A Study on Existence : Two Approaches and a Deflationist Compromise [1 ed.] 9781443891707, 9781443850681

Citation preview

A Study on Existence

A Study on Existence: Two Approaches and a Deflationist Compromise By

Giuliano Bacigalupo

A Study on Existence: Two Approaches and a Deflationist Compromise By Giuliano Bacigalupo This book first published 2017 Cambridge Scholars Publishing Lady Stephenson Library, Newcastle upon Tyne, NE6 2PA, UK British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Copyright © 2017 by Giuliano Bacigalupo All rights for this book reserved. No part of this book may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN (10): 1-4438-5068-3 ISBN (13): 978-1-4438-5068-1

To Jule

TABLE OF CONTENTS

Preface ........................................................................................................ xi Acknowledgements .................................................................................. xiii List of Tables ............................................................................................ xiv Introduction ................................................................................................. 1 Part One: The Non-Property View Chapter One ................................................................................................. 8 Hume: No Addition 1.1 Attempts at Urbanizing Hume ......................................................... 8 1.2 The Most Perfect Assurance of Being ........................................... 11 1.3 The Most Clear and Conclusive Dilemma ..................................... 13 1.4 On External Existence.................................................................... 14 1.5 A First Occurrence of the Paradox of Non-Existence .................... 15 1.6 To Exist and to Be Believed .......................................................... 17 1.7 Objections: Thinking about Non-Existents .................................... 18

 Chapter Two .............................................................................................. 20 Kant: Not a Real Predicate 2.1 Real and Logical Predicates ........................................................... 20 2.2 Pars Destruens: Existence Is Not a Property ................................. 22 2.3 Comparison with Hume and Frege ................................................ 24 2.4 Pars Construens: Existence and Possible Perception .................... 26 2.5 Kant, Neo-Meinongianism and the Ontological Argument ........... 28 2.6 Objections: Existence and Possibilities .......................................... 29 Chapter Three ............................................................................................ 33 Brentano: Acceptance and Rejection 3.1 Mental In-Existence ....................................................................... 33 3.2 To Judge Is to Accept or Reject ..................................................... 35 3.3 Brentano’s Existential Reformulation of the Square of Opposition .................................................................................. 38

viii

Table of Contents

3.4 Hume and Brentano on Existence and Belief/Acceptance ............. 40 3.5 Twardowski on Contents and Objects of Ideas .............................. 41 3.6 Twardowski and the Property-View of Existence.......................... 45 3.7 Objections: To Judge and to Judge Correctly ................................ 46 Chapter Four .............................................................................................. 49 Frege: A Second-Order Property 4.1 The Meaningless Reading of “to Exist” ......................................... 50 4.2 Existence and the Particular Quantifier.......................................... 51 4.3 The Self-Evident Reading of “to Exist” ......................................... 52 4.4 Singular Statements and the Sense/Reference Distinction ............. 54 4.5 Stabilizing Frege’s Account ........................................................... 56 4.6 A Second Occurrence of the Paradox of Non-Existence ............... 57 4.7 Digression on Russell and Quine ................................................... 59 4.8 Objections: Sweeping Existence under the Carpet of Quantification ............................................................................ 62 Part Two: The Property View Chapter Five .............................................................................................. 66 Meinong: Objects and Objectives 5.1 Meinong and Brentano ................................................................... 66 5.2 Meinong’s Solution to the Paradox of Non-Existence ................... 68 5.3 Terminological Remarks ................................................................ 71 5.4 Being-Objectives and So-Being-Objectives and their Independence................................................................... 72 5.5 Meinong’s B-Strategy .................................................................... 74 5.6 Russell’s Objections: The Paradoxes of Characterization ............. 76 5.7 Meinong’s Answers to the Paradoxes of Characterization ............ 78 5.8 Objections: Meinong’s Retreat from Predicate Logic.................... 80 5.9 MacColl and the Early Russell on Existence ................................. 82

 Chapter Six ................................................................................................ 85 Routley, Parsons, and Jacquette: An Extra-Nuclear Property 6.1 Almost a New Solution to the Paradox of Non-Existence ............. 86 6.2 On Impossible Objects and Contradictory Statements ................... 88 6.3 Constitutive and Extra-Constitutive Properties .............................. 90 6.4 Nuclear and Extra-Nuclear Properties ........................................... 92 6.5 Quine’s Possible Man in the Doorway........................................... 93 6.6 Answer to Quine’s Challenge ........................................................ 96 6.7 Objections: Ad Hocness ................................................................. 98

A Study on Existence: Two Approaches and a Deflationist Compromise

ix

Chapter Seven.......................................................................................... 102 Rapaport and Zalta: A Brand New Relation 7.1 Rapaport: Existence as a Two-Place-Relation ............................. 102 7.2 Zalta: Existence as Being Spatially Located ................................ 104 7.3 The Unrestricted Characterization Principle ................................ 105 7.4 Objections: Fregeanism under Disguise....................................... 106 Chapter Eight ........................................................................................... 109 Priest: Modal Meinongianism 8.1 The Perfectly Ordinary Property of Existence ............................. 109 8.2 The Representing-Operator .......................................................... 111 8.3 Constant Domains ........................................................................ 112 8.4 Objections: Existence and Modal Contexts ................................. 113 Interlude Chapter Nine............................................................................................ 118 Free Logics: The Existence-Predicate 9.1 The Existence-Predicate............................................................... 118 9.2 Negative, Neuter and Positive Free Logics .................................. 120 9.3 Supervaluations and Superinterpretations .................................... 123 9.4 Free Dialogic Logic ..................................................................... 125 9.5 Objections: Free Logics and Fregeanism ..................................... 130 Part Three: The Deflationist Compromise Chapter Ten ............................................................................................. 136 General Existential Statements 10.1 A Raw Intuition.......................................................................... 136 10.2 Fregeanism ................................................................................. 139 10.3 Neo-Meinongianism .................................................................. 140 10.4 The Attempt at a Compromise: A Deflationary Account of Existence........................................... 142 10.5 A Second Raw Intuition ............................................................. 146 10.6 Deflationism and Meta-Ontology .............................................. 147

 Chapter Eleven ........................................................................................ 150 Modal Existential Statements 11.1 Actualism and Possibilism ......................................................... 150 11.2 The Rationale behind Actualism and Possibilism ...................... 153 11.3 The Modal Raw Intuition ........................................................... 155

x

Table of Contents

11.4 A Second Modal Raw Intuition ................................................. 158 11.5 Presentism and Contingentism ................................................... 159 Chapter Twelve ....................................................................................... 160 Intentional Statements 12.1 Propositional Attitudes Reports ................................................. 160 12.2 Objectual Attitudes Reports ....................................................... 161 12.3 A Further Objectual Attitude Report.......................................... 163

 Chapter Thirteen ...................................................................................... 165 Singular Existential Statements 13.1 The Raw Intuition, again ............................................................ 165 13.2 Vindicating the Raw Intuition .................................................... 166 13.3 The Trilemma about Singular Existential Statements ................ 167 13.4 Proper Names and Individuating Properties............................... 168 13.5 The Trilemma, again .................................................................. 170

 Concluding Remarks ............................................................................... 172 Bibliography ............................................................................................ 175 Index ........................................................................................................ 185

PREFACE

My interest in the problem of existence was born from dissatisfaction with what I was hearing and reading on this topic as a philosophy student. Most philosophers endorsed the startling slogan that everything existed, yet were providing a rather plausible narrative to support it. Conversely, a small but raucous group of philosophers endorsed the rather plausiblesounding slogan that some things exist while others do not, yet provided an astonishing narrative to back it. I was thus naïve enough to think that it should be possible to have both: a plausible narrative and a plausible slogan. This led me to embark on writing a PhD thesis on the problem of existence, which–after some considerable revision–developed into this book. Whereas some level of acquaintance with (modal) propositional and (modal) first-order logic might be helpful for some chapters (especially, Chapters 9, 10 and 11), this is not–by any means–required to follow the thread of the discussion. Besides the one between logic and philosophy, I have also tried to eschew another compartmentalization, namely the one between systematic and historical approaches. I hope philosophers focusing on either one of them might find some things of interest in this study. While working on my thesis, and, later, on this book, I had the opportunity of being part of some very different, yet equally lively and welcoming intellectual communities: the Philosophy Department and the UMR “Savoirs, Textes, Langage” of the University of Lille 3, where I participated in different seminars and defended my PhD in January 2016 under the supervision of Shahid Rahman; the Philosophy Department of Seattle University, where I worked as a lecturer from 2009 to 2012; the Law Department and the Philosophy Department of the University of Constance, where I was a member of an interdisciplinary project between law and logic under the supervision of Matthias Armgardt from 2012 to 2015; and, finally, the Philosophy Department of the University of Geneva, where I am currently working in a project on the philosophy of Anton Marty directed by Laurent Cesalli and Kevin Mulligan. Glancing back over these eventful years, I cannot but start by thanking Shahid Rahman. Without his guide and encouragement, I would never have dared to cross the dangerous waters of the riddle of existence. I

xii

Preface

would also like to thank Burt Hopkins: my time as a lecturer at Seattle University in the Philosophy Department directed by him has been decisive to shape my approach to philosophy. I am equally most grateful to the members of my PhD thesis committee, which, besides the already mentioned Shahid Rahman, included Arkadiusz Chrudzimski, Claudio Majolino, Francesco Orilia and Juan Redmond. I hope that the present work does justice to at least some of their careful and helpful remarks. For their engaged and pleasant discussions, I am grateful to the students of two “existential” seminars (one at Seattle University and the other at the University of Constance). I would also like to thank the audiences at the 7th ECAP (University of Milan, Italy, 1-6 September 2011), at the 14th CLMPS (Nancy, France, 19-26 July 2011), at the SIFA conference (L’Aquila, Italy, 3-5 September 2014), and at the Workshop Brentano in Early Analytic Philosophy (Institut Jean Nicod, Paris, France, 20 October 2014, organized by Uriah Kriegel) where I presented parts of this work. Special thanks to Jochen Briesen, Eléonore Le Jallé, Tilman Süchting, and Emiliano Trizio for reading and commenting upon parts of this work, as well as to two anonymous reviewers for the journal Argumenta: if the final chapters of this study are to some extent successful, I owe it to their excellent comments. I would also like to express my sincere gratitude to Kallina Barclay Temperini for her patient linguistic revision of the final manuscript. Last but not least, great many thanks to Carlo Vita for his permission to expose some of his non-existent pebbles on the cover of this book. Out of fear of presenting an incomplete list, I will not attempt to name all my friends and colleagues with whom I had countless and enjoyable exchanges–bis auf eine Ausnahme: thanks to Juliane Lippmann; no pun on the topic of this book might capture my gratefulness for your encouragement and your scrutinizing glances when confronted with the umpteenth solution to the puzzle of existence.

ACKNOWLEDGEMENTS

The material in Chapter 10, 11, and 12 is taken–with minor modifications– from the following paper, and is reprinted here with the permission of the publisher: “Whose Existence? A Compromise to the Fregean/Neo-Meinongian Divide.” Argumenta, 2, 1 (2016): 5–24.

LIST OF TABLES

Chapter 3: Table 3-1 Existential and Psychological Formulations Table 3-2 Conditional Statements Chapter 9: Table 9-1 Particle Rules for Quantifiers Table 9-2 Validity of Existential Generalization Table 9-3 Validity of Specification Table 9-4 Invalidity of Existential Generalization Table 9-5 Invalidity of Specification

L’existence est ailleurs. (André Breton, Manifeste du Surréalisme)

INTRODUCTION

The problem of existence is reputed to be one of the most intractable in philosophy, so that it does not pale even when compared to the mind-body problem. To avoid misunderstandings, however, we should hasten to point out that by the problem of existence philosophers do not mean the question as to why we, or for that matter, the universe exist, or where we come from, or where we are headed. To borrow the categories which have been applied to the mind-body problem, one may think of these questions as the soft problem of existence: if we are patient enough, one day (natural) science will provide us with the answers to these questions–and to a not negligible extent it has already done so. No, what philosophers mean by the problem of existence may be labeled as the hard problem: i.e., the question as to which place we should attribute to the notion of existence within our categorical grammar. More precisely, the issue in question is whether the notion of existence should be interpreted as expressing a property of objects (i.e., a first-order property, as opposed for instance to second-order ones), which would thus put it on a par with other garden-variety properties such as being round, being a circle, being heavy, etc.; or whether the term ‘existence’ and its cognates should be taken to express something radically different from a first-order property. The question as to whether or not we should interpret existence as a property will guide us throughout this study (if not specified otherwise, by ‘property’ I mean ‘first-order property’). Yet evidently, in order to distinguish between the views according to which existence is a property from those that deny it, I must specify the notion of property at stake. Throughout this study, I rely on a conception of property borrowed from Frege’s “Dialogue with Pünjer” (Frege 1883?, 3; 14 [54; 62]): a property is something which enables us to divide the domain of objects into two classes–those that, circularly speaking, instantiate this property, and those that do not. Take, for instance, the rather uncontroversial property of being red: we can make sense of red as a property because we may use it to put certain objects under one column–i.e., the column of red objects–and the others under a different column–i.e., the column of objects that are not red. This is the characteristic I am going to rely upon to distinguish a property from what is not a property.

2

Introduction

Besides spelling out the conception of property assumed by this study, it is crucial to distinguish between two different strategies one may rely upon to deny the property-status to existence. The first, more immediate one would be to argue for the fact that everything exists. Indeed, if everything existed, the notion of existence would not allow for any distinction within the domain of objects. A pleonastic property is, if not a contradictio in adiecto, something very different from the view of property at the heart of this study.1 On the other hand, one might also argue that nothing exists and therefore existence is not a property, since– once again–we would not be able to rely on existence to draw a distinction within the domain of objects. This, however, seems to be rather an impervious road to follow: none of the philosophers addressed here ever ventured on it. Thus, I am not going to consider it as a viable strategy. Instead, a second viable strategy is the following: someone might argue that existence does not apply to objects, but rather, to something categorically different. Objects, then, would simply not be–so to speak–in the line of business of existence. To sum up, we thus have an a- and a b-strategy, which we may rely upon in order to put forward a non-property view of existence. To return to the metaphors of the two columns, if one follows the a-strategy, no object will find a place in the column of non-existing objects; if one follows the b-strategy, the column of existence and the column of nonexistence are to be filled in with something essentially other than objects. As we shall see, these two strategies need not be mutually exclusive, but they may actually complement one another instead. The structure of this study is as follows. Part One focuses on the attempts at interpreting existence as something other than a property, developed by David Hume (Chapter 1), Immanuel Kant (Chapter 2), Franz Brentano (Chapter 3) and Gottlob Frege (Chapter 4). Part Two turns to the philosophers who have been most effective at arguing that existence should be considered a property of objects. These are Alexius Meinong (although–as will be seen–with due qualification) (Chapter 5), the Nuclear Neo-Meinongians Richard Routley, Terence Parsons and Dale Jacquette

 1

I would like to stress that this is just a matter of definition. I obviously do not wish to claim that, by endorsing this definition of property, I have refuted the approaches to existence as a formal or pleonastic property, as defended for instance by Salmon and Nakhnikian (1957), Salmon (1987), Williamson (1998; 2013), Mendelsohn (2005), Branquinho (2012) and, at least partially, Miller (1975; 1986) and Voltolini (2012). The only thing that follows, instead, is that, from the perspective taken by this study, such approaches are not considered as propertyviews of existence.

A Study on Existence: Two Approaches and a Deflationist Compromise

3

(Chapter 6), the Dual Copula Neo-Meinongians William Rapaport and Edward Zalta (Chapter 7), and the Modal Neo-Meinongian Graham Priest (Chapter 8). In the Interlude between the second and the third part, I address the family of free logics (Chapter 9). Finally, in Part Three, I develop a deflationist approach to existence first in the context of general statements (Chapter 10), then in the context of modal (Chapter 11), intentional (Chapter 12) and singular statements (Chapter 13). Paradoxically, I will argue here that there is no nature of existence, so that the term “existence” and its cognates express neither a property of objects nor any other substantive notion. Historically–I should note–the non-property view may have found expression well before Hume and all the way back to Plato and Parmenides. Indeed, in a famous fragment (On Nature, fragment 2), Parmenides warned us that the path of non-being leads us nowhere–which may be interpreted as a poetic way of expressing the view that being is not a property. Metaphorically speaking, the path of non-red does lead to something, namely to objects which are not red, so that red may be deemed a property. But the path of non-being leads nowhere, since no object is without being. Thus, being is not a property, and, more precisely, it is not a property because everything exists (i.e., the a-strategy). Yet it is not at all clear whether Parmenides’ notion of being may be interpreted as existence–a problem which is inherited by Plato’s Parmenidean passages in the Sophist and other dialogues. For this reason, I avoid any attempt at interpreting these texts in the present study. Another chapter in the history of philosophy that will not be addressed in the present study is the discussion by Aristotle and within the Aristotelian tradition on the distinction between essence and existence–a discussion which might also be reconstructed as a non-property view of existence (see Nelson 2012). As rich as this debate certainly was, it did not influence the philosophical discussion on existence of modern philosophy, and thus, in contemporary philosophy too, traces thereof are hard to find. As for many other philosophical problems, it seems that also here Descartes has been able to oblige those who came after him to think in other categories than the Aristotelian ones. As it happens, Hume is the first philosopher who has provided us with a clear formulation of the nonproperty view in modern philosophy–which is the reason this study opens with a chapter on him. Moreover, we will see how Kant, Brentano, and Frege have all followed in Hume’s footsteps to different extents. The property view of existence may be traced back before Meinong as well. For instance, precursors of this position may be found in Thomas Reid (see Routley 1980, 835–50), or even in Medieval philosophy (see

4

Introduction

Priest 2005, 68–81). What is undeniable, though, is that it is first and foremost through Meinong’s influence that the contemporary approaches to existence as a property of objects have taken shape. Thus, it is all but mandatory to start the second part of this study with him. In fact, all the other authors discussed in the second part considered themselves to be Neo-Meinongians: Parsons, Routley, Jacquette, Rapaport, Zalta and Priest, all read Meinong’s pages on existential statements and developed their theories under their sign. The analysis contained in the first two parts will leave us with two main competing theories: Frege’s and Routley’s. These two theories will be seen as the most convincing explanations of existence, i.e., respectively, as something that is and something that is not a property of objects. The problem, however, will be that the two main contenders do not provide us with any decisive argument against each other, so that the question about which theory one should ultimately choose seems to boil down to a matter of intuitions. More specifically, if someone gives priority to our intuitions about the syntactical appearance of existential statements, he will tend towards Routley’s solution; if, on the other hand, someone privileges the intuition according to which statements of the form “something is x” are equivalent to statements of the form “there are (there exist) xs,” he will tend toward Frege’s view that the notion of existence is captured by the particular (so-called “existential”) quantifier. This stalemate will first lead me to explore the family of free logics as a possible alternative to both Fregeanism and Routley’s version of NeoMeinongianism. The conclusion of the chapter, however, will be that free logics are best considered as variations to the Fregean approach to existence: to them, existence still remains a matter of quantification. In addition, free logics do not offer us any new philosophical ammunition against Neo-Meinongianism. Finally, in Part Three, I develop what I would like to consider a compromising solution. Relying on analysis of general existential statements in natural language, I argue that we should endorse a version of deflationism about existence. This deflationism differs from the one recently advanced by Thomasson (2013) insofar as it relies on what I call the existence equivalence schema, which follows the blueprint of the wellknown truth equivalence schema. It is this schema which will allow us to say, with the Fregean philosophers, that existence is not a discriminating property of objects, and, with the Neo-Meinongian philosophers, that it is not the case that existence is a matter of quantification. The reader may be surprised by the fact that, in Part Three, the discussion of general statements precedes the discussion of singular ones.

A Study on Existence: Two Approaches and a Deflationist Compromise

5

The reason for this is that in the last decades the hard problem of existence has often been identified with the problem of singular existential statements (see, for instance, Salmon 1998, 1). The approach defended in the last part of this study, however, goes against this trend: the hard problem of existence is first of all the problem about general statements. Once this problem has been addressed, the solution to singular statements follows almost automatically, albeit at some theoretical costs. The fact that this study closes by arguing for a version of deflationism about existence will probably also surprise many readers–or at least it has surprised its author. But, after all, should we really be so surprised? Do we have any idea of existence? Are we sure that there is a nature of existence hiding behind our everyday use of the word “existence” and its cognates which is waiting to be discovered? Perhaps all the philosophers discussed in the present study, no matter whether they endorsed the property or the non-property view, were–in this respect–chasing a chimera.

PART ONE THE NON-PROPERTY VIEW

CHAPTER ONE HUME: NO ADDITION

As already addressed in the Introduction, the non-property view of existence may be traced back all the way to Antiquity. Yet Hume is the first modern philosopher who provided us with a clear formulation of this position. His approach, moreover, had a decisive impact on both Kant and Brentano, and at least indirectly, i.e. through Kant, on Frege. Accordingly, Hume deserves to come first on our reading list. However, one should deal carefully with this matter. Hume does not explicitly argue for the view that existence is not a property. Rather, he argues for the claim that the idea of existence makes no addition to the idea of an object. Nevertheless, given the view of property this study relies upon, the two formulations are equivalent. As we will see, by arguing that the idea of existence makes no addition to the idea of an object, Hume means that we cannot rely on existence to draw any distinction within the domain of objects. And, as addressed in the Introduction, a property is (at least) this: something which allows us to divide the domain of objects into two classes.

1.1 Attempts at Urbanizing Hume At the beginning of the section of the Treatise “The Ideas of Existence and of External Existence,” Hume writes: There is no impression nor idea of any kind, of which we have any consciousness or memory, that is not conceiv’d as existent; and ‘tis evident, that from this consciousness the most perfect idea and assurance of being is deriv’d. (Hume 2000, 48 [1.2.6.2])

Hume’s claim about being or existence (he seems to use these terms synonymously in this passage) is prima facie very puzzling: every impression and every idea–i.e., everything that can be an object of our mind in Hume’s psychology–is conceived as existent. What is puzzling

Hume: No Addition

9

about this view is the easiness with which we may find counterexamples to it: there are many things I can think about, of which it is not true that I conceive them as existent, such as for instance, Santa Claus, Sherlock Holmes, or–to borrow an example from Hume himself–the New Jerusalem. Thus, the reader is left wondering whether Hume could really mean something so blatantly false. Indeed, it is very tempting to try to urbanize Hume’s claim, i.e. to reinterpret or reword the claim so that it loses its puzzling character. A first attempt at urbanizing Hume is put forward by Tweyman (1992, 141). According to him, when Hume writes “there is no impression nor idea of any kind […] that is not conceived as existent,” he does not literally mean existence, but rather, possible existence. In other words, what Hume is aiming at is nothing other than the well-known metaphysical principle that if something is conceivable, then it is possible. If this interpretation were granted, the quote would lose its puzzling character. Indeed, it is much less controversial to claim that everything we may think about is–at least–possibly existent than to claim that everything we may think about actually does exist. For instance, one may argue that Santa Claus, Sherlock Holmes and the New Jerusalem enjoy this diminished kind of existence, at least as long as we can conceive them and, thus, they are not impossible. This interpretation, however, does not do justice to Hume’s position, as reported in the previous quote: it is by thinking about every idea and every impression that we derive “the most perfect idea and assurance of being.” How could we derive the most perfect idea and assurance of being from something that is–if not always–at least very often a mere possibility? Even if we were to subscribe to an extreme form of realism about possibilities, such as for instance David Lewis’ (1986) realism about possible worlds, we would probably refrain from endorsing such a position. Hence, what Hume addresses here must be something other than the metaphysical principle that everything conceivable is possible. Moreover, the reader may notice that Hume very explicitly endorsed the conceivability approach to (the epistemology of) modalities in a previous section of the Treatise: if we can think about something, then it is possible (Hume 2000, 26 [1.2.2.8]). Thus, it would be very awkward if he were to restate the same principle in such a convoluted form just a few pages later, and with no reference to his previous endorsement. These two reasons should be sufficient to cast doubts on Tweyman’s attempt to defuse the puzzling character of Hume’s claim. Something more substantive than mere possible existence must be at stake here.

10

Chapter One

Cummins (1991, 63; 77) developed a second strategy to urbanize Hume. According to Cummins, we should restrict the scope of Hume’s claim to impressions and simple ideas: Hume does not literally mean that every impression and every idea conveys the idea of existence; rather, this function is only fulfilled by impressions, no matter whether simple or complex, and ideas of a specific kind, i.e. simple ones. The first and main motivation behind Cummins’ interpretation is an application of the principle of charity: if we were to take Hume’s passage at face value, he would appear to be blatantly contradicting himself–or at least Cummins takes this to be the case. The contradiction would derive from the fact that Hume previously acknowledged that some complex ideas are not copies of original impressions, as for instance in the case of the already mentioned idea of the New Jerusalem. Thus, clearly, such ideas cannot provide us with any assurance of being. By contrast, as soon as we reinterpret the claim as targeting only impressions and simple ideas, we may rule out all the troubling counterexamples, such as the New Jerusalem. Better still, Hume’s copyprinciple (i.e., the principle that there is no simple idea that is not a copy of a simple impression) would help secure the fact that this kind of idea always conveys us an “assurance of being.” The idea of the New Jerusalem is not a copy of any impression. But all the simple ideas that compose this complex idea are themselves derived from impressions and, thus, would carry over an assurance of being. However, also Cummins’ interpretation runs into problems. First and foremost, Hume’s own examples of things that cannot but be conceived as existent clearly involve non-simple ideas, as for instance the idea of God (see the quote below, section 1.6). Could it really be the case that Hume not only forgets to specify that he is referring to simple ideas, but–over and above that–also forgets to provide the right kind of examples? This strikes me as a very uncharitable reading of Hume. Secondly, Cummins’ approach seems to suggest that, if we consider simple ideas, they are conceived as existent because of the principle that every simple idea is a copy of an impression. But this would be a very indirect and highly speculative way by which ideas are conceived as existent (notice, too, that Hume seems to allow for some exceptions to the copy-principle) (Hume 2000, 9–10 [1.1.1.10]). In addition, if Hume was really trying to convey what Cummins attributes to him, he would have formulated his view in a doubly misleading way. Not only should Hume have explicitly restricted the claim to impressions and simple ideas; but he should also have added that only impressions are immediately conceived as existent, whereas simple ideas are conceived as existent in a mediate

Hume: No Addition

11

way, namely insofar as they are copies of simple impressions. For these reasons, I suggest that we put aside this second attempt at urbanizing Hume as well.

1.2 The Most Perfect Assurance of Being It is often the case that a picture cannot be deciphered if we stand too close to it. So let us take a step back and consider where the controversial passage stems from. As already noted, we are at the very beginning of the section of the Treatise called “The Ideas of Existence and of External Existence.” Once this is taken into proper account, it seems only natural to interpret Hume as not referring to the idea of external existence at the very beginning of the section. This assumption is further confirmed by the fact that, at the end of the section, he will explicitly come to speak about (alleged) external existence. Thus, following this thread, it seems safe to assume that Hume is not talking here of the existence of what may have caused our impressions or of what may correspond to our ideas (i.e., external existence). Once this is taken into account, the two attempts at urbanizing Hume addressed in the previous paragraph fall prey to the same mistake: both Tweyman and Cummins interpret Hume as discussing external existence. Indeed, the possible existence referred to by Tweyman can only be a possible external existence. Cummins, on the other hand, attributes to impressions–no matter whether simple or complex–and simple ideas priority in conveying the notion of existence because he, too, is thinking about external existence. Indeed, impressions and simple ideas convey the notion of existence because, respectively, they grant us access to externally existing things and because they are copies of something that grants us this access.2 But what, then, is the kind of existence Hume is talking about at the very beginning of the section, if not external existence? As far as I can see, the answer must be the following: Hume is addressing what to him is the more primitive notion of existence, namely the existence of impressions and ideas themselves.3

 2 Berto (2013) also falls prey to the same temptation of rewording Hume’s claim so that it applies to external existence. After having provided the quote of the controversial passage, he comments it as follows: “This sounds a bit confusing: the point would rather be that whatever we have an impression of, we have the impression or idea of an existent thing” (Berto 2013, 12). 3 Bricke (1991, 163), in his answer to Cummins, briefly considers this interpretative option, but only to discard it. The reason he offers is that such a

12

Chapter One

If we interpret Hume as putting forward a claim about impressions and ideas themselves, such a claim suddenly loses its puzzling character. On this conception, Hume would simply be stating that every time we think of an impression or an idea, this impression or idea exists within our mind, and, therefore, while we reflect upon it, the impression or idea conveys to us the idea of existence. Thus, we can no longer count on Santa Claus, Sherlock Holmes or the New Jerusalem as counterexamples: every time we think of such ideas, these ideas evidently exist within our mind and thus we can only conceive them as existent. Even better, if we follow this interpretation, we can explain why Hume–pace Cummins–is not at all interested in giving a priority to impressions with respect to ideas as those objects of thought that yield us the most perfect assurance of being: both are equally qualified to fulfill this function. In the present context, the principle that simple ideas are copies of simple impressions is irrelevant. Finally, we can also see how–pace Tweyman–the notion of possibility is not part of the picture: impressions and ideas both actually exist in our mind while we are thinking about them. True, someone may want to argue that this is not the common way of stumbling upon the idea of existence: it is not by realizing that every impression or idea we have is existent that we form our everyday notion of existence. To the contrary, everyone would agree that it is by thinking of alleged external objects that we first form the notion of existence. However, it does not seem to be the case that Hume intended to provide us with a theory about how we develop the notion of existence. His is not a genealogy of existence. Rather, what he is telling us is where we may find the “most perfect idea and assurance of being,” which, according to his psychology, is–so to speak–in our head.

 principle is not something with which an opponent of Hume could be expected to agree. Consequently, Bricke moves on to one more attempt at urbanizing Hume. To him, we should understand the claim that every idea and impression is conceived as existent as follows: “One has the experience as of something that is F if that experience is as of the existence of something that is F.” The first problem with this line of reasoning, however, is that Hume does not say that he is putting forward an uncontroversial, largely shared principle. To the contrary, the only relevant question is whether the claim made by Hume is consistent with his philosophical project–which it is. Secondly, and more crucially, it is difficult to see how Bricke’s recasting of Hume’s claim may yield us the required assurance of being: we would be left with an “as if”-assurance of being, i.e., a hypothetical one. Yet a hypothetical assurance of being is no assurance at all.

Hume: No Addition

13

1.3 The Most Clear and Conclusive Dilemma In the previous paragraph, I have argued that we should interpret Hume as making a claim about ideas and impressions themselves: these are always conceived as existent. And the reason for this is that, while we are thinking about them, such ideas and impressions clearly must exist. This, however, is only the beginning of Hume’s discussion of existence. In fact, Hume is relying on this insight to shed light on the very meaning of the word “existence” or, in his own terminology, to shed light on what the idea of existence really consists in. Immediately after the previous quote, Hume sets up the following dilemma: From hence we may form a dilemma, the most clear and conclusive that can be imagin’d, viz. that since we never remember any idea or impression without attributing existence to it, the idea of existence must either be deriv’d from a distinct impression, conjoin’d with every perception or object of our thought, or must be the very same with the idea of the perception of the object. (Hume 2000, 48 [1.2.6.2])

Again, we should be very careful not to interpret Hume as making claims about external existence, i.e. about what may correspond to an impression or to an idea. Instead, he is again referring to ideas and impressions themselves. Otherwise, we would end up with the same problems that were discussed in the previous paragraph: we simply would not be able to make sense of the claim that “we never remember any idea or impression without attributing existence to it.” Once this worry is set aside, we may provide a straightforward interpretation of the dilemma. Since we attribute existence to every object of thought or perception–i.e., all the impressions and ideas we have–one of the two following options must hold: either we derive from a part of the object of thought the idea of existence, i.e., every object includes within itself a distinct impression of existence; or the idea of existence and the idea of the object are simply one and the same thing. The dilemma is then easily resolved by Hume by means of the principle according to which, if an object includes within it a distinct impression x, we should be able to think of the same object without x. Thus, if the idea of existence were a distinct impression included in every object, we should be able to think of every object without this impression and, thus, we would not derive the idea of existence from it. But this cannot be the case, since it would flatly contradict the principle that everything we can think of is conceived as existent. Thus, the dilemma

14

Chapter One

leads us to conclude that the idea of existence is one and the same thing as the idea of the object. We are finally in a position to address the famous Humean claim that existence makes no addition to the idea of any object. Indeed, this is simply another way to reformulate the conclusion of the dilemma: To reflect on anything simply, and to reflect on it as existent, are nothing different from each other. That idea, when conjoin’d with the idea of any object, makes no addition to it. (Hume 2000, 48 [1.2.6.4])

We have seen how the idea of existence cannot be subtracted from any object. But what cannot be subtracted clearly cannot be added, either.4

1.4 On External Existence The time has come to address a possible concern. If Hume is referring to the existence of ideas or impressions themselves all along, he is not providing us with any general theory of existence. Instead, what he is giving us is a theory of the most primitive and certain notion of existence–of course within the framework of his psychology. But then the claim that existence makes no addition to an object may not be true in full generality, but only if we restrict its scope to the impressions or ideas we are thinking about. Most prominently, existence may add something to the objects that those impressions or ideas represent or correspond to. Yet, as we shall soon see, within Hume’s theoretical framework this distinction is jeopardized. When Hume tackles the notion of external existence at the end of the section in question, he pays tribute to one of his main influences, i.e.

 4

It is interesting to remark that McGinn, even though only as a side note, provides a radically different interpretation of what we may label as Hume’s non-addition principle. According to him, the non-addition principle is derived from the fact that existence is not a perceivable property of objects. By this he means that, no matter whether we perceive or imagine an object, this object may present us with “the same sensory appearance.” For instance, “hallucinated pink rats look an awful lot like existent pink rats” (McGinn 2001, 45). Although suggestive, this approach is misleading: Hume is not saying that existence adds nothing because, for instance, we cannot find any perceivable property that distinguishes a hallucinated pink rat from an existent pink rat. As it happens, Hume is simply not interested in what may be the perceivable properties of these two rats. Instead, what he is telling us is that regardless of whether we are having an impression of a pink rat or a hallucination of a pink rat, both the impression and the hallucination exist. Once more, then, Hume is not talking of the object that may be represented by impressions and ideas, but he is talking of impressions and ideas themselves.

Hume: No Addition

15

bishop George Berkeley. To Hume, as to Berkeley before him, the distinction between ideas or impressions and something external that corresponds to them and exists independently is–to say the least– problematic. In his own vivid wording: Let us fix our attention out of ourselves as much as possible: Let us chase our imagination to the heavens, or to the utmost limits of the universe; we never really advance a step beyond ourselves, nor can conceive any kind of existence, but those perceptions, which have appear’d in that narrow compass. (Hume 2000, 49; [1.2.6.8])

To go back to our examples, according to Hume, every time we think of Santa Claus, Sherlock Holmes or the New Jerusalem, we think of existing perceptions (ideas or impressions) within the “narrow compass” of our mind. Thus, we simply do not have any notion of so called external existence, but only a notion of the existence of impressions and ideas themselves. Notice, moreover, that this passage confirms the interpretation given above as to why every impression and every idea conveys the notion of existence. It is the existence of the impressions and ideas themselves (i.e., the existence of perceptions) which is at stake: “nor can [we] conceive any kind of existence, but those perceptions, which have appear’d in that narrow compass.”

1.5 A First Occurrence of the Paradox of Non-Existence The time has come now to ask ourselves to what extent the non-property view of existence can be attributed to Hume. This study relies on a conception of property as something which enables us to divide the domain of objects into two classes: namely, those that instantiate it and those that do not. Now, Hume has provided us with a theory according to which everything we may think of exists. Hence, existence is clearly not a property, because it does not fulfill the function of dividing the domain of objects into two classes. We are thus confronted with a first instance of what was labeled as the a-strategy. Hume’s view that existence makes no addition and, consequently, that it is not a property, leads rather straightforwardly to the paradox of nonexistence. This paradox is, indeed, nothing but the other side of the coin of the a-strategy:5

 5

A very similar formulation of the paradox may be found in Fitting and Mendelsohn (1998, 168).

16

Chapter One

(1.1) If we think about something non-existent, we think about it. (1.2) If we think about something, this something exists. (1.3) Thus, if we think about something non-existent, it exists. Premise (1.1) being analytic, it is uncontroversial. In addition, as I have discussed at length, Hume seems to be endorsing premise (1.2), i.e. the premise characteristic of the a-strategy. Thus, it seems to follow that any thought about non-existents is contradictory, or, in other words, that it is impossible to think about non-existents (1.3). If existence makes no addition to an object of thought, this also means that it cannot be subtracted from it. But can it really be the case that Hume embraces the paradox of nonexistence? The problem here is that Hume repeatedly speaks of nonexistence in his Treatise, so that he would always be contradicting himself in those passages. Moreover, if we look beyond the Treatise and take into consideration the refutation of the ontological argument in Dialogues Concerning Natural Religion (Part IX), we find Hume confidently stating that “there is no being whose non-existence implies a contradiction” (Hume 1947, 189) (notice that “being” and “existence” cannot be used synonymously in this instance, as was the case in the first quote). Confronted with this evidence, Williams (1988, 18–21) concludes that Hume does indeed blatantly contradict himself every time he speaks of non-existence. Yet it is hard to fathom how Hume could really have been so blind to such a contradiction. I would suggest that the following passage of the Treatise provides at least a hint towards a strategy that may sidestep the paradox. While discussing the relation of contrariety, Hume writes: no two ideas are in themselves contrary, except those of existence and nonexistence, which are plainly resembling, as implying both of them an idea of the object; tho’ the latter excludes the object from all times and places, in which it is supposed not to exist. (Hume 2000, 15 [1.1.5.6])

For several reasons, this passage is difficult to understand. In the first place, it is plainly circular, for it explains the idea of non-existence by relying on the idea of non-existence itself (“the latter excludes the object from all times and places, in which it is supposed not to exist”). Moreover, also the notion of exclusion (from all times and places) seems to be too close to the notion of non-existence to have any explanatory power in the present context. Be that as it may, Hume is telling us that the ideas of existence and non-existence are not too far apart. Rather, they are “plainly

Hume: No Addition

17

resembling, as implying both of them an idea of the object.” Where do they differ, then? The most interesting part of Hume’s answer lies in the intuition that we are dealing with “contraries in themselves.” This, as he goes on to elucidate, means that they are not found to be contrary by experience, as for instance in the case of hot and cold, or water and fire. Now, although the notion of contrariety at stake remains rather mysterious, it may hint to a way out of the paradox. While thinking of non-existent things, we think of the contrary in itself–whatever this may mean–of a given idea. For instance, while thinking of Santa Claus as nonexistent we think of the contrary in itself of the (existent) idea of Santa Claus. To this extent, it may be possible for us to think of non-existence.

