminarians.