Synthese Library Studies in Epistemology, Logic, Methodology, and Philosophy of Science Volume 393 Editor-in-Chief Otávio Bueno, University of Miami, Department of Philosophy, USA Editorial Board Berit Brogaard, University of Miami, USA Anjan Chakravartty, University of Notre Dame, USA Steven French, University of Leeds, UK Catarina Dutilh Novaes, University of Groningen, The Netherlands
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Andrea Iacona Logical Form Between Logic and Natural Language 123
Andrea Iacona Center for Logic, Language, and Cognition, Department of Philosophy and Education University of Turin Turin, Italy Synthese Library ISBN 978-3-319-74153-6 ISBN 978-3-319-74154-3 (ebook) https://doi.org/10.1007/978-3-319-74154-3 Library of Congress Control Number: 2017964660 Springer International Publishing AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. The book may be divided into three parts. The first part (Chaps. 1, 2, and 3) provides the historical background. The idea of logical form goes back to antiquity, in that it stems from the recognition that a pattern of inference can be identified by abstracting away from the specific content the sentences that instantiate it. The most important developments of this idea took place in the twentieth century, as they derive from some seminal works that mark the beginning of the analytic tradition. Under the influence of those works, logical form became a separate object of inquiry and started being regarded as crucial to philosophical investigation. The second part (Chaps. 4, 5, and 6) is the core of the book. Its aim is to show that, contrary to what is commonly taken for granted, no unique notion of logical form can play the two theoretical roles that are usually associated with the use of the term logical form. At least two notions of logical form must be distinguished: according to one of them, logical form is a matter of syntactic structure; according to the other, logical form is a matter of truth conditions. As will be suggested, in the sense of logical form that matters to logic, logical form is determined by truth conditions. v
vi Preface The third part (Chaps. 7, 8, and 9) develops the point made in the second part and shows some of its implications. First it outlines an account of validity that accords with the view that logical form is determined by truth conditions. Then it shows that the distinction between two notions of logical form suggested in the second part provides an interesting perspective on some debated issues concerning quantification. The case of quantified sentences is highly representative, because the same distinction may be applied in similar way to other important issues. Most of the ideas expressed in the book have been presented and discussed at talks, seminars, and graduate classes at the Heinrich Heine University Düsseldorf, the University of Aberdeen, the University of Barcelona, the University of Bochum, the University of the Caribbean, the University of L Aquila, the Hebrew University of Jerusalem, the University of Milan, the National Autonomous University of Mexico, the University of Padua, the University of Parma, the University of Rome III, and the University of Turin. Some parts of the book actually emerged as answers to questions posed by members of those audiences. In particular, I would like to thank Axel Barceló Aspeitia, Andrea Bianchi, Victor Cantero Flores, Stefano Caputo, José Díez, Christopher Gauker, Mario Gómez Torrente, Héctor Hernández Ortíz, Dan López de Sa, Genoveva Martí, Manolo Martínez, Elisa Paganini, Roberto Parra Dorantes, Victor Peralta Del Riego, Luis Rosa, Sven Rosenkranz, Gil Sagi, Giuliano Torrengo, Achille Varzi, and Elia Zardini. I am also especially grateful to Guido Bonino, Pasquale Frascolla, Diego Marconi, Massimo Mugnai, Carlotta Pavese, Mark Sainsbury, Marco Santambrogio, Daniele Sgaravatti, Ori Simchen, Alessandro Torza, Alberto Voltolini, Tim Williamson, and to various anonymous referees for their comments on parts of previous versions of the manuscript. There was much to be learned from their helpful and accurate remarks, and I really hope that I have learned enough. The second and the third part of the book are drawn from published papers, with the due adjustments, refinements, and terminological changes. More specifically, Chaps. 4 and 5 are based on Two Notions of Logical Form, Journal of Philosophy (2016), which originates from elaborations of Logical Form and Truth- Conditions, Theoria (2013). Some parts of Chap. 7 are derived from Validity and Interpretation, Australasian Journal of Philosophy (2010). Chapter 8 is drawn from Quantification and Logical Form, published in the volume Quantifiers, Quantifiers, and Quantifiers, Springer (2015). Finally, Chap. 9 is drawn from Vagueness and Quantification, Journal of Philosophical Logic (2016). I thank the editors for their permission to use the materials of these papers, which are listed in the final bibliography, respectively, as Iacona (2010c, 2013, 2015, 2016a,b). The last acknowledgment is the most important. My gratitude goes to Camila and Leonardo, for all the time that I took away from them while I was absorbed in writing this book. Words can hardly describe the strange sensation of emptiness that I feel for not having been there even when I was there. Andrea Iacona
Contents 1 The Early History of Logical Form... 1 1.1 Preamble... 1 1.2 Aristotle... 2 1.3 The Stoics... 4 1.4 Logic in the Middle Ages... 6 1.5 Leibniz s Dream... 8 2 The Ideal of Logical Perfection... 11 2.1 Frege... 11 2.2 Russell... 16 2.3 Wittgenstein... 19 2.4 A Logically Perfect Language... 22 2.5 The Old Conception of Logical Form... 24 3 Formal Languages and Natural Languages... 27 3.1 Tarski s Method... 27 3.2 Davidson s Program... 30 3.3 Montague Semantics... 32 3.4 The Current Conception of Logical Form... 34 3.5 Two Open Questions... 37 4 Logical Form and Syntactic Structure... 39 4.1 The Uniqueness Thesis... 39 4.2 Intrinsicalism... 40 4.3 LF... 42 4.4 Semantic Structure... 44 4.5 Relationality in Formal Explanation... 46 4.6 Further Clarifications... 50 5 Logical Form and Truth Conditions... 53 5.1 The Truth-Conditional Notion... 53 5.2 Truth Conditions and Propositions... 55 5.3 Adequate Formalization... 58 vii
viii Contents 5.4 A Truth-Conditional Account... 61 5.5 Logical Form as a Property of Propositions... 63 5.6 Extrinsicalism... 66 6 Logical Knowledge vs Knowledge of Logical Form... 69 6.1 Preliminaries... 69 6.2 Logical Identity and Logical Distinctness... 70 6.3 Distinct Objects Must Be Denoted by Distinct Names... 71 6.4 Distinct Names Must Denote Distinct Objects... 74 6.5 Logical Knowledge... 80 6.6 Linguistic Competence and Rationality... 81 7 Validity... 85 7.1 Interpretations of Arguments... 85 7.2 Validity and Formal Validity... 87 7.3 The Sorites... 90 7.4 The Fallacy of Equivocation... 92 7.5 Context-Sensitive Arguments... 95 8 Quantified Sentences... 99 8.1 Two Questions About Quantified Sentences... 99 8.2 Quantifiers... 102 8.3 Meaning and Truth Conditions... 104 8.4 The Issue of First Order Definability... 105 8.5 Two Kinds of Formal Variation... 108 8.6 Conclusion... 110 9 Further Issues Concerning Quantification... 111 9.1 Two Kinds of Indeterminacy... 111 9.2 Precisifications of Quantifier Expressions... 113 9.3 First Order Definability Again... 117 9.4 Logicality... 120 9.5 Quantification Over Absolutely Everything... 123 9.6 Unrestricted Quantification and Precision... 124 Afterword... 127