1.6 To Exist and to Be Believed A second, at least partial, way out of the paradox of non-existence may be found in Hume’s discussion of the nature of belief. Clearly Hume, while addressing the notion of belief, is establishing a link to the prior discussion of existence: But I go farther; and not content with asserting, that the conception of the existence of any object is no addition to the simple conception of it, I likewise maintain, that the belief of existence joins no new ideas to those, which compose the idea of the object. When I think of God, when I think of him as existent, and when I believe him to be existent, my idea of him neither increases nor diminishes. (Hume 2000, 66 [1.3.7.2])

At first sight, it seems as if the discussion about belief were to follow exactly the same pattern as the one about existence: when I think of God, of the existing God and of the God I believe in, nothing changes in the idea I have in my mind. Even a belief is not something that may be added or subtracted from the idea of an object–one is tempted to conclude. Yet Hume clearly wants to uphold the intuition according to which we believe some things and disbelieve others. In order to uphold this intuition, Hume is again confronted with a dilemma. Ideas can differ only in two respects: because of their object and because of their vivacity or vividness, i.e. they may approximate the vivacity of impressions or they may be considerably less vivid. Moreover, we know that there has to be a difference between ideas we believe in and ideas we do not believe in. But we also know that this difference cannot be located at the level of the object of the idea: whether I believe in God or I do not, I will have the same idea of God. Thence it follows that the difference between ideas we believe in and ideas we do not believe in can

18

Chapter One

only be accounted for in relation to the difference in their vivacity or vividness. To believe in something is thus equivalent to having a vivid or lively idea of it (see Hume 2000, 67 [1.3.7.5]). We may now go back to the problem of non-existence. As noted above, Hume’s answer to the question as to how we may think of nonexistent objects remains rather mysterious. By contrast, Hume provides us with a clear answer to the question as to how we may disbelieve an object. This happens every time I have a non-sufficiently vivid idea of the object. Even though it is hard to make sense of the non-existence of Santa Claus, we may at least make sense of our disbelief in Santa Claus. Hume’s insights into the notions of existence and belief lead to a capital consequence for the interpretation of the logical notion of judgment, i.e. the mental event associated with a statement. As Hume points out in a crucial footnote (Hume 2000, 67 [1.3.7.5]), the traditional view of the mental act of judging as the separation or union of different ideas must be abandoned. The reason is that all existential judgments falsify this definition: the statement “God is” is not associated to a union of ideas, but just to one idea; i.e., the idea of God. But what then is the necessary and sufficient condition for a judgment? Clearly, it has to be the manner of conceiving an object, i.e. its vividness. If it is a vivid conception, then we have a judgment of belief or assent; if, on the other hand, we have a non-vivid conception, then we have a judgment of disbelief, or, as Hume also says, a dissent. As will be seen in the relevant chapter, this line of reasoning will play a crucial role in Brentano’s approach to judgments and existence.

1.7 Objections: Thinking about Non-Existents Two different steps may be distinguished in Hume’s analysis of existence. To begin with, we are confronted with a first instance of what, in the Introduction, I have labeled as the a-strategy to deny existence the status of property: every object is an existent object. For this reason we cannot rely on the idea or property of existence to draw any distinction within the domain of objects. As it happens, the idea of an object and the idea of an existent object are one and the same thing. It should be highlighted that this claim is strictly linked to Hume’s view that everything we can think of is either an impression or an idea, which, as such, exists within “the narrow compass of our mind.” What is problematic about this approach is that it seems to lead directly into the pitfalls of the paradox of non-existence: it is hard to see how we may still vindicate our intuition that we may think of non-existent objects.

Hume: No Addition

19

Hume does, indeed, hint at a possible way out, by bringing into play the notion of a contrariety in itself between existence and non-existence. But some further details would be needed in order to understand Hume’s cursory remark. The second step is the introduction of a distinction between this trivial notion of existence and the notion of belief: to think of something as existing is different from believing something. Even though belief, as existence, makes no addition to an idea, it is always possible to believe or disbelieve what we think. The reason for this is that belief is explained by Hume as the vividness of an idea, and disbelief as its non-vividness– something which may be relied upon to draw a distinction between ideas. Thus, even though within Hume’s theory it is hard to make sense of our thoughts about non-existents, we may at least compensate this shortcoming by means of our disbeliefs about objects. Yet everyone–and, apparently, Hume too–would still like to be able to draw a distinction between thinking about non-existent things and disbelieving things. To conclude, most of us would readily agree that there is something peculiar about existence, especially if one compares it to other, as it were, garden-variety properties such as being red, being heavy, being a living being, etc. Hume, thus, presented us with a first attempt at rationalizing this difference. His approach, however, does not hit the goal, for we do not get a clear explanation of how it is possible to think of non-existents, or to deny the existence of something.

CHAPTER TWO KANT: NOT A REAL PREDICATE

Kant’s discussion of existence may be seen as pointing backwards to Hume and, perhaps more poignantly, as foreshadowing Frege. It is indeed tempting to interpret Kant as following Hume’s footsteps, to the extent that both claim that existence makes no addition. In fact, Kant says something slightly different: namely, that existence does not enlarge the concept of an object; Hume, on the other hand, says that existence makes no addition to the idea of an object. Yet someone may consider the difference in the respective formulations to be a minor one. In addition, it is perhaps even more tempting to see Kant as anticipating Frege’s famous claim that existence is not a first-order predicate, but rather, a secondorder one. As it happens, even in this case Kant says something slightly different, namely that existence is not a real predicate. But then again, someone may want to argue that a real predicate is a first-order one, and a non-real predicate a second-order one.1 In this chapter, I argue that there is not much substance behind either of these similar word choices. Nevertheless, Kant agrees with Hume and Frege at least to this extent: he, too, deems existence to be something other than a property of objects. Hence, he fully deserves to be dealt with in the first part of this study.

2.1 Real and Logical Predicates To Kant, the quagmire of the philosophical discussion about existence is due to a failure to properly take into account the distinction between real and logical predicates. More precisely, once this distinction is put into

 1 See, for instance, Frege (1976, 176) himself, as well as Bennett (1974, 228–240), Sluga (1980, 88), Haaparanta (1986, 278–279), Williams (1988, 29–30), Forgie (2000) and Reed (2007, 169). Contrary views may be found in Hintikka (1986), Sullivan (1991, 146), Chakrabarti (1997, 43–44), Mendelsohn (2005, 121–149) and Rosefeldt (2011).

Kant: Not a Real Predicate

21

place, the apparently valid but deeply puzzling ontological proof of the existence of God may be put to rest: to Kant, this famous argument is based upon a wrong construal of the very notion of existence. Ironically, however, the distinction between real and logical predicates has given birth to its own quagmire rather than putting an end to the discussion. My suggestion is to sort things out by interpreting “logical” as standing for “syntactical” and drawing a clear line between what pertains to the syntactical and what to the semantic level. A logical predicate–says Kant–is everything that occupies the merely logical–i.e., syntactical–position of a predicate. Kant mentions statements where the subject is predicate of itself, i.e. self-identity statements, as an example. Indeed, in “Superman is Superman,” the second occurrence of “Superman” occupies the merely logical–i.e., syntactical–position of a predicate, even though its meaning–this time not syntactically but semantically speaking–is an object.2 A real predicate, on the other hand, is–in Kant’s words–“a predicate which goes beyond the concept of the subject and enlarges it” (Kant 1998, 567 [B 624 = A 596]).3 This definition should clearly be interpreted semantically. But what might be a semantic reading of the notion of a real predicate, if not that it expresses a property? I will thus take it as a Working Hypothesis (WH) that the couple logical/real predicate should be interpreted as follows: (WH) A real predicate is a term that stands in the syntactical position of a predicate and expresses a property of the subject of the statement. A merely logical predicate is a term that stands in the syntactical position of a predicate without expressing a property of the subject of the statement. On the basis of (WH), I am going to resist the temptation to map the distinction between merely logical and real predicates to the famous Kantian distinction between analytic and synthetic judgments (see for instance Abaci 2008, 580–91). True, we are tempted to say that statements with real predicates express synthetic judgments, whereas statements with merely logical predicates express analytic judgments. But, according to (WH), the two planes should be kept apart. This may be shown by means

 2

The reader may notice that, according to Kant, it seems that in the statement “Superman is Superman,” the logical (i.e., syntactical) predicate is “Superman” and not “is Superman.” This has to be so because “is Superman” clearly does not refer to an object. 3 The original reads: “ein Prädikat, welches über den Begriff des Subjects hinzukommt und ihn vergrößert.”

22

Chapter Two

of a variation on the previous example. If I say “Superman is Clark Kent,” “Clark Kent” occupies a merely logical position of a predicate, for what it means is an object. The identity statement, however, is obviously not an analytic, but rather, a synthetic one: we may only establish its truth by relying on experience (let us assume Superman is not a fiction). Thus, we should not think of statements with a merely logical predicate as being analytic. But should we not at least maintain that statements with real predicates express synthetic judgments? After all, the characterization of a real predicate is in the vicinity of the characterization of the predicate in a synthetic judgment as “lying entirely outside the concept” of the subject (Kant 1998, 130 [B10=A 6]). According to (WH), however, this vicinity is misleading. While discussing the notion of a real predicate, Kant does not focus his interest on whether the predicate actually lies inside or outside the concept of the subject. Rather, he seems to be interested in the fact that the predicate may enlarge the concept of the subject. This does not rule out that the addition may actually be redundant, as in “a golden mountain is golden.”

2.2 Pars Destruens: Existence Is Not a Property Let us turn back to existence. To Kant, existence should not be considered a real predicate. So, according to (WH), Kant is telling us that the verb “to exist” simply occupies the syntactic position of a predicate, as for instance in the proposition “God exists,” but without expressing a property of the subject, i.e. God. From this perspective, there would be a clear analogy between a statement such as “God exists” and identity statements: as the second occurrence of (say) “God” in “God is God” is in the position of a predicate without expressing a property, so is the term “exists” in “God exists.” The classifying of “to exist” as a mere logical predicate raises at least two questions. First, how does Kant argue for it? Clearly, some strong reasons are needed. Indeed, the fact that “exists” does not express a property is not as evident as with the second occurrence of “God” in “God is God” or with the occurrence of “Clark Kent” in “Superman is Clark Kent.” Secondly, what else could be expressed by “exists” if not a property? Clearly, it cannot be an object as in the case of “God” and “Clark Kent.” But what then is its meaning? Partial answers to these questions may be found in the following passage:

Kant: Not a Real Predicate

23

The proposition God is omnipotent contains two concepts that have their objects: God and omnipotence; […] Now if I take the subject (God) together with all its predicates (among which omnipotence belongs), and say God is, or [it is] a God,4 then I add no new predicate to the concept of God, but only posit the subject in itself with all its predicates, and indeed posit the object in relation to my concept. (Kant 1998, 567 [B 627 = A 599])

From a contemporary perspective, we may interpret Kant as putting forward a paraphrase strategy. According to him, in order to interpret statements such as “God exists,” we should move from (2.1) to (2.2): (2.1) God exists. (2.2) I posit the object in relation to the complete concept of God. By (2.2), moreover, I assume Kant to mean something like the following: (2.3) I posit the object that instantiates all the properties expressed by the complete concept of God. This appears as the most plausible way of making sense of the relation between concept and object: an object stands in relation with a concept if and only if it instantiates it; or, in the case of a compound concept, an object stands in relation with a concept if and only if it instantiates all the properties expressed by the concept. Other relations that may hold between objects and concepts are hard to imagine. Kant’s paraphrase strategy is a first important confirmation of (WH). While moving from (2.1) to (2.2) (and 2.3), we no longer find the expression “to exist” in the syntactic position of a predicate that expresses a property of God. Instead, the expression “to exist” has simply disappeared and its meaning seems now to be captured by the notion of positing (for this is the only available candidate for it).5 The term “to posit,” in turn, takes the syntactic position of a predicate that expresses a

 4

The translation reads here: “there is a God,” which seems to suggest that the original says “es gibt einen Gott.” But since the original does not say “es gibt einen Gott,” but rather “es ist ein Gott,” it is preferable to provide a literal translation. This is especially the case since the “there is”-formulation triggers unwarranted Fregean associations. True, “it is a God” is not a fluent English rendition. But the original “es ist ein Gott” is not fluent German, either. 5 As noted by Adaci (2008, 581), in his pre-critical text The One Possible Basis for a Demonstration of the Existence of God (1763), Kant explicitly identifies the notion of being with the notion of positing.

24

Chapter Two

property of the cognitive agent (the “I”). Hence, if “Clark Kent” in “Superman is Clark Kent” is a mere logical predicate because it expresses an object and not a property, “exists” in “God exists” is a mere logical predicate because it does not express a property of God, but rather, a property of the cognitive agent. According to this interpretation, existential statements remain plain categorical statements where a property is attributed to an object. They are problematic only insofar as they do not–so to speak–wear the object and the property which are at stake on their sleeves.6 We may now briefly address what is hiding behind Kant’s stance on existence as something that cannot be added to the concept of an object. Provided the paraphrase strategy is correct, we have already seen why this is the case: existence adds something to the concept of the cognitive agent, i.e. the hidden subject of existential statements (i.e., 2.2 or 2.3), and not to the concept of the apparent grammatical subject (i.e., 2.1). True, one might be tempted to argue that–to a certain extent–the concept of the apparent subject is being changed too, namely to the extent that it is posited by me. This, however, seems closer to what contemporary philosophers like to call a Cambridge-change to distinguish it from real, full-blown changes of properties.

2.3 Comparison with Hume and Frege It may be helpful to turn to a brief comparison between Kant’s analysis of existence and the views endorsed by Hume and Frege. As addressed at the beginning of this chapter, there seem to be reasons to interpret Kant as moving in Hume’s footsteps, as there seem to be reasons to interpret him as a forerunner of Frege. Let us start with Hume. To Hume, the idea of existence makes no addition to our ideas, because every idea is existent. To Kant, on the other hand, existence makes no addition to the concept of an object because existence is simply not–so to speak–in the line of business of objects. Thus, the similarity in their formulations remains a very superficial one. This should be clear from the fact that only Hume’s view seems to lead to the paradox of non-existence. For Kant, on the other hand, this problem

 6

Martin (2006, 55) reaches the different conclusion that, according to Kant, existential statements do not express the attribution of a property to an object, or– more generally–they do not express a combination of ideas. As Martin (2006, 44– 46) is aware of, however, this stands in conflict with the fact that Kant upholds the traditional view that every statement or judgment expresses a combination of concepts.

Kant: Not a Real Predicate

25

does not arise: according to him, we may very well think of non-existents, namely as long as we are not “positing,” or, more precisely, as long as we are doing the contrary of positing the object–whatever this may be (more on this below). Again, we have a clear sign that the two philosophers are in fact following completely different lines of reasoning. It is only because of some similar choices of words–in the first place the English expression of “enlarging” and its semantically related German counterpart “vergrössern”–that the two positions seem to converge. This notwithstanding, there is a tendency in the literature to attribute to Kant something like the Humean thesis on existence. For instance, both Mendelsohn (2005, 122) and Reicher (2005, 197–199) argue that Kant endorses a view of existence as a redundant property of objects. As Mendelsohn writes while commenting upon the famous example of the hundred existing thalers, “[w]hatever one imagines, one imagines to exist: when one imagines one hundred thalers, one imagines they have the existence property (even though they might not).” This is a thesis which has an intuitive appeal and may be relied upon to argue that existence is a redundant property of objects. Notice, moreover, that Mendelsohn’s reading of Kant comes very close to a possible interpretation of the Humean principle discussed above (see above, section 1.1). The problem, however, is that it is hard to see what in Kant’s wording supports this interpretation. Let us turn to Frege. Upon first inspection, there seems to be less friction between his account and the one defended by Kant. As we will see in more detail in the relevant chapter, according to Frege, existential statements which do not involve proper names have to be rephrased as “there is an x,” where x stands for a concept. To wit, if we interpret “God” as a concept, “God exists” should be interpreted as “there is a God.” In addition, since the object of the statement is indifferent (it simply has to be something), one may as well speak of it as a statement about the instantiation of a concept: “There is a God” says that the concept of God has the property of being instantiated at least once. Consequently, the mysterious first-order property of existence is interpreted away by means of the more familiar second-order one of being instantiated (at least once). Existence–so to speak–is in the line of business not of objects, but of concepts. Now it seems that Kant and Frege at least agree with respect to the negative part of their thesis: to Kant, too, existence is not in the line of business of objects. Or, as he frames it: Existence is not a predicate which goes beyond the concept of the subject and enlarges it. This is strictly linked to Kant’s attempt to dispel the illusion that existence is about

26

Chapter Two

objects, by reducing it to the notion of positing. Also in this respect, we may say that Kant and Frege are not too far apart. The notion of positing and the notion of having instances both fulfill an analogous function: they are meant to lift the veil of illusion on existence as a property of objects. But a crucial question still lingers: does the notion of positing mean, if not the same, something relevantly similar to Frege’s notion of having instances? What should be highlighted, at this point, is that Kant, as of yet, has said nothing about the notion of positing. But it seems that Kant’s reformulation of existential statements such as “I posit the object in relation to my concept” already excludes the Fregean reading. As argued above, “I posit the object in relation to the complete concept of God” (2.2) should be interpreted as “I posit the object that instantiates all the properties expressed by the complete concept of God” (2.3). And–if this is the case–Kant is distinguishing the notion of positing–whatever it may be– from the notion of having instances. Thus, if we concentrate on the positive side of their approach, the Kantian and the Fregean strategy seem to fall apart. Nevertheless, in order to substantiate this line of reasoning we need to explore Kant’s notion of positing.

2.4 Pars Construens: Existence and Possible Perception The foregoing discussion has left us with one open question. What does the talk about positing an object really mean? The answer is provided by the following passage: For through its concept, the object would be thought only as in agreement with the universal conditions of possible empirical cognition in general, but through its existence it would be thought as contained in the context of the entirety of experience; thus through connection with the content of the entire experience the concept of the object is not in the least increased, but our thinking receives more through it, namely a possible perception. (Kant 1998, 568 [B 629 = A 601])

According to Kant, through a concept we think of an object as possible, in the sense that it is possible according to the general conditions of empirical knowledge. Existence, on the other hand, is something through which we think of the object as an object of experience. But this, instead of adding something to the object, adds something to our thought: namely, a possible perception. This passage provides the key as to how to interpret the notion of positing. Since to say “x exists” is tantamount to saying “I posit x,” and–as

Kant: Not a Real Predicate

27

the passage clearly states–to say “x exists” is also tantamount to saying “it is possible for me to perceive x,” it follows that to say “I posit x” is also tantamount to saying “it is possible for me to perceive x.” From this perspective, the statement “God exists” (2.1) is explained by the statement “I posit the object that instantiates all the properties expressed by the complete concept of God” (2.3). In turn, “I posit the object that instantiates the properties expressed by the complete concept of God” should be explained as (2.4): (2.4) It is possible that I perceive the object that instantiates all the properties expressed by the complete concept of God. This is in fact what Kant has already expressed elsewhere, when saying that “perception […] is the sole characteristic of actuality” (Kant 1998, 325 [B 273 = A 225]).7 By taking this step, Kant goes all the way towards interpreting existential propositions as being–in the last instance–propositions about the possible perceptions of a thinking agent. This move definitely pulls Kant away from Frege. The notion of positing has clearly nothing in common with the second-order property of having instances. Instead, in order to discover the essence of existence, we have to look at the agent who is putting forward existential judgments and his possible perceptions. Notice, moreover, that since a given possible perception does not seem to be analytically contained within the concept of a thinking agent, Kant vindicates the intuitive synthetic character of existential judgments. If the subjectivist stance pulls Kant away from Frege, it brings him–at least to some extent–closer to Hume. True, Kant does not share the view that we can only think of existents, as Hume seemed to. However, for both philosophers it is the cognitive agent which takes the center of the stage. In Hume, this is the case because of the existing impressions and ideas within the narrow scope of a mind; in Kant, this is the case because of the possible perceptions of a thinking subject. Finally, the explanation of the notion of positing through the notion of possible perception provides us with a second confirmation of (WH). If the verb “to exist” really expresses the notion of positing, and, in turn, the notion of positing is tantamount to the notion of a possible perception of a thinking agent, the verb “to exist” only occupies the syntactical position of

 7

Chakrabarti (1997, 38) already drew attention to this quote. The same point is also discussed at length by Abaci (2008, 587–593).

28

Chapter Two

a predicate, without expressing a property of the object. Indeed, what it really expresses is a property of the agent.

2.5 Kant, Neo-Meinongianism and the Ontological Argument It has been suggested by Chakrabarti (1997, 38) and Rosefeldt (2011, 348) that, in agreement with what was argued above, Kant is indeed not a Fregean. The reason adduced by both Chakrabarti and Rosefeldt, however, is that to them Kant’s approach is in the vicinity of the Neo-Meinongian distinction between nuclear and extra-nuclear properties–a distinction which will be addressed in detail in the second part of this study. As Chakrabarti says, “[t]he idea of a predicate which is always to remain outside the ‘inner determinations’ of an object, and yet can be ascribed to it informatively, is closer to Meinong’s idea of an extra-nuclear predicate […] than to Frege’s notion of a second-order predicate” (Chakrabarti 1997, 38). Chakrabarti correctly highlights this similarity between the Kantian and the Meinongian approach. First, existence is informative, i.e., it is always possible to deny the existence of something. Second, existence must nonetheless be relegated–metaphorically speaking–outside the “inner determinations” of objects. One should, however, also highlight the differences. As the very notion of an extra-nuclear property suggests, to Neo-Meinongian philosophers such as Routley (1980) and Parsons (1980) existence does indeed express a property of objects: by means of the notion of existence we can divide the domain of objects into two classes: i.e., existent and non-existent ones. It is in this sense that existential statements are informative to them. To Kant, on the other hand, existence does not express a property of objects, and existential statements are informative because they tell us something about the agent putting forward these statements, i.e., which his possible or impossible perceptions are. Thus, once we spell out what is hiding behind the metaphor of lying outside the inner determinations of objects, we discover two very different approaches. A second reason adduced by Chakrabarti and Rosefeldt to bring Kant closer to the Neo-Meinongian philosophers is related to the ontological proof of the existence of God. A very primitive rendition of the ontological argument may run as follows:8

 8

Obviously, the inference is valid only if the T-axiom of modal logic is granted: from “it is necessary that p” we may infer “p.”

Kant: Not a Real Predicate

29

(2.5) Existence is part of the concept of God. (2.6) If a property P is part of the concept of x, then it is necessary that x instantiate P. (2.7) It is necessary that God exist. (2.8) God exists. There are of course slightly different paths that lead to the premise (2.5). For the purpose of the present discussion, however, we do not need any details as to what is hiding behind (2.5). What is important is to stress that Neo-Meinongians reject (2.5) because existence is not a nuclear, but rather, an extra-nuclear property. Kant, on the other hand, rejects (2.5) because existence is not a real predicate, but rather, a merely logical one. Because of this analogy in the strategy to block the ontological argument, both Chakrabarti and Rosefeldt want to see a link between the notions of real and nuclear predicate, on the one hand, and of logical and extranuclear property, on the other hand. But then again, this analogy seems to me to be misleading. To understand why Kant rejects (2.5), it is not enough to say that to him existence is not a real but a logical predicate. What needs to be added is that to Kant existence is not at all in the line of business of the prima facie objects of existential statements. Once again, if this is taken into account, the stark difference between Kant’s approach and the Neo-Meinongian one comes to the fore. We must therefore conclude that the analogies between the Kantian and the Neo-Meinongian approach remain rather superficial and fall short of proving any substantial convergence between these two positions. As it happens, the divide between Kant and Neo-Meinongians is the same divide between the first and the second part of this study: according to the latter, existence is a property of objects, whereas according to the former this is not the case.

2.6 Objections: Existence and Possibilities Let me summarize Kant’s approach to existence. The first step consists in a pars destruens: Kant denies that the term “existence” (and its cognates) expresses a property of the object allegedly at stake in the existential statement, even though he concedes that it seems to be a predicate of that same object. The second step of Kant’s discussion is–not surprisingly–a pars construens. Although it does not express a property of the object

30

Chapter Two

allegedly at stake, “exists” is not meaningless according to Kant. First, the verb “to exist” is interpreted by the term “positing”: “x exists” means “I posit the object that instantiates the properties expressed by the (complete) concept of x.” Second, the notion of positing is interpreted by recurring to the notion of the possibility of being perceived: what “I posit the object that instantiates the properties expressed by the concept of x” means is “it is possible for me to perceive the object that instantiates the properties expressed by the concept of x.” As in the case of Hume, we are thus confronted with a shift of focus towards the thinking agent. It is, however, only in the case of Kant that we may speak of a first occurrence of what I have labeled as the b-strategy: existence does not characterize objects, but rather, the possibility of a thinking subject. Thus, under the column of existence we should not write existent objects, but rather, the possible perception of a given subject. Conversely, under the column of nonexistence we should not list the non-existent objects, but the impossible perceptions of a given subject. Let us now turn to some objections. For one, it is indeed easy to think of situations where the statement “x exists” is true whilst the statement “it is possible to perceive x” is false. Some objects may simply not be perceivable. Thus, the series of equivalences upon which Kant seems to rely (from 2.1 to 2.4) is jeopardized. Yet someone may argue that it is indeed the case that everything that exists has to be–at least in principle– perceivable. From this perspective, for instance, one would have to say that, even in the case of God, if he exists, he has to be perceivable. Kant seems ready to make this very strong assumption: [O]ur consciousness of all existence […] belongs entirely and without exception to the unity of experience, and though an existence outside this field cannot be declared absolutely impossible, it is a presupposition that we cannot justify through anything. (Kant 1998, 568 [B 629 = A601]).

It is perhaps with this kind of passage in mind that Richard Routley qualified Kant’s view of existence not only as “subject-relativism” but also as “human chauvinism” (Routley 1980, 181).9

 9

Abaci (2008, 591), on the other hand, draws attention to the following point. An existential statement needs not to express that a direct perception of the object at stake is possible. Rather, it may simply express that it is possible to perceive something causally linked to the object at stake. This weakening, however, does not substantially change the picture. Why should it be more plausible to say that every existent object should be at least indirectly perceivable? Take for instance Lewis’ possible worlds: we cannot perceive them, neither directly nor indirectly.

Kant: Not a Real Predicate

31

However, even the strong epistemological premise just considered is not enough to render Kant’s view immune from the following objection: one may think of situations according to which the statement “x exists” is false but the statement “it is possible to perceive x” true. Indeed, many things that do not exist could very well be perceived. To take a less controversial example than God, I assume we all agree that a golden mountain does not exist. Yet we could very well conceive a possible situation in which we perceive a golden mountain. Hence, the equivalence postulated by Kant is once again jeopardized. The obvious reply to this second objection would run as follows: Kant has a different notion of possibility in mind, which does not allow for the truth of a statement of the form “x does not exist and it is possible to perceive x.” But then the question we should raise would be the following: In which sense is he speaking of possibility? The answer would have to be that Kant is implicitly narrowing the scope of possibilities to possibilities about actually existent objects: the only situations which are–in the relevant sense–possible are those in which we have exactly the same set of existing objects as in the actual situation. But this would clearly make the Kantian reasoning circular: “x exists” is explained by reducing it to “it is possible to perceive x.” But, in turn, we have to add the condition that the statement “it is possible to perceive x” is true if and only if x exists. Thus, we have not moved one single step further in explaining the notion of existence. To return to the example of the golden mountain: If someone were to raise the objection that a golden mountain does not exist but it is possible to perceive a golden mountain, what might Kant’s answer be? It seems to me that he would have to say that it is only possible to perceive a golden mountain if it is actually the case that a golden mountain exists. We must therefore conclude that the possibility of perceiving something is, if perhaps a necessary, at least not a sufficient condition for the existence of something. It might indeed be false that something exists and that it is not possible to perceive this something (i.e., there are no unperceivable objects). However, one has to grant that it may be true that something does not exist but it is possible to perceive this something, namely in case we are considering an alternative situation in which we have a different set of existent things. It is also worth noticing that the interpretation of existential statements as the possibility of someone’s perception presupposes the existence of the

 Yet this does not stand in the way of considering them to be existing–as Lewis does.

32

Chapter Two

perceiver, or at least of the perception. In turn, the existence of the perceiver or perception would thus have to be explained as the possibility of being perceived, and so on ad infinitum. All these arguments are pointing towards the very plain fact that the notion of perception is of no use towards explaining the notion of existence. What we could claim, on the other hand, is–far more modestly– that perception is the privileged way we have to establish whether something exists or not. But Kant clearly wanted to say something more than this. If the pars construens of Kant’s approach to existence has to be rejected, his pars destruens cannot–as it stands–be upheld either. As it happens, the only reason we may have to endorse the pars destruens would be the strength of the pars construens. Kant’s discussion does not provide any further reason to accept his claim that existence is just a merely logical predicate. One may, obviously, grant, along with Kant, that we all have a strong intuition that there is something peculiar about existence, which sets it apart from what we usually consider to be a property. The problem with this intuition, however, is that Kant, as Hume before him, has not provided us with a convincing explanation thereof.

CHAPTER THREE BRENTANO: ACCEPTANCE AND REJECTION

The interest in Brentano as a decisive figure for contemporary philosophy established itself rather late, and his approach to existence is not usually addressed in studies on this subject.1 However, Brentano deserves our attention as a philosopher who forcefully argued against the property-view of existence. Moreover, as will be seen, his approach is in several respects very much indebted to Hume. There is also a further reason for which Brentano should not be missing in the present study: he, Brentano, played a crucial role in the development of the thought of Meinong, i.e., the philosopher who is commonly regarded as the champion of the property-view of existence;–it is, indeed, owing to Brentano’s suggestion that Meinong wrote his Habilitationsschrift (Meinong 1877) on Hume. And even though Meinong showed a strong strive for independence from the very beginning of his philosophical career, his approach to existence is best understood against the background of Brentano’s. This chapter will also devote two paragraphs to Kasimir Twardowski, who, like Meinong, was a student of Brentano. Twardowski is relevant in the present context for his attempt to amend some key elements of Brentano’s approach and for at least hinting towards the possibility of interpreting existence as a property of objects.

3.1 Mental In-Existence Brentano’s approach to existence is intimately connected to his theory of judgment. Before addressing Brentano’s theory of judgment, however, we should devote a few words to the famous passage on mental inexistence in his Psychology from an Empirical Standpoint. The reason for this is twofold: on the one hand, judgments according to Brentano are a kind of

 1

Only very recently, Kriegel (2015) has drawn attention to Brentano’s theory of existence as an alternative to other more commonly acknowledged approaches.

34

Chapter Three

mental phenomenon; thus, before addressing the more specific notion of judgment, we should say something about what a mental phenomenon is according to him. On the other hand, and more cogently, Brentano’s approach to intentionality seems to rely–at least prima facie–on a notion of existence, or more precisely on what he refers to as “intentional (or mental) inexistence.” Brentano writes: Every mental phenomenon is characterized by what the Scholastics of the Middle Ages called the intentional (or mental) inexistence of an object, and what we might call, though not wholly unambiguously, reference to a content, direction towards an object (which is not to be understood here as meaning a thing) or immanent objectivity. Every mental phenomenon includes something as object within itself, although they do not all do so in the same way. In presentation, something is presented, in judgment something is affirmed or denied, in love loved, in hate hated, in desire desired and so on. (Brentano 1874, 115 [88])

As his brief recapitulation at the end of the paragraph clearly states, this passage should be understood in the first place as putting forward the following claim: “The intentional in-existence of an object [is] a general characteristic of mental phenomena which distinguishes this class of phenomena from the class of physical phenomena” (Brentano 1874, 118 [91]). The problem, however, is how to interpret the notion of intentional or mental inexistence. Two options are on the table: either the notion of intentional inexistence of an object implies that the object has to literally in-exist, i.e., to exist within the mind (Sauer 2006 labels this the KrausChisholm interpretation); or we should take the expression as a mere façon de parler, as suggested for instance by Chrudzimski and Smith (2004, 205).2 The question as to which horn of the hermeneutical dilemma one should take is difficult to assess. This is especially the case if one also takes into consideration the lectures held by Brentano in the 80s and 90s (especially Brentano 1982).3 What is uncontroversial, however, is that

 2

Authors who have explicitly argued that the notion of mental inexistence should not be taken literally are Antonelli (2000; 2001, 395–405), Brandl (2005), Münch (1993, 76–78) and Sauer (2006). Chrudzimski (2001, 13–26; 2004, 124–138; 2007, 8) takes a more nuanced position, but he agrees that there is no element in Brentano’s Psychology obliging us to read the notion of mental inexistence literally. 3 Chrudzimski (2001, 10–49; 2003, 124–175; 2007, 8–37) argues that in his lectures Brentano defended an explicit ontological interpretation of the notion of immanent or mentally inexistent objects, albeit under the new label of the

Brentano: Acceptance and Rejection

35

Brentano later on in his career explicitly rejected the literal reading of mental inexistence (the passage quoted above stems from Brentano’s Psychology, published in 1874, whilst the following text was first published in 1911 in the appendix to the second volume of the Psychology): If someone thinks of something, the one who is thinking must certainly exist, but the object of his thinking need not exist at all (Brentano 1911, 123 [272])

From this perspective, it would be better to avoid any reference to the notion of intentional inexistence while formulating Brentano’s Intentionality Thesis: (IT) Something is a mental phenomenon if and only if it is directed towards an object. According to this interpretation, (IT) should be considered existentially neutral: mental phenomena are those phenomena which are directed towards an object, no matter whether this object is existent or non-existent. As we shall see, this is also the interpretation of (IT) which best suits Brentano’s theory of judgment. For these reasons–namely Brentano’s own retrospective interpretation and the consistency with his theory of judgment–I am going to rely on (IT) as capturing the central claim behind the famous passage on mental or intentional inexistence.

3.2 To Judge Is to Accept or Reject As already addressed in the previous section, Brentano’s discussion of the notion of existence is intimately connected to his discussion of the notion of judgment. Here one should start by noticing that, in his Psychology, Brentano argues at length against the then still orthodox notion of judgment as the mental event of uniting or separating ideas. To him (Brentano 1874, 276–7 [161–2]), as to Hume before him, existential statements play a crucial role in rejecting this view, though in a somewhat different way. Brentano’s first step is to deny that the union or separation of ideas is a sufficient condition for a judgment (see Chrudzimski 2001, 51–2; 2007, 38). For instance, the phrase “a learned man” (when pronounced) surely

 “intentional correlate” (intentionales Korrelat) or of the “meaning” of a name as opposed to its “reference.”

36

Chapter Three

expresses two ideas joined together, but it does not express a judgment. In order to have a judgment we need something more, namely what Brentano labels as acceptance (Anerkennung) and rejection (Verwerfung) of ideas.4 Thus, the statement “a man is learned” (when asserted) expresses a judgment because it does not express a mere combination of ideas, but rather, the acceptance of the combination of the idea of a man with the idea of someone learned. On the other hand, the statement “a man is not learned” expresses the rejection of the combination of ideas of a man and of someone who is learned. More precisely, what is approved or rejected are not the ideas, but rather, the objects of the ideas, since by the term “idea” (Vorstellung) Brentano understands the mental phenomenon of representing, and by object or content of the idea, that towards which the mental phenomenon of representing is directed. On the background of the interpretation of judgments as mental phenomena of acceptance and rejection, Brentano is in a position to show that the union or separation of ideas is not even a necessary condition for a judgment (see again Chrudzimski 2001, 51–2; 2007, 38). In order to prove this, Brentano relies on the principle that if you accept a whole, then you have to accept its parts, too. For instance, the judgment expressed by the statement “a learned man exists” is not only a mental phenomenon of accepting the existence of a learned man (i.e., the whole) but also of accepting the existence of a man (i.e., a part of the whole). Yet, if this were the case, a statement of the form “A exists” would not only express the acceptance of an existing A, but also the acceptance of A (“A” should be understood as a variable for any indefinite or definite description; there is no place for proper names in Brentano’s philosophical grammar). But at this point he will rhetorically ask: In which respect does the acceptance of the existence of A differ from the acceptance of A? To him, there clearly is no difference. Thus he concludes: “So we see that the affirmation [Anerkennung] of A constitutes the true and complete sense of this proposition [“A exists”], and that A alone is the object of the judgment” (Brentano 1874, 277 [208]). The same conclusion is even more striking if negative existentials are taken into consideration. If “A does not exist” is interpreted as a denial of the combination of a property of existence with A, then we would not yet

 4

The English translation (Brentano 1994) renders freely the German terms of “Anerkennung” and “Verwerfung” as “affirmation” and “denial.” I prefer the more literal translation, especially because it does not give rise to the strong linguistic associations of the terms “affirmation” and “denial.” Although it may be expressed through linguistic affirmations and denials, a judgment according to Brentano is something totally independent of language.

