Formal Languages In Logic: A Philosophical And Cognitive Analysis

FORMAL LANGUAGES IN LOGIC Formal languages are widely regarded as being, above all, mathematical objects, and as producing a greater level of precision and technical complexity in logical investigations because of this. Yet defining formal languages exclusively in this way offers only a partial and limited explanation of the impact which their use (and the uses of formalisms more generally elsewhere) actually has. In this book, Catarina Dutilh Novaes adopts a much wider conception of formal languages so as to investigate more broadly what exactly is going on when theorists put these tools to use. She looks at the history and philosophy of formal languages, and focuses on the cognitive impact of formal languages on human reasoning, drawing on their historical development, psychology, cognitive science, and philosophy. Her wide-ranging study will be valuable for both students and researchers in philosophy, logic, psychology, and cognitive and computer science. catarina dutilh novaes is Assistant Professor at the Faculty of Philosophy of the University of Groningen, The Netherlands. She is the author of Formalizing Medieval Logical Theories (2007). FORMAL LANGUAGES IN LOGIC A Philosophical and Cognitive Analysis CATARINA DUTILH NOVAES cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge cb2 8ru, UK Published in the United States of America by Cambridge University Press, New York www.cambridge.org Information on this title: www.cambridge.org/9781107020917 © Catarina Dutilh Novaes 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data Novaes, Catarina Dutilh. Formal languages in logic : a philosophical and cognitive analysis / Catarina Dutilh Novaes. p. cm. isbn 978-1-107-02091-7 (hardback) 1. Formal languages. 2. Reasoning. 3. Cognition. I. Title. qa267.3.n68 2012 511.3–dc23 2012015483 isbn 978-1-107-02091-7 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate. Contents page vii Acknowledgements 1 Introduction 9 part i 1 11 12 16 28 Two notions of formality 1.1 The formal as de-semantification 1.2 The formal as computable 1.3 Conclusion