Brentano: Acceptance and Rejection

37

have denied A, for the rejection of a whole does not imply the rejection of its parts. Yet, according to Brentano, when we say “A does not exist” we want to express a rejection of A, so that A alone, and not a combination of A and existence, is the only object of our judgment (Brentano 1874, 277 [209]). Two capital conclusions follow from this line of reasoning. First, since judgments may be directed to only one object, as in the case of the acceptance of a man, the union and separation of ideas is not even a necessary condition of judgments. Judgments may thus be simply defined as the acceptance or rejection of an object of an idea. Judgments are still dependent upon ideas, but not because they combine them. Rather, judgments are dependent upon ideas because they consist in taking a certain attitude with respect to the object presented by the idea, namely accepting or rejecting it. As Brentano says, a judgment is a certain way in which we may be directed towards an object.5 The second crucial consequence of Brentano’s arguments is that the notions of acceptance and rejection entirely capture the notions of existence and non-existence respectively. As we have seen, if I say “A exists,” the true sense of this statement is “A is accepted”; and if I say “A does not exist” the true sense of this statement is “A is rejected.” Brentano reaches the same conclusion in a more explicit way by relying on the following trilemma: (3.1) The idea of existence is derived from sensation (3.2) The idea of existence is an innate idea (3.3) The idea of existence is an idea of reflection. Since Brentano rejects both (3.1) (sensation does not provide any idea of existence), and (3.2) (Brentano, who moves in the footsteps of British empiricism, is skeptical about innate ideas), we are only left with (3.3). As Brentano (1874, 279 [210]) writes, the idea of existence “is derived from inner experience, and we acquire it only with reference to judgments.” To paraphrase Quine, we may say that to be is to be accepted and not to be is to be rejected.6

 5

According to Brentano, also impersonal statements such as “it rains” should speak in favor of his approach to judgment. For a discussion of impersonal statement in this context, see the series of articles by Brentano’s student Anton Marty (1884; 1895). 6 Vallicella (2001, 315) denies that Brentano is identifying existence with acceptance because this would lead to a “lunatic form of idealism.” Brentano,

Chapter Three

38

3.3 Brentano’s Existential Reformulation of the Square of Opposition Brentano’s approach to existence implies that every statement, since it expresses a judgment of acceptance or rejection, may be restated in an existential form. If I say “God is omnipotent” I express my acceptance of an omnipotent God. The same judgment, thus, may also be expressed by the statement “an omnipotent God exists,” for the true sense of this statement is, once more, “an omnipotent God is accepted.” Similarly, “God is not omnipotent” and “the omnipotent God does not exist” have exactly the same meaning, i.e., “an omnipotent God is rejected.” Brentano even takes these considerations further and shows how the categorical statements of the traditional square of opposition may all be cast as existential statements (see Table 3-1, where I rely on the traditional scholastic labels of the four kinds of categorical statements). Table 3-1 Existential and Psychological Formulations

 Classic Formulation

Existential Formulation

Psychological Formulation

A

All men are mortal

No immortal man exists

An immortal man is rejected

I

Some man is ill

Some ill man exists

An ill man is accepted

E

No stone is living

No living stone exists

A living stone is rejected

O

Some man is not learned

Some unlearned man exists

An unlearned man is accepted

 however, is not arguing for the dependence of the world from the thinking subject (i.e., idealism). He simply says that what we mean by the word “existence” and its cognates are our mental events of acceptance or rejection. These two things should not be confused. The fact that Brentano defines existence via the notion of acceptance, and non-existence via the notion of rejection, is highlighted by Chisholm (1982, 20). Chisholm also notes that one may be tempted to speak of Brentano’s affirmation (i.e., acceptance) as an “affirmation ‘as existing’.” Strictly speaking, however, this way of talking is misleading, for the notion of existence, and thus the term “existence,” is explained away by the notion of affirmation. See also the critical remarks by Geach (1965, 458–459), and Simons (1994, xviii).

Brentano: Acceptance and Rejection

39

Particular affirmative propositions (I) and universal negative propositions (E) pose no problem to the equivalence between the categorical and the existential formulation. Affirmative universal (A) and particular negative (O) propositions, however, have to be reinterpreted as negative universal and particular propositions, respectively. The reason behind the reduction of (A) deserves special attention. It would indeed be very awkward to rephrase “all men are mortal” as “all mortal men exist.” Indeed, the fact that all mortal men exist would not even exclude the possibility that some immortal men exist, too–which seems to be what is ruled out by the statement that all men are mortal. Moreover, this reduction would render the truth of the sentence dependent upon the existence (or, more precisely, acceptance) of mortal men–which seems unwarranted. To Brentano, even if there are no men, “all men are mortal” should be considered as a true statement (he thus abandons subalternation) (see Brentano 1874, 285 [215–6]). Brentano thus opts for reinterpreting universal statements as universal negations of existence.7 Finally, according to Brentano conditional statements, too, may be reformulated as existential statements. We should simply apply the reduction as in Table 3-2. Table 3-2 Conditional Statements Classic Formulation

Existential Formulation

Psychological Formulation

If a man acts wrongfully, he harms himself

There is no such thing as a man who acts wrongfully and does not harm himself

A man acting wrongfully and not harming himself is rejected

This is crucial because the rules of inference usually linked to conditionals such as modus ponens and modus tollens need to be reinterpreted as rules about relations between mental events of acceptance and rejection. For instance, if I reject aman who actswrongfully and does not harm himself, and I accept a wrongfully acting man, then I also have to accept a man

 7

Later in his life, Brentano will give a slightly more complicated interpretation of the different categorical propositions, in order to accommodate it with what is usually labeled his “reism” (see Brentano 1911, 145–158 [291–300] and Brandl 2014 for discussion).

40

Chapter Three

who harms himself. Since we are mainly interested in Brentano’s theory of existence, though, we need no longer follow him on this very steep path.8

3.4 Hume and Brentano on Existence and Belief/Acceptance Let us now turn to some differences as well as similarities between Hume and Brentano. As we have seen, Hume does not reduce existence and nonexistence to belief and disbelief, or assent and dissent, respectively. He hints, however, to a connection.9 Brentano–we may then say–is following Hume’s hint and attempts a straightforward reduction. A direct consequence of this approach is that, in Brentano’s conceptual framework, we are not confronted with any paradox of non-existence. Since “x exists” expresses the acceptance of x and “x does not exist” the rejection of x, there is nothing tautological in the first statement and nothing contradictory in the second one. True, according to a literal interpretation of the passage on intentional in-existence, Brentano, like Hume before him, seems to be committed to the view that every object of thought somehow exists within the mind. But it is clear that, even if he ever held such a view, it did not take him long to abandon it. And this for a very simple reason: namely, that this view would not be consistent with his theory of judgment. As he writes: if he [the thinking agent] is denying something, the existence of the object is precisely what is excluded whenever his denial is correct” (Brentano 1911, 123 [272]).10 Going back to the comparison between Brentano and Hume, what both agree upon is that judgments do not consist in the act of uniting or separating (objects of) ideas, but rather, in something which supervenes

 8

It is noteworthy how the paradoxes of material implication make their appearance under disguise in Brentano’s logic: if I reject a wrongfully acting man, then I also reject any conjunction including a wrongfully acting man; and if I reject a man who does not harm himself, then I also reject any conjunction including a man who does not harm himself. Brentano’s existential reduction of statements is discussed by Simons (1992a, 46; 1992b, 259–264; 1996, 307; 2004, 52). 9 According to Geach (1965, 458), Hume too is reducing existence to the notion of belief. However, this interpretation does not seem to be entirely accurate. 10 This passage immediately follows the quote given above at the end section 3.1. Chrudzimski (2001, 79; 2007, 48) on the other hand, suggests that Brentano’s theory of judgment need not clash with an ontologically loaded interpretation of the immanent or mentally inexistent object. The reason for this is that the judgment, even though directed at the mentally inexistent object, may metaphorically “extend” (verlängern) the intentional relation and yield us something other than the mentally inexistent object. We do not have any textual evidence that may lead us to attribute this view to Brentano, though.

Brentano: Acceptance and Rejection

41

upon (objects of) ideas, either single or composed. Hume talks of belief and Brentano of acceptance/rejection. However,–and here we come to a further major difference–Brentano does not follow Hume in his reduction of belief to the vividness of an idea. Brentano’s strategy is thus to take acceptance and rejection to be primitive notions.11 On this conception, there is only some room for analogies with other kinds of mental events: as we may like or dislike the object of an idea, so we may accept or reject the object of an idea. The analogy is appropriate to the extent that (a) both judgments and emotions (i.e., likings and dislikes) are mental phenomena strictly linked to an idea and therefore to its object, and that (b) the notions of liking and disliking–like the ones of acceptance and rejection–are irreducible to other notions (Brentano 1874, 290–5 [222–5]). This leads to a third major difference between Hume and Brentano. As we have seen, Hume considers existence and non-existence to be “in themselves contrary.” To Brentano, on the other hand, they are, as it were, contrary by experience, like heat or coldness: it is by means of the experience of reflecting upon the opposite mental events of acceptance and rejection that we gain these notions.

3.5 Twardowski on Contents and Objects of Ideas Before assessing Brentano’s approach to existence, let us now turn to his student Kasimir Twardowski and the amendments he suggested to the Brentanian picture. Indeed, if such amendments are convincing, they should be taken into consideration while assessing Brentano’s approach. In his most famous publication On the Content and Object of Presentations (1894), Twardowski argues that we should–as the title suggests–introduce a distinction between the content of a presentation or idea and its object. More precisely, but only as a first approximation, we may say that according to Twardowski the content is the component of an idea in virtue of which the idea is about a given object. In other words, it is by means of its content that an idea is directed towards an object. Now, Twardowski follows the Brentanian view according to which every mental phenomenon essentially involves a presentation. Thus, the introduction of the distinction between contents and objects of presentations automatically leads to the following revision of the Intentionality Thesis. According to Twardowski, instead of (IT), we should say something like (IT´):



11 It should be pointed out, however, that already Hume seemed to be moving in this direction in his Enquiry (see Owen 2003).

42

Chapter Three

(IT´) Something is a mental phenomenon if and only if it is directed towards an object by means of its content. However, as will be seen further on, Twardowski will not simply argue for the introduction of a distinction between the content and object of ideas. Rather, he will also suggest that the same distinction may be drawn in the case of judgments: judgments, too, have what may be labeled as a content which must be distinguished from the object of the judgment itself. Moreover, according to Twardowski, the notion of the content of a judgment should to a certain extent clarify the relation between judgments, i.e., acts of acceptance and rejection, and the notion of existence. But let us first focus upon ideas. Twardowski starts by clarifying the distinction between contents and objects of ideas by means of an analogy with paintings: the content of an idea fulfills a function analogous to that of the colors and shapes on the canvas of a painting (see Twardowski 1894, 12–20 [11–17]). More precisely, as the colors and shapes on a canvas yield us the depicted object, so does the content of an idea with respect to its object. For instance, in my idea of the golden mountain there has to be something similar to the colors and shapes on the canvas of a painting representing a golden mountain. Otherwise, as a canvas that has not been painted yet, the idea would simply not represent anything. But what is it that speaks in favor of this assumption, namely, that ideas should have as their constituents something like the colors of a painting? Twardowski defends this assumption by relying on three arguments (clearly the analogy with paintings is not an argument): an argument from spatiality, an argument from co-reference, and an argument from existence. The argument from spatiality, which Twardowski credits to Benno Kerry, runs as follows: the content of a presentation cannot be spatial, for the content is part of an essentially non-spatial mental event, but the object of a presentation may be spatial. For instance, the idea of a golden mountain is the idea of an object that has the spatial properties of being golden and being a mountain; but the content of the idea clearly can have neither of those spatial properties. Thus, we should distinguish between contents and objects of presentations (Twardowski 1894, 30–31 [28–29]). This argument, however, presupposes that there is something like the mental content of a presentation, so it cannot be considered as a compelling argument for the distinction between contents and objects of

Brentano: Acceptance and Rejection

43

ideas. At most, the argument may prove that if there are contents of ideas, they are–at least in certain cases12–distinct from the objects of these ideas. The argument from co-reference relies on the assumption that some ideas may be different but nevertheless be directed towards the same object. The example provided by Twardowski is the idea of Mozart’s birthplace and the idea of the former Roman city Jovavum: these ideas, albeit evidently different, are directed towards the same object, i.e., the city of Salzburg. Such examples should compel us to postulate something like the contents of ideas as being something different from their objects. Otherwise, how could we account for the difference between ideas directed towards the same object (Twardowski 1894, 31–2 [29–30])? It is important to stress that this argument presupposes a further assumption, namely the disjunction that ideas may either differ because of their objects or because of their content. Schematically, the argument would take the following shape: (3.4) If an idea A and an idea B are different, they either differ because of their object or because of their content. (3.5) The idea of Mozart’s birthplace and the idea of the former Roman city of Jovavum are different. (3.6) The idea of Mozart’s birthplace and the idea of the former Roman city of Jovavum do not differ because of their object. (3.7) Thus, the idea of Mozart’s birthplace and the idea of the former Roman city of Jovavum differ because of their content. The problem with this line of reasoning, however, is that the premise (3.4) is rather questionable and presents the clear trait of a false dilemma. Indeed, ideas may differ not only because of their objects and contents, but also because they represent the same object relying on a different set of properties. Different properties of the object–in this case Salzburg–may account for the difference in ideas.13 Let me explain what I mean. If we had an object with one and only one property but still different ideas of it, then we might be forced to postulate

 12

As noted by Jacquette (1987, 197–198), the argument is not fully generalizable, since some ideas may be about other ideas, which thus may really have the same properties. 13 This objection was put forward by Grossmann (1974, 50–51). Jacquette (1987, 191–199) also criticized this argument because it is not fully generalizable (see previous footnote).

44

Chapter Three

something like a content of an idea. Or, alternatively, if we had an object with a certain set of properties, and two ideas of it which are aimed at exactly this set of properties while still being different, we would have to assume something like a mental content. Yet both antecedents are clearly absurd, so that there is no reason to postulate such things.14 Let us now turn to the third and last argument for the distinction between contents and objects of ideas. To Twardowski, if we truthfully deny the existence of an object, then the object of the presentation upon which our judgment is based does not exist. Yet the content of the idea upon which this judgment is based must exist. Thus, the object and the content of an idea must be different (Twardowski 1894, 34 [30]). Now, the problem with the latter argument is that, like the first one, it begs the question: it presupposes that every idea has a content, by means of which we present an object. We therefore must conclude that the distinction between contents and objects of presentations is not warranted, so that we should in any case prefer (IT) to (IT´). Of course, Twardowski may argue that the fact that ideas have contents by means of which they are directed towards objects is evident in and by itself. However, as is always the case with intuitions, we are not compelled to follow him. This is especially true since it seems preferable to follow Brentano and take the fact that every idea is directed towards an object as primitive. What deserves some further attention is whether Twardowski is attempting to amend Brentano also in respect to his approach to existence. Here it is important to notice that Twardowski fully endorses Brentano’s view of judgments as mental events of accepting or rejecting the object of an idea. However, Twardowski assumes that the distinction between content and object should be applied not only to ideas, but to judgments as well. As addressed above, this does not follow automatically from the revision of (IT) as (IT´): one may consistently hold that only ideas have contents, whereas judgments do not. Yet Twardowski does not follow such a path. The main reason for his choice seems to be that the notion of content of a mental phenomenon, once applied to judgments, may explain the strong link between the notion of judgment and the notion of existence.

 14

Twardowski considers also the converse of this argument, which he credits again to Kerry. A content of an idea should be distinguished from its object because in the case of general ideas different objects may be represented by the same content. This argument, however, is discarded by Twardowski since he rejects the assumption according to which general ideas are ideas that represent different objects (see Twardowski 1894, 34 [31]).

Brentano: Acceptance and Rejection

45

To Twardowski, the content of a judgment is in a certain sense what we mean by existence (see Twardowski 1894, 8–9 [6–7]). The approach to existence as the content of a judgment is a very mysterious one. But we need not here attempt a clarification of what Twardowski may have actually meant by this. In fact, since the distinction between content and object was already rejected at the level of ideas, there is no good reason to grant such a distinction at the level of judgments, either. We should, instead, stick to the orthodox Brentanian view of existence as acceptance (and non-existence as rejection), without trying to introduce some mysterious entity that might explain the strong link between existence and acceptance.

3.6 Twardowski and the Property-View of Existence Chrudzimski (2007, 113–115) draws attention to a further aspect in which Twardowski seems to abandon the Brentanian orthodoxy. To Chrudzimski, Twardowski is moving towards introducing a full-blown metaphysical distinction between, among others, existent and non-existent objects. The crucial quote, which summarizes the result of the analysis in § 7 of his essay, is the following: Everything that is presented through a presentation, that is affirmed or denied through a judgment, that is desired or detested through an emotion, we call an object. Objects are either real or non real; they are either possible or impossible objects; they exist or do not exist. What is common to them all is that they are or that they can be the object (not the intentional one) of mental acts […]. Everything which is in the widest sense “something“ is called “object,” first of all in regard to a subject, but then also regardless to this relationship. (Twardowski 1894, 40 [37])

Indeed, it is a fact that Twardowski allows here for a metaphysical perspective, i.e., a perspective from which objects are not considered as objects of ideas, but simply as objects, regardless of whether or not they are represented by a cognitive agent. Moreover, it is also a fact that, from this perspective, Twardowski is introducing a distinction between existent and non-existent, as well as a distinction between possible and impossible, real and non-real objects (we would rather speak of concrete and nonconcrete objects), so that existence, as well as possibility and reality, seems to be reduced to a property. However, the question we should be asking ourselves in this connection is one of priority. Is Twardowski attributing a priority to the metaphysical perspective, where for instance the domain of objects may be

46

Chapter Three

divided into two classes, i.e.: existent and non-existent ones? Or should we rather say that the metaphysical perspective always acts, as it were, parasitically upon the psychological one, which says that existence should be interpreted as something strictly linked to the mental act of acceptance? It seems to me that the only way to provide a consistent interpretation of Twardowski is to follow this second path: if the metaphysical perspective had the priority, it would no longer make any sense to interpret existence as the mental act of accepting (or the content of such a mental act of accepting); one should rather move on to interpret existence as a plain property of objects. On the other hand, if priority is given to the psychological perspective, one could always allow for a derived metaphysical perspective, where one distinguishes between existent and non-existent objects. As Twardowski (1894, 37 [34]) states, it is psychology that “turns into metaphysics,” which seems to imply that taking the opposite path from metaphysics to psychology would be misleading.15 Nevertheless, what must be granted is that the passage by Twardowski quoted above, even though it does not endorse a property-view of existence, may at least tempt others into exploring such a path. This is in fact a question that will have to be addressed in the chapter on Meinong: to what extent can we understand Meinong as someone who followed Twardowski’s hints towards the possibility of considering existence a property of objects?

3.7 Objections: To Judge and to Judge Correctly As already noted, Brentano’s approach to the notion of existence may be captured by paraphrasing the famous Quinean slogan: To be is to be accepted and, consequently, not to be is to be rejected. This is a clear second instance of what was labeled as the b-strategy (the first one being

 15

The view defended by Twardowski presents interesting similarities with the line of reasoning of Brentano’s 1889 lecture “On the Concept of Truth.” Here Brentano (1930, 24 [14]) writes: “Let us say that the area to which affirmative judgment is appropriate is the area of the existent […] and that the area to which the negative judgment is appropriate is the area of the non-existent.” At the same time, however, Brentano (1930, 27 [15–16]) stresses the fact that these are mere tautologies, which, as such, do not lead us to any metaphysical hindsight (see also Brentano 1889, 76–77). And, indeed, how could it be otherwise? Since Brentano interprets the statement “A exists” as “I accept A,” to say that “I accept A corresponds to the existence of A” is equivalent to saying “I accept A corresponds to my acceptance of A.”

Brentano: Acceptance and Rejection

47

the Kantian account): existence is not in the line of business of objects, but rather, in the line of business of expressing a certain kind of mental events. We may now turn to consider some objections. As pointed out above, if existential statements are understood as statements about acceptance and rejection, we end up with the following problem. The truth of the statement “God exists” does not seem to be connected to the truth of the acceptance of God: it may very well be the case that someone accepts God even though the statement “God exists” is false. From a different perspective, one may note that, when two persons are arguing as to whether God exists or not, they are not arguing as to whether they accept God, for both would concede the latter but not the former. Another problem raised by Brentano’s approach was highlighted by Geach (1965, 458–459). We have to grant that we may say “God exists” without asserting it, as for instance in “either God exists or everything is permitted.” Yet Brentano does not seem to be in a position to make sense of such an embedded, non-asserted existential statement. In Brentano’s later texts as well as in the series of articles on impersonal statements by his student Anton Marty, we may find an answer to the objections we have just raised. According to Marty (1884, 33; 39), we should not interpret “to exist” as simply meaning “to be accepted” but rather as meaning “to be correctly accepted” (the same claim may also be found in Brentano 1930, 45 [27–28 footnote]; 79 [47], and Brentano 1911, 147 [283]).16 Thus, when we argue as to whether God exists, we argue whether it is correct to accept God. Similarly, “either God exists or everything is permitted” should be re-interpreted as “either it is correct to accept God or everything is permitted.” Clearly, the new account allows us to vindicate the truth-values of the statements at stake. This strategy is hardly satisfying, though. Intuitively, when we say that something exists we are not judging the correctness of judgments. More precisely, neither the element of a second-order judgment nor the normative element seems to play any role in our affirmation of existence. Sure, the truth-equivalence is preserved every time we substitute “to exist” with “to be correctly accepted.” But the meaning-equivalence remains very dubious. A final remark should address the risk of circularity. If “God exists” really means “it is correct to accept God,” we seem entitled to raise the question as to what corresponds to this acceptance, i.e. in virtue of what this acceptance is correct. The answer cannot be the intentional object

 16

Kriegel (2015) only focuses on this more refined approach to existence. Noting the analogy to metaethical expressivism about the notion of the good, Kriegel characterizes Brentano’s position as “metaontological expressivism.”

48

Chapter Three

God, for–as we have seen above–such an object is indifferent to being. So, one is tempted to answer that it is God’s existence or the existent God which makes this acceptance correct. But then we would be moving in a circle. Brentano, however, rejected the possibility of developing any correspondence-theoretic approach to truth. To him, the only criterion for truth must be epistemic: a judgment is true if and only it is evident, or at least possibly evident.17 As long as we concede the viability of such a definition of truth, we may grant to Brentano that the problem of circularity does not arise. To conclude, as with Hume and Kant, the shortcomings of Brentano’s account of existence cannot be overlooked. What Brentano, as Hume and Kant before him, give expression to, however, is how deeply rooted our intuition is that the notion of existence should not be interpreted as a property of objects. No matter how hard we look at our objects of thought, we do not seem to find anything akin to a property of existence. For this very reason, one is tempted to say, these philosophers turned their attention from the object of thought to the thinking agent.

 17

Chrudzimski (2001, 50–89) has shown that this evidence-based approach to truth is preeminent throughout Brentano’s philosophical production. The only text by Brentano where he seems to move away from this evidence-based approach is his 1889 lecture “On the Notion of Truth” (Brentano 1930, 3–29 [2–17]).

CHAPTER FOUR FREGE: A SECOND-ORDER PROPERTY

Frege is rightly considered the champion of the view that existence is not a property. In addition, he is the first philosopher to rely on a double strategy to defend this stance: in a first sense, existence is not a property because everything exists (the a-strategy); in a second sense, existence is not a property because it is not in the line of business of objects (the bstrategy). Moreover, what sets Frege apart from all previous philosophers is that he does not try to interpret existential statements as statements about the thinking subject putting forward the statement, be it his impressions and ideas, his possible perceptions or his mental event of accepting and rejecting. Nothing could be farther from Frege than such an approach–which was probably the very reason he himself was so alien to the philosophy of his time. But–as we now know–times were changing: Frege has grown to become the most influential figure for the debate on existence and much else in contemporary philosophy. Another crucial aspect of Frege’s account that sets him apart from the philosophers we have considered so far is the attention he pays to the logical structure of existential statements. More precisely, he advocates an essentially different account for existential statements that are singular in form, i.e. statements about a definite object, and general existential statements, i.e. quantified statements. As we shall see further on, the reason Frege relies on both the a- and the b-strategy is that he applies different strategies to these two kinds of existential statements. Finally, this chapter also addresses the amendments to the Fregean approach that were suggested by Russell and Quine, which target the relation between quantified and singular statements: both Russell and Quine take steps towards closing the gap between general and singular statements, and thus strive for a more uniform treatment of existence than the one advanced by Frege.

Chapter Four

50

4.1 The Meaningless Reading of “to Exist” The posthumously published text “Dialogue with Pünjer on Existence” yields the best insight into Frege’s view of existence (see Mendelsohn 2005, 101). This unorthodox text (a few fragments of a dialogue followed by a 3-page commentary) sees Frege arguing against his colleague and theologian Bernhard Pünjer and should be dated somewhere between the publication of the Begriffsschrift (1879) and the publication of the Grundlagen (1884) (see Mendelsohn 2005, 113). The debated question is, in the first place, whether in statements of the form “there are xs” the meaning of the expression “there are” captures the meaning of the expression “exist” in statements of the form “some xs exist.” As will be seen presently, however, this question is strictly linked to the more familiar one as to whether existence should be deemed a property. One of the examples discussed by Frege and Pünjer is the following: (4.1) There are men. (4.2) Some men exist. It would seem rather uncontroversial to claim that “there are” in (4.1) captures the meaning of “exist” in (4.2). For what else could be at stake in statements of the form “there is x” (in German: es gibt) if not existence? So Pünjer clearly reputes himself to be on the safe side while endorsing this approach. Yet, surprisingly, Frege goes on a crusade against this apparently innocuous claim. Why does Frege take issue with Pünjer? To Frege, the real meaning of “there is” is not captured by the expression “to exist”, as Pünjer believes, but by the form of the particular judgment (die Form des partikulären Urteils),1 i.e., from a linguistic perspective, by the expression “some” or “something” (Frege 1883?, 15 [62]). His reasoning relies here on the universal substitution of “some”-statements and “there are”-statements. Every statement with a particular quantification may be cast as a “there is”-statement, just as for instance “some material objects are light” is truthequivalent to “there are light material objects”; and conversely, every “there is”-statement may be cast as a particular statement. In other words, what drives Frege to consider the existential meaning of “there is” as

 1

Frege talks of judgments (Urteil) throughout the dialogue, but we should not interpret the term psychologically. In fact, everything he says may very well be formulated in the terminology of statements or propositions.

Frege: A Second-Order Property

51

captured by the particular quantifier “something” is that the corresponding statements seem to be truth-equivalent. But what, then, is the function of the verb “to exist” if the existential meaning is already captured by “something”? Frege’s answer is ingenious: Like the “it” in it is raining, the “exist” in “men exist” has to be understood as a mere auxiliary. As language feeling at loss for a grammatical subject, invented “it,” so here, feeling at loss for a grammatical predicate, it has invented “exist.” (Frege 1883?, 15 [62])

On this assumption, Frege can argue that Pünjer is simply misled by the grammatical predicate “to exist,” and does not see that the meaning of “there is” is already captured by the expression “something.” It is, however, not clear why Pünjer–or anyone else for that matter–should endorse this ad hoc view of the predicate “to exist.”

4.2 Existence and the Particular Quantifier If the view that “there is” is equivalent to “something” is not taken into due account, the Fregean definition of existence as a second-order property, as formulated in § 53 of The Foundations of Arithmetic, cannot be adequately accounted for. Existence–he says in this work–is a property of concepts (Frege 1884, 65–65 [64–65])–i.e., a second-order property. However, it should be pointed out that this is in the first place an appropriate characterization of the particular quantifier “something” and not of “existence”: it is “something” and not “existence” which expresses a property of a concept in the first place. Only because according to Frege “something”-statements always convert to “there is”-statements, we may then proceed to say that existence is a property of concepts. Why the quantifier “something” is considered by Frege a property of concepts requires some explanation. According to Frege’s categorical grammar, the quantifiers “something” and “everything” are second-order functions, which take as their argument a first-order function expression about an indeterminate object of which a property or concept is predicated (i.e., a so-called “open sentence”). Accordingly, when we say “everything is a man” or “something is a man,” we mean that the fact of being a man is true of no matter which indeterminate object, or at least for one indeterminate object respectively (Frege 1879, see also Dummett 1973, 34–53). It is with this notion of quantification in mind, i.e. the notion at the heart of classical predicate logic, that we should understand the view that “something” expresses the second-order property that a property is

52

Chapter Four

instantiated at least once. Now, no specific claim about existence has been made so far. However, given Frege’s view that particular statements can all be cast as “there are”-statements, the characterization of the quantifier “something” indirectly captures a notion of existence, namely the notion of existence implied by “there are”-statements.2 Following this assumption, the expression “something is a man” does not simply say that the property of being a man is true of at least one indeterminate object, but that it is true of at least one indeterminate existing object. Or, in other words, the second-order property of having at least one instance means that a concept is being instantiated by at least one indeterminate existing object. This cursive notion of existence, moreover, should not be confused with the meaning of the grammatical predicate “to exist,” which prima facie may appear to be a first-order property, since–as pointed out above– “to exist” is simply devoid of any meaning. To Frege, there is no predicate of existence, but only the existential quantifier. This is indeed the controversial part of the thesis advanced by Frege.

4.3 The Self-Evident Reading of “to Exist” As we have seen above, to Frege, the notion of existence is entirely captured by the expression “there are” or “something.” On the other hand, the expression “to exist” and its cognates are simply a fill-in which our language invented out of a sense of grammatical uniformity. This is a clear instance of the b-strategy: language misleads us into thinking that existence is in the line of business of objects, for we are led by it to believe that this notion is expressed by the verb “to exist”; yet existence is in the line of business of concepts, since it is captured by the expression “some,” i.e., the property of concepts of having at least one instance. It is important, however, to notice that Frege does not seem to be entirely consistent, for in the same text he also defends the view according to which the grammatical predicate “to exist” does indeed have a meaning: “to exist,” besides being interpreted as a mere expletive, is also interpreted as having a self-evident (selbstverständlich) meaning. Moreover, by qualifying the meaning of “to exist” as self-evident, Frege addresses the fact that, no matter what we replace for “x,” the expression “x exists” is always true. Thus, the following analogy with self-evident statements comes to the surface:



2 The same point was made by McGinn (2001, 21) with respect to Russell, who couches Frege’s insight within the new terminology of propositional functions.

Frege: A Second-Order Property

53

Neither in “A is identical with itself” nor in “A exists” does one learn anything new about A. Neither statement can be denied. (…) They do not assign A to one of two classes in order to mark it off from some B which does not belong to that class. The point in saying “A is identical with itself” can only be to express the logical law of identity; the point cannot be to impart any further knowledge on A. (Frege 1883?, 14–15 [62])

As the reader will have noticed, this is nothing but an instance of the astrategy to deny the status of a property of existence: existence does not allow us to draw any distinction between the domains of objects since, no matter what A is, it is always true that A exists. There seems to be a tension between Frege’s declination of the a- and the b-strategy: to say that “to exist” is a mere expletive is hardly to reconcile with the claim that it means something self-evident. Here, however, we should pay attention to the fact that the self-evident meaning comes into play only when we are dealing with singular statements, i.e., statements about a definite object. The “A” in “A exists,” where “exists” has a self-evident meaning, is a variable for a proper name. It may for instance be substituted with “Sachse,” as in (4.3): (4.3) Sachse exists. On the other hand, the “x” in “x exists,” where “exists” is a mere expletive, is a variable for a quantified expression such as in (4.2). Once this is taken into consideration, we can also understand the logical law which is at stake in singular existential statements: it is the law according to which every proper name has to refer to an object. In Frege’s own words: If Sachse exists is supposed to mean “The word ‘Sachse’ is not an empty sound, but ‘designates’ something,” then it is true that the condition “Sachse exists” must be satisfied. But this is not a new premise, but the presupposition of all our words. […] The rules of logic always presuppose that the words we use are not empty […]. (Frege 1883?, 11 [60])

“Sachse exists” thus simply is an instance of our presupposition that words have a meaning, which in the case of proper names is identical to the object referred to: in this case, the individual . The same considerations also apply to singular statements that do not rely on proper names, but rather, on a definite description to refer to a definite object. As Frege will clearly state in his Foundations of Arithmetic (1884, 87–88 footnote [87–88]), expressions of the form “the P,” where P is a simple or compound property, in order to be considered meaningful, have to designate something. Frege is indeed careful to point out that what

54

Chapter Four

holds for definite descriptions does not hold for the concepts embedded in it. This, however, does not change anything to the fact that a statement such as (4.4), too, should be deemed self-evident: (4.4) The gymnasium teacher of Frege exists. Now, if the expletive-reading of existence seemed somewhat ad hoc, one cannot fail to notice that the self-evident reading of existence seems to be flat out false: it is all too easy to find examples of true singular negative existentials, such as for instance in “Santa Claus does not exist” or “Sherlock Holmes does not exist.” Or, in other words, it flies in the face of our linguistic practice to say that “Sherlock Holmes” and “Santa Claus” are not part of our language.

4.4 Singular Statements and the Sense/Reference Distinction Let us now turn to a possible improvement of Frege’s account of singular existential statements. As Mendelsohn (2005, 117) notes, Frege’s strategy to deal with statements such as (4.3) is strongly reminiscent of his approach to identity statements in the Begriffsschrift. As (4.3), in order to be informative, has to be interpreted meta-linguistically, so the statement “a=b” is informative because it says something about the signs “a” and “b”; namely, that they refer to the same object. From this perspective, it also becomes very tempting to argue–as Mendelsohn does–that the distinction between sense (Sinn) and reference (Bedeutung), as spelled out in Frege (1892), may serve not only to more convincingly address the informativeness of identity statements–as Frege did–but the informativeness of existential statements, as well. This seems to be the very direction in which the well-known passage on Odysseus is moving: The sentence “Odysseus was set ashore at Ithaca while sound asleep” obviously has a sense. But since it is doubtful whether the name “Odysseus”, occurring therein, has a Bedeutung, it is also doubtful whether the whole sentence does. Yet it is certain, nevertheless, that anyone who seriously took the sentence to be true or false would ascribe to “Odysseus” a Bedeutung, not merely a sense; for it is of the Bedeutung of the name that the predicate is affirmed or denied. Whoever does not admit the name has a Bedeutung can neither apply nor withhold the predicate. But in that case it would be superfluous to advance to the Bedeutung of the name; one could be satisfied with the sense, if one wanted to go no further than the thought. If it were a question only of the sense of the sentence, the thought, it would be needless to bother with the Bedeutung of a part of the sentence; only the

Frege: A Second-Order Property

55

sense, not the Bedeutung, of the part is relevant to the sense of the whole sentence. The thought remains the same whether “Odysseus” has a Bedeutung or not. (Frege 1892, 32–33 [157])

Here Frege endorses in clear terms the view that names have what he calls a sense, and this even though the reference may be lacking. Of course, statements with names lacking a reference can neither be true or false according to Frege, for statements imply a predication and the predication is something that takes place at the level of the reference of the name, and not at the level of its sense. Nevertheless, the fact that names have a sense allows us to rescue at least the intuition according to which names such as “Santa Claus” are not mere empty sounds like “blituri,” and therefore contribute to the meaning of the sentence in which they are embedded. Now, the problem according to Mendelsohn is that Frege, even when he already had the conceptual tools at his disposal to provide a more sophisticated account, never abandoned his meta-linguistic interpretation of singular existential statements. More precisely, Mendelsohn (2005, 119) argues that Frege could have vindicated our intuition that statements such as (4.3) are informative by dealing with them “at the level of sense, not at the level of reference.” Mendelsohn is most certainly right in highlighting how the distinction between sense and reference may help improve upon Frege’s account of singular existential, as provided in his dialogue with Pünjer. It would indeed be very worrisome if a term such as “Odysseus” not only could not be used to form any properly true or false statement, squarely falling outside what we consider to be language. As noted by Mendelsohn (2005, 119), this would for instance imply that we would not be in a position to make sense of the fact that (4.5) provides different information than (4.6): (4.5) Odysseus exists. (4.6) The cleverest of the Achaeans exists. On the other hand, as soon as we introduce the distinction between sense and reference, we might say that (4.5) is indeed different from (4.6) because “Odysseus” and “the cleverest of the Achaeans” express a different sense.3

 3

The reader will remember that to Frege definite descriptions have to be dealt with in the same way as proper names. This insight will even lead Frege (1892, 27 [153]) to claim that every designation of a definite object is in a logical sense a proper name. Thus, if we introduce the distinction between sense and reference of

56

Chapter Four

This notwithstanding, one cannot fail to point to the fact that, even if Frege’s approach to singular existentials were to be amended along the lines suggested by Mendelsohn, we would not be in a position to come to the rescue of the kind of informativeness which we intuitively attribute to statements such as (4.3), or for that matter, (4.4), (4.5) and (4.6). The reason we consider (4.3) and the like informative is not only that we mean something by it, or that (4.3) expresses a thought, but that what we say may be true or false. As addressed at the end of the previous section, it seems a plain truth that Santa Claus and Sherlock Holmes do not exist. In his amendment of Frege, on the other hand, Mendelsohn seems ready to sacrifice this intuition.

4.5 Stabilizing Frege’s Account Let us for a moment set aside the problematic aspects of Frege’s account addressed above: the ad-hocness of the expletive-reading and the strongly counter-intuitive character of the self-evident reading of the predicate “to exist.” Because of the difference in how singular and general existential statements are treated, Mendelsohn characterizes Frege’s approach as “fundamentally instable” (Mendelsohn 2005, 117): we would wish for only one definitive answer to what existence is, and not two entirely different ones. The latter point may be highlighted by considering a statement such as (4.7): (4.7) Sachse and something red exist. Can we plausibly maintain that the verb “to exist” in (4.7) has two meanings at the very same time, namely the self-evident one and the expletive one? Mendelsohn’s suggestion is that we should give precedence to the selfevident meaning. He starts by noticing that Frege is wrong in considering the notion of existence, as captured by quantification, as not being about objects at all. To the contrary, since “some” means that a concept is instantiated by an object at least once, the definition of “some” presupposes the notion of object. Thus, we should rather look on the side of the object in order to gain insight into the notion of existence. But this is what the self-evident notion of existence is all about: to Mendelsohn, it

 (grammatical) proper names, this distinction should be applied to definite descriptions, too.

Frege: A Second-Order Property

57

establishes a strong link between existence and objects. More precisely, we should understand the self-evident notion of existence as a universal or pleonastic property of objects (Mendelsohn 2005, 118). Thus, quantification captures existence only because every object exists (see Mendelsohn 2005, 120–121). From such a perspective, we may thus say that the verb “to exist” always means a pleonastic property of objects, and so a statement such as (4.7) is no longer problematic. Finally, as already addressed in the previous paragraph, Mendelsohn believes that it is enough if we apply Frege’s theory of sense to vindicate the intuition that false singular existentials are at least part of our language, i.e., they have meaning and are not mere empty sounds. The meaning of existence at stake in such statements, however, is still the selfevident one. In what follows, I will partly go along with Mendelsohn’s suggestion. I agree with him insofar as we may improve upon Frege’s account if we consider the verb “to exist” to have, unequivocally, the self-evident meaning. However, as already addressed in the Introduction, I prefer to avoid the talk of a universal or redundant property–as Frege did: either something allows us to divide the domain of objects into two classes, and then we may consider it a property, or this is not the case.4

4.6 A Second Occurrence of the Paradox of Non-Existence Let us return to Frege’s argument against Pünjer. As addressed at the beginning of the chapter, Pünjer defends the view that “to exist” is neither an expletive nor the expression of a self-evident meaning. In other words, “to exist” expresses a property which, as such, divides the domain of

 4

Russell endorses the same position as Frege and considers it a category mistake to talk of a predicate (i.e., something that expresses a property) that cannot but apply to everything. Answering the question as to why we should not introduce a redundant or universal predicate of existence, Russell (1918/1919, 206) says: “No, there is not an idea that will apply to individuals. As regards the actual things there are in the world, there is nothing at all that you can say about them that in any way corresponds to this notion of existence. It is a sheer mistake to say that there is anything analogous to existence that you can say about them… There is no sort of point in a predicate which could not conceivably be false. I mean, it is perfectly clear that, if there were such a thing as this existence of individuals that we talk of, it would be absolutely impossible for it not to apply, and that is the characteristic of a mistake.” Mendelsohn, on the other hand, is following another tradition which does not consider it to be a category mistake to talk of a pleonastic property. This tradition goes back at least to Salmon and Nakhnikian (1957) (see above, Introduction, footnote 1).

58

Chapter Four

objects into two classes: namely, those that have it and those that do not. In order to defend this view, Pünjer goes through a series of definitions of existence as being perceivable,5 being an object of an idea that is not an illusion, or being an object of an idea that arises from an affection of the ego (Frege 1883?, 13 [61–2]). All these clarifications of the meaning of the predicate “to exist” clearly stand in the tradition of modern subjectivist philosophy and seem in fact to permit a division of the domain of objects. Frege, however, needs no long digression into the quandaries of the subjectivism of modern philosophy in order to settle the matter. To him it is enough to remind Pünjer of the equivalence between “something” and “there is.” Frege’s argument runs as follows: (4.8) If “to exist” expresses a property, then something does not exist. (4.9) If something does not exist, then there is an object that does not exist (4.10) If “to exist” expresses a property, then there is an object that does not exist Premise (4.8) follows from the definition of a property as something which divides the domain of objects into two classes; (4.9) follows from Frege’s claim that the meaning of “there is” is captured by the expression “something”; (4.10) follows from (4.8) and (4.9) by hypothetical syllogism. Moreover, since Pünjer agrees that “existence” means the same as “there is,” (4.10) cannot but be a contradiction. So, the antecedent of (4.8), namely that “to exist” expresses a property, must be false.6

 5

This is in fact Kant’s view, even though a caveat should be added. As addressed in Section 2.6, existence does not allow for a division of the domain of objects, but in the first place for a division between possible perceptions and impossible ones. 6 Frege puts forward the argument relying on Pünjer’s definition of existence as being an object that does not arise from an affection of the ego. The result is obviously the same: “F[rege]: Do you admit that there are objects of ideas, where these ideas have not been caused by something affecting the ego? P[ünjer]: Yes. F.: Do you admit that objects of ideas which have not been caused by something affecting the ego do not exist? P.: Yes. F.: Then it follows that there are objects of ideas–ideas which have not been caused by something affecting the ego–which do not exist. Now if you are using the word ‘exist’ in the same sense as the expression ‘there is’, then you have at the same time asserted and denied the same predicate of the same subject” (Frege 1883?, 8–9 [58–9]).

Frege: A Second-Order Property

59

To Pünjer’s credit, however, one should notice that he was not taken aback by Frege’s argument. As he clearly points out, the equivalence between “something” and “there is” can only be granted if by “something” one already presupposes “something existing,” which does not seem to be warranted (see Frege 1883?, 10 [59]). But with this remark we are already moving towards possible objections to Frege’s approach.

4.7 Digression on Russell and Quine Before assessing Frege’s approach to existence, we need to consider some well-known amendments. As addressed above, one reason for being unsatisfied by Frege’s account is that he seems to be telling a very different story for general and singular existential statements. As we have already seen, Mendelsohn suggests a strategy to overcome this instability in Frege’s account, but at the obvious price of giving up our intuition that singular existentials may be true or false. There is, however, a second path that allows one both to provide a unified account of existence and to rescue the intuition that singular existential statements are genuinely informative. Yet these advantages, as is often the case, come at a price: this path leads to the view that singular statements are such only prima facie, for they should rather be construed as general ones under disguise. This can be achieved as soon as one provides an alternative, non-Fregean interpretation of proper names and definite descriptions. Let us start with definite descriptions. One may still defend the view that (at least some) proper names presuppose a reference to a definite object, so that they yield us genuine singular statements, but that definite descriptions are–so to speak–in an entirely different line of business. This is the approach developed by Bertrand Russell. In his article “On Denoting,” Russell (1905) draws attention to a counterintuitive consequence of Frege’s view: all statements which embed definite descriptions that do not denote anything can be deemed neither true nor false. But at least in some cases we would resist such a conclusion, as for instance in the case of the following statement: (4.11) The present King of France is bald. To Russell (1905, 483–484), there must be a way to vindicate the intuition that (4.11) is indeed a false statement and not merely the expression of a thought to which neither truth nor falsity can be attributed. Russell’s suggestion is well-known. Definite descriptions are not “genuine constituents” of the propositions, but rather, they should be analyzed and reduced to something more fundamental. More precisely,

60

Chapter Four

Russell proposes to analyze every definite description of the form “the P,” where P stands for the property or properties embedded in the description, as the conjunction of the two following claims: (4.12) There is some x which has the property P. (4.13) For every y, if y has the property P, then y is identical with x. The claim (4.12) assures us that there is an indefinite object which has the property P. On the other hand, (4.13) is intended to capture the notion that the object is a definite one. It is easy to see how according to this theory, (4.11) is no longer truth-valueless but false. If we apply Russell’s theory of definite descriptions, (4.11) should be reformulated as (4.14): (4.14) There is some x, which has the property of being the present King of France, and for every y, if y has the property of being the present King of France, then y is identical with x, and x is bald. This statement is indeed false because it contains the false claim that there is a present King of France. However, this reduction only works as long as we agree that the notion of uniqueness of the object is equivalent to the notion of being a definite object, as Russell himself believed. This may be disputed, especially because of the following counterintuitive consequence: a definite description would be false (or, more precisely, the statement of which it is a part would be false), if there were more than one thing which instantiated the concept linked to the definite description. Frege (1892, 40 [162–163]), for one, wanted to avoid such a consequence (see Pelletier and Linski 2009) and thus ruled out the possibility of analyzing away definite descriptions. It is tempting to depart from Frege in an even more drastic way: we may deny, not only definite descriptions, but also proper names the status of genuine constituents of a statement. One way of doing so would be to interpret proper names as hidden definite descriptions and then interpret the definite descriptions along Russellian lines. As it happens, this is something which was already suggested by Russell himself (1905, 491). However, Russell never claimed this strategy should be applied across the board to all proper names, but only to proper names that lack a (Fregean) reference. From this perspective, Russell’s approach seems inevitably ad hoc: he wants to uphold the intuition that singular existentials with proper

Frege: A Second-Order Property

61

names may be true or false. However, if they are false, then they are not really singular, but rather, they should be analyzed as general statements.7 The step to altogether eradicating names from our language as something that refers to definite objects and thus yield us singular statements was clearly taken by Quine. To him (Quine 1948, 28–29), every proper name has to be interpreted as a hidden Russellian definite description containing one or more predicates. In the limit case, the description may even consist of one primitive predicate. To give his example, if one were unsatisfied by the interpretation of “Pegasus” as “the winged horse that was captured by Bellerophont,” the definite description “the Pegasizing thing” would still be available. If, as Quine suggests, both definite descriptions and proper names are interpreted away, we end up with a language where there are no more singular statements, i.e., statements about a genuine singularly determined object. As addressed above, this is the price that one must pay to follow this path. Notice, moreover, that in such a fully analyzed language, there is room left only for the self-evident meaning of “to exist.” Every time we have an alleged singular existential such as (4.3), we should, if no description is available, interpret it as (4.15), which is true: (4.15) Something Sachsizes and exists. And if we have a negative singular existential such as (4.16), we should interpret it as (4.17), which again is true: (4.16) Pegasus does not exist. (4.17) It is not the case that something Pegasizes and exists. The advantage of such an approach is that, pace Frege and Mendelsohn, prima facie singular existential statements cease to have to be considered trivially true. The price we have to pay, on the other hand, is a separation between a surface form and a deeper logical form of our language. The question which remains unanswered, however, is the following: What is the meaning of the expression “to exist” and its cognates in our everyday, non-analyzed language? Yet Russell and Quine were probably not so interested in the way we speak.

 7

Because of Kripke (1972/1980), the view that names should always be interpreted away is often attributed to Russell. Yet Kripke (1973) himself corrected this misunderstanding of Russell.

62

Chapter Four

4.8 Objections: Sweeping Existence under the Carpet of Quantification Frege’s crucial insight about existence is that particular quantification captures existence. Why should this be the case? According to Frege, his view offers the best explanation as to why statements with particular quantification may be cast as “there are”-statements. We may thus say that existence appears under disguise in our language, namely as the expression “some” or “something,” or, more overtly, as the expression “there is.” Once this first step is taken, we are of course left with the following problem: What does existence mean when it appears, as it were, in person, i.e., as the verb “to exist” and its cognates? Frege tells us a rich story. First, if the expression “to exist” makes its appearance in a general statement, it may in fact be a mere expletive, a grammatical invention that fills a gap in order to yield us a grammatical statement. Second, if the expression “to exist” makes its appearance in a singular statement, the verb “to exist” expresses something self-evident, something that, like the law of self-identity, is always true. In this chapter, we have also considered some strategies to simplify the Fregean picture of existence. Mendelsohn suggests that the notion of existence may be fully captured by the self-evident meaning of “to exist”: every object exists. It is only, as it were, indirectly–because quantification is quantification over the domain of existent objects–that quantification captures the notion of existence, too. On the other hand, Russell and Quine show us a strategy to avoid the counterintuitive consequences of this approach, namely that all singular negative existentials are automatically false. In order to do so, they introduce a distinction between the superficial structure of our language and a hidden logical language. It is at the deep logical level that “to exist” has a self-evident meaning. Let us now turn to possible objections. The crucial and at the same time controversial aspect of Frege’s theory is the claim that particular quantification captures the notion of existence. As we have seen, the reason he provides is that “some”-statements and “there”-are statements seem to be equivalent. However, a plain linguistic fact seems to jeopardize this account: it is perfectly fine to say that some things do not exist, as in for instance “something which is a golden mountain does not exist,” or in “something which is a round square does not exist.” Frege does not seem to have any better argument to reject these examples than once again relying on his claim that quantification implies existence, so that if statements such as “something that is a golden mountain does not exist” or “something that is a round square does not exist” were literally true, they

Frege: A Second-Order Property

63

would lead to the paradox of non-existence. But this line of reasoning is clearly question-begging. Notice, moreover, that we may also rely upon singular negative existentials to argue that quantification does not imply existence. We all would agree that statements such as “Santa Claus does not exist” or “Sherlock Holmes does not exist” are true, from which it seems to be safe to generalize and infer that “something does not exist” (this point is stressed by Routley 1980).8 The adjustments we find in Russell and Quine do not change anything substantial to this picture. True, if we follow Russell and Quine, we avoid the gap between the analysis of singular and general existential statements, of course at the price of distinguishing between our ordinary language and an analyzed one where singular statements are interpreted away. The upshot, however, is that one gives even more weight than Frege to the role of quantification. More precisely, to Quine, the only means we have to reach out to reality is quantification, for all the direct bridges (i.e., definite descriptions and proper names) are cut off. But then again, neither Russell nor Quine provide us with new arguments to explain why particular quantification should be given an existential interpretation.9 Moreover, their reduction of some or all proper names to quantified statements leaves their strategy vulnerable to the objections put forward by Kripke (1972/1980) and Donnellan (1972)–though this is a discussion into which I had rather not enter in the present context. The same considerations also apply to Mendelsohn’s approach. As it happens, Mendelsohn (2005, 113) has forcibly made the point that Frege does not provide us with any (good) reason to interpret existence as a second-order property, i.e., as quantification.10 The same, however, applies to his interpretation of existence as a universal or pleonastic property in turn.

 8

More recently, this line of argument has been endorsed by Crane (2013, 28–51). What is important to notice about his approach, however, is that Crane does not deny that from a statement such as, for instance, “some characters in the Bible do not exist” we may infer “there are characters in the bible that do not exist.” Instead, what he denies is that “there is” has any existential meaning (Crane 2013, 42). He even goes on to use exactly the same analogy we found in Frege: “there is” is merely a filling-in construction, precisely like “it” in “it rains” (Crane 2013, 43). 9 McGinn (2001, 21) notices that Russell and those who followed him did not present any argument to the effect that “something” implies “there is.” 10 Mendelsohn (2005, 111) refers to a letter by Frege to Anton Marty where the former seems to suggest having an argument to defend his view. Yet, since this argument is nowhere to be found, Mendelsohn labels this letter as “one of the great teasers of modern philosophy.”

64

Chapter Four

Nevertheless, we need to be careful and distinguish between the fact that Frege or those that followed in his footsteps have not convincingly argued for this theory and the fact that this theory may be false. As it happens, the theory may very well be true. The problem is that we as yet have no substantial reason to endorse this theory. More precisely, we do not have any non-circular reason to discard alleged counter-examples to this approach, namely statements of the form “x does not exist,” no matter whether “x” stands for a quantified expression, a definite descriptions or a proper name. The most we could do to directly defend such a stance seems to be to invoke what Russell (1918/1919, 170) labeled as a “robust sense of reality.” But perhaps there is at least one indirect reason to endorse Frege’s approach, namely that theories which try to take statements of the form “x does not exist” at face value involve contradictions or lead to severely counter-intuitive consequences. Thus, it is time now to turn the tables and assess those theories that interpret existence to be a property of objects.

PART TWO THE PROPERTY VIEW

CHAPTER FIVE MEINONG: OBJECTS AND OBJECTIVES

It is very tempting to think of Meinong as the champion of the view of existence as a property of objects. The reason for this is that many of his well-known statements seem to move in this direction. According to Meinong, for instance, objects qua objects are beyond being and nonbeing (Meinong 1904, 12 [86]). How should we interpret this claim if not as a metaphorical way of saying that existence or being is a property of objects? The same is true of Meinong’s infamous claim that “there are things of which it is true that there are no such things” (Meinong 1904, 9 [83]). If we look away from the paradoxical character of this claim–of which he was very well aware–Meinong seems to suggest that the domain of objects may be divided into two classes: namely, those that exist and those that do not. Thus, again, existence seems to be reduced to a property of objects. However, as will be argued in this chapter, there is more than one problem with the above interpretation of Meinong. It is nevertheless appropriate to start the second part of this study with an account of his approach: even though Meinong does not really endorse the property-view of existence, the step from his approach to the property one is indeed a very short one. Moreover, Meinong does offer us some powerful arguments that may be relied upon to endorse the property view. In this sense, it is legitimate for the contemporary philosophers who are going to be discussed in the following chapters–and who will actually defend the property-view–to enlist him as major influence.

5.1 Meinong and Brentano As already addressed, Meinong was one of Brentano’s students. He attended his courses in Vienna (1875–1878) and under his recommendation undertook a thorough study of Hume’s philosophy, which then led to his Habilitationsschrift by the title Hume-Studien I (Meinong 1877). Thus, it should not come as a surprise that the

Meinong: Objects and Objectives

67

Intentionality Thesis (IT) plays a crucial role in Meinong’s writings. At the beginning of his most famous article–quasi a manifesto of his philosophy– “On the Theory of Objects,” we may read: [N]o one fails to recognize that psychological events so very commonly have this distinctive “character of being directed to something” (auf etwas Gerichtetsein) as to suggest very strongly (at least) that we should take it to be a characteristic aspect of the psychological as opposed to the nonpsychological. (Meinong 1904, 3 [77])

True, in this passage Meinong carefully avoids a full endorsement of (IT). But the reason for this is not so much that he has some actual reservations with respect to the principle, as the fact that in the present context he does not need to fully commit himself to it. In fact, the real aim of the article is not to provide a definition of the proper object of psychology, but rather– as the title says–to expose the principles of what Meinong calls the “Theory of Objects” (Gegenstandstheorie). As will be shown presently, this theory is strictly linked to his approach to the notion of existence. Even though in many respects Meinong did indeed follow in Brentano’s footsteps, he was anything but a herald of Brentanian orthodoxy. For one thing, Meinong endorsed Twardowski’s introduction of the distinction between the content and the object of ideas (see Meinong 1899; Chrudzimski 2007, 115–118).1 But this should not be seen as a major breach with Brentanian orthodoxy, especially if one does not interpret Brentano’s in-existent objects as existing psychological entities, i.e., as what Twardowski calls the content of the idea. Another, more dramatic way in which Meinong distances himself from his mentor is by introducing a new class of psychological phenomena which were not considered by Brentano, i.e. assumptions. To Meinong, assumptions should take something like a middle ground position between

 1

As Chrudzimski notices, however, there is a crucial difference between the Twardowskian and the Meinongian notion of content of an idea. To Twardowski, such contents play the role of the meaning of nominal linguistic expressions, whereas to Meinong the meaning of a nominal linguistic expression is simply the object referred to by the linguistic expression. If we go back to Bacon’s famous example, the meaning of the word “Sun” is not the idea of the Sun, but rather, the Sun himself. This reference-theory of meaning is clearly endorsed by Meinong (1910) (see Morscher and Simons 2001, 436). It is only in his very last book on possibility and probability that Meinong (1915) moves towards the introduction of mediating semantic entities between the linguistic signs and the referred objects. These mediating entities, however, are closer to a Fregean sense than to Twardowski’s content, in that they are non-psychological (see Simons 1995).

68

Chapter Five

ideas and judgments. Accordingly, Meinong rejects the Brentanian tripartition of mental phenomena into ideas, judgments and emotions. The rationale behind the introduction of this fourth class of mental events is that assumptions cannot be reduced to ideas, for they are either affirmative or negative–something that cannot be said of ideas. At the same time, assumptions cannot be reduced to judgments, for they do not involve any belief (see Meinong 1910, 1–5). The most decisive breach with Brentanian orthodoxy, however, is due to Meinong’s clear and unabashed endorsement of a correspondence theory of truth. In fact, already the view that truth and falsity should not be considered as exclusive properties of judgments, but also belong to assumptions, moves towards questioning the Brentanian epistemic definition of truth (a judgment is true if evident or if it is at least possibly evident).2 But Meinong clearly goes beyond this: to him, both judgments and assumptions are true if and only if there is something out there which makes them true. Paraphrasing Russell’s talk of a robust sense of reality, we may say that Meinong has a robust sense of truth. Now, the first obstacle for every correspondence theory of truth is no other than the paradox of non-existence: how can a true negative existential statement be true because it refers to an object out there, when it is precisely a statement which requires the non-existence of the object?3 This is the problem that Meinong addresses in a crucial chapter of his main work On Assumptions and that will lead him to develop his own interpretation of the notion of existence.4

5.2 Meinong’s Solution to the Paradox of Non-Existence Let us start by fleshing out the details of Meinong’s interpretation of the paradox of non-existence. As is usually the case, the specific way in which a given problem is framed already hints at how it is going to be solved.

 2

See above, section 3.7. Meinong speaks of “bedeuten,” which may be more literally translated as “to mean” rather than “to refer.” Yet this difference is irrelevant since Meinong (1910) endorses a reference-theory of meaning (see above, footnote 1). 4 To be more precise, this problem is addressed in the 10th chapter of the first edition of Über Annahme (Meinong 1901), which was reworked into the third chapter of the strongly revised second edition (Meinong 1910), to which I am going to refer throughout this chapter. Notice that Meinong, like Brentano, would not speak of the truth of statements, but rather, of the truth of judgments as what is expressed by (asserted) statements. For simplicity, I am going to abstract from this complication in my discussion. 3

Meinong: Objects and Objectives

69

According to Meinong, the paradox arises because of three crucial assumptions: (i) There are true negative existential statements; (ii) Statements are true because something existing makes them true; and (iii) what makes a statement true is the object (or objects) referred to by the statement. Schematically, this new version of the paradox runs as follows: (5.1) Statements of the form “x does not exist” are true. (5.2) A statement is true if and only if something existing makes it true. (5.3) What makes a statement true is the object referred to by the subject of the statement. (5.4) Statements of the form “x does not exist” are true if and only if the object referred to by the subject exists. The premises (5.1), (5.2) and (5.3) together imply (5.4). But (5.4) is of course a contradictory statement. For instance, if we consider the statement “a golden mountain does not exist,” this statement would be true if and only if a golden mountain existed. It is worth pointing out how Brentano would have dealt with the paradox as it is framed by Meinong. To him, the solution could not be easier: given his epistemic approach to truth, he would simply uphold (5.1) but reject both (5.2) and (5.3). This path, however, is clearly not available to Meinong. According to him, we should uphold a correspondencetheoretic approach to truth–which is clearly what the two premises are about. It is also worth considering how Frege would deal with this version of the paradox: to him, we should simply reject the assumption that negative existentials may be true, and thus let (5.1) fall. Negative existentials are contradictory, therefore they should be expunged from our language. To truly deny the existence of something is impossible. What we can do, however, is to say that such and such properties are not instantiated (in the case of general statements) or that a given grammatical expression is–in a sense–empty (in the case of singular statements). This, however, is rather a brutal way of handling the paradox and may be compared to a Procrustean bed: instead of changing the bed (i.e., our premises about what makes our statements true) we amputate the body that does not fit it (i.e., our language or the way we speak). But let us return to Meinong. To begin with, he clearly rejects the Procrustean approach: we should change our premises about truth, rather

70

Chapter Five

than amputate our language.5 The problem, however, is that there is not much room left for changing the premises so that (i) the paradoxical conclusion is blocked and (ii) a version of the correspondence theory of truth is upheld. To stick to mythological metaphors, we may thus interpret Meinong as someone who tries to navigate the perilous waters of the paradox of non-existence without falling prey to Scylla (the Brentanian epistemic interpretation of truth) or Charybdis (the Fregean amputation of language). Yet the specific version of the paradox of non-existence concocted by Meinong points in the direction of a possible fix. What is crucial to Meinong is that the intuition behind an objective notion of truth as correspondence may be broken down into two elements, namely (5.2) and (5.3). This puts him in a position to suggest that the real problem is not, generally, a problem of the correspondence theory, but, more specifically, a particular understanding of it, namely (5.3). According to Meinong we may uphold (5.2) and block the paradox by means of a minor adjustment to (5.3). More precisely, we should drop the intuition that it is the object referred to by the subject of the statement that makes a statement true. Rather, what makes a statement true is the object referred to by the statement as a whole. Furthermore, the object referred to by the statement as a whole is something which–in a first approximation– may be labeled as a fact (Tatsache) (Meinong 1910, 42–3 [37–38]). Schematically, Meinong’s strategy to block the paradox is tantamount to letting (5.3) fall and putting (5.3b) in its place: (5.3b) What makes a statement true is the fact referred to by the statement. From (5.2) and (5.3b) we can no longer infer (5.4) but only (5.4b): (5.4b) Statements of the form “x does not exist” are true if and only if the fact referred to by the statement exists. Going back to the previous example, it is no longer the case that the statement “a golden mountain does not exist” is true if and only if– paradoxically–there is a golden mountain, but if and only if –innocuously– there is the fact that a golden mountain does not exist.

 5

Meinong was not acquainted with Frege’s work. He was, however, acquainted with Fregean-like strategies that relied on interpreting away negative existentials as something that does not really refer to non-existent objects (see Meinong 1907, 39). Moreover, Meinong also explicitly endorsed what we may call the antiProcrustean principle: the facts of ordinary language show us the way to the right semantics and metaphysics (see Meinong 1904, 41 [103]).

Meinong: Objects and Objectives

71

The circumstance that Meinong really provides a solution to the paradox of non-existence may come as a surprise to some reader. Was it not the case that, according to Meinong, “there are some objects of which it is true that there are no such objects”? Yet, as already suggested at the beginning of the chapter, this would be a misunderstanding: in the passage of his article “On the Theory of Objects” from which this statement comes, Meinong is simply reporting the judgment of “those who like paradoxical modes of expression” (Meinong 1904, 8–9 [82–83]). And, as Meinong says in the following pages (Meinong 1904, 9–10 [83–84]), the mistake of those who like contradictions arises from their misguided conception that the object referred to by the subject of a statement is what makes a statement true, i.e. (5.2).6 The solution to the paradox of non-existence advanced by Meinong requires that not only the truth of negative existential statements, but also the truth of affirmative existential statements be explained by the existence of the relevant facts. The statement “there is snow” is true not because snow exists, but rather because it is a fact that there is snow. Moreover, the same approach has to be applied to predicative statements. A predicative statement such as “a tree is green” is also true because the fact, to which the statement as a whole refers, exists. Meinong also made some steps towards interpreting conditionals, and thus–arguably–disjunctions, too, within the framework of his semantics of facts. But since this element of his semantics did not go beyond simple suggestions, we may avoid discussing it in the present context.

5.3 Terminological Remarks After the key reasoning of Meinong has been spelled out, it is helpful to make some remarks about terminology. For one thing, Meinong chooses not to speak of “facts,” but rather, of “objectives” as the objects referred to by statements. The rationale for this is that, according to him, facts are by definition existent: the claim that a fact exists is analytically true. Yet false statements cannot refer to a fact, since otherwise they would be true. As a consequence, he introduces the term “objective” to address the object of a statement as something that may or may not exist, and reserves the term “fact” to refer to an existing objective. Accordingly, a true statement is such because it refers to an existing objective (i.e. a fact), whereas a false

 6

Examples of ascribing this view to Meinong can be found both among sympathetic readers (e.g., Chisholm 1972, 25) and less sympathetic ones (e.g., Ryle 1972, 7).

72

Chapter Five

statement is false because it refers to a non-existent objective. In addition, this neologism also serves the purpose of hinting at an analogy: as the subject of a statement refers to an object, so the statement as a whole refers to an objective (Meinong 1910, 44 [38]; 69 [55]; 97–105 [74–79]). The second terminological remark bears upon to the notion of existence. By “existence” Meinong intends the kind of being that may pertain to spatiotemporal objects, whereas the kind of being proper to abstract or ideal objects is labeled as “subsistence” (Bestand). Objectives are abstract objects, i.e., entities which cannot be located in space and time. He provides the following example: his desk is a spatiotemporal object, which may thus exist, but the objective that his desk exists cannot be located in space and time. Thus, objectives are not things that may or may not exist, but things that may or may not subsist (Meinong 1910, 63– 69 [51–55]). Once this terminology has been put into place, Meinong’s own version of the correspondence theory of truth (MCT) may be spelled out as follows: (MCT) A statement is true if and only if it refers to a subsisting objective, and is false if not.7

5.4 Being-Objectives and So-Being-Objectives and their Independence The Meinongian definition of truth draws no distinction between the truthconditions for predicative and existential statements. Both kinds of statements are true if and only if the relevant objective subsists. However, predicative and existential statements are made true by two essentially different kinds of objectives: the latter are true because of the subsistence of the relevant being-objectives (Meinong calls them “Seins-Objektive”), whilst the former are true because of the subsistence of the relevant sobeing-objectives (Soseins-Objektive) (Meinong 1910, 72 [57]). So-being-objectives are the objectives that yield us what we commonly regard as the relation of instantiation. Being-objectives, on the other hand, are essentially different: they do not tell us whether or not an object instantiates the property of existence. But how should we understand the

 7

While providing his definition of truth, Meinong (1910, 93–94 [71–72]) introduces a further distinction between the ontological notion of objective and the epistemological one of pseudo-objective. I leave this complication aside in the present discussion.

Meinong: Objects and Objectives

73

notion of existence at stake in being-objectives? Meinong’s answer to this question is adamant yet puzzling. As he repeats on several occasions, the opposition between existence and non-existence does not really bear upon the object, but rather upon the objective: the fact that an object exists is explained by means of the subsistence of the corresponding beingobjective (Seinsobjektiv); conversely, the fact that an object does not exist is explained by means of the subsistence of the corresponding non-beingobjective (Nichtseinsobjektiv). As Meinong says, “the opposition between being and non-being is primarily a matter of the objective and not of the object” (Meinong 1904, 12 [86]). It is from this perspective that the famous Meinongian remark addressed at the beginning of the chapter should be understood: objects are beyond being and non-being. This does not suggest that objects may be divided into two classes, i.e., those that exist and those that do not exist, but rather, that existence (or more generally, being) must be explained in terms of objectives (see Findlay 1963, 75; 102–103; Rapaport 1978, 157 and Poli 2001, 351). Once the distinction between being- and so-being-objectives has been put into place, Meinong is also careful to notice that we should refrain from introducing the following principle about their relation: a given sobeing-objective subsists if and only if the relevant being-objective subsists as well. It is easy to see how the introduction of this principle would be tantamount to saying that, if something instantiates a property, then it must exist. This is a very deep intuition we seem to share and upon which, for instance, the famous Cartesian cogito ergo sum is arguably built. I instantiate the property of thinking, therefore I exist. However, there is no place for such an intuition in Meinong’s philosophy. Meinong has two reasons for rejecting this intuition. First of all, this is mandated by the very solution he has provided to the paradox of nonexistence. Negative existentials may be literally true–i.e., they really are about a given object, of which they say that it does not exist. And since negative existentials are, if not always, at least very often general negative existentials, i.e., they sort out an object by means of its properties, this implies that the object really must have those properties.8 For instance, the

 8 Unlike Frege, Meinong focuses solely on general existential statements. The reason seems to be that to him objects may always be reduced to bundles of properties (see Grossmann 1974, 76; Orilia 2002, 88). True, he often talks of the golden mountain or the round circle. But the use of the definite article is simply anaphoric and should not be read as implying a singular statement as opposed to a general one. Accordingly, throughout the chapter I am relying exclusively upon examples of general statements.

74

Chapter Five

following statement is really a statement about something that instantiates the properties of being golden and a mountain: (5.5) A golden mountain does not exist. The second reason is strictly linked to the first one. According to Meinong, we should rescue what may be labeled as analytic statements about nonexistent objects, such as for instance: (5.6) A golden mountain is golden and is a mountain. This statement has to be true no matter whether the golden mountain exists. Or, relying on the conceptual tools of Meinong’s semantics, (5.6) refers to a subsisting objective even though (5.7) does not: (5.7) A golden mountain exists. In order to stress his rejection of the intuition at stake, Meinong introduces what he calls the Principle of Independence of Being from Being-So (PI) (see Meinong 1904, 8 [82]):9 (PI) An objective of so-being may subsist independently of the subsistence of any being-objective. Of course, the fact that objectives of so-being are independent of objectives of being does not imply that Meinong rejects any relation between objectives. To the contrary, the whole project of his semantics and metaphysics moves towards explaining relations of inference between statements as relations of dependence among objectives. What characterizes his metaphysics of objectives, however, is the rejection of a specific kind of dependence by means of the introduction of (PI).

5.5 Meinong’s B-Strategy The previous paragraphs have provided us with an overview of Meinong’s semantics and metaphysics (the metaphysics implied by his semantics is what Meinong labels as his Theory of Objects).10 The overview, moreover,

 9

Meinong credits Ernst Mally for the first formulation of the principle. One should note that Meinong has rather an idiosyncratic understanding of the notion of metaphysics: to him metaphysics is an a posteriori, thence empirical, investigation of what exists (see Meinong 1904, 486 [79]). This is clearly not the 10

Meinong: Objects and Objectives

75

has highlighted the role of the paradox of non-existence in the development of this theory: Meinong’s semantics is best understood as the upshot of his solution to the paradox of non-existence. The distinction between objects and objectives, between being-objectives and so-beingobjectives, as well as the crucial principles that connect or do not connect these objectives–all this is a straightforward consequence of the solution of the paradox. Once the Meinongian semantics has been presented in its essential traits, we may thus address the crucial question for us, namely whether, according to this theory, existence is a property or not. If we focus primarily on one part of the story of Meinong’s account, it is indeed very tempting to see him moving in this direction. Since Meinong upholds the view that negative existential statements refer to objects, it seems that Meinong is introducing a genuine distinction between existent and nonexistent objects. The statement “a golden mountain does not exist” really refers to a non-existent mountain. As it happens, this is the standard interpretation of Meinong.11 However, one should also take into due consideration the second part of the story, namely that what makes a statement true is a (subsisting) objective and not an object. Moreover, we have also seen how Meinong explicitly states that existence is in the first place a matter of the objective and not of the object. Thus, what we are confronted with is not a genuine division of the domain of objects into two classes, i.e., existent and nonexistent ones. Instead, Meinong is advocating a division between two kinds of objectives: on the one hand we have being-objectives, and on the other we have non-being-objectives. The distinction between existent and non-existent objects is thus only parasitic and derived with respect to the distinction between these two kinds of being-objectives.12 Of course, someone may argue that the point I am trying to make is not a crucial one: does it really make much difference whether we draw a line between existent and non-existent objects or between being-objectives and non-being-objectives? But according to Meinong there is indeed a

 sense of metaphysics I am assuming when I talk of metaphysics as something implied by a given semantics. 11 Examples of interpreting Meinong as introducing a genuine distinction between existent and non-existent objects are the following: Chisholm (1972), Grossmann (1974), Lambert (1983, 25), Simons (1992c, 164), Jacquette (1996, 23–26), Orilia (2002, 81–92), Reicher (2005, 260; 2014), Rosefeldt (2006, 14–21) Chrudzimski (2007, 179–250), Marek (2013, section 4.3.2). 12 This point was already made, as quoted above, by Findlay (1963, 102–103), Rapaport (1978, 157) and Poli (2001, 351).

76

Chapter Five

considerable difference: only if we take objectives to be primitive and explain the existence or non-existence of objects in terms of being- and non-being-objectives will we be able to avoid the paradox of nonexistence. In fact, if one were to explain the notion of being-objective and non-being-objective by means of existent objects and non-existent objects, respectively, we would again be stuck with the paradox: a non-existent object in and by itself cannot make a negative existential statement true, for it does not exist. Going back to the categories employed in the first part of this study, it is now easy to see how we should classify Meinong’s approach to existence as further instance of the b-strategy. Under the column of existence and non-existence we should not write down objects, but objectives, and more precisely being-objectives and non-being-objectives. Existence is not really in the line of business of objects, but rather, in the line of business of objectives. This does not mean that we can no longer talk of existent or non-existent objects. However, the talk of existent and non-existent objects is just a secondary and derived way of talking. From this perspective, Meinong is following in Brentano’s and Kant’s footsteps: they are all relying exclusively upon the b-strategy to deny the propertystatus to existence. Just as Brentano and Kant had no quarrel with the talk of existent and non-existent objects, neither does Meinong. But this should not be conflated with an endorsement of the property-view of existence.13 The crucial circumstance is that all these authors, in one way or another, attempt to explain existence away: Kant reduces existence to the possibility of being perceived, Brentano to the mental event of accepting an object, and, finally, Meinong to being-objectives.

5.6 Russell’s Objections: The Paradoxes of Characterization A full account of Meinong’s theory can only be provided if Russell’s (1905) objections are taken into account. The reason is that these objections obliged Meinong to add some crucial–and somewhat puzzling– details. Russell correctly saw how Meinong committed himself to upholding what is now known as the Unrestricted Characterization Postulate or Unrestricted Characterization Principle (for the introduction of the term, see Routley 1980, 46): every well-formed subject of a statement must refer



13 The same would of course also apply to Twardowski, since, as was discussed above (3.5), he is an orthodox Brentanian with respect to his approach to existence.

Meinong: Objects and Objectives

77

to an object, as, for instance, in “a golden mountain,” “the round square,” or “the present King of France.” As we have already addressed above, Meinong did in fact consider himself in a position to defend this approach, for he was confident that his theory successfully addressed the paradox of non-existence. Yet Russell was able to point to other unwelcome consequences. The Unrestricted Characterization Principle is unrestricted in that it puts no restriction on how the description may be constituted–besides the fact that it must be grammatically well-formed. Somewhat more formally, (UCP) may thus be expressed as follows: (UCP) For any condition ij, an object satisfies this condition.14 This is the very intuition Meinong wanted to save while addressing the paradox of non-existence: statements may always be taken at face value as referring by means of their subjects to a given object (or more than one), with no restriction on the specific kind of subject in question. Russell, however, points to two paradoxes that arise from (UCP) and may thus be labeled as the paradoxes of characterization. First, if the expression “a round square” refers to something that is round and square, and we assume–as everyone would be ready to concede–that if something is square then it is not round, we end up with the contradiction, i.e., the paradox that the round square is round and not round.15 Schematically, this may be put as follows: (5.8) A round square does not exist. (5.9) If something is round and square then something is round and not round. (5.10) Something is round and square. (5.11) Something is round and not round.

 14 For the time being, I am going to abstract from the problem as to whether Meinong is committed to an even stronger version of (UCP), namely that for any condition ij, an object satisfies exactly this condition. 15 As will be seen further on (see section 6.2), one may want to distinguish between a weaker predicative contradiction “the round square is round and not round” and a stronger propositional contradiction “it is the case that the round square is round and it is not the case that the round square is round.”

78

Chapter Five

We would all agree that (5.8) and (5.9) are the case. Now, by (UCP) and (5.8) we may infer (5.10). Finally, by modus ponens, we may infer (5.11) from (5.9) and (5.10), which is a clear instance of a contradiction. I will label this paradox as the First Paradox of Characterization. The Second Paradox of Characterization is linked to the consequences of embedding the notion of existence in a description that, as Russell phrases it, does not denote anything. For instance, “an existing golden mountain” does not denote anything, or, in other terms, an existent golden mountain does not exist. Yet, according to the Characterization Principle, it follows that an existing golden mountain exists. Schematically: (5.12) An existing golden mountain does not exist. (5.13) An existing golden mountain exists. (5.14) An existent golden mountain exists and does not exist. By (UCP), (5.13) follows from (5.12), and by (5.12) and (5.13) we may infer (5.14), i.e. a contradictory statement. The Second Paradox of Characterization comes very close to the paradox of non-existence. But it is precisely for this reason that one should stress the fact that it is built on different premises: the paradox of nonexistence relies on the premise that reference implies existence, whereas the Second Paradox of Characterization relies on the premise that descriptions refer to objects that instantiate the properties expressed by the predicates embedded in their description. Both premises, then, lead to the same conclusion, namely that something exists and does not exist.

5.7 Meinong’s Answers to the Paradoxes of Characterization Even though Russell’s arguments do not tackle the core of the theory (in the first place that we should distinguish between objects and objectives), Meinong was not caught off guard. As far as the First Paradox is concerned, Meinong notices that the Principle of Non-Contradiction was never intended to apply to impossible objects, but only to possible or existing ones (Meinong 1907, 16–7). Thus, the fact that the round square is round and not round does not give rise to any problem–at least as long as we allow for true statements about impossible objects. Notice, moreover, that impossible objects do not pose a threat in Meinong’s eyes, since these are not what makes statements about them true. What makes

Meinong: Objects and Objectives

79

statements about impossible objects true are once again subsisting objectives. With respect to the second paradox, Meinong answered by introducing a deeply puzzling distinction–as Russell (1973, 81) did not fail to notice. To Meinong, an expression such as “an existing golden mountain” does not refer to an object that (really or actually) exists, but rather, to an object which enjoys a diminished kind of existence (Meinong 1910, 140–141 [105–106]). In a later text, Meinong will label this diminished existence as “contemplative existence” (Meinong 1915, 282). Meinong, moreover, notices that existence shares this complexity with other modalities, such as for instance possibility: although I may contemplate its possibility, it is not by simply characterizing the round square as possible that I can fabricate a possible round square. The same may be said about impossibility and necessity. Meinong’s answer to the Second Paradox of Characterization leads to a restriction of (UCP): characterizations yield us objects only insofar as they do not embed the modal notions of existence, possibility and impossibility, or–as Meinong calls it–as long as they do not embed a modal moment. More precisely, in the case of modal notions, the Characterization Principle yields us only contemplative modalities. We may say that Meinong is thus conceding to Russell that (UCP) is untenable, and we should instead uphold the Modal Characterization Principle (MCP): (MCP) For any condition ij that does not embed modal notions, an object satisfies this condition. In the next chapters, we will be able to explore Meinong’s counterarguments and their reception. For now, suffice it to notice that we have learned something more about his view on existence: according to Meinong, it is a modal moment that, like every modal moment, comes either in its full-blown form or in a watered down one. Notice, however, that to Meinong the modal moment is something which should not be deemed a property of objects, but rather, a property of the objective (Meinong 1910, 80–97 [63–74]). Meinong thus does not abandon his belief that existence is something which in the first place pertains to a certain kind of objectives, i.e. being-objectives. To conclude, one should also note that Meinong does not restrict himself to addressing the objections raised by Russell, but also strikes back by raising a methodological concern. According to Meinong, in order to formulate his objections, Russell is forced to consider statements that allegedly refer to such things as golden mountains and round squares. Thus, by default, he is acknowledging the possibility of referring to non-

80

Chapter Five

existent objects (see Meinong 1907, 17–18). This, however, does not seem to be a fair assessment of Russell’s objections. What the paradoxes of characterizations are pointing at is that from certain grammatical statements and the (UCP) some contradictions would follow. This is a perfectly legitimate instance of a reduction to the absurd, which, as such, does not commit Russell to any of the absurd premises. As it is too easy to discard Meinong’s theory because it allegedly leads to the contradiction that there are things of which it is true that there are no such things, so it is too easy to discard Russell’s objections because they presuppose what they intend to refute.

5.8 Objections: Meinong’s Retreat from Predicate Logic In this chapter, we have found a middle path between Brentano and, more generally, the subjectivism proper of modern philosophy and Frege’s own breed of objectivism. On the one hand, the notion of existence is not explained by means of the cognitive agent’s putting forward an existential statement. On the other hand, existence is not reduced to the second-order property of having instances (in the case of general statements) or to a meta-linguistic notion (in the case of singular statements). One single step is decisive for this middle-ground solution. Meinong advances a semantics of facts–or, more precisely, of objectives–that defuses the paradox of nonexistence: a negative existential statement is true if and only if it refers to a subsistent objective. As addressed above, this middle ground solution should be considered as an instantiation of the b-strategy: under the column of existence and non-existence we should write down, respectively, subsistent being-objectives and subsistent non-beingobjectives, and not existent and non-existent objects. Existence is not in the line of business of objects. As we have already seen, Russell raised two powerful objections to Meinong’s approach, but even though Meinong’s answers are hardly satisfying, one cannot speak of knock-down blows (see Simons 1992c, 186). Be it as it may, Meinong’s answers are not much more than a sketch, which clearly stands in need of further developments. Thus, I take it to be fairer to assess Meinong’s theory with respect to what can properly be considered its cornerstone, i.e., the distinction between objects and objectives and the strictly related solution to the paradox of non-existence. In any case, the following chapters will provide us with more than one opportunity to come back to Meinong’s answers to the paradoxes of characterization. So let us put them aside for the time being.

Meinong: Objects and Objectives

81

From the perspective of the semantics of objectives, a first problem which deserves to be addressed is the following. Since a true negative existential statement has to refer to a subsisting objective, it is difficult to see how the object, which is a part of the objective, should not in its turn have to exist. Or, in other words, how could something non-existent be a part of something that subsists? Meinong addresses this question in his article on the Theory of Objects by denying that we are dealing here with a plain part/whole relation (Meinong 1904, 10–11 [84–5]). Facts are essentially different from objects, insofar as the latter are spatiotemporal, whereas the former are abstract. Thus, it would make no sense to consider something spatial as literally being a part of something non-spatial. Even if one considers this answer satisfactory–Russell (1905, 532; 1973, 80) did not–, the introduction of the notion of objective as a solution to the paradox of non-existence raises a further problem. As noted by Brentano (1911, 147 [228]), the ontology of objectives leads to an infinite multiplication of (subsisting) objectives for every true statement.16 Indeed, if it is true that lions exist, than it is also true that the fact that lions exist obtains, and so on and so forth. Now, according to Meinong, all these statements seem to need a different objective as truth-maker: the objective , the objective , and so forth. Meinong’s (1910, 71 [56]) reply to this objection was that we should consider the subsistence of higher-order objectives as dependent on the subsistence of lower-order ones. These two objections already point to problematic aspects of Meinong’s theory. From the perspective of this study, however, the crucial objection runs as follows. What Meinong’s strategy is tantamount to is an attempt at solving the paradox of non-existence by means of a retreat from a semantics for predicate logic to a semantics for propositional logic. But this cannot be considered a viable solution, since the paradox arises only insofar as we try to analyze the inner structure of predicative and existential statements and assess the difference between them. To say that predicative and existential statements refer, respectively, to so-beingobjectives and being-objectives does not bring us any closer to understanding the difference between existential and predicative statements. One may say that these are just new labels for the old problem. In fact, Meinong still owes us an answer to the question as to where the difference lies between the two kinds of objectives and as to the actual meaning of existence. And since we do not have a rationale as to where

 16

Much later on, this point will also be made by Rapaport (1978, 157).

82

Chapter Five

the difference between so-being-objectives and being-objectives may be, neither have we learned anything new about the meaning of existence. Critics of Meinong have mostly followed Russell’s remarks in “On Denoting” and focused on the so called jungle of objects introduced by him,17 such as the aforementioned golden mountain, the round square or the existing golden mountain with watered-down existence. What went mostly unnoticed is how this jungle is innocuous in Meinong’s eyes, since he relies on the objectives to do, as it were, all the heavy-lifting. Moreover, the upshot of relying so much on the notion of objective is anything but a jungle. Instead, one may even say that Meinong shares Quine’s (1948, 23) taste for desert landscapes and ultimately reduces reality to a system of homogenous abstract objects. Of course, as soon as one discards Meinong’s distinction between objects and objectives as an effective tool to deal with the notion of existence, what we are left with is an interpretation of existence as something which very much resembles a property of objects. From this perspective, one may add, the standard reading of Meinong is vindicated. One should also note that, as soon as we blend out objectives, Meinong provides us with original and at the same time powerful insights that may be relied upon to argue for a property-view of existence. Indeed, no one before Meinong has been as eloquent at questioning one of the deepest intuitions about existence that we have, namely that instantiation presupposes existence. True, as I hope this chapter was able to show, Meinong’s agenda was not thereby to defend a property-view of existence. With this caveat in mind, the label of Neo-Meinongianism is not out of place for the theories that will be addressed in the next chapters. Even though only Neo-Meinongians will take the daring step of interpreting existence as a property of objects, Meinong does provide them with powerful ammunitions to defend such an approach. Nevertheless, Meinong is anything but the champion of the property view of existence he is often portrayed as. This is one of those myths of historiography that deserve to be debunked.

5.9 MacColl and the Early Russell on Existence One final question deserves to be addressed in the present chapter: if not Meinong, who then deserves the title of the champion of the property-view of existence? One option would simply be to attribute this title to the

 17

On the history of criticizing Meinong’s theory by referring to it as a jungle, see Jacquette (1996, 16–17).

Meinong: Objects and Objectives

83

philosophers that are going to be discussed in the next chapters, in the first place Routley and Parsons. But this would not be a fair assessment of the historical situation either. The reason for this is that the early Russell and the Scottish philosopher Hugh MacColl are the ones who really deserve this label. According to MacColl (1902; 1905a; 1905b; 1906), the domain of objects should be divided into two classes: those that have real existence and those that do not have a real existence but a merely symbolic one (see Rahman 2011). Moreover, since MacColl’s notion of real existence should capture the everyday notion of existence, we are confronted with a clear reduction of existence to a property of objects. The notion of a mere symbolic existence, on the other hand, is supposed to be a redundant notion true of both existent and non-existent objects, which–as such– cannot really be deemed a property. Barack Obama has a real existence, Santa Claus has not. Yet both share a symbolic existence. But let us turn to Russell. MacColl’s distinction between symbolic and real existence is mirrored by the early Russell’s distinction between being and existence in his Principles of Mathematics. Here we read that being is that which belongs to any object of thought, whilst “existence is a prerogative of some only amongst beings” (Russell 1903, 449; see Rahman 2011). Barack Obama exists, Santa Claus does not. Yet both share in being. Once this is taken into proper account, we may notice that it has been a matter of historical circumstance that, when Russell converted to the Fregean view of existence, he decided to present his paradoxes of characterizations as objections to Meinong’s position. In fact, these very paradoxes may be relied upon to target MacColl’s position–something which is in fact addressed by Russell (1905, 491)–as well as Russell’s own early position. The reason for this, however, is not that Meinong provides the same interpretation of the notion of existence as MacColl and the early Russell. To the contrary, on this matter the theories present us with a deep disagreement. As we have seen, according to Meinong existence is not a property of objects, but rather, something which pertains to the objective. Instead, the reason these paradoxes are effectively targeting these different theories is that all of them presuppose (UCP). It is also worth mentioning that Meinong himself admitted he was tempted to attribute a kind of being to non-existent objects. And if such a minimal yet universal notion of being is introduced, there is clearly no longer any need for the epicycles of the Meinongian semantics of objectives. Going back to the formulation of the paradox of non-existence

84

Chapter Five

at the beginning of the chapter, Meinong might as well have let (5.3) stand as it is and instead dropped (5.2) in favor of (5.2b): (5.2b) A statement is true if and only if something that has minimal being makes it true. However, Meinong discarded such an option, and for a very good reason, too. The introduction of a minimal notion of being would have led to a notion of being with no negative counterpart–something which he was not ready to accept (Meinong 1910, 79–80 [61–62]). Even though Meinong does not say it explicitly, the reason for which such a solution cannot be accepted is rather obvious. First, it has a clearly ad hoc character. Second, the paradox of non-existence would simply resurface once again under the vestiges of the paradox of non-being. Are we not evidently capable of thinking of something entirely beingless, just as we are capable of thinking of something non-existent? From this perspective, Meinong was indeed justified in venturing on the path of his semantics of objectives. As we shall see, however, at least some Neo-Meinongians consider the introduction of a minimal notion of being to be harmless, and therefore follow MacColl and the early Russell.

CHAPTER SIX ROUTLEY, PARSONS, AND JACQUETTE: AN EXTRA-NUCLEAR PROPERTY

Within mainstream 20th century English speaking philosophy, Russell’s objections were considered–and to a certain extent still are–as having buried Meinong’s theory (see Ryle 1972, 7). In addition, it looks as if the refutation of Meinong grew up to become a founding myth of what is usually labeled as analytic philosophy: it is what defines an entire school of thought (see Perszyk 1993,1–2). From this perspective, it is easy to see how tempting it is to gloss over the fact that Russell himself was–so to speak–more Meinongian than Meinong: a founding myth with a sinful grandfather is harder to sell. However, there is at least one strong intuition that backs up both Meinong’s and Russell’s (as well as MacColl’s) early theories, and in fact constitutes one of the main motivations behind them: general existential statements seem to be informative, and this without having to go secondorder–pace Frege, the converted Russell, and Quine; and singular existentials, too, seem to be informative without having to go metalinguistic. When we say that Santa Claus does not exist, or that a golden mountain does not exist, it looks as if we are learning something about Santa Claus and about a golden mountain. Now, the heretic philosophers labeled as Neo-Meinongians–heretic because they come from the lines of analytic philosophers–are less interested in resurrecting Meinong’s theory, than in coming to the rescue of this very intuition. If one were to stick with the obituary metaphoric, to Neo-Meinongians the intuition that existential statements are informative statements with respect to the very objects they are purportedly about was buried alive. By contrast, what is really dead to them is Meinong’s notion of objective. The same also applies to Meinong’s answers to what we have labeled as the paradoxes of characterization: no Neo-Meinongian is going to resurrect them. As it happens, what Neo-Meinongians are really coming to the rescue of is the theory of the early Russell or MacColl. In this chapter, I address Richard Routley’s, Terence Parsons’, and Dale Jacquette’s version of Neo-Meinongianism. These authors all build

86

Chapter Six

upon a distinction between nuclear and extra-nuclear properties and the classification of existence as an extra-nuclear property of objects. We are thus for the first time confronted with the explicit thesis that existence is a property of objects, albeit an extra-nuclear one. In order to distinguish this first family of Neo-Meinongianism from the ones addressed in the following chapters, I follow Berto (2013) in adopting the label of Nuclear Neo-Meinongianism.

6.1 Almost a New Solution to the Paradox of Non-Existence As noted above, the intuition that Routley, Parsons and Jacquette want to rescue is in the first place that negative existentials can be true, and affirmative ones false–and this without having to go second-order or metalinguistic. However, since they do not resurrect Meinong’s notion of objective,1 they are from the outset confronted by the problem of having to provide a different solution to the paradox of non-existence. Nuclear Neo-Meinongianism provides the most straightforward possible solution: negative existentials are true because non-existent objects make them true. Thus existential statements become very similar to ordinary predicative statements. A statement such as “a rose in the garden is not red” is true if and only if a rose in the garden does not instantiate the property of being red; similarly, a statement such as “a golden mountain does not exist” is true if and only if a golden mountain does not instantiate the property of being existent. This solution did not go unnoticed before the advent of NeoMeinongianism; it was just set aside without much after-thought. For instance, Meinong implicitly discards this option, since according to him only existing or, more precisely, subsisting objects may fulfill the role of truth-makers. And the reason behind this choice is that only subsisting objects can guarantee for a robust sense of truth. But there is an easy answer to these preoccupations: one simply has to follow the early Russell (1903, 455) and distinguish between being and existence: “Existence is a prerogative of some only amongst beings.” Or, which is tantamount to the same, one may also follow MacColl (1902; 1905a; 1905b; 1906) and distinguish between symbolic existence and real existence: every object has at least symbolic existence, but only some objects enjoy real existence (see Rahman 2010). Both approaches are indeed only terminologically

 1

While Jacquette and Parsons simply do not resort to objectives in their theories, Routley explicitly rejects the notion (Routley 1980, 4; 855–856).

Routley, Parsons, and Jacquette

87

different, since they both introduce what I have called a minimal though universal notion of being. Going back to the Neo-Meinongians, Parsons squarely follows in the footsteps of the early Russell and MacColl. To Meinong–as we have seen– the statement that there are things of which it is true that there are no such things was indeed contradictory. To Parsons, this statement is true as long as we disambiguate between two alleged meanings of the expression “there is.” In its first instance, it refers to the minimal though universal notion of being, whereas in the second one it refers to the non-universal notion of existence. And since existence becomes a kind of being (i.e., not everything that has being has existence), there is no contradiction in saying that there are things of which it is true that such things do not exist (Parsons 1980, 5–9).2 Routley and Jacquette, for their part, follow a slightly different path. They have no issue with letting what was formerly a robust sense of truth fall–something to which the early Russell, MacColl, Parsons, but also Meinong held on to. Accordingly, they avoid any distinction between being and existence of objects: to them, negative existential statements are simply made true by non-existent objects, period. One could thus say that Routley and Jacquette are not just reviving the strategy of the early Russell and MacColl, but they are also borrowing an essential element from Meinong’s theory: objects may lack any kind of being whatsoever. However, one cannot stress enough how Meinong was confident he was in a position to defend this view only because of the introduction of those theoretical entities he labeled as objectives. Thus, Routley really does provide us with a new solution to the paradox of non-existence–a solution which was then endorsed by Jacquette as well. The difference between Parsons’ approach on the one hand and Routley’s and Jacquette’s on the other is highlighted by the formalism to which their theories are linked. If Parsons may still rely on the classical, Fregean, existentially loaded couple of quantifiers (i.e., “‫ ”ݔ׌‬and “‫׊‬x”), Routley and Jacquette introduce a new couple of existentially neutral quantifiers, which, together with the predicate of existence “‫ܧ‬,” may be used to define standard existentially loaded quantifiers (read “ܲ‫ ”ݔ‬as the particular, existentially neutral quantifier, and “ܷ‫ ”ݔ‬as the universal, existentially neutral quantifier; see Routley 1980, 176): ‫ ܣݔ׌‬ൌௗ௘௙ ܲ‫ݔ‬ሺ‫ܧ‬Ǩ ‫)ܣ ـ ݔ‬

 2

Parsons thus returns to Frege’s formulation of the paradox of non-existence (see above, section 4.4.), but upholds the view that “to exist”-statements and “there are”-statements are not synonymous.

88

Chapter Six

‫ ܣݔ׊‬ൌௗ௘௙ ܷ‫ݔ‬ሺ‫ܧ‬Ǩ ‫ܣ ר ݔ‬ሻ Of course, both Routley and Jacquette could very well have maintained the standard couple of quantifiers and could have changed the way we should “read” them instead. But since they thought that by then the reading of “‫ ”ݔ׌‬as “there is an x” (where “there is” is given an existential interpretation) was too far ingrained in the mind of philosophers and logicians, they preferred to introduce an altogether new symbolism. And, indeed, this symbolism is very helpful to bring to the fore the difference not only with respect to the standard Fregean approach, but also with respect to the unorthodox one developed by Parsons.

6.2 On Impossible Objects and Contradictory Statements As previously mentioned, not only do Nuclear Neo-Meinongians abandon the notion of objective, thus having to provide a different solution to the paradox of non-existence, but they are also unimpressed by Meinong’s solutions to the paradoxes of characterization. Let us start with the first one. It seems rather harmless to object to Russell that the Principle of NonContradiction is not universal, since it clearly does not apply to contradictory objects, and thus no consistency restriction should be applied to the Characterization Principle. Yet Meinong might have underestimated the power of the Characterization Principle, (or more precisely its unrestricted version UCP). For instance, as Routley noted, the principle enables us to construct a characterization that leads to a denial of the Principle of Non-Contradiction in full generality. In order to do so, one simply has to build the following characterization: “The object which is such that the Principle of Non-Contradiction does not apply.” Even worse, the characterization principle is so powerful that it may yield us a trivial logic without further ado. All we need is just to build the characterization “the object which is such that every statement is true” (Routley 1980, 505). Because of the problems just mentioned, Neo-Meinongians try to strike a balance between dropping altogether Meinong’s intuition that some objects are indeed impossible and the very unwelcomed consequence of paraconsistency and trivialism.3

 3

Routley also spends some time trying to explore the alternative of going paraconsistent, while at the same time avoiding the pitfall of trivialism (Routley 1980, 347–360). Since he does not flesh out the details of such an approach, I am not going to address it in the present context.

Routley, Parsons, and Jacquette

89

The main tenet of the approach to the threat posed by impossible objects is the following: Routley, Parsons and Jacquette all allow for characterizations of impossible objects, and thus also allow for the truth of statements such as “the round square is round and square.” What they try to achieve, however, is to block the inference from a statement about an impossible object to a corresponding propositional contradiction. To wit, given the statement (say) (6.1) we are not in a position to infer (6.2): (6.1) The round square is round and square. (6.2) It is the case that the round square is square and it is not the case that the round square is square. Differences in strategy come into play as soon as we consider how the inference from a statement about an impossible object to a propositional contradiction is blocked. Parsons blocks the inference by rejecting the principle that if something is square then it is not the case that this something is round. More generally, to him each time we have an object with allegedly contradictory properties, we should drop the principle according to which these properties are contradictory. We may thus say that, according to Parsons, impossible objects are objects with only apparently contradictory properties, i.e., objects that have contradictory properties only according to certain conceptual schemes–as for instance Euclidean geometry in the case of the round square. What this approach clearly rules out is that inherently contradictory characterizations such as “the non-square square” yield us any object (Parsons 1980, 42 footnote). This is tantamount to a restriction of the Characterization Principle: we may not characterize objects with truly or immediately contradictory properties. This strategy–one should notice–is forced upon Parsons by his Russellian stance: non-existent objects have being; but being clearly cannot be contradictory. Routley and Jacquette, by contrast, try to save what we may call truly and not just apparently impossible objects: the round square is truly round and not round. They both come to the rescue of this intuition by arguing against the implication that if the round square is not round, then it is not the case that the round square is round. Again, more generally, what they are both aiming at is a strong separation between predicate negation and propositional negation (Routley 1980, 272; Jacquette 1996, 114–115). And since they interpret the law of non-contradiction as a principle of propositional logic, they can claim that they are able to save both Meinongian impossible objects and the Principle of Non-Contradiction in its full generality.

90

Chapter Six

Clearly, also this second strategy presupposes a strong restriction of the Characterization Principle, namely that propositional contradictions cannot be inferred from statements about impossible objects. Moreover, propositional contradictions cannot be embedded in a characterization: the characterization “the object such that it is the case that p and it is not the case that p” is not a well-formed characterization. All the authors we are considering thus admit that the Characterization Principle cannot be upheld in its unrestricted version. As we shall soon see, the Second Paradox of Characterization will oblige them to introduce further restrictions.

6.3 Constitutive and Extra-Constitutive Properties Nuclear Neo-Meinongians rely on a distinction between nuclear and extranuclear properties (Routley 1980, 496; Parsons 1980, 44; Jacquette 1996, 85–86) to block the Second Paradox of Characterization–a distinction which is supposed to be Meinongian in spirit. As a matter of fact, Routley, Parsons and Jacquette all claim that the distinction between nuclear and extra-nuclear properties is inspired by Meinong’s distinction between konstitutorische and außer-konstitutorische Bestimmungen. I thus start by providing an analysis of Meinong’s pair of notions. It is not entirely transparent what Meinong means by “konstitutorische und außer-konstitutorische Bestimmungen,” whose English effective but somewhat free translation as nuclear and extra-nuclear properties is due to John Findlay (1963, 176).4 These concepts are the result of an elaboration on a similar distinction advanced by Meinong’s student Ernst Mally and address the problematic barrier between what is really part of the object and what is attributed to it because of the cognitive agent’s psychological relation to the object. More precisely, constitutive properties are part of the nature of the object–where we should be careful not to understand “nature” as meaning the sum of the necessary properties of the object (see Jorgensen 2002, 32). Extra-constitutive properties, on the other hand, are attributed to the object because of our subjective way of grasping it (see Meinong 1915, 177). A few examples may prove helpful. If we take an object and refer to it first with the expression “a red thing” and then with the expression “an ivory red ball,” it seems innocuous to assume that the switch of

 4

Findlay clarifies in a footnote how he had to find a term other than “constitutive” to render the German “konstitutorisch,” since he had already used the term to render Meinong’s notion of “konstitutiv.”

Routley, Parsons, and Jacquette

91

expressions does not affect the nature of the object itself. The properties of the object remain exactly the same (I assume the object satisfies both descriptions). What really changes is that our way of grasping the object is more or less complete.5 For instance, since the second expression lists more properties of the object, it allows for a more complete hold on the object. Now, the property of being more or less complete is ausserkonstitutorisch, i.e., it applies to our way of grasping the object–something which is in this case strictly related to a linguistic expression. Things are somewhat more complicated, though, because the property of being complete may have both a constitutive and an extra-constitutive function. To Meinong, this is particularly true since to him some objects are complete and some are incomplete (see Meinong 1915, 178). Thus, one and the same property may be used to characterize the object or the way we grasp the object, i.e., something strictly related to the linguistic expression. A second example provided by Meinong is the property of being simple. If I say “the red thing is simple,” I may express the way of grasping the object through the expression “the red thing,” i.e., the fact that I am referring to an object relying on an expression with only one predicate. Yet the same predicate “simple” may also be used to characterize an object, namely an object that has only one property. In this case, however, it would be contradictory, since a simple red thing would not be simple but complex (it would instantiate two properties).6 Without launching here on a scholarly discussion of Mediaeval logic, we may notice that the phenomenon addressed by Meinong bears a strong resemblance to the scholastic notion of simple supposition (supposition simplex): we may talk about, and thus attribute properties to intentions of the soul or concepts and not, as is usually the case, objects. This analogy is only relevant insofar as it points to the circumstance that we are not really dealing with a distinction between two kinds of properties, but rather, with an ontological distinction between concepts (or something concept-like) and objects. Properties become constitutive if attributed to objects, and extra-constitutive if attributed to concepts or concept-like entities.7

 5

Contemporary philosophers may want to add that, if a change occurs, it is a Cambridge change: the object changes to the extent that someone has referred to it in a new way. 6 For a discussion of this paradox, see Reicher (2005, 261–262; 2014, section 4). 7 Jorgensen (2002, 31) already suggested that we are not–strictly speaking–dealing with a distinction between two kinds of properties.

Chapter Six

92

6.4 Nuclear and Extra-Nuclear Properties Let us now return to Nuclear Neo-Meinongianism. The distinction between constitutive and extra-constitutive properties undergoes a metamorphosis in the hands of Routley, Parsons and Jacquette. Here comes Parsons’ list of examples of predicates which express extra-nuclear properties (Parsons 1980, 23): Ontological: “exists,” “is mythical,” “is fictional” Modal: “is possible,” “is impossible” Intentional: “is thought about by Meinong,” “is worshipped by someone” Technical: “is complete”8 In contrast, examples of predicates which express nuclear properties are “being red,” “being human,” “having a beard,” etc. It is at first glance clear that this distinction cannot have much in common with Meinong’s distinction between constitutive and extraconstitutive properties: according to Routley, Jacquette, and Parsons, the distinction is really about kinds of properties and not about kinds of objectivities to which properties may be ascribed. In other words, it is not what an extra-nuclear property is ascribed to, which makes an extranuclear property out of it; rather it is the property by itself that is extranuclear. The same is of course true of nuclear properties. Since Neo-Meinongians do not really take over Meinong’s distinction, we are confronted with the following problem: how can we ground the difference between nuclear and extra-nuclear properties? What is the legitimacy of this distinction? Everyone would agree that there is a sense to the scholastic notion of supposition simplex and thence to the distinction drawn by Meinong between constitutive and extra-constitutive properties. Yet we cannot rely on this notion to defend the distinction between nuclear- and extra-nuclear properties. Neo-Meinongians are aware of an explanatory gap. However, they are confident we can rely on intuitions to sort extra-nuclear properties from nuclear ones. As Parsons says, what is considered by everyone as a normal property of an object should be considered to be nuclear; if otherwise, it should be considered as extra-nuclear (Parsons 1980, 24; for similar considerations, see Routley 1980, 264–265).

 8

Routley (1980, 266) provides an almost entirely overlapping list.

Routley, Parsons, and Jacquette

93

Once this intuitive distinction is taken for granted, one simply needs to limit the scope of the Characterization Principle to nuclear properties, thus avoiding the Second Paradox of Characterization. This Nuclear Characterization Principle (NCP) may be formulated as follows: (NCP) For any condition ij that does not embed extra-nuclear properties, an object satisfies this condition. By means of (NCP), we may for instance say that the description “an existent golden mountain” does not yield us an existing golden mountain, because existence is not a nuclear property (Parsons 1980, 44; Routley 1980, 496; Jacquette 1996, 85–86).9 In addition, problems similar to the Second Paradox of Characterization are addressed by means of the notion of extra-nuclear properties. For instance, simply by characterizing an object as mythical or fictional, we do not chase things out of existence (see characterizations such as “the fictional Barack Obama”). Or, to give an example related to intentional properties, the characterization “the golden mountain thought about by Barack Obama” does not yield us any object because an intentional property is embedded in it. Yet it is not difficult to see that the intuitive distinction between nuclear- and extra-nuclear properties constitutes the ill-concealed Achilles’ heel of this first breed of Neo-Meinongianism.

6.5 Quine’s Possible Man in the Doorway One last piece of information is missing before we can assess Nuclear Neo-Meinongianism. As we have seen, Meinong was able to profit from Russell’s objections in order to flesh out some crucial details of his theory. There is, however, one more objection, which Meinong was not in a position to take into account simply because it arrived too late. What I

 9

If Routley, Jacquette and Parsons all rely on an intuitive distinction between nuclear and extra-nuclear properties, their paths part with respect to the question as to whether the watered-down versions of extra-nuclear properties should be allowed or not. As we have seen, this was a notion that Meinong applied to the modal moment: existence, possibility and necessity all come in two forms, a fullblooded one and a watered down one. Thus, the description “an existent golden mountain” does yield us an existent golden mountain, precisely insofar as we are dealing with a watered down existence. Routley (1980, 496) and Jacquette (1996, 85–86) reject this strategy, though. Only Parsons (1980, 44) recurs to Meinong’s notion of a watered-down version of modal notions, and generalizes it to all extranuclear properties (modal notions are a subset of extra-nuclear properties) (see Berto 2013, 125).

94

Chapter Six

have in mind is Quine’s famous argument of the possible man in the doorway. Now, if this objection arrived too late for Meinong, the same cannot be said for Neo-Meinongianism. So, let us first address the objection and then turn to the reply provided by Routley, Parsons and Jacquette. Quine’s target of criticism is the fictional philosopher Wyman, whereby Wyman is usually interpreted as being a placeholder for Meinong. To be fair, however, this identification should not be taken for granted (see Routley 1980, 413 footnote 3). Nevertheless, at least one objection raised by Quine against Wyman seems to accurately target Meinong’s or Neo-Meinongian positions (Routley 1980, 414–416), at least as long as possibility is interpreted as non-existence: Wyman’s slum of possibles is a breeding ground for disorderly elements. Take, for instance, the possible fat man in that doorway; and, again, the possible bald man in that doorway. Are they the same possible man, or two possible men? How do we decide?” (Quine 1948, 23)

The point Quine is striving to make is strictly linked to a problem addressed by Russell (1905) while putting forward his theory of descriptions. As a first approximation, we may consider the problem about identities of non-existents as a specification of a more general question about non-existents, already implicitly addressed by Russell. It is thus worth considering this more general problem. Russell’s theory of descriptions was not only meant to address the puzzle of non-existence, but in the first place concerns the Law of Excluded Middle (LEM) in statements that involve non-denoting definite descriptions (see Russell 1905, 490). To give his example, prima facie neither (6.3) nor (6.4) seems to be true, thereby violating (LEM): (6.3) The present King of France is bald. (6.4) The present King of France is not bald. His theory of description, however, provides an almost clear-cut answer to this problem. The definite description in (6.3) should be contextually interpreted so as to yield us (6.3b): (6.3b) There is some x which has the property of being the present King of France and for every y, if y has the property of being the present King of France, then y is identical with x, and x is bald.

Routley, Parsons, and Jacquette

95

This statement is clearly false, since there is no such thing as a bald present-day King of France. With (6.4) the matter is somewhat more complicated. According to Russell, the negation in (6.4) may be interpreted as internal–which would mirror the grammatical statement–or as external. If the first option is privileged, we would end up again with a false statement, since (6.4b) is as false as (6.3b): (6.4b) There is some x which has the property of being the present King of France and for every y, if y has the property of being the present King of France, then y is identical with x, and x is not bald. As there is no bald present-day King of France, neither is there any nonbald present-day King of France. However, if the negation is given an external interpretation, the statement becomes true, as (6.4c) shows: (6.4c) It is not the case that there is an x which has the property of being the present King of France and for every y, if y has the property of being the present King of France, then y is identical with x, and x is bald. Of course, we may avoid the epicycles of Russell’s theory of descriptions as well as the alleged ambiguity of our language between internal and external negation if we declare all statements with non-denoting definite descriptions as false or senseless. However, as already noted above (section 4.7), this seems to be a very drastic solution. Thus, it is difficult not to side with Russell in discarding this option. On the other hand, if one follows a Meinongian position, we are confronted with a different kind of problem. From a Meinongian or Neo-Meinongian perspective, we simply do not seem to be in a position to assess whether (6.3) or (6.4) is true. The reason for this is that the Characterization Principle does, indeed, only say that any description yields us an object that satisfies this description; but how can we establish whether this object satisfies a property which is not embedded in its description? This may be labeled as the Problem of Underdetermination. It is important to note that Russell did not raise this objection to Meinong’s theory. This step was taken by Quine. He does not raise this problem in general, though, but with respect to a specific kind of statements, namely identity ones. The problem raised by Quine is that a Meinongian philosopher cannot tell us whether (6.5) or (6.6) are true:

96

Chapter Six

(6.5) The fat man in the doorway is identical with the bald man in the doorway. (6.6) The fat man in the doorway is not identical with the bald man in the doorway. Because we cannot assess whether (6.5) or (6.6) are true, non-existent objects are “a breeding ground for disorderly elements.” Russell, however, had already given us the conceptual tool to notice that non-existent objects are “a breeding ground for disorderly elements,” since they more generally lead to what I have called the Underdetermination Problem. Whereas Quine’s slogan is “no entity without identity,” a more general slogan would be “no entity to which the Law of Excluded Middle does not apply.” There is, however, a sense in which Quine’s objection to non-existent objects is something more than just a specification of the one implicit in Russell’s line of reasoning. In order to see this, it is sufficient to recall the most intuitive approach to the notion of identity, i.e., Leibniz’s Law of Indiscernibles: (LLI) Two objects are identical if and only if for every condition ij, both satisfy ij or neither satisfies ij. From this perspective, we may say that identity is not just a property among others, but something which supervenes upon other properties. And, if this is the case, we should not say that non-existent objects are underdetermined with respect to identity statements as well as with respect to statements involving other conditions. Rather, we should say that it is because non-existent objects are underdetermined that we cannot assess their identities. (Of course, the underdetermination should be restricted to conditions other than identity, since otherwise this line of reasoning would be trivial). Indeed, if we were be able to assess whether the non-existent fat man in the doorway is bald or not, we would also be able to assess the identity at stake. In this sense, Quine’s objection may be located at the same level of generality as the one that may be derived from Russell’s line of reasoning. Be that as it may, Neo-Meinongian philosophers need to provide an answer to this challenge.

6.6 Answer to Quine’s Challenge The introduction of the distinction between extra-nuclear and nuclear properties proves–once more–to be decisive. According to Nuclear Neo-

Routley, Parsons, and Jacquette

97

Meinongianism, two objects are identical if and only if they share exactly the same set of nuclear properties (see Parsons 1980, 28; Jacquette 1996, 101), or if and only if there is a coincidence in extensional properties–as Routley (1980, 414) prefers to word it. Thus, the identity criterion for nonexisting objects should be the same as the one at stake with existing objects, since the question as to whether or not objects exist is irrelevant while discussing their identity. The same of course would hold for other extra-nuclear properties: whether an object is fictional or not, mythical or not, thought about or not, all this is irrelevant to establish the identity of such an object. This principle may be labeled as the Nuclear Identity Principle (NIP) and expressed as follows: (NIP) No two objects have exactly the same nuclear properties. This, though, is not enough to fully address the challenge raised by Quine. In fact, we cannot yet answer the question as to whether the non-existent bald man in the doorway is identical with the non-existent fat man in the doorway. Indeed, how might we know whether the two expressions refer to an identical object that instantiates the nuclear properties of being bald and being fat or to two different men, one of them fat and one of them bald? The Neo-Meinongian way to address this further concern is by means of a strengthening of (NCP). This may be labeled as the Strong Nuclear Characterization Principle: (SNCP) For any condition ij that does not embed extra-nuclear properties, an object satisfies exactly this condition. Once (SNCP) has been introduced, the Quinean rhetorical question may be answered as follows: the description “the fat man in the doorway” does not refer to the same object as the description “the bald man in the doorway,” since the former refers to an object that satisfies exactly the condition of being a bald man, whereas the latter refers to an object that satisfies exactly the condition of being a fat man. The price one has to pay in order to meet the challenge raised by Quine is rather a high one: descriptions may yield us objects that violate (LEM), namely in the case of non-existent objects.10 The fat man in the doorway is neither bald nor not bald; and the bald man in the doorway is neither fat nor not fat. They are, however, fully determined objects: for every

 10

At least starting from his work on probabilities, Meinong (1915), too, considered unproblematic the introduction of incomplete objects, i.e., objects that violate (LEM).

98

Chapter Six

condition ij, we may say whether or not they satisfy this condition. To this extent, non-existent objects are not disorderly. If we go back to (NIP), one may notice that this principle, too, is rather problematic. Indeed, why should extra-nuclear properties be irrelevant while establishing the identities of objects? The reason, however, lies at hand: if also extra-nuclear properties were to become relevant while addressing the identity of objects, this would lead to non-existent doubles of existent objects. For instance, if extra-nuclear properties were relevant for identities, this would mean that the characterizations “the existent golden mountain” and “the non-existent golden mountain” might characterize two different objects. And if this were the case, then we would be confronted with the very awkward situation in which both statements would be true, namely that the golden mountain does not exist and that the golden mountain exists. But we obviously do not want any doubles of existing or non-existing objects. Thus, the extra-nuclear property of existence has to be considered irrelevant to the identity criterion of an object. We can have only one golden mountain, either an existent or a non-existent one. The same line of reasoning, then, may be applied to all extra-nuclear properties, so that we end up with the identity criterion defended by Routley, Parsons and Jacquette.

6.7 Objections: Ad Hocness As addressed at the beginning of the chapter, the first and crucial motivation behind Neo-Meinongian theories such as Routley’s, Parsons’ and Jacquette’s is to rescue the crucial intuition behind Meinong’s theory: existential statements are informative without having to be reinterpreted as statements about instantiations of concepts or about the reference of one of its terms. For instance, when someone says that Santa Claus or a golden mountain does not exist, we do in fact learn something about Santa Claus and a golden mountain–provided of course these statements are true. This is the very intuition that also the early Russell and MacColl tried to vindicate. To refer back to the mythological metaphor of the previous chapter, Routley, Parsons and Jacquette, like Meinong, the early Russell and MacColl before them, defend an anti-Procrustean stance: our existential statements may be taken at face value and do not have to be amputated from our language as trifling or contradictory (in the case of singular statements) or as second-order ones (in the case of general statements). The details of Nuclear Neo-Meinongianism follow almost automatically from its anti-Procrustean aspiration. First, existence is

Routley, Parsons, and Jacquette

99

deemed a first-order property, since it is something that objects may or may not instantiate. This is tantamount to a deviation from the theory defended by Meinong and an endorsement of the strategy of MacColl or the early Russell. On this conception, the paradox of non-existence is simply the result of the unwarranted premise that the domain of objects is a domain of existent objects, i.e., that existence does not permit any partitioning within the domain of objects. Secondly, a principle of characterization must be introduced to secure the reference to non-existent objects, but at the same time restricted, in order to avoid the paradoxes of characterization. Most notably, the Characterization Principle cannot be applied to obtain objects that lead to violations of the Principle of NonContradiction, and it must be restricted to so-called nuclear properties. Let us turn to possible objections. First, it is important to remember that according to Parsons an object may or may not instantiate the property of existence, but every object instantiates being. In contrast, Routley and Jacquette reject any distinction between being and existence. As the reader will remember, Meinong, too, rejected such a distinction: a universal notion of being did not make any sense to him–and, we may add, neither did it make any sense to Frege and the later Russell. Moreover, as pointed out above, such a distinction would open the door to a new paradox of being. Sure enough, every statement such as “a golden mountain does not exist” would be unproblematic and thus spared by Procrustes’ axe. Yet every statement such as “a golden mountain has no being” would automatically be contradictory and, as such, would have to be amputated. There is no getting rid of Procrustes. This line of reasoning may thus be applied to Parsons’ strategy as well. Routley and Jacquette, instead, do provide us with a more satisfactory solution of the paradox of non-existence, even if at the price of abandoning a robust sense of truth. Some sentences are true even if there is literally nothing that makes them true. However, if one is caught in the trilemma of either amputating our language, or introducing questionable ontological entities as the objectives, or abandoning the robust sense of truth, is this really the worst choice one may make? Even with respect to the First Paradox of Characterization, we may say that Routley’s and Jacquette’s versions of Meinongianism have the upper hand with respect to Parsons’. Since some objects simply have no kind of being whatsoever, there is prima facie no problem in having true contradictions about them. Consequently, sentences like “the round square is round and square” or even “the round square is round and not round” can both be true.

100

Chapter Six

Parsons, in contrast, is forced to develop a particular interpretation of negation in order to save the truth of the Meinongian statement “the round square is round and square” and at the same time avoid the inference to “the round square is round and not round.” This strategy, moreover, falls short of handling intrinsic contradictory definite descriptions–as Parsons readily admits. Finally, the weakness shared by Routley, Jacquette and Parsons is linked to the distinction between nuclear and extra-nuclear properties. As suggested above, this is the ill-concealed Achilles’ heel of the first kind of Neo-Meinongianism. The usual objection here bears upon the ad hoc character of these notions (Priest 2005, 83; Kroon and Voltolini, 2011, section 1.2.3.; Berto 2013, 126): the only reason that really speaks in favor of this conceptual distinction is that it allows for a solution to the Second Paradox of Characterization or variations thereof. Nevertheless, the ad-hocness of a conceptual distinction does not mean that it has to be false. As Wittgenstein noticed, explanations come to an end somewhere. But then, how should we assess Nuclear Meinongianism and, more specifically, how should we decide between Nuclear NeoMeinongianism and its most plausible alternative until now, namely Fregeanism? Or, in other words, how could we take sides with respect to the question whether or not existence is a property of objects? The problem I am trying to point out is that the choice between Frege on the one hand, and Routley and Jacquette on the other, seems to boil down to a matter of intuitions.11 You either start with the intuition that objects need to be existent, and thus sacrifice the appearance that existential statements are informative statements about objects; or you start with the intuition that the appearance of existential statements should be upheld, and then introduce a distinction between objects that instantiate existence and objects that do not. If you give precedence to one intuition, you will become a Fregean; if you follow the other, you will become a Nuclear Neo-Meinongian. But exactly as Frege was not in a position to give us any reason to back up his view of objects as existents, so Nuclear Neo-Meinongians provide us with no reason to uphold the appearance of existential statements. But could Routley and Jacquette not point to a decisive advantage of their approach with respect to the Fregean alternative, namely that the very

 11 Perszyk (1993, 178) makes the same point with respect to the debate between Russell and Meinong. Similar points have been made by Lewis (1990: 27–28) and van Inwagen (2008: 54). To say that the rival theory is unintelligible, as Lycan (1979: 290) consider it to be the case with Neo-Meinongianism (see Priest 2008a), may also be seen as pointing towards an irreducible clash of intuitions.

Routley, Parsons, and Jacquette

101

appearance of language speaks in their favor? This may very well be the case. This advantage is, however, relativized by the epicycles to which a Neo-Meinongian semantics is obliged, i.e., the introduction of (NCP) and (NIP) and the ad-hocness of the distinction between nuclear- and extranuclear properties. Apparently, we have reached a stalemate.

CHAPTER SEVEN RAPAPORT AND ZALTA: A BRAND NEW RELATION

Rapaport and Zalta confront us with a second version of NeoMeinongianism which does not operate with the nuclear/extra-nuclear distinction. Instead, the essential trait of Rapaport’s and Zalta’s theories is the introduction of a distinction between two kinds of predication. More precisely, these authors distinguish two kinds of relations which may obtain between objects and properties, which are both–ambiguously– expressed by the copula “is”: the familiar relation of instantiation and the less familiar one of encoding (Zalta) or constitution (Rapaport). This is a highly unusual undertaking–which explains why the label of Dual Copula Neo-Meinongianism is appropriate to them (see Kroon and Voltolini 2011). For sure, it is very commonsensical to distinguish, for instance, between the meaning of the copula as predication and as identity–and examples of this distinction go all the way back to Plato–or between the meaning of the copula as predication or existence. Rapaport and Zalta, however, stand rather isolated in their attempt to introduce a relation between objects and properties other than the one of instantiation. Despite this difference, the main tenet of the Dual Copula NeoMeinongianism is the same as in the Nuclear one. Rapaport and Zalta, too, purport to come to the rescue of the intuitions behind Meinong’s theory: existential statements are first-order informative statements, and thus it is possible to negate the existence of something. Again, it is only to this limited extent that Rapaport and Zalta may be considered Meinongians, for–like Parsons, Routley and Jacquette before them–they are neither interested in resurrecting the notion of objective nor the notion of modal moment. Nevertheless, as will be shown further on, Dual Copula NeoMeinongians give a new twist to the view of existence as a property.

7.1 Rapaport: Existence as a Two-Place-Relation Rapaport’s theory puts forward a solution to the paradox of non-existence, relying explicitly on an encompassing theory of thought or intentionality,

Rapaport and Zalta: A Brand New Relation

103

and not simply on a theory of language. The theory of thought defended by Rapaport is a version of representationalism: theoretical entities which mediate between the subject and the “world” are introduced. To Rapaport, every thought is directed toward an M-Object (where the “M” should stand for Meinongian) that may or may not stand in a two-place relation with an ordinary object. For instance, if I think about the golden mountain, I am thinking of an M-Object to which no ordinary object corresponds. On the other hand, if I am thinking about Rapaport’s golden ring, I am thinking about an M-Object to which an ordinary object corresponds. In order to specify this two-place relation and clarify what M-Objects are, Rapaport builds upon a distinction put forward by Hector-Neri Castañeda (1974) between two kinds of predication, i.e., two kinds of relation between an object and a property: namely, “constitution” and “exemplification.”1 According to this distinction, we should think of Mobjects as being constituted by properties, and of existing or actual objects as exemplifying properties. For instance, the M-Object to which the expression “the golden mountain” refers is constituted by the properties of being a mountain and being golden. Yet only the actual object with which the M-Object might be in a two-place relation can exemplify these properties (Rapaport 1978, 160). We may now further specify the twoplace relation as follows: an M-object is in the relevant two-place relation with an ordinary object if and only if the latter exemplifies the properties that are the constituents of the former (Rapaport 1978, 165). With this conceptual apparatus at hand, Rapaport is in a position to interpret negative existential statements as first-order statements. When we affirm that something does not exist, what we really mean is that nothing stands in the appropriate two-place relation with a given M-object. For instance, the statement “a golden mountain does not exist” means that no object stands in the appropriate two-place relation with an M-object whose constituents are the properties of being a mountain and being golden. And since nothing stands in this relation to this M-object, the statement in question is indeed true. Rapaport’s declination of Neo-Meinongianism–we ought to point out– does not interpret existence as a (unary) property, but as the holding of a two-place relation. Under the column of existence we should put Mobjects that stand in a two-place relation with an ordinary object, whereas under the column of non-existence we should put those M-objects that do not. Hence–surprisingly–Rapaport’s strategy seems to move towards an

 1

Castañeda was also inspired by Meinong, although very loosely. For a discussion of his theory, see Orilia (2002, 147–159).

104

Chapter Seven

instance of the b-strategy (I will come back to this at the end of the chapter).

7.2 Zalta: Existence as Being Spatially Located Zalta, like Rapaport before him, also develops an approach to existence which is strictly linked to a more general theory of intentionality. More precisely, Zalta endorses a version of representationalism which is very close to Rapaport’s. To Zalta, every thought is directed in the first place toward an abstract object (short: A-object), which thus plays the role of Rapaport’s M-objects. Out of a sense of symmetry, however, Zalta wants to avoid the picture according to which sometimes the A-object is in a given two-place relation with something else, but this is not always the case. Thus, to Zalta, every A-object is in a one-to-one correlation with another object, the only difference being that this second object may either be a spatial object or, yet again, an A-object (Zalta 1988, 111). In order to clarify what A-objects are, Zalta, too, relies on a distinction between two kinds of predication. His primary source, though, is neither Rapaport nor Castañeda, but rather, it is Meinong’s pupil Ernst Mally. According to the latter, properties may either be “exemplified,” which is the case of ordinary, spatial objects, or they may be “encoded,” which is the case of A-objects (Zalta 1988, 15). On this conception, we have a slightly different interpretation of negative existentials than the one put forward by Rapaport. The statement “a golden mountain does not exist” is true not because there is no twoplace relation between an A-object and the corresponding spatial object, but rather, because the object which is a golden mountain is an abstract, i.e., non-spatial one. Thus, existence is no longer interpreted as a twoplace relation, but as a property identical with the property of being abstract or spatially located (Zalta 1988, 21). Since he preserves the interpretation of existence as a (unary) predicate, Zalta may seem closer to Nuclear Neo-Meinongianism. Yet there is no denying that interpreting existence as being spatially located also moves in a direction foreign to the aspiration of Nuclear NeoMeinongianism. Non-existent objects become abstract objects, i.e., something essentially similar to numbers–provided one considers numbers to be abstract objects. Non-existent objects are thus made ontologically innocuous. It is no longer the case that only some objects enjoy existence whereas others do not. Instead, some objects enjoy existence, and others enjoy abstractness.

Rapaport and Zalta: A Brand New Relation

105

This yields a straightforward solution to the paradox of non-existence which very much resembles Parsons’: no matter whether objects are spatial or abstract, they always have being. But then again, one should notice that, according to Parsons, non-existent objects have no positive characterization other than the fact of having being. Zalta, by contrast, tells us that non-existent objects have the additional positive property of being abstract (see Reicher 2014, section 5.4). Being an extensive monograph, Zalta’s exposition of his approach is much more detailed than Rapaport’s. Among other things, he draws attention to the fact that A-objects, too, exemplify properties–in the first place the property of being abstract. In addition, Zalta also develops a modal logic according to which objects that encode properties are necessarily such. And since objects that encode properties are abstract, and such objects are non-existent, it follows that, indeed rather counterintuitively, non-existent objects are necessarily so (Zalta 1988, 19).2 For the scope of the present discussion, however, we may leave these details aside.

7.3 The Unrestricted Characterization Principle The distinction between two kinds of predication does not only allow us to defuse the paradox of non-existence, but it also provides ammunitions against Russell’s objections. Let us start with the First Paradox of Characterization. Both Rapaport and Zalta are not worried by a statement such as (7.1): (7.1) An existent golden mountain is existent. The reason for this is that every property may be attributed to the object in a second, radically different way. So, according to them, we are able to uphold the position according to which every characterization yields us an object. All we need to say is that the controversial object at stake does not exemplify the properties used in the description but, rather, it is simply constituted by them, or it encodes them. An existing golden mountain is really existent, to the extent that the property of existence is encoded by it or constitutes it. As for the First Paradox of Characterization, Rapaport and Zalta can simply say that the Principle of Non-Contradiction applies only to

 2

Berto’s (2013, 135–136) criticism targets this aspect of Zalta’s theory.

106

Chapter Seven

exemplified properties, but not to the second kind of predication (Rapaport 1984, 261–262; Zalta 1988, 120–123). The solutions of the paradoxes of characterization put forward by Dual Copula Neo-Meinongianism seem to have a crushing advantage with respect to the first kind. On the one hand, Rapaport and Zalta need not rely on the allegedly ad hoc distinction between nuclear- and extra-nuclear properties. On the other, they are not obliged to introduce impossible objects in their semantics or to limit the Characterization Principle to noncontradictory properties, nor to characterizations that do not embed propositional contradictions. In fact, one is tempted to sum up this difference by saying that Zalta’s and Rapaport’s theories do not require any qualification of the Characterization Principle, but may uphold its unrestricted version (URC). However, there are ways to challenge this assessment of the second kind of Neo-Meinongianism.

7.4 Objections: Fregeanism under Disguise Not many words are required to summarize this second breed of NeoMeinongianism: everything happens in one single step. The introduction of mediating abstract entities and the strictly connected distinction between two kinds of object-property relations provide straightforward solutions to the paradox of non-existence, as well as to both paradoxes of characterization. Sure enough, as philosophers are keen to say, this comes at relevant ontological costs. Yet–however unusual the distinction between two kinds of predication may be–the introduction of mediating entities follows a well-established philosophical tradition, i.e. representationalism. And one may argue that, as soon as representationalism is granted, we also have to grant a distinction between two kinds of predications. But let us start with the solutions to the paradoxes of characterization. Rapaport’s and Zalta’s theories seem to present the most striking advantage with respect not only to the ones developed by Routley, Parsons and Jacquette, but also to those expressed by Meinong, the early Russell or MacColl: they are in a position to uphold (UCP). As it happens, their theories can deal effectively with both paradoxes of characterization, solely by relying on the distinction between two kinds of predication. The problem, however, is that (UCP) or its cognates were intended to apply to the exemplification of properties. Once a second kind of predication is introduced, the principle is essentially altered. More precisely, as one can see from the following reflection, it would be more accurate to say that no (UCP) finds its way in Rapaport’s and Zalta’s theory.

Rapaport and Zalta: A Brand New Relation

107

Dual Copula Neo-Meinongianism relies on the assumption that our language is equivocal–a view that implicitly acknowledges that we may disambiguate the way we speak. Rapaport and Zalta, after all, are constantly discriminating between expressions where the predication should be read in one way or the other. Yet, as soon as we do this, the paradoxes of characterization strike back with a vengeance. For instance, the disambiguated definite description “the object that exemplifies the property of being a mountain and of being golden” can yield us no object. The same is obviously the case with the disambiguated contradictory denoting phrase “the object that exemplifies the properties of being round and square” (see Byrd 1986, 247 and Berto 2013, 135).3 One must concede that, within this disambiguated language, the Characterization Principle is indeed unrestricted as long as only the encoding of properties or the being constituted by properties is considered.4 But since the principle was always meant to address the exemplification of properties, it is hard to see how this may still be labeled as the Characterization Principle. Let us now turn to the solution to the paradox of non-existence. Even though Rapaport and Zalta provide a rather different interpretation of the notion of existence, it is important to stress how they both agree on a distinction between existence and being. Both authors would agree that negative existentials can be true because there are objects that do not exist. To Rapaport, this is the case because there are M-objects that do not stand in the appropriate two-place relation to an ordinary object. To Zalta, this is the case simply because there are A-objects. From this perspective, Dual Copula Neo-Meinongianism comes very close to the kind of theory put forward by Parsons, the early Russell or MacColl: Rapaport, Zalta and Parsons all agree on something that was explicitly rejected by Meinong: namely, that we may solve the paradox of

 3 Zalta (1988, 35–36) foresees this objection and claims a) that statements involving notions of his theory such as being an A-object, exemplifying or encoding are not genuine natural language data and b) that counter-examples to his theory may be construed only within natural language data. Thus, “the object that exemplifies the properties of being round and square” cannot constitute a counterexample to his theory. But, as Menzel (1992, 1150) notices in his review of Zalta’s book, this position is not unproblematic: “If there are such things as he purports, they are no less appropriate as potential subjects of discourse in natural language than quarks, black holes, or any other highly theoretical entity.” 4 This is not entirely accurate, since in order to avoid the Clark-Rapaport paradox some restrictions need to be put in place (see Rapaport 1978, Zalta 1983, and Jacquette 1996, Appendix A).

108

Chapter Seven

non-existence by saying that all objects have being, but only some of them exist. The problem, however, is that this is not a solution of the paradox but–as was already noted in the previous chapter–simply a deferral of it. Rapaport’s and Zalta’s solution of the problem of non-existence, just like Parsons’, the early Russell’s or MacColl’s solution before them, is unsatisfactory because the paradox resurfaces again under a different form: namely, as the paradox of non-being. There are, however, even more serious problems which are raised by Rapaport’s and Zalta’s solution to the paradox of non-existence. In the case of Zalta’s version of Neo-Meinongianism, we are confronted with the awkward situation in which every statement of the form “x does not exist” is always true, no matter what “x” stands for. The reason for this is that Zalta endorses (URC) with respect to the encoding of properties. Thus, no matter which properties are embedded in the description of an object, there will always be an A-object that encodes these properties. This problem is avoided by Rapaport’s version of NeoMeinongianism, because he does not interpret existence as a unary predicate. The price he has to pay for this, however, is that existential statements are no longer about those objects to which they seem to be referring. As a consequence, Rapaport is giving up the very intuition at the heart of both Meinong’s theory and Neo-Meinongianism: namely, that we should uphold the appearance of existential statements. Instead, what we end up with is a Fregeanism under disguise. Indeed, why can we not interpret Rapaport’s M-objects as concepts and the relation that holds or does not hold with an ordinary object as a relation of instantiation? The difference seems to become a merely terminological one. Rapaport’s approach, as (a part of) the Fregean one, is thus best understood as an instance of a b-strategy. Existence is not really in the line of business of dividing the domain of objects into two classes. In the light of these last remarks, the verdict has to be that the interpretation of existence put forward by Routley and Jacquette remains the best available theory of existence as a first-order property. Rapaport and Zalta, on the other hand, may be considered as having simply argued for a richer ontology, leading either to the unwelcome consequence that every negative existential statement is true, or to a kind of Fregeanism under disguise. Thus, Rapaport and Zalta cannot help us to find a way out of the stalemate between Nuclear Neo-Meinongianism and Fregeanism addressed at the end of the previous chapter.

CHAPTER EIGHT PRIEST: MODAL MEINONGIANISM

Although following in many respects his mentor Routley, Graham Priest’s version of Neo-Meinongianism deserves to be treated separately. Like the other Neo-Meinongians before him, Priest wants to save existential statements from Procrustes’ axe. What is specific about his approach, however, is that Priest’s solutions to the paradoxes of characterization are strictly tied to a possible-worlds semantics framework: hence the label of Modal Meinongianism (see Berto 2013, 137 and Kroon 2012). Relying on a modal framework, Priest purports to defend the most daring version of Neo-Meinongianism. To him, existence is not a first-order property of a specific kind, but rather a perfectly ordinary one. Accordingly, no gerrymandered distinction between nuclear and extra-nuclear properties needs to be introduced. In Modal Meinongianism–we may say–there is no caveat to the claim that existence is a property.

8.1 The Perfectly Ordinary Property of Existence As just addressed, Priest did not stop half-way on the path to consider existence a property. To him, it is no longer the case that, albeit a property, existence is not like most of the other properties. To the contrary, since he criticizes the ad-hocness of the notion of extra-nuclear properties, Priest sets out to do what Routley dared not: “The noneist strategy [i.e., the admission of non-existent objects] requires us to suppose that existence is a perfectly ordinary predicate” (Priest 2005, 14). If Priest radicalizes Routley’s view of existence as a quasi-ordinary property, he follows him in denying any kind of being to non-existents. Formally, this is achieved by means of the introduction of a couple of existentially neutral quantifiers, i.e., the same approach as in Routley and Jacquette (Priest 2005, 13–14). As already discussed above, this approach yields us the most convincing solution to the paradox of non-existence, for every theory that distinguishes between being and existence is inevitably confronted by the paradox of non-being. Thus, once the paradox of non-

110

Chapter Eight

existence has been put aside, let us turn to Priest’s approach to the paradoxes of characterization. Priest’s strategy to deal with the paradoxes of characterization involves several steps. The first step is rather unexpected: not every object can be non-existent, but only those objects that do not instantiate existenceentailing properties. As in the case of the distinction between nuclear and extra-nuclear properties, Priest acknowledges that he is not in a position to provide a definition such that, for every property x, we may know whether it is existence-entailing or not. Instead, like Routley, Parsons and Jacquette before him, he too assumes the notion to be an intuitive one. Intuitive examples of existence-entailing properties are: being red, being tall, being kicked, and the like. If and only if something exists, it can instantiate these properties. On the other hand, examples of properties that do not entail existence are: being thought about, being imagined, being identical and the like: both existent and non-existent objects may instantiate these properties. Nevertheless, Priest (2005, 59–60) is confident that his distinction is commonsensical enough and does not present an overt ad hoc character. The result of the introduction of the notion of existence-entailing properties puts a heavy constraint on what it is that can be an object of a negative existential. For instance, each time we say that a winged horse does not exist, that all winged horses do not exist or that the winged horse Pegasus does not exist, these statements would have to be–strictly speaking–contradictory and thus false. The reason for this is obvious enough: intuitively, the properties of being winged and being a horse fall within the class of existence-entailing properties, so that no non-existent object may instantiate them. On this conception, negative existential statements are possibly true– i.e., non-contradictory–only if they have bare quantifications as a subject (e.g., “some object does not exist”), proper names (e.g., “Pegasus does not exist”), or subjects that embed only non-existence entailing properties (i.e., “some object that is thought about does not exist”). Here, no existenceentailing property is attributed to these objects, so that the corresponding negative existential statements may indeed be true. Upon further inspection, however, these negative existential statements may become controversial, too. In fact, one may argue that some existence-entailing property is required in order to understand such statements. Otherwise, how would we know what we are speaking about? So, eventually, we may be forced to throw all negative existentials overboard. This problem of Priest’s theory was labeled as the

Priest: Modal Meinongianism

111

underdetermination of non-existing objects (see Nolan 2008, 191–193):1 since these objects are stripped of all existence-entailing properties, how can we still know what we are speaking about while denying the existence of something? However, it would be too soon to assess the impact of this objection, for we have not yet considered the crucial trait of Priest’s approach, i.e., its modal dimension.

8.2 The Representing-Operator So far, Priest’s version of Neo-Meinongianism does not seem to fare very well. Rather surprisingly, it does not seem in a position to give us what every Neo-Meinongian theory promises, namely a way to save existential statements from Procrustes’ axe. Most negative existentials seem indeed contradictory according to his theory. An unsympathetic reader, moreover, might point out that the rest look pretty much senseless. Let us see how the modal dimension of Priest’s theory dramatically changes this rather worrisome picture. It is in the first place in connection with the Characterization Principle that the modal framework is brought to bear by Priest. It seems that the solution to the paradox of non-existence already compels Priest to throw the principle overboard. As it happens, already at this stage his theory is immune from the paradoxes of characterization: it is not the case that every characterization yields us an object. What Priest must do at this point, then, is not so much to restrict the principle in order to avoid the paradoxes. To the contrary, he must sneak the principle back in to earn the label of Neo-Meinongianism in the first place.2 Priest’s strategy is to say that the Characterization Principle will only hold as long as the characterization takes up the position of the variable y in an expression of the form “x represents y.”3 The reason the principle holds under this condition is that the expression “x represents y” is formally interpreted as an operator on a possible-worlds modal semantic framework. Intuitively speaking, according to Priest’s definition, the operator of representing is understood as a relation between the world inhabited by the representing subject and a set of worlds in which things are as they are (partially) represented to be (Priest 2005, 84–85).

 1

This problem of underdetermination should not be confused with the one raised by Quine’s objection (see above, section 7.5). 2 As Reicher (2014, section 5.2) writes “it is worth noting that the postulation of existence-entailing properties is an implicit rejection of Meinong’s principle of independence, which is one of the cornerstones of Meinongian object theory.” 3 Berto (2013, 180) talks here of a regimentation of the principle.

112

Chapter Eight

Once such a formal apparatus is put into place, it should be clear how the expression (say) “a golden mountain” may refer to an object that is both golden and a mountain as soon as it is embedded in the construction “I represent a golden mountain.” Moreover, within this construction, there is no problem in saying that the expression “a golden mountain” refers to something existing. In fact, it would have to, since the properties of being golden and being a mountain are intuitively existence-entailing–and this without there being any need for a golden mountain in the actual world. At this point, one might argue that this approach does not yield us anything close to the Characterization Principle as it was endorsed by Meinong: the golden mountain was deemed to be golden and a mountain here and now, so to speak, and not in alternative worlds. Yet it is important to notice that considerations of intentionality played a crucial role in Meinong’s stance on non-existing objects. It was primarily because he considered himself capable of thinking of golden mountains or round circles that Meinong was drawn to the assumption that the golden mountain and the round circle should be considered as genuine objects on a par with existent ones. Thus, Priest’s strategy may be interpreted as providing a modal interpretation of this intuition.

8.3 Constant Domains We may now see how Priest’s interpretation of the Characterization Principle puts him in a position to come to the rescue of the negative existential statements that his theory–at least prima facie–seemed to need to rule out as contradictory. It is still the case that, literally speaking, the statement (for instance) (8.1) cannot be true: (8.1) A winged horse does not exist. However, a minimal paraphrase may suffice to come to the rescue of this statement, namely (8.2): (8.2) An object I represent as being a winged horse does not exist. The latter statement, to the contrary of (8.1), may indeed be true. In order to comprehend how this last statement can be true, however, we have to turn to some technical details of the modal framework. Priest adopts a possible-worlds semantics with constant domains: the domain of objects associated to a world does not change while moving

Priest: Modal Meinongianism

113

from one world to another.4 In such a context, the truth-conditions of the statement (for instance) (8.2) should be construed as follows: the representing agent is in a relation with a denizen of the actual world that does not exist and has no existence-entailing properties; this very same object, however, has the properties of having wings, being a horse, and thus also being existent in a set of non-actual worlds. Finally, if something like Kripke’s causal theory of reference of proper names is assumed–as in Priest’s case (2005, 141–144)–this object may even be named; for instance, in the case of Pegasus.5 We should add that Priest’s semantics also envisions impossible worlds, which are crucial in order to avoid any further restriction to the comprehension principle: contradictory characterizations, too, may refer to an object, at least as long as this object lies within the scope of the representing-operator. For instance, “I represent a round square” expresses the relation between a subject that is representing something and an object that is both round and square in the appropriate impossible worlds, of course via a non-existent object in the actual world. Notice, moreover, that the same strategy would also work with the more challenging impossible objects addressed in the previous chapters. For instance, Priest is in a position to quarantine the object such that the Principle of NonContradiction does not hold–as long as this object lies within the scope of a representing-operator and the representing-operator expresses a relation to an impossible world.

8.4 Objections: Existence and Modal Contexts In this chapter, we have seen how Priest radicalizes Routley’s approach to existence: existence becomes an ordinary predicate. The price to pay for this radicalization, however, is the introduction of a paraphrase strategy. Whereas to Routley, “a golden mountain does not exist” is a well-formed negative existential that may for instance find a one-to-one translation into the formal language, to Priest what such a statement really means is “I represent an object that does not exist which is a golden mountain,” where the representing-operator is formally interpreted as a relation within a constant domains possible-worlds semantics. This paraphrase is required since being golden and being a mountain are existence-entailing

 4

For a description of possible-world semantics with constant domains, see below, section 12.1. 5 Within such a setting, Quinean problems of identity of non-existents clearly become innocuous.

114

Chapter Eight

properties, so that they can only be instantiated in alternative worlds in which the represented object exists. Finally, the non-classical extension of this semantics through impossible worlds enables Priest also to have impossible objects in the scope of the representing-operator. We have already addressed one challenge to Priest’s approach, namely the underdetermination problem: we can truly deny existence of only those objects that do not instantiate existence-entailing properties; but once objects are stripped of said existence-entailing-properties, we are left with just a handful of properties that do not seem sufficient to determine an object, as for instance being thought about or being identical. This objection, however, can to a certain extent be blocked by means of the (im)possible-worlds semantics developed by Priest. True, objects of which we truly deny existence can have no existence-entailing property. But we may still say quite a lot about them, for instance that they are represented by one or more cognitive agents as having such and such properties. And, given a version of the causal theory of names, we may name them, too. The object named Pegasus, for instance, would instantiate the properties of having wings and being a horse in a set of possible worlds. Or, at least, Pegasus would instantiate these properties in an impossible world, namely in the case in which the represented winged horse is taken to be an impossible object. Since the underdetermination problem does not seem to be decisive, let us put it aside, and focus on the paraphrasing strategy enforced by Priest instead. First, let us address an objection raised by Kroon (2012, 29). A statement such as “a flying horse does not exist” has to be rephrased as “an object I represent as being a flying horse does not exist,” for the properties of being a horse and being flying are existence-entailing. The problem raised by Kroon will now be the following: we would all agree that every paraphrase strategy should be in a position to preserve the truth-value of the statements at stake; yet Priest’s paraphrase does not meet this requirement. Whereas we all agree that it is the case that a flying horse does not exist, it may very well be false that an object I represent as being a flying horse does not exist. Indeed, I may just be representing my existing dog Fido as something that instantiates the property of being a winged horse in a set of possible (or even impossible) worlds.6

 6

Priest’s answer was to deny that there was anything troubling with this consequence: the operator of representing might either involve (actually) existent or non-existent objects (personal conversation, reported by Kroon 2012, 31). Yet the picture is indeed troubling since–as noted above–it fails to fulfill a crucial requirement for every paraphrase strategy.

Priest: Modal Meinongianism

115

Following Kroon’s lead, one may raise a further objection, namely that Priest’s approach to existential statements seems to involve an asymmetry. Whereas a statement such as (8.1) has to be paraphrased as (8.2), a statement such as (8.3) seems fine as it stands according to Priest: (8.3) A lion exists. Since the object is an existent one, it may very well instantiate the property of being a lion. But is a theory that suggests such an asymmetric reading of existential statements still plausible? Of course, Priest might object that nothing stands in the way of paraphrasing the affirmative existential statement as well, thus mirroring the strategy that has to be employed with (most) negative existential statements. But then we would end up with the same problem addressed by Kroon. If we paraphrase (8.3) as (8.4), it is no longer the case that the following statement must be true: (8.4) An object I represent as being a lion exists. Indeed, nothing stands in the way of saying that what I represent is a nonexistent object that instantiates, at a set of non-actual worlds, the property of being a lion. Again, the paraphrase strategy would not be in a position to preserve the intuitive truth-value of the paraphrased statement. Both these objections point to what I take to be the crux of Modal Meinongianism. To Priest, existential statements very often if not always have an implicit modal dimension. Yet, after some inspection, it becomes clear how problematic such an approach really is. For instance, when we say that something round and square does not exist, we are not at all interested in an object that has the modal properties of being possibly–or more precisely impossibly–round and square. To the contrary, it is the property of being actually round and square that is of relevance here. More generally, it is only how things actually are which is relevant to the assessment of the truth of plain existential statements such as the one just considered; alternative situations, on the other hand, are simply not part of the picture. As Crane (2013, 75) noted (although not in the context of a discussion of Modal Meinongianism), “fix the facts about everything in the world, and you will have fixed the truth of negative existential.” The epicycles of Modal Meinongianism, thus, run into troubles because they try to overrun this basic insight. With Priest’s attempt at reducing existence to a perfectly ordinary firstorder property we have covered the most influential attempts at interpreting existence as a property. And since the version of

Chapter Eight

116

Meinongianism developed by Priest leads to several problems, the verdict remains the same as in the last chapters: the most convincing interpretation of existence as a first-order property is the one that relies on the notion of extra-nuclear properties. More precisely, the most convincing kind of NeoMeinongianism is the one developed by Routley and endorsed by Jacquette, for it avoids the problematic distinction between being and existence. Accordingly, we are left with two main rival theories: Frege’s view of existence as a second-order property, and Routley’s or Jacquette’s approach to existence as a first-order property. These are, so far, the two most convincing interpretations of existence we have encountered–or, at least, I have tried to argue so. .

INTERLUDE

CHAPTER NINE FREE LOGICS: THE EXISTENCE-PREDICATE

In this chapter, I provide a brief overview of a family of approaches to existence which may be considered as an alternative to Fregeanism and Neo-Meinongianism: free logics. It is important to underline how free logics are, as logics, formal. From this perspective, it is imperative to distinguish between the formal model in and by itself (e.g., one specific kind of free logic) and the philosophical interpretation of the model (see Bencivenga 1986, 147–148). In fact, the real question which we are concerned with in this chapter is how to interpret and assess philosophically the introduction of a predicate of existence in free logics, or, if there is none, which place is, so to speak, implicitly assigned to existence. As we shall see, whereas the most common version of free logics, namely negative free logic, seems to follow closely some intuitions that may be traced back to Frege, the same cannot be said of other, more sophisticated and recent approaches. Arguably, these are candidate theories which might help us break the stalemate between Fregeanism and Neo-Meinongianism, i.e., the upshot of the first two parts of this study.

9.1 The Existence-Predicate As we saw in Chapter 4, in his Dialogue with Pünjer, Frege is in the first place defending the view according to which existence is captured by quantification. However, this approach is also strictly linked to the view that the meaning of the English verb “to exist” is self-evident: no matter which objects we are talking about, it is true of this object that it exists. Conversely, to deny the existence of an object is contradictory: no matter which object we are talking about, it is false to say that such an object does not exist. If we introduce a formal language where lower case letters are the counterpart of proper names of objects (so-called individual constants), the particular Fregean–and thus existential–quantifier and, finally, the identity sign, this self-evident meaning of existence may be defined as follows (see Hintikka 1966):

Free Logics: The Existence-Predicate

119

‫ܧ‬Ǩ ሺܽሻ ൌௗ௘௙ ‫ݔ׌‬ሺ‫ ݔ‬ൌ ܽሻ Clearly, in a language where individual constants are names of objects, the predicate is self-evident, in the sense that it is true of every individual constant. Another way to put it would be to say that in such a language, for every individual constant a, the presupposition of existence holds: (PE)

‫ݔ׌‬ሺ‫ ݔ‬ൌ ܽሻ

This logical principle, moreover, is strictly linked to two further principles, namely specification (S) and existential generalization (EG):1 (S)

‫ ߮ݔ׊‬՜ ߮ሾ‫ݔ‬Ȁ݇ଵ ሿ

(EG)

߮ሾ‫ݔ‬Ȁ݇ଵ ሿ ՜ ‫߮ݔ׌‬

If every object within the domain of objects satisfies a condition, then a given object satisfies this condition, too (S). And if a given object satisfies a condition, then there is something that satisfies this condition (EG). However, as already addressed in Chapter Four, there is something deeply unsatisfactory in interpreting the meaning of “to exist” as selfevident, or, as some philosophers are wont to put it, as expressing a universal or pleonastic property. Indeed, our everyday language confronts us with blatant counter-examples to such an interpretation. As we have seen, Frege attempts to address this problem by going meta-linguistic. In order to make sense of prima facie true denials of existence, such as for instance “Odysseus does not exist,” we may interpret them as statements about a grammatical expression: what true denials of existence tell us is that a given grammatical expression, for instance “Ulysses,” is a mere empty sound. Or, if one were to introduce the distinction between sense and reference, one might say that the name “Ulysses” has a sense but no reference. Following Frege’s lead, one may thus want to develop a formal language where individual constants do not simply represent names of (existent) objects, but may also represent proper names as empty sounds, or as terms with a sense but without a reference. In such a setting, one would clearly have to give up the logical truth of (PE), (S) and (EG). Now, free logics are called free in the first place because they do not uphold the logical truth of (PE): they are logics free of the assumption that for every

 1

The arrow “՜” stands for the inference-relation. I use the horse-shoe “‫ ”ـ‬for material implication.

120

Chapter Nine

particular term there is something to which this term refers.2 In other words, terms may be empty. The upshot is that now the definition of the formal predicate of existence E! no longer yields us something self-evident, or, if you like, a universal property. Thus, it makes perfect sense to interpret statements of our ordinary language such as, for instance, “Ulysses does not exist” as ̱‫ܽܧ‬. Furthermore, the reader may notice how this approach presents a striking advantage with respect to the amendments to Frege’s approach introduced by Russell and Quine. It is no longer the case that the truth of grammatical statements of the form “x does not exist,” where x stands for a proper name or a definite description, has to be defined with respect to the truth of the statements resulting from the logical analysis of their proper name or definite description. Free logics thus seem to put us in a position to close the gap between ordinary language and the analyzed logical language that was introduced by Russell and Quine. Historically, this is one of the main motivations behind the exploration of free logics, i.e., to avoid the epicycles introduced by Russell and Quine (see Leonard 1956).

9.2 Negative, Neuter and Positive Free Logics In this paragraph, I will follow the standard distinction between negative, neuter and positive free logics (see Lambert 1960). Negative free logic is called negative because every atomic proposition with so-called “empty” (singular) terms is false. Syntactically, free logic only differs from classical logic because of the introduction of an existence-predicate and an identity-sign. The intuition as to what an empty term really is, however, may only be understood by considering the semantics for negative free logic.3 [D1] A model M for negative free logic is a tuple ‫ܦۃ‬ǡ‫ ۄܫ‬where D is the domain of quantification and I a partial function (i.e., a function which is not defined for every singular term). [D2] Interpretation for negative free logic: 1. For every singular term k, either ‫ܫ‬ሺ݇ሻ belongs to D or ‫ܫ‬ሺ݇ሻ is not defined.

 2

To be more precise, free logics are free of existential assumptions with respect to both particular and general terms, i.e., predicates (see Lambert 1960). 3 I follow the exposition of the semantics provided by Fontaine and Redmond (2012). Only the truth-definitions for the relevant truth-connectives are defined. The other connectives are defined as usual.

Free Logics: The Existence-Predicate

121

2. For every n-ary predicate P, I(P) is a n-tuple of members of D. 3. Every member of D has a name. [D3] Truth in the model for negative free logics: 1. ܸெ ሺܲ݇ଵ ǡ ǥ ǡ ݇௡ ሻ ൌ ͳ if and only if ‫ܫ‬ሺ݇ଵ ሻǡ ǥ ǡ ‫ܫ‬ሺ݇௡ ሻ are defined and ‫ܫۃ‬ሺ݇ଵ ሻǡ ǥ ǡ ‫ܫ‬ሺ݇௡ ሻ‫ܫ א ۄ‬ሺܲሻ. 2. ܸெ ൫݇௜ ൌ ݇௝ ൯ ൌ ͳ iff ‫ܫ‬ሺ݇௜ ሻand ‫ܫ‬൫݇௝ ൯ are defined and ‫ܫ‬ሺ݇௜ ሻ is the same as ‫ܫ‬൫݇௝ ൯. 3. ܸெ ሺ‫ܧ‬Ǩ ݇௜ ሻ ൌ ͳ iff ‫ܫ‬ሺ݇௜ ሻ is defined. 4. ܸெ ሺ‫߮ݔ׊‬ሻ ൌ ͳ iff ܸெ ሺ߮ሾ‫ݔ‬Ȁ݇௜ ሻሿ ൌ ͳ for every ݇௜ such that ‫ܫ‬ሺ݇௜ ሻ is defined. 5. ܸெ ሺ‫߮ݔ׌‬ሻ ൌ ͳ iff ܸெ ሺ߮ሾ‫ݔ‬Ȁ݇௜ ሻሿ ൌ ͳ for at least one ݇௜ such that ‫ܫ‬ሺ݇௜ ሻ is defined. We may now understand what an empty term is according to negative free logic: empty terms are those terms for which no interpretation function is defined and which, thus, lead to the invalidation of the principles (PE), (S) and (EG). Neuter free logic differs from negative free logic only insofar as it attributes an undetermined truth-value to all atomic statements with empty terms, thus abandoning the framework of two-valued logics. A limitation of both negative and neuter free logic is that statements which seem to be analytically true turn out to be false, as for instance in ݇௜ ൌ ݇௜ , when the interpretation function of ݇௜ is not defined. This is the main motivation behind the development of positive free logic. In order to allow for true atomic propositions with singular terms, which negative free logic considers empty, positive free logic is obliged to introduce a reference for such terms, too. This is achieved by means of a distinction between an inner domain, on which the quantifiers range, and an outer domain, on which the quantifiers do not range: every singular term refers to an object either in the inner or in the outer domain. The semantics will thus take the following form: [D4] Interpretation for positive free logic: 1. For every singular term k, I(k) belongs to ‫ܦ‬ଵ ‫ܦ  ׫‬ை Ǥ 2. For every n-ary predicate P, I(P) is a n-tuple of members of ‫ܦ‬ଵ ‫ܦ  ׫‬ை Ǥ 3. Every member of ‫ܦ‬ଵ ‫ܦ  ׫‬ை has a name. [D5] Truth in a model for positive free logic: 1. ܸெ ሺܲ݇ଵ ǡ ǥ ǡ ݇௡ ሻ ൌ ͳ if and only if ‫ܫۃ‬ሺ݇ଵ ሻǡ ǥ ǡ ‫ܫ‬ሺ݇௡ ሻ‫ܫ א ۄ‬ሺܲሻ. 2. ܸெ ൫݇௜ ൌ ݇௝ ൯ ൌ ͳ iff ‫ܫ‬ሺ݇௜ ሻand ‫ܫ‬൫݇௝ ൯ is the same as ‫ܫ‬൫݇௝ ൯. 3. ܸெ ሺ‫ܧ‬Ǩ ݇௜ ሻ ൌ ͳ iff ሺ݇௜ ሻ ‫ܦ  א‬ଵ .

Chapter Nine

122

4. ܸெ ሺ‫߮ݔ׊‬ሻ ൌ ͳ iff ܸெ ሺ߮ሾ‫ݔ‬Ȁ݇௜ ሻሿ ൌ ͳ for every ݇௜ such that ‫ܫ‬ሺ݇௜ ሻ ‫ܦ  א‬ଵ . 5. ܸெ ሺ‫߮ݔ׌‬ሻ ൌ ͳ iff ܸெ ሺ߮ሾ‫ݔ‬Ȁ݇௜ ሻሿ ൌ ͳ for at least one ݇௜ such that ‫ܫ‬ሺ݇௜ ሻ ‫ܦ  א‬ଵ . As with negative free logic, principles (PE), (S) and (EG) are invalidated. This, however, is achieved not through an introduction of an asymmetry in the interpretation function, but through an asymmetry in the semantics, namely the distinction between an inner domain, over which the quantifiers range, and an outer domain, over which quantifiers do not range. Because of this limitation in the range of the quantifiers, these two domains may be intuitively understood as the domains of existent and nonexistent objects. It is worth noticing how positive free logic leads to a most dramatic failure of (EG): in negative and neuter free logic, (EG) fails only because we have true non-atomic propositions with empty terms; in positive free logic, (EG) fails because we have true atomic propositions about nonexistent objects. This difference may be highlighted if one considers the Principle of Predication (PP), namely that for every property P and every individual constant ݇௜ , the following holds: (PP)

ܲ݇௜ ՜ ‫ݔ׌‬ሺ‫ ݔ‬ൌ ݇௜ ሻ

This principle is upheld by negative and neuter free logic but invalidated by positive free logic. Most philosophers, and non-philosophers too, will usually wince at the idea that (PP) may be given up: it seems one of the strongest intuitions we have that if something instantiates a property, then it exists. However, we have already seen how Meinong and the NeoMeinongian philosophers were capable of questioning the hold this intuition has upon us. Now, positive free logic provides us with a further framework in which this premise may be abandoned without further ado. But, then, the preoccupation arises that the difference between positive free logic and, for instance, the Neo-Meinongian approach developed by Routley is merely terminological. As noted by Priest (2008b, 295), we only have to introduce a second couple of quantifiers that range both over the inner and the outer domain, and may thus be labeled as outside quantifiers. Once we have outside quantifiers, quantification in and by itself no longer captures the notion of existence. In such a context, moreover, the most promising path to distinguish between the two couples of quantifiers would be to introduce a Neo-Meinongian first-order predicate of existence, whose extension is provided by the inner domain.

Free Logics: The Existence-Predicate

123

9.3 Supervaluations and Superinterpretations As addressed above, one of the main motivations behind the move from negative or neuter to positive free logic was to save the tautological character of identity statements. It would in fact be welcomed if the truth value of (instances of) ݇௜ ൌ ݇௜ did not depend on whether ݇௜ refers to an existing object or not. However, positive free logic pays too high a price to accommodate this intuition, namely by providing a theory which is de facto Neo-Meinongian. But is it not possible to uphold the intuition about identity statements without going down the path of Neo-Meinongianism? Bencivenga’s own version of free logic–to which I now turn–may be interpreted exactly as an attempt at finding such a compromise. Bencivenga builds upon van Fraassen’s models that distinguish between partial valuations, classical extensions and supervaluations. So, let us start with a brief characterization of van Fraassen’s model (again, for the reconstruction I am relying on Fontaine and Redmond 2012): -

-

Partial valuations allow for truth-value gaps (some propositions are false, some are true, and some are neither true nor false). Classical extensions are obtained by considering all arbitrary assignments to propositions lacking a truth-value which are consistent with the truth-conditions (i.e., if a given proposition is arbitrarily made true, then any disjunction containing this proposition will be made true, too). A proposition is true according to the supervaluation if it is true in all classical extensions, false if it is false in all classical extensions, and neither true nor false if it takes on different values in different classical extensions.

Within such a model, the notions of logical consequence and validity are then defined as follows: Logical consequence: A proposition is a logical consequence of another proposition if there is no partial valuation, each classical extension of which makes all the premises true and the conclusion false. Validity: A proposition is valid according to supervaluation if there is no partial valuation the classical extension of which renders that proposition false. The upshot of van Fraassen’s model is that we may come to the rescue of logically true sentences, even if such sentences do not have a truth-value

Chapter Nine

124

in the original partial evaluation. Let us consider the following instance of the law of non-contradiction: (9.1)

ܲ݇௜ ‫̱݇ܲ ש‬௜

Now, we assume that ܲܽ does not get a truth-value in a given partial evaluation, because the term is an empty one. Nevertheless, we may still say that (9.1) is valid because it will turn out to be true in all classical extensions of the partial valuation. Bencivenga may now be understood as exporting the core idea of van Fraassen’s model from the propositional level of logical analysis to the level of denotation. To him, we should not operate with the arbitrary attribution of truth-values to statements that are originally valueless–i.e., classical extensions–but with an arbitrary assignment of denotation to empty names. This can be done in the following way. We start with a partial model U consisting of a domain D and an interpretation I which is partial with respect to singular terms. This partial model is clearly an analogue of van Fraassen’s partial valuations. For every sentence, where this sentence contains an empty term, one has to consider all extensions of U which attribute an arbitrary denotation to the empty term at stake. Thus, van Fraassen’s classical extensions become extensions of the partial model U and its interpretation I. Finally, if a statement has empty terms, it is considered true at U if and only if it is true in all classical extensions. This may be seen as the limit of the analogy with van Fraassen’s model: whilst van Fraassen was interested in supervaluations for the sake of a definition of logical truth, Bencivenga relies upon superinterpretations not just to develop a theory of logical truth, but also for a theory of truth simpliciter (see Bencivenga 1986, 176). The superinterpretation allows us to assign a truth-value to a statement that otherwise would have none. The difference between the theory of validity put forward by van Fraassen and Bencivenga’s theory of truth may be highlighted as follows. To Bencivenga, (9.1) is not simply valid but it is true even if the term at stake (݇௜ ) is an empty one. The same applies to identity statements with empty terms: that ݇௜ ൌ ݇௜ , where ݇௜ is an empty term, is true in the model U because it is true in all superinterpretations of U. At this stage of the development of the formal system, however, Bencivenga is confronted with the following problem: his model validates both (EG) and (S). For instance, ‫ ݔܣݔ׊‬՜ ‫݇ܣ‬ଵ , where ݇ଵ is an empty term in the partial model U, becomes true in the partial model U since it is true in all possible supervaluations of U. Indeed, no matter which arbitrary denotation we attribute to ݇ଵ , it will always be the case that in every

Free Logics: The Existence-Predicate

125

supervaluation ‫݇ܣ‬ଵ . But validating (S) and (EG) would then make of Bencivenga’s model something other than a free logic: as we have been observing since the very beginning of this chapter, free logics are characterized by the failure of (EG) and (S). Moreover, the reason these principles should fail is that they are strictly linked to the failure of (PE), thence to rescuing the intuition that existence is not something selfevident. Thus, Bencivenga needs to find a strategy to invalidate (EG) and (S) within his model. Bencivenga’s solution to this problem comes at the price of some gerrymandering: if there is a conflict between the partial model U and its extensions, we should give priority to the valuation attributed by the partial model. As Bencivenga (1986, 181) says, “we must not forget the purely instrumental character of the extensions in question, and in particular we must not let them prevail over the information [the partial model U] already gives.” Bencivenga thus provides us with the desideratum of a free logic that is in a position to uphold the truth of statements involving empty terms, and at the same time is in a position to vindicate (PP). This, however, is not the only reason behind such a framework. To Bencivenga, it is crucial that, philosophically, we think of the extensions of the model as counterfactual situations in which the original empty terms have a denotation. Thus, the identity ݇௜ ൌ ݇௜ , where ݇௜ is, according to the partial model, empty, is true because, if ݇௜ had a denotation, it would be true. The same reasoning would of course apply to (9.1): where ݇௜ is again an empty term according to the partial model, ܲ݇௜ ‫̱݇ܲ ש‬௜ is true because, if ݇௜ had a denotation, the sentence would be true. The advantage of this counterfactual reading of the extensions of the model is that it neutralizes the commitment to non-existent objects proper of neuter free logic. Instead, as Bencivenga (1986, 182) says, his model simply presupposes that “there are different structures, and different sets of objects exist in them.” As it should be clear, Bencivenga is here directly concerned with the philosophical problem upon which this study focuses and argues–or, more precisely, assumes–that existence should not be deemed a property of objects: the set of objects cannot be divided into the two classes of existent and non-existent ones.

9.4 Free Dialogic Logic Building upon suggestions derived in the first place from Bencivenga, Rahman and others (Rahman, Rückert and Fischermann 1997; Rahman 2001; Fontaine and Redmond 2012) have developed a free dialogic logic.

126

Chapter Nine

Thus, before the specificity of this kind of free logic can be addressed, a few words should be spent to introduce the dialogical framework. The dialogical approach is committed to the view that the meaning of logical constants and the validity of formulas may and should be analyzed pragmatically, i.e., by means of the moves that are allowed within a dialogue where an agent P (the proponent) puts forward and defends a principle thesis and an agent O (the opponent) attacks the main thesis of P. From this perspective, we are not confronted with a standard semantics that maps names and relationships “into the world,” but, if any, with a semantics which is provided by the agents P and O doing things with linguistic signs (see Rahman, Rückert and Fischermann 1997, 3). Meaning–following Wittgenstein’s slogan in his Philosophical Investigations–is use. Since free logics are logics that deny principles such as (EG) and (S), it is helpful to start by providing the dialogic rules that allow us to uphold such principles. This will also provide us with an opportunity to get acquainted with the dialogical framework. First of all, one should note that rules in dialogic logic–i.e., what determines which moves are or are not allowed in the dialogue–are of two different kinds: namely, particle rules and structural rules. The particle rules are stated independently of the agent, i.e., they apply in the same way to P and to O and establish the local semantics. Structural rules, on the other hand, regiment the kind of moves that are permissible for P qua P or O qua O and provide what may be labeled as the global semantics of the dialogue. Now, the rules for quantification, which validate an implicational form of (EG) and (S), are particle rules; more precisely, for an arbitrary ij, the particle rules that establish the local semantics for quantifiers are presented in Table 9-1.4 Table 9-1 Particle Rules for Quantifiers Utterance

Attack

Defense

X - ! - ‫߮ݔ׌‬

Y-?‫׌‬

X -! – ߮ሾ‫ݔ‬Ȁ݇ଵ ሿ

X - ! - ‫߮ݔ׊‬

Y - ? ‫׊‬Ȁ݇ଵ

X -! – ߮ሾ‫ݔ‬Ȁ݇ଵ ሿ

Intuitively, this means that, in the case of the universal quantifier, either of the two agents (no matter whether P or O) may challenge the other’s utterance by choosing an individual constant and asking to instantiate the formula. On the other hand, in the case of the existential quantifier, Y may



4 For a full exposition of the dialogical rules, see Rahman and Keiff (2005), Fontaine and Redmond (2008), and Keiff (2009).

Free Logics: The Existence-Predicate

127

attack X’s utterance by asking him to provide an instantiation of the formula. From this perspective, there is no limit to the individual constants which are available to both players. However, one should notice that, from the perspective of global semantics, the standard rules for dialogic logic (which are rules for both classical and intuitionistic logic) do indeed set a limit to the availability of individual constants on the proponent’s part. Only the opponent may introduce singular terms, whereas the proponent may only “copy-cat” the individual constants introduced by the proponent: [SR-3] (structural rule for individual constants) Only O may introduce singular terms. We may now see how the principles (EG) and (S) (or their implicational formulation) are validated by the rules for standard and intuitionistic dialogic logic (see Table 9-2 and Table 9-3, respectively; the numbers on the outside row indicate the temporal order of the move, whilst those in the inside row indicate what is challenged by the move). Table 9-2 Validity of Existential Generalization O

1 3

‫݇ܣ‬ଵ ?‫׌‬

P ‫݇ܣ‬ଵ ‫ݔܣݔ׌ ـ‬ ‫ݔܣݔ׌‬ ‫݇ܣ‬ଵ

0 2

0 2 4

Table 9-3 Validity of Specification O

1 3

‫ݔܣݔ׊‬ ‫݇ܣ‬ଵ

P

0 2

1

‫݇ܣ ـ ݔܣݔ׊‬ଵ ‫݇ܣ‬ଵ ? ‫׊‬Ȁ݇ଵ

0 4 2

The principles are validated because in both cases the proponent has a winning strategy at his disposal. In the case of (EG), the opponent challenges the conditional by conceding the antecedent, which forces the proponent to utter the consequent. Then the opponent challenges the existential quantifier of the consequent. Yet, since the proponent has already introduced the singular term ݇ଵ , the proponent is in a position to counter the attack. In the case of S, on the other hand, the proponent simply has to challenge the antecedent with respect to the thesis’

Chapter Nine

128

individual constant ݇ଵ , which forces the opponent to concede the consequent of the conditional, too. As addressed, the structural rule (SR-3) of dialogic logic is decisive for the validation of (EG) and (S). Thus, if we are interested in invalidating these principles, the most natural thing to do in a dialogical framework is to impose some constraints on the application of this rule. More specifically, these constraints take the form of the structural rule called the Introduction Rule, whereby the notion of introduction is defined below as [D6]. [D6] Introduction–A singular term ݇ଵ played by X is said to be introduced if and only if: 1. X utters the formula ߮ሾ‫ݔ‬Ȁ݇ଵ ሿ while defending a formula of the form ‫ ߮ݔ׌‬and has not been used to attack or to defend a quantifier before, 2. X chooses ݇ଵ by means of the move ‫ۃ‬ǫ‫׊‬Ȁ݇ଵ ‫ ۄ‬while challenging a formula of the form ‫ ߮ݔ׊‬and ݇ଵ has not been used to attack or to defend a quantifier before. [SR-6] Introduction Rule: Only O is allowed to introduce singular terms. As Fontaine and Redmond (2012, 196) say, “the intuition captured by this rule is that the availability of singular terms is determined by the choices of the opponent.” But that is not all. The upshot of [SR-6] is that the domain of existent objects is constituted by concessions of the opponent: only the individual constants introduced by the opponent are, as Redmond and Fontaine phrase it, “ontologically loaded.” Let us see how (EG) and (S) are invalidated by means of the Introduction Rule in (Table 9-4) and (Table 9-5), respectively. Table 9-4 Invalidity of Existential Generalization O

1 3



‫݇ܣ‬ଵ ?‫׌‬

P

0 2

‫݇ܣ‬ଵ ‫ݔܣݔ׌ ـ‬ ‫ݔܣݔ׌‬

0 2

Free Logics: The Existence-Predicate

129

Table 9-5 Invalidity of Specification O

P ‫݇ܣ ـ ݔܣݔ׊‬ଵ

1

‫ݔܣݔ׊‬

0

0 4

In the case of (instances of) (EG), (P) cannot defend himself from the attack on the quantifier (move 3) since ݇ଵ was not introduced by O: move 1 is neither an attack on a universal quantification nor a defense from a challenge on an existential quantifier. On the other hand, in the case of (S) the opponent cannot attack the universal quantifier of move 1, since no individual constant has been introduced yet. At this level of specification, free dialogic logic captures the invalidation of (EG) and (S) characteristic of negative and positive free logic (in neuter free logic these principles are not invalid but undetermined). However, there is a drawback to this approach: as it stands, it seems to be too restrictive, in that it invalidates every existentially quantified formula. Indeed, the proponent has no winning strategy in such cases, because the domain is possibly empty (technically, this means that the logic is not only free but also inclusive). In order to avoid this consequence, Fontaine and Redmond introduce a symbolic move, which takes place every time the domain is possibly empty. As in the standard framework, an individual constant may always be introduced by the proponent, but merely in a symbolic move. Philosophically, the fact that an individual constant is introduced only symbolically means that the decision about the ontological status of the individual constant at stake is– so to speak–suspended. To go back to Fontaine and Redmond’s phrasing, the individual constant is not ontologically loaded. The introduction of a symbolic move leads to dropping [SR-6] in favor of [SR-FLS], which again must be coupled to some definitions: [D7] An individual constant is said to be totally new if and only if it does not occur in the initial thesis, or if it has not been previously introduced. [D8] We call symbolic constant an individual constant which is totally new or an individual constant occurring in the initial thesis [D9] An individual constant is said to be ontologically loaded if and only if it has been introduced by O. [SR-FLS] While defending an existential quantifier or challenging a universal quantifier, P must use totally new individual constants or individual constants previously introduced by O.

130

Chapter Nine

According to the new rule [SR-FLS], (EG) and (S) are still invalid and the corresponding dialogues still look like the one presented above. What changes is the explanation as to why the proponent has no winning strategy. In the case of (EG), the proponent cannot answer the challenge in move 3, because the required individual constant is neither totally new, nor was it introduced by the opponent. The same holds with respect to (S): the proponent loses because he is not in a position to affirm the consequent. It is important to notice that free dialogic logic always presupposes a dynamic domain of discourse, no matter whether [SR-FLS] or [SR-6] is applied. The domain of discourse is not “a static collection of data given by the model” but, instead, it is “a result from the dialogue conceived as a process of construction” (Fontaine and Redmond 2012, 194). True, free dialogic logic with [SR-FLS] puts forward substantive constraints on the introduction of new individual constants or, more precisely, on the kind of constants that are introduced, but this does not preclude the domain of discourse from being a dynamic one.

9.5 Objections: Free Logics and Fregeanism Let us attempt an assessment of the free logics addressed in this chapter. As far as neuter free logic is concerned, I have already highlighted how it cannot be philosophically distinguished from a Neo-Meinongian approach. The first question I would like to raise is thus whether negative or neuter logic yield us an alternative to both Fregeanism and Neo-Meinongianism. Only at a later stage, will I then turn to Bencivenga’s development of free logic and to the free dialogical approach to existence as being chosen (by the appropriate agent in a dialogue and within the appropriate context). With respect to negative and neuter free logic, their formal semantics clearly points in one direction: we are still moving within the safe borders of the Fregean interpretation of existence. As was the case with Frege, every object exists, so that existence cannot be deemed a property. True, negative free logic allows for a predicate of existence; but this predicate simply tells us whether a given name refers or not. In other words, we are dealing here with the formal counterpart of Frege’s philosophical insights that the predicate of existence may be something other than self-evident, as long as one allows for a meta-linguistic interpretation thereof. Formally, the philosophical intuition that “x exists” means “x refers” may in fact be easily expressed as ‫ݔ׌‬ሺ‫ ݔ‬ൌ ܽሻ. To ask whether a exists is to ask whether a is identical with something that falls within the scope of quantification.

Free Logics: The Existence-Predicate

131

Someone may want to go even further than that: the difference between negative and neuter free logic may be traced back to different and not entirely consistent claims that one can find in Frege. If more weight is attributed to the intuition put forward in the Dialogue with Pünjer, according to which singular negative existentials may become a truthvalue if interpreted meta-linguistically, one clearly will end up with negative free logic: singular existentials are either true or false. If, on the other hand, we were to follow the suggestions of the passage on Ulysses in the article “On Sense and Reference,” one would clearly lean towards neuter free logic. Even though names are not empty in the sense that they are empty sounds–they do indeed have a sense–singular existentials embedding such empty names are neither true nor false. It has also often been noted that one may find a striking agreement between negative free logic and the results–but not the method–of amending Frege by means of Russell’s analysis of definite description and proper names (see Bencivenga 1986, 171). As negative free logic allows for empty terms, so the theory of description allows for non-denoting definite descriptions and names. Moreover, both theories lead to the result that every statement which encodes an empty name or a non-denoting definite description is false, with the exception of course of negative existential statements. But this should not come as a surprise. As it happens, Russell developed his approach by firmly rooting it in the footsteps of the Fregean analysis of quantification. Moreover, Russell, like Frege before him, also attempted to reconcile this approach to quantification and the unwelcomed consequence that negative existentials seem to become senseless. Finally, from the philosophical point of view, we may notice that negative and neuter free logics do not provide us with any new arguments to defend the rejection of the property view of existence. The only thing that negative and neuter free logic accomplish is to show us how a formal model that operates with a non self-evident predicate of existence may be developed, which remains faithful to the Fregean intuition that existence is really captured by quantification. The problem, however, still remains that the Fregean argument to defend this philosophical position was defective. Let us now turn to the version of free logic developed by Bencivenga. From the point of view of the philosophical debate on existence, Bencivenga, too, provides us with a clear instance of a Fregean approach: the division between existent and non-existent objects is eschewed by his system. Indeed, in the partial model, which is clearly intended to represent things as they actually are, we are dealing with a domain of existing

132

Chapter Nine

objects only.5 True, Bencivenga allows for empty terms to acquire a denotation in an alternative scenario. However, this does not imply any distinction of the domain of objects into two classes, i.e., existent and nonexistent ones. Instead, we are simply dealing with alternative situations where we are confronted with different sets of existing objects. This is exactly the philosophical point Bencivenga relies upon to defend his own version of free logic. But, then again, the question remains unanswered: how do we know that we should not consider the domain of (actual) objects as something that should be divided into two classes, namely existent and non-existent? Finally, let us consider free dialogic logic. The difference between free dialogic logic and the other kinds of free logics considered so far is that the former invalidates the crucial principles (S) and (EG) by means of dialogic rules and not by means of a (set-theoretic) semantics. These rules, moreover, lend themselves to be interpreted as implying a view of existence as the function of a choice within a dialogue. Now, as the semantics for free logics allows us to make sense of the fact that existence is not a self-evident predicate, so the dialogical rule [SR-FLS] allows us to make sense of the fact that not every individual constant introduced in a dialogue is ontologically loaded. Nevertheless, free dialogic logic agrees with the other non-dynamic, i.e., referentialist logics insofar as quantification is still understood as existentially loaded (see Fontaine and Redmond 2012, 198).6 From this perspective, free dialogic logic, too, is still moving within safe Fregean territory. A more general remark is now called for. Free logics–from a philosophical perspective–all agree with Frege that quantification is existential. This, however, as Frege already recognized, clashes with several intuitions we have, in the first place with the intuition that statements of the form “x does not exist,” where x is a proper name, may be true. The solution suggested by free logics is thus the following: since giving up the quantificational view of existence is not an option, we should simply change the logical rules or, if one prefers, the meaning of quantification, by invalidating (EG) and (S). Once this is done, we can no longer infer from “x does not exist” that, contradictorily, “there is an x that does not exist.” The problem, however, is that we have no substantial

 5

It is appropriate to bring into play the modal notion of actuality, since Bencivenga clearly intends his model to be interpreted modally: supervaluations represent counterfactual scenarios. 6 In a footnote, Fontaine and Redmond point out how the formulation of free dialogic logic by Rahman (2011) relies on two different kinds of quantifiers: ontologically and non-ontologically loaded.

Free Logics: The Existence-Predicate

133

reason as yet to interpret quantification as existentially loaded. Moreover, one may notice that, from the point of view of ordinary language, a statement of the form “x does not exist” may be true, no matter whether “x” stands for a proper name, a definite description or a quantificational expression. Indeed, this is the crucial insight upon which all versions of Neo-Meinongianism discussed in the Second Part rely. Thus, from a NeoMeinongian perspective, the approach developed by the free logicians cannot but be seen as a “halfway house” (Routley 1980, 79). To conclude, none of the free logics provide us with a viable alternative to Fregeanism and Neo-Meinongianism, for free logics turn out to be minor modifications within the Fregean paradigm (of course, with the exception of positive free logic). Moreover, free logics do not provide us with any additional argument in favor of Fregeanism. Thus, the stalemate is not broken yet. This will be the goal of the third and final part of this study.

PART THREE THE DEFLATIONIST COMPROMISE

CHAPTER TEN GENERAL EXISTENTIAL STATEMENTS

The discussion of the previous chapters has left us with two main options on the table with respect to the problem addressed by this study: either existence is interpreted as a notion which is essentially captured by quantification (Frege), or it is interpreted as an almost ordinary property of objects (Routley, Jacquette). Moreover, as things stand right now, the choice between these main competitors seems to boil down to a question of so-called intuitions: so far, no definitive argument that may help us settle the issue has been presented. In the following chapters, I am going to develop an argument that purports to break this stalemate by striking a middle path between Fregeanism and Nuclear Neo-Meinongianism (from now on, simply: NeoMeinongianism). This, however, may only be achieved on a step by step basis. In the present chapter, I am going to build an argument that relies upon an analysis of quantified, i.e., general statements. If you like, you may think of this argument as proving–if anything–something about a hypothetical language without proper names and definite descriptions. In addition, what we have to blend out from this language are both modal and intentional statements. In Chapter 11, I then show how the line of reasoning of Chapter 10 may be declined so as to apply to modal contexts. In Chapter 12, I address the challenge raised by intentional statements about indeterminate objects. Finally, in Chapter 13, I provide a further declination of the same argument of Chapters 10 and 11 to alleged singular statements. At the end of the third part of this study, we will thus have reconstructed, piece-by-piece, our everyday natural language.

10.1 A Raw Intuition Let me start with a terminological remark. Throughout these last chapters, by “existential statement” I am referring to a statement in which the verb “to exist” is embedded. Hence, my characterization is a strictly linguistic one. This I take to be the most suitable definition of existential statements since every statement which does not wear, so to speak, its existential character on its sleeve may be cast as a statement with the verb “to exist.”

General Existential Statements

137

For instance, a statement such as “an existing dog is on the street” is meaning-equivalent with the statement “a dog on the street exists.” Or the statement “there are some dogs,” where existence seems to be expressed by the expression “there are,” is also meaning-equivalent to the statement “some dogs exist.” Finally, the same applies to statements in which the noun “existence” is embedded: the statement “the existence of dogs is uncontroversial” may be rephrased as “it is uncontroversial that dogs exist.” Notice, moreover, that I am consciously leaving statements with a particular quantification out of this list: I am refraining from saying that “something is x” is meaning-equivalent to “there are xs” or “some xs exist.” Indeed, this is what Fregeanism and Neo-Meinongianism are arguing about, so that we cannot and should not take it for granted. The other equivalences, on the other hand, I take to be theoretically neutral. Now, even before getting started on any philosophical lucubration about existential statements, I assume we would all agree that there is something peculiar about existential statements. And, in fact, the previous chapters may be considered a list of attempts at rationalizing this difference. The question with which I would like to start is thus the following: How can we give more substance to this shared intuition about the peculiarity of existential statements without bringing into play a given philosophical theory about them? Can we really do no better than saying that this is our intuition? In other words, what I am looking for is some pre-theoretical intuition about the difference in the behavior of existential statements and non-existential ones, which may be the reason for our shared intuition about the peculiarity of the former–or, if not the reason, at least a reason. First, let us consider the two following existential statements: (10.1) Something red does not exist. (10.2) It is not the case that something red exists. It seems to me that there is a very strong connection between these two statements: if one of them is true, the same holds for the other, and conversely, if one of them is false, so is the other. At least prima facie, (10.1) and (10.2) mutually imply one another. Or, in more technical terms, the internal negation seems to be interchangeable with the external one. Let me provide a few more standard examples to substantiate this claim. To say that something which is golden and a mountain does not exist (shorter: a golden mountain does not exist) is equivalent to saying that it is not the case that a golden mountain exists. To say that something which is round and square does not exist (shorter: a round square does not exist) is

138

Chapter Ten

equivalent to saying that it is not the case that a round square exists (and so on and so forth). Someone may challenge the reading just advanced since it seems easy to point to a situation in which both (10.1) is true and (10.2) false. As it happens, the actual state of things seems to be just the right one to accomplish this feat. We would all agree that, on the one hand, red dragons do not exist and, on the other hand, some red things, such as for instance traffic lights, do. Thus, why not assume that (10.1) is true because red dragons do not exist, while (10.2) is false because a red traffic light exists? However, I take this to be a misconstrual of (10.1). If someone were talking about red dragons, he would have to make it explicit. Thus, he should not say “something red does not exist” but rather “something which is a red dragon does not exist.” But this would be a very different claim than affirming (10.1). The same point may be clarified in the following way. While having coffee with a friend of mine, we stumble upon the topic of redness, upon which I claim “something red does not exist!” My friend then objects to my claim by pointing to the traffic light in front of the coffee shop. But then I go on to say that, of course, red traffic lights exist, but red dragons do not–which should be enough to make my claim warranted. What would my friend’s reaction to this explanation be? I suppose he would give me an incredulous stare and say something along the following lines: “OK, what you really meant was that a red dragon does not exist. Yet this is a rather irrelevant remark to the topic of redness which we were just starting to discuss.” Let us now turn to a very similar pair of sentences which, however, are not existential: (10.3) Something red is not round. (10.4) It is not the case that something red is round. I gladly concede that this second pair, as probably the first, too, may sound awkward. Below, I provide a possible coffee shop scenario in which they may be uttered. Now, the difference between this second couple of statements and the first one is striking. Notwithstanding the very similar structure, we have lost the mutual–and for that matter any kind of– implication: the truth of (10.3) is compatible with both the truth and the falsity of (10.4). Conversely, the truth of (10.4) is compatible with both the truth and the falsity of (10.3). For it could always be the case that nothing is red. In other words, internal and external negations are no longer interchangeable.

General Existential Statements

139

True, someone may be tempted to interpret (10.3) as a hidden hypothetical, namely as really meaning that if something is red then it is not round. It may then be argued that such a hypothetical would indeed imply (10.4). Please set this interpretation aside: (10.3) should be read literally. An example of a literal reading of (10.3) and (10.4) is the following. I am still sitting in the same coffee shop as before and my friend points out that something red is round, namely the red traffic light. Without having any intention to contradict him, but just for the sake of conversation, I then say that it is also true that something red is not round, namely the red sports-car parked in the second row. This is the pretheoretical linguistic intuition about the peculiarity of existential statements with which I wish to start my discussion. I would like to stress that I am very well aware that not everyone would share this intuition. This is especially the case with philosophers, whose intuitions about existential statements have already been thwarted in one direction or another by their own theory about existence. Moreover, philosophers may stress that it is only on the background of a theory about existence that we may test the mutual implication of (10.1) and (10.2). For these reasons, I am labeling the intuition in question as the raw intuition. Now, I assume that even those who reject the raw intuition or have qualms about it should be interested in why one may have such an intuition. Thus, I will ask them to indulge me for a little while. I will come back to their worries at the end of section 10.4.

10.2 Fregeanism Having introduced you to the raw intuition, I would like to explore how a Fregean and a Neo-Meinongian philosopher might make sense of it. This, moreover, will provide us with the opportunity to rehearse some theses and arguments of these two arch-enemies. Let us start with Fregeanism. As already addressed in previous chapters, according to this approach, we should go Procrustean and amputate (10.1) from our language. As classical logic (the formal arm of Fregeanism) teaches us, there is only room for a universal predicate of existence in our formal language, which–as we have already seen in section 9.1–may be defined by means of quantification and identity (Hintikka 1966): ‫ܧ‬Ǩ ሺܽሻ ൌௗ௘௙ ‫ݔ׌‬ሺ‫ ݔ‬ൌ ܽሻ Thus, the formalization of (10.1), if we take the verb “to exist” as expressing the predicate of existence, would yield us a contradictory

Chapter Ten

140

statement (see, e.g., Lewis 1990, 25), which should be formalized as follows: (10.1*) ‫ݔ׌‬ሺܴ‫ܧ ׽ר ݔ‬Ǩ ‫ݔ‬ሻ On the other hand, (10.2) may be formalized without further ado into the somewhat redundant (10.2*): (10.2*) ‫ݔ׌ ׽‬ሺܴ‫ܧ ר ݔ‬Ǩ ‫ݔ‬ሻ Thus, according to Fregeanism, the puzzle of the raw intuition is resolved to the extent that, while stating (10.1), we cannot really mean what we say. Rather, if we are reasonable agents, what we mean is (10.2). Or, from a different perspective, one may prefer to say that language is misleading because both (10.1) and (10.2) express the same logical form (10.2*).1 What is the philosophical reason for the Fregean approach to the raw intuition, namely that we should get rid of (10.1)? As it happens, it is nothing over and above the strong intuition which philosophers and nonphilosophers alike seem to share, namely the Principle of Predication (PP), (see above, section 9.2). Informally, if something instantiates a property, then it exists. Arguably, this is the principle Russell (1918/1919, 170) had in mind while talking of a robust sense of reality. A most common formulation of the principle is to say that statements of the form “something is such and such” are equivalent to statements of the form “there is such and such a thing” (see Frege 1883?, 63).

10.3 Neo-Meinongianism Let us turn to a short summary of the Neo-Meinongian strategy. NeoMeinongianism rejects (PP), which, with some terminological bias, is labeled as “the Ontological Assumption” (Routley 1980, 21): non-existent objects may instantiate properties. Thus, the domain of objects is divided into two classes, namely, existent and non-existent ones. As a consequence, quantification is existentially neutral in that it has to range over all objects. To a Neo-Meinongian such as Routley, (10.1) does not

 1

McLeod (2011, 260) rightly stresses this second option: a Fregean philosopher does not have to claim that the expression “some” in natural language always must have existential import (although Frege himself did). However, the difference between the two strategies is minimal. If pressed, a Fregean may only provide the following answer to the question as to why the superficial grammatical form (10.1) should be seen as hiding the deep logical structure (10.2*), namely that otherwise it would have to be interpreted as the contradictory (10.1*).

General Existential Statements

141

have to be interpreted away or even be amputated from our language. Rather, (10.1) finds a streamlined logical interpretation as (10.1**), which relies on the Neo-Meinongian, existentially neutral particular quantifier “ܲ‫”ݔ‬: (10.1**)

ܲ‫ݔ‬ሺܴ‫ܧ ׽ר ݔ‬Ǩ ‫ݔ‬ሻ

The fact that Neo-Meinongianism is in a position to provide such a streamlined logical interpretation of (10.1) does indeed count as one of the main advantages of this position, as stressed by Routley (1980, 31-32). The logical form of (10.2), on the other hand, turns out as follows: (10.2**)

‫ݔܲ ׽‬ሺܴ‫ܧ ר ݔ‬Ǩ ‫ݔ‬ሻ

Notice that a Fregean philosopher cannot refute a Neo-Meinongian philosopher by recurring to (PP). The problem is that Neo-Meinongians reject (PP), so that this strategy would be question-begging. From our perspective, instead, the problem a Neo-Meinongian is confronted with is the following: he has to show how some additional premises are responsible for the fact that from (10.1) we may infer (10.2), and the other way around–premises which should of course not allow to infer (10.4) from (10.3) and (10.3) from (10.4). One such premise is the Strong Nuclear Characterization Principle (SNCP) (see above, section 6.6):2 (SNCP) For any condition ij that does not embed extra-nuclear properties, an object satisfies exactly this condition. We need not enter again into the details as to why (SNCP) must be restricted to nuclear properties and strengthened so that the object instantiates no other property besides those embedded in the characterization (the object satisfies the condition exactly). Here, I would simply like to point out how (SNCP) is needed in order to make sense of the raw intuition. Indeed, it is only if we concede (SNCP), or something sufficiently close to it, that we are in a position to say that, if a given condition ij is not satisfied by an existing thing, then it is satisfied by a non-existing one. And this is exactly what we need in order to infer (10.1) from (10.2). One should note that (SNCP) leads to an inconvenience with respect to the second couple of statements: (SNCP) would by itself validate (10.3), so that if (10.4) is true, so is (10.3). A Neo-Meinongian is thus led to

 2

See Parsons (1980, 19), Routley (1980, 260–264), and Jacquette (1996, 85–86).

142

Chapter Ten

reinterpret the quantification in (10.3) and (10.4) as implicitly restricted to existing objects. Otherwise we could not think of a situation in which (10.4) is true but (10.3) is not.3 The real problem, however, is that Neo-Meinongianism is not in a position to make sense of the inference from (10.1) to (10.2). As far as I can see, a Neo-Meinongian philosopher has only one option to rescue this inference. He must sacrifice (10.1) and reinterpret it as really meaning “everything which is red does not exist.” In other words, a NeoMeinongian philosopher has to take the superficial structure of (10.1) to be misleading, since what is really expressed should be formalized relying on the Neo-Meinongian universal quantifier “ܷ‫”ݔ‬: (10.1***)

ܷ‫ݔ‬ሺܴ‫ܧ̱ ـ ݔ‬Ǩ ‫)ݔ‬

Indeed, it is clear that this reading of (10.1) would vindicate both inferences, from (10.1) to (10.2) and from (10.2) to (10.1). This, however, dramatically relativizes the advantage of Neo-Meinongianism vis-à-vis Fregeanism: the former, exactly as the latter, is forced to reinterpret (10.1) and extract an allegedly deeper logical form to make sense of the raw intuition. The crucial purported advantage, stressed both by Meinong and Neo-Meinongians, that their approach does justice to the superficial grammatical structure of our language is, at least to some extent, jeopardized.

10.4 The Attempt at a Compromise: A Deflationary Account of Existence What should we do? Should we give preference to our intuition that predication implies existence and thus amputate (10.1) as contradictory? Or should we rather deem existence to be an almost perfectly ordinary discriminating property of objects and strongly revise our understanding of (10.1), so that its real meaning is captured by (10.1***)? To me, both look like bad solutions: they both are Procrustean in the sense that they force us to amputate some statements (in the case of Fregeanism) or stretch them so as to make them almost unrecognizable (in the case of NeoMeinongianism). (The reader will remember that the legendary bandit had two opposite ways of torturing his victims, either by amputating their limbs if they did not fit the Procrustean bed, or by stretching them if they did not fill it up.) In other words, neither of the two options is really in a

 3

As Routley (1980, 27) says, “existential loading is a contextual matter.”

General Existential Statements

143

position to do justice to the raw intuition. So, the question should rather be: Is there really no better option? My suggestion will be the following. We can avoid all amputations and reach a streamlined interpretation of the raw intuition by exploring a third possible explanation of existence. To wit, we should abandon the assumption, shared by both accounts, that existence has a nature which we may be searching for, be it that of a notion captured by quantification or of a discriminating property. More generally, following Lewis (1970, 19), we should rather say that there is no connection between the notion of existence and any aspect of the world, be it a property or anything else. Instead, we should consider existence to be a redundant notion, whose meaning is entirely exhausted by the following Existence Equivalence Schema (EES) and its negative counterpart, the Non-existence Equivalence Schema (NES): (EES) n exist(s) if and only if sn. (NES) n do(es) not exist if and only if it is not the case that sn. As the reader will have noticed, (EES) and (NES) follow the blueprint of the equivalence schemata of the deflationary account of truth and falsity:

is true if and only if p and

is not true (false) if and only if it is not the case that p. Not surprisingly, however, there are crucial differences. First, “n” should be understood as a variable for any particular quantified nominal expression, no matter whether in singular or plural form (e.g., “something red” or “some red things,” respectively). Second, “sn” should be understood as a variable for the sentence which may be extracted from the nominal expression in question (e.g., “something is red” or “some things are red”).4 Finally, a further important difference is that (EES) and (NES) do not involve any metalinguistic shift: there is no device to name linguistic entities, be it sentences or propositions (the square brackets). One may wonder at this point whether we may apply the equivalence schemata to existential statements with universally quantified nominal expressions such as “everything red exists” or “everything red does not

 4

How, then, are we supposed to interpret “something exists” and “something does not exist”? The sentence we may extract from “something” may only be “something is somehow” or “something is of some kind.” Thus, (EES) and (NES) yield us, respectively, “something is of some kind” and “it is not the case that something is of some kind.” See below, section 10.6, for further discussion of this pair of statements.

144

Chapter Ten

exist.” These, however, strike me as ill-formed statements which no one really makes use of.5 A further remark is required. The equivalence relation I take to be expressed by (EES) and (NES) is neither an extensional, material one, nor a metaphysical, necessary one. Instead, it must be an analytical equivalence. Only from such a perspective may we say that there is no connection between the notion of existence and any aspect of the world, and that we are, instead, dealing with a redundant notion. Indeed, since nothing expresses a notion of existence on the right-hand side of the equivalence, we may say that the notion of existence is redundant on the left-hand side. By way of clarification, let us apply (EES) and (NES) to “something red exists” and “something red does not exist” (i.e., 10.1), respectively: (10.5) Something red exists if and only if something (is) red. (10.6) Something red does not exist if and only if it is not the case that something (is) red. In both (10.5) and (10.6), “something is red” is the sentence which may be extracted from the nominal expression “something red” (I highlight this by putting the sentence-forming device, i.e., the copula, in parenthesis). The deflationist theory I propose is that there is nothing more to be said about existence than what (EES) and (NES) and their instantiations tell us. Now, from the perspective of our line of reasoning, the crucial advantage of the deflationary account of existence which we have just proposed lies in the streamlined explanation of the raw intuition. Indeed, if we apply (EES) to (10.2) we get: (10.7) It is not the case that something red exists if and only if it is not the case that something is red. It follows thence that both (10.1) and (10.2) are equivalent with another since the application of (NES) to (10.1) and (EES) to (10.2) shows that they are both equivalent to a third, identical statement: “it is not the case that something is red.” We have thus explained their mutual implication.

 5

As far as other natural language quantifiers different from the particular and universal ones are concerned, it seems to me that we may apply (EES) and (NES) to them as well. For instance, the quantified existential statement “at least one red thing exists” would yield us by application of (EES) “at least one red thing exists if and only if at least one thing is red.”

General Existential Statements

145

Another way to state the same point would be to say that (NES) reveals to us why (10.1) is not really a case of internal negation: (10.1) is really equivalent to a statement with external negation. One may indeed think of the syntactical predicate “to exist” as a linguistic device to stress the external negation, in the case of negative statements, and to stress the absence of negation, in the case of affirmative statements. Yet nothing is really added to the content of the statement, since the expression “to exist” does not refer to a property or nature. This, moreover, is all we need in order to explain the different behavior of (10.3) and (10.4), since (10.3) really confronts us with an internal negation and a predicate which is not merely syntactical but actually adds something to the content of the statement. The crucial argument developed in this section may now be cast as a trilemma. Let us assume that we want to make sense of the raw intuition. The verb “to exist” expresses a notion captured by quantification, a discriminating property, or a redundant concept whose whole meaning is entirely captured by (EES) and (NES). If “to exist” expresses a notion captured by quantification, then we have to amputate (10.1) as contradictory. If “to exist” expresses a discriminating property, then we have to stretch our language, for (10.1) can no longer be taken at face value and hides a universal quantification instead. Finally, if the meaning of “to exist” is entirely captured by (EES) and (NES), then we need neither amputate nor stretch (10.1). Moreover, if the meaning of “to exist” is entirely captured by (EES) and (NES), then we need not revise the general rule according to which internal negation is not interchangeable with external negation, since (10.1) no longer constitutes a case of genuine internal negation. Furthermore, since I assume that (i) we neither want to amputate nor stretch our language, and (ii) we also have an interest in upholding the general rule that internal and external negation are not interchangeable, we should conclude that the meaning of the syntactical predicate “to exist” is entirely captured by (EES) and (NES). Let us now return to any qualms the reader may have with the raw intuition. To such a reader we may say that the deflationary account of existence we have just put forward is not essentially dependent upon endorsing the raw intuition. One may very well not share the intuition that (10.1) and (10.2) imply one another. They are, after all, problematic statements, where it is perhaps out of place to rely on intuitions to determine their entailment-relations. Rather, they are statements which should be interpreted in the light of a theory. But then again, even abstracting from the raw intuition, we still have an interest in following the deflationary account of existence. The reason is that going deflationist

146

Chapter Ten

provides us in any case with a good compromise between Fregeanism and Neo-Meinongianism. On the one hand, by going deflationist, we avoid the problem of Fregeanism highlighted by Neo-Meinongians: negative existentials of the form “something such and such does not exist” are no longer contradictory. (I thus assume that we have at least an intuition about the non-contradictory character of such statements.) On the other hand, we equally avoid any Neo-Meinongian distinction between existent and nonexistent objects and the epicycles which have to be coupled to this distinction, i.e., the target of the objections raised by Fregean philosophers. It is because the theory concedes something to both contenders that the deflationist approach to existence should be seen as a compromise.

10.5 A Second Raw Intuition As remarked at the end of the last section, I am persuaded that the deflationary account of existence is independent of a pre-theoretical endorsement of the raw intuition. But what I cannot and do not want to say is that the account is independent of any linguistic intuition: if the account is convincing, it has to be in conformity with other intuitions a given speaker may have. In other words, the application of (EES) and (NES) to existential statements in the vernacular should not lead to counterintuitive results. Or, at least, we must reach a kind of reflective equilibrium between our intuitions and the deflationary account of existence, so that some intuitions support the theory, while the theory itself should help establish other intuitions. In the next three chapters, I address some existential statements which may seem, in this respect, especially problematic. Presently, however, I would like to draw attention to a second intuition which seems to support the deflationary account of existence. Let us consider the following pair of statements: (10.8)

Something round and square does not exist.

(10.9)

Something round does not exist.

Here it may very well be the case that the former is true and the latter is false (the implication goes only the other way round). Yet things are rather different with the following pair of non-existential statements: (10.10) Something round and heavy is not red.

General Existential Statements

147

(10.11) Something round is not red. Evidently, the former implies the latter: if (10.10) is true, so is (10.11). How would the Fregean and the Neo-Meinongian approach deal with this further raw intuition? As with the previous one, Fregeanism and NeoMeinongianism would lead, respectively, to an amputation and stretching of our language. If we follow the Fregean approach, we would simply have to amputate statements such as (10.8) and (10.9) from our language. If we follow Neo-Meinongianism, on the other hand, we should stretch (10.8) to “everything round and square does not exist.” In this case, the inference to (10.9) would clearly not be allowed. If we follow the third way, instead, we may rescue all our intuitions about these statements and at the same time provide an explanation for the alleged bad behavior of existence. The application of (NES) to (10.8) and (10.9) yields us (10.12) and (10.13), respectively: (10.12) Something round and square does not exist if and only if it is not the case that something (is) round and square. (10.13) Something round does not exist if and only if it is not the case that something (is) round. We may now spell out the reason as to why (10.8) does not imply (10.9). As a look at the right-hand side of (10.12) and (10.13) will show, the reason is that the falsity of a conjunction does not imply the falsity of the conjuncts. Thus, we have once more seen how the deflationary view of existence fares better than Fregeanism and Neo-Meinongianism in–as it were–cashing out a pre-philosophical linguistic intuition.

10.6 Deflationism and Meta-Ontology As addressed in the Introduction, Thomasson (2014) recently defended a version of deflationism about existence, which, moreover, she links to a quietist approach to some ontological debates, such as for instance the existence of numbers. In this section, I would like to draw attention to some crucial differences between the version of deflationism I am advocating and Thomasson’s. These differences, however, should not hide the common ground between Thomasson’s deflationism and mine: we both share the anti-metaphysical stance according to which it is pointless to search for any deep nature of existence. If we focus on the theory itself, Thomasson’s deflationist approach to existence is characterized by establishing a strong link to deflationism

148

Chapter Ten

about the semantic notions of truth and reference: “the concepts of truth, reference, truth-of, and existence are all interlinked by trivial rules, and deflationisms about any of these notions stand or fall together” (Thomasson 2014, 198). More precisely, Thomasson sees a strong link between the notion of existence and the notion of reference, which she ties by means of the equivalence schemata “ refers if and only if n exists” and “

refers if and only if Ps exist” (whereby “n” stands for any singular term and “P” for any general term different from existence). Then, via the notion of reference, the notion of existence may be tied to the notion of truth to form what Thomasson labels as a “conceptual circle.” The kind of deflationism defended in this chapter, by contrast, is independent of deflationism about truth and reference, which of course may be seen as an advantage (if you are a deflationist about truth and reference) or a drawback (if you are not). In addition, the semantic notions of reference and truth are simply not part of the picture I have presented. This strikes me as a clear advantage of the approach I am defending. In fact, we all have a fairly good understanding of existential claims, but only philosophers are familiar with the semantic notion of truth and, especially, reference. Turning to the meta-ontological implications, Thomasson (2014, 204– 206) explicitly develops her brand of deflationism as providing us with a path to “easy ontology.” According to this perspective, some ontological questions may be solved by looking at the world. For instance, to know whether red things exist, we have to rely on our conceptual competence and see whether the concept red refers to anything, i.e., whether we have instances of red things. Furthermore, other, less trivial, ontological questions such as the one targeting the existence of numbers, should be seen as trivial inferences from uncontroversial truths, which do not involve the concept at issue (for instance, from “there are three cups on the table” to “the number of cups on the table is three”). Thomasson, thus, broadly follows in Carnap’s (1950) footsteps and draws a distinction quite close to the one between internal and external questions to a given conceptual framework. The deflationism defended in this paper, by contrast, is not motivated by, and does not have this kind of meta-ontological implications. True, I would agree that in order to assess the question as to whether red things exist we have to look at the world (notice, though, that I am not bringing into play the notion of reference). But when, for instance, numbers are taken into consideration, the theory defended here does not prescribe any procedure. We may only say–via the application of (EES)–that something

General Existential Statements

149

which is a number exists if and only if something is a number. The question whether some things are numbers, however, remains open and a legitimate object of ontological dispute. What, however, is clearly ruled out by the deflationist view of existence defended here is both a Fregean and a Neo-Meinongian approach to ontology. The answer to the question which defines ontology, namely “what exists?”, should neither be “everything” nor “the things which happen to have the property of existing.” These are signs of a misunderstanding of the question. Instead, in order to understand the ontological question correctly, we must look at possible answers to it, as for instance in “something red exists” or “numbers exist.” All these answers tell us that something is somehow or of some kind (red, number, etc.). Thus, what the question of ontology really means is: what is of what kind? This should be seen as the result of the application of (EES): we have answered the question as to what exists if and only if we have answered the question as to what is of what kind (in other words, the sentence that has to be extracted from the subject “what” is “what is of what kind?”). And, if the outcome of such an investigation is that nothing is of any kind, we may move to the nihilist claim that nothing exists, or, equivalently, that it is not the case that anything exists; if, on the other hand, at least something is of some kind, we may confidently state that at least something exists (in other words, the sentence that has to be extracted from the bare subject “something” is “something is of some kind”).6

 6 See above, footnote 4. These considerations lead to the following interpretation of (PP): “if something instantiates a property, then this something exists” yields us, by application of (EES), “if something instantiates a property, then this something is of some kind.” According to this interpretation, (PP) is certainly true but rather vacuous.

CHAPTER ELEVEN MODAL EXISTENTIAL STATEMENTS

Within the contemporary debate on the metaphysics of modality, one finds a stark opposition that, in many respects, recalls and in fact overlaps with the one upon which this study is focused, i.e., the opposition between actualism and possibilism. Just as a Fregean-minded philosopher argues that existence is captured by quantification, so will an actualist philosopher argue that actuality or actual existence is captured by quantification. In other words, to say that something is not actually existing is as contradictory as saying that something does not exist. The possibilist philosopher, on the other hand, has no problem in considering actual existence as something that allows us to distinguish between two kinds of objects: some things are actually existent, some are not. This seems to be nothing but a rehearsing of the Neo-Meinongian view about existence: actual existence is a property of things. Nevertheless, as we shall see, there are good reasons to keep the two debates separate. In this chapter, I briefly present the debate between actualism and possibilism. Then I address to what extent this debate is very close to, and indeed overlaps with the debate between Fregeanism and NeoMeinongianism. Finally, I argue that the problem which lies at the heart of the debate between actualism and possibilism may be solved by relying on the deflationist view of existence developed in the previous chapter. As it happens, the very same argument that was developed in relation to nonmodal contexts may be applied to modal contexts as well.

11.1 Actualism and Possibilism Since the debate between actualism and possibilism is a debate as to how the modal notion of actual existence should be interpreted, it usually takes place on the background of the standard approach in logic to modalities, i.e., possible-worlds semantics. Moreover, since the problem of actualism and possibilism does not arise at the propositional level of analysis, but rather, at the object level, the kind of semantics that is of relevance here is a possible-worlds semantics for the lower predicate calculus. As addressed

Modal Existential Statements

151

above, the dispute between actualism and possibilism poses the question whether objects may be divided into actual and non-actual ones. Now, within possible-worlds semantics, the most straightforward approach to the lower predicate calculus is a semantics that operates with constant domains: while moving from one world to the other, the domain of objects remains the same. This approach may be labeled as the Simplest Quantified Modal Logic (SQML), and its characterization runs as follows (see Menzel 2014). The language of first-order modal logic results by adding the necessity operator “Ƒ” to the lower predicate calculus and by adding the definition of the possibility operator “¸” as ̱Ƒ̱‫݌‬. The language of SQML will thus consist of the two modal operators, variables, individual constants, n-place predicates, atomic formulas, as well as the usual logical constants. The semantics, on the other hand, is defined as follows. [D1] An interpretation I for SQML is a 4-tuple ‫ܹۃ‬ǡ‫ݓ‬଴ ǡ ‫ܦ‬ǡ ܸ‫ ۄ‬where 1) ܹ is a non-empty set, which intuitively represents the set of possible worlds. 2) ‫ݓ‬଴ is a distinguished member ܹ that intuitively represents the actual world. 3) ‫ ܦ‬is a non-empty set, which intuitively represents a set of individuals. 4) ܸis a function that assigns appropriate semantic values to the constants and predicates in the lexicon of L, specifically (a) for constants ț, V(ț) ‫ א‬D and (b) for n-place predicates ʌ, V(ʌ) ‫א‬ {f | f : W ĺ Ե(Dn)}. That is, V maps each n-place predicate to a function that, for each world w ‫ א‬W, yields the set of n-tuples of individuals to which ʌ applies at w. Intuitively, V determines the extension of the predicate ʌ at each possible world, thereby representing the modal intuition that the things that exemplify a given property like being a politician can differ from world to world. [D2] Assignments and denotations for SQML: 1) A variable assignment, or, more simply, an assignment, (relative to I) is any total function from the set of variables into D. Given an assignment f, for any variable Į and any individual a ‫ א‬D, let f[Į,a](Į) = a and let f[Į,a](ȕ) be the function that is exactly like f except that it assigns a to the variable Į (that is, more exactly, f[Į,a](ȕ) = f(ȕ) for variables ȕ other than Į). 2) Given an assignment f, we define the denotation function dI,f determined by I and f to be a function on the terms IJ of L such

152

Chapter Eleven

that, if IJ is a constant, then dI,f(IJ) = V(IJ) and if IJ is a variable, then dI,f(IJ) = f(IJ). [D3] Truth in the model for SQML: Truth in our interpretation I is defined as a special case of truth at a world under a given variable assignment f, which is defined recursively as follows. Let ij be a formula of L and w a world in W: 1) If ij is ʌIJ1…IJn, then ij is trueI,f at w iff ‫ۦ‬dI,f(IJ1), …, dI,f(IJn)ۧ ‫א‬ V(ʌ)(w). 2) If ij is IJ1=IJ2, then ij is trueI,f at w iff dI,f(IJ1) = dI,f(IJ2). 3) If ij is ~ȥ, then ij is trueI,f at w iff ȥ is not trueI,f at w. 4) If ij is (ȥ ‫ ـ‬ș), then ij is trueI,f at w iff either ȥ is not trueI,f at w or ș is trueI,f at w. 5) If ij is ‫׊‬Įȥ, then ij is trueI,f at w iff, for every a ‫ א‬D, ȥ is trueI,f[Į,a] at w. 6) If ij is Ƒȥ, then ij is trueI,f at w iff, for every world wƍ ‫א‬W, ȥ is trueI,f at wƍ. 7) ij is trueI at w iff ij is trueI,f at w for every variable assignment f. 8) ij is trueI iff ij is trueI at the actual world w0 of I. 9) ij is logically true, or valid, iff ij is trueJ for all interpretations J of L. A set ī of formulas of L entails ij if, for every interpretation J of L, ij is trueJ if every member of ī is trueJ. These definitions sort out a class of modal languages in conjunction with a method to interpret them, which together yield us SQML. Finally, the proof-theory (i.e., the complete system of axioms as well as inference rules) for SQML is provided by the combination of the proof-theory for First Order Logic with identity and S5 propositional modal logic. The most prominent characteristic of SQML is that it assumes that the same set of objects is correlated to every world. In other words, no distinction is made between the domain of a given world and the overall domain D. In fact, one may think of SQML as a semantics with a function dom that assigns to each world w the same domain dom(w) identical with the overall domain D. On the background of SQML, the dispute between actualism and possibilism takes the following form. An actualist is a philosopher who interprets the domain associated with every world, and thus the overall domain in SQML, as a domain of actual objects: (A)

Everything actually exists.

If we introduce a unary predicate of existence ‫ܧ‬Ǩ in the language of SQML, this may be expressed as follows:

Modal Existential Statements

(A*)

153

‫ܧݔ׊‬Ǩ ‫ݔ‬

Moreover, since A is obviously conceived as a necessary truth, (A) and (A*) also hold under necessitation: (NA)

It is necessary that everything actually exist.

(NA*) Ƒ‫ܧݔ׊‬Ǩ ‫ݔ‬ Finally, it is easy to see which definition of ‫ܧ‬Ǩ would validate the actualist principles (A*) and (NA*), namely the same definition a Fregean philosopher would give of existence (if he were pressed and indeed agreed to provide one): ‫ܧ‬Ǩ ሺܽሻ ൌௗ௘௙ ‫ݔ׌‬ሺ‫ ݔ‬ൌ ܽሻ The possibilist philosopher, on the other hand, is someone who interprets the overall domain D, and thus the domain associated to every world, as a domain of objects that may either be actual or non-actual. Thus, his approach may be characterized by the rejection of (A*) and (NA*), which in turn implies the rejection of the definition of existence hidden behind these principles. Again, the dispute between actualism and possibilism is a dispute as to whether actual existence is something that divides the domain of objects into two sets, or something that is essentially captured by quantification.

11.2 The Rationale behind Actualism and Possibilism So far, we have seen how the dispute between the actualist and the possibilist view exactly parallels the dispute between the views of existence as captured by quantification or as captured by a (discriminating) property. Let us see whether this parallelism also holds once we take into account the reasons leading to endorse one view over the other. The main intuition behind the actualist approach is that for a statement to be true, something actual has to be there in order to make this statement true. Now, what actual object might make a statement such as the following one true? (11.1)

Something that might be an alien is not actually existing.

Formally: (11.1*) ‫ݔ׌‬ሺτ ‫ܧ̱ ר ݔܣ‬Ǩ ‫ݔ‬ሻ

154

Chapter Eleven

Indeed, for such a statement to be true, we should be able to go through the list of objects and, as it were, show the object of which it is the case that it might be an alien but is not actual. But this is obviously impossible. We are thus confronted with the same problem that leads a Fregeanminded philosopher to reject statements of the form “something such and such does not exist.” An actualist is a philosopher who declines Fregean worries in a modal context. And these worries are the motivation behind the definition of actual existence by means of the identity principle and quantification, and the consequent rejection of (11.1*), as a contradictory statement. Let us now turn to the possibilist option. As the Neo-Meinongian argues that statements of the form “something such and such does not exist” are perfectly intelligible as they are and thus should not be amputated from our language, a possibilist argues that we can in fact make perfect sense of a statement such as (11.1). More precisely, as the NeoMeinongians argue that (say) the negative existential “something that is a flying horse does not exist” is really a statement about something that is a flying horse, which–it just so happens–does not instantiate existence, so the possibilist will argue that (11.1) is a statement about something that might be an alien, which–it just so happens–does not instantiate the property of being actually existent. Furthermore, the possibilist may provide us with the following narrative to corroborate the intuition that (11.1) may indeed be true: the aliens at stake in (11.1) are so radically different from any actually existent life-form that no specimen of an actually existent thing can be an alien. In other words, the situation we are confronted with is essentially different from the one that may be concealed behind (say) (11.2): (11.2)

Something might have been a flying pig

Here one may argue that this statement is indeed about actual pigs, of which it is true that they might have acquired wings, provided for instance the evolution had taken a slightly different path from the one it actually took. Now, all this does not apply to the first conjunct of (11.1). This statement is true even though nothing actually existing might be an alien. If we grant the assumptions required to construct the alien-scenario, then we have a rationale as to how (11.1) really makes sense. More precisely, the possibilist has provided us with a rationale as to how (11.1) may be true. And if we agree that (11.1) may be true, we should also concede that actual existence is a property that applies to some objects but not to others. Given this brief presentation of the main intuitions behind the possibilist approach, we may characterize the relation between possibilism

Modal Existential Statements

155

and Neo-Meinongianism as follows: possibilism is a specific form of NeoMeinongianism which claims that non-existent objects may instantiate at least one kind of properties, i.e. modal ones. If the Neo-Meinongian is a philosopher who rejects what, in first-order logic, is captured by the Principle of Predication (PP), the possibilist is a philosopher who at least allows for some violations of (PP), namely with respect to modal properties.1 In addition, since the possibilist does not have to reject (PP) in its full scope, neither does he need a full blown Neo-Meinongian Characterization Principle (i.e., SNCP), but merely a Characterization Principle restricted to consistent modal properties.2 This may be labeled as the Possibilist Characterization Principle and formulated as follows: (PCP) For any condition ij that embeds consistent modal properties, an object satisfies this condition. As it happens, one may even say that the Characterization Principle needed by a possibilist (i.e., PCP) comes for free within SQML: the intuition expressed by (PCP) is usually taken for granted in every philosophical interpretation of modal logic. This is why possibilism is a far less controversial theory than Neo-Meinongianism. However, as we have just seen, there is a fundamental point on which possibilism must agree with Neo-Meinongianism: non-existent objects may instantiate one kind of properties, i.e., modal ones. It seems to me that, philosophically, this is a strong enough reason to argue that a possibilist should not rely on the Fregean quantifiers (i.e., “‫ ”׌‬and “‫ )”׊‬but rather on the NeoMeinongian ones (i.e., “P” and “U”) in their formalizations.

11.3 The Modal Raw Intuition In what follows, I am not going to address the different strategies at the disposal of an actualist philosopher, which may allow to uphold A* and

 1

To be more precise, one should point to the fact that a possibilist is forced to grant that objects which do not actually exist may instantiate at least one nonmodal property, i.e., the universal property of being self-identical (provided we accept the talk of a universal property). 2 Williamson (2013, 19–22) makes the same remark about the metaphysical position he advocates, i.e., necessitism: what necessitism shares with NeoMeinongianism is that non-concrete objects (read: non-existent objects) may instantiate some properties; however, they differ insofar as necessitism does not require any characterization principle.

Chapter Eleven

156

NA*, while at the same time doing justice to some of the intuitions invoked by the possibilist.3 Instead, I would like to show how we may rely on the same line of reasoning of the previous chapter to address the dispute between actualism and possibilism. First, let us consider a pair of existential modal statements: (11.3)

Something that might be red does not exist.

(11.4)

It is not the case that something which might be red exists.

As with the non-modal version of the raw intuition, we may again say that at least some of us share the intuition that there is a strong connection between (11.3) and (11.4): they mutually imply one another. Notice, moreover, that this would not be the case if we were dealing with something other than existence, and more precisely what everyone would consider a garden-variety property: (11.5)

Something that might be red is not round.

(11.6)

It is not the case that something which might be red is round.

Everyone would agree that the truth of (11.5) would simply have no relevance whatsoever for the truth or falsity of (11.6), and vice versa. I am aware of the fact that this second intuition (the difference in behavior of 11.3 and 11.4 vis-à-vis 11.5 and 11.6) is perhaps even more problematic than the one discussed in the previous chapter: fewer readers are probably going to share it. Yet, as in the case of the first raw intuition, I kindly ask the reader who does not share this intuition to play along until the end of this section. Once more, the question we should now ask ourselves is the following: why is it the case that in (11.3) internal negation is interchangeable with the external one? The dilemma we are facing takes the following form. One option would again be to get rid of such oddities. This would be the path chosen by the actualist. As it happens, if we formalize (11.3) as (11.3*), we will be stuck with a contradiction: (11.3*) ‫ݔ׌‬ሺτ ܴ‫ܧ̱ ר ݔ‬Ǩ ‫ݔ‬ሻ An actualist could only make sense of (11.4), even though he would consider it partially redundant:

 3

For a survey of these options, see Menzel (2014).

Modal Existential Statements

157

(11.4*) ̱‫ݔ׌‬ሺτ ܴ‫ܧ ר ݔ‬Ǩ ‫ݔ‬ሻ Again, as in the non-modal setting, a Fregean, actualist philosopher has two available strategies: he may either say that (11.3) is contradictory and should therefore be amputated from our language. Or he may say that (11.3) is just a misleading formulation of the logical form (11.4*). What would the possibilist alternative look like? According to possibilism, (11.3) is no longer a contradiction since it may be formalized as (11.3**) with a non-existentially loaded quantification and a discriminating property of existence: (11.3**) ܲ‫ݔ‬ሺτ ܴ‫ܧ̱ ר ݔ‬Ǩ ‫ݔ‬ሻ Furthermore, (11.4) and its formalization as (11.4**) would no longer be redundant: (11.4**) ̱ܲ‫ݔ‬ሺτ ܴ‫ܧ ר ݔ‬Ǩ ‫ݔ‬ሻ But how can a possibilist vindicate the fact that (11.3) and (11.4) mutually imply one another? If we start again by focusing on the inference from (11.4) to (11.3), we may see how (PCP), i.e. the modal watered-down version of (SNCP), would again validate the inference. As in the nonmodal setting, however, the real problem for Neo-Meinongianism or possibilism is the direction of inference from (11.3) to (11.4). True, the same option would of course be available as in the non-modal setting, namely reinterpreting (11.3) as meaning “everything that might be red does not exist.” This, of course, would lead to abandoning the straightforward (11.3**) in favor of (11.3***): (11.3***) ܷ‫ݔ‬ሺτ ܴ‫ܧ̱ ـ ݔ‬Ǩ ‫ݔ‬ሻ Thus, the possibilist (just like the Neo-Meinongian in a non-modal setting) is forced to sacrifice (11.3), or more precisely, he has to stretch it to the point that it is no longer recognizable. Having thus introduced the modal raw intuition and explained the challenge it poses to both actualism and possibilism, the stage is set for introducing the deflationary view of existence. The reader will have probably already guessed the thesis that I am going to put forward: the inferences which are at stake in statements about actual existence can easily be accounted for as soon as we apply our equivalence schema (NES). We thus may move away from (11.3) and (11.4) on to, respectively, (11.7) and (11.8):

158

Chapter Eleven

(11.7)

Something which might be red does not exist if and only if it is not the case that something might be red.

(11.8)

It is not the case that something which might be red exists if and only if it is not the case that something might be red.

The mystery as to how internal negation is interchangeable with external negation is now easily dispelled. As in the previous case, the predicate “to exist” does not express any property or nature. Rather, it may be considered a stylistic device to stress negation in the case of negative statements, or, alternatively, the absence of negation in the case of affirmative statements. This, again, is the crucial difference between existence and roundness: (11.5) is a genuine instance of internal negation. The advantages of the deflationist approach to existence may thus be confirmed in the modal setting: as soon as we abandon the premise that the verb “to exist” really expresses a property or a nature, there is no longer any need to amputate or stretch our language. But what if the reader does not share the modal raw intuition? As with the non-modal raw intuition, I would argue that he still would have an interest in endorsing the deflationist approach. The reason is that going deflationist provides–once again–a good compromise between the modal cousins of Fregeanism and Neo-Meinongianism: namely, actualism and possibilism. On the one hand, we avoid the problem of actualism, that is to say that negative existentials of the form “something which might be such and such does not exist” become contradictory (I thus assume that we have at least an intuition about the non-contradictory character of such statements). On the other hand, we equally avoid the possibilist distinction between existent and non-existent objects and the problems which are coupled to this distinction. Thus, the reader who were to choose this perspective may accept the entailment relations between (11.3) and (11.4) in the light of this theory and without having to rely on blind intuitions.

11.4 A Second Modal Raw Intuition Let us now turn to a modal version of the second raw intuition discussed in the previous chapter: (11.9)

Something that might be an alien and conscious is not actually existent.

(11.10) Something that might be conscious is not actually existent

Modal Existential Statements

159

As with the non-modal version, there is no implication from (11.9) to (11.10), but only from (11.10) to (11.9). Things are relevantly different if we consider statements about plain, everyday properties: (11.11) Something that might be round and square is not red. (11.12) Something that might be round is not red. How would the actualist and the possibilist approaches deal with this further raw intuition? As with the previous intuitions, actualism and possibilism would lead, respectively, to an amputation and stretching of our language. If we follow the actualist approach, we would simply have to consider (11.9) and (11.10) contradictory or ill-formed. If we follow Neo-Meinongianism, on the other hand, we should reinterpret (11.9) as “everything round and square does not exist.” In this case, the inference to (11.10) would clearly not be allowed. If we follow the third way, instead, we may rescue all our intuitions about these statements and at the same time provide an explanation for the alleged bad behavior of existence. The application of (NES) to (11.9) and (11.10) yields us (11.13) and (11.14), respectively: (11.13)

Something round and square does not exist if and only if it is not the case that something (is) round and square.

(11.14)

Something round does not exist if and only if it is not the case that something (is) round.

We may now spell out the reason as to why (11.9) does not imply (11.10): as in the non-modal setting, the falsity of a conjunction does not imply the falsity of the conjuncts.

11.5 Presentism and Contingentism To conclude this chapter, it is worth noticing that the deflationist approach to existence may be declined in tensed contexts as well. Here we would have to say that the statement “something that was red does not exist” and “it is not the case that something that was red exists” intuitively imply one another (or, more prudently, one might have an intuition to this effect). Then, the same line of reasoning would lead us to deflationism, regardless of worries we might have about the intuition in question. Deflationism about existence thus opens the path for a compromise between the tensed declinations of Fregeanism and Neo-Meinongianism, i.e., what are sometimes labeled, respectively, as presentism and contingentism.

CHAPTER TWELVE INTENTIONAL STATEMENTS

Intentional statements give rise to two well-known puzzles: failure of substitutivity of co-referring terms and failure of existential generalization. However, both puzzles are linked to the assumption that there are such things as genuine singular statements in our language. And, since for the time being I am abstracting from singular statements, I will set those two puzzles aside. The challenge raised by intentional statements in the present context is thus a different one, and has rather to do with the distinction between de re and de dicto readings. More precisely, if it could be shown that we have de re intentional statements about non-existent objects, this would imply that Neo-Meinongians are right after all: the class of objects may be divided into two classes, namely, existent and non-existent ones.

12.1 Propositional Attitudes Reports Let us first consider a couple of intentional statements involving the notion of belief: (12.1)

Meinong believes that something is a golden mountain.

(12.2)

Meinong believes that something which is a golden mountain does not exist.

This is a paradigmatic example of what are often labeled as propositional attitudes reports, i.e., what is expressed by an intentional verb followed by a that-clause. One should add that both (12.1) and (12.2) are true: historically, Meinong really held those beliefs. Now, Neo-Meinongianism would provide us with a de re interpretation of these two intentional statements. Not only (12.1) and (12.2) are true, but also (12.3): (12.3)

Something is such that Meinong believes that it is a non-existent golden mountain.

A Fregean philosopher, however, would clearly resist such an interpretation. To him, Meinong’s belief described in (12.2) is inconsistent

Intentional Statements

161

in that it implies by (PP) that there is something which is a golden mountain and does not exist. Similarly, Meinong’s belief in (12.1) is interpreted as false: it is not true that there is something which is a golden mountain. Thus, even though (12.1) and (12.2) are true, this does not mean that (12.3) is true, as well. Or, in other words, we should reject the de re reading. The deflationist view of existence, finally, is more generous towards Meinong and Neo-Meinongianism because it avoids any reference to (PP). The belief in (12.2) is not inconsistent. Nevertheless, the belief in (12.2) contradicts the belief in (12.1) for the very reason that to say that a golden mountain does not exist is, by (EES), tantamount to saying that it is not the case that something is a golden mountain. Thus, the deflationist view of existence allows for a different, more lenient, diagnosis of Meinong’s inconsistency. This diagnosis, however, does enough work to block the de re reading of the intentional statements in question: (12.1) is not about a golden mountain because Meinong’s belief that something is a golden mountain is false, and (12.2) is not about a golden mountain even though Meinong’s belief that a golden mountain does not exist is true.1

12.2 Objectual Attitudes Reports But let us turn to a more challenging example of intentional statements of imagining: 2 (12.4)

Meinong imagines a golden mountain.

This is a paradigmatic example of what are often referred to as objectual attitude reports, i.e., what is expressed by a transitive intentional verb. The reason imagination is more challenging than belief is that in this case it seems that something really is a golden mountain; namely, what is imagined by Meinong. Does Meinong not have a golden mountain, as it were, “in front of his eyes” while imagining it? Moreover, since we all

 1

The same applies to Meinong’s belief that a golden mountain is golden, since this implies the belief that something is a golden mountain. This belief is not about a golden mountain either, because it is false. (Of course, Meinong’s belief would turn out to be true if interpreted hypothetically: if something is a golden mountain, then it is golden.) 2 The example is equivalent to the one by Priest (2008b, 296) of John imagining an ugly monster. Priest considers such examples to be crucial evidence in favor of Neo-Meinongianism.

162

Chapter Twelve

assume that golden mountains do not exist, it seems that we have provided a scenario in which both (12.5) and (12.6) are true: (12.5)

Something is a golden mountain.

(12.6)

A golden mountain does not exist.

Or, in other words, it appears that in the case of the objectual attitudes such as imaginings we are forced to accept a de re reading of the intentional statement in question. This may be seen as a decisive argument for Neo-Meinongianism and thus a refutation of the deflationism I am advocating. Nevertheless, are we sure we know enough about imagination to draw such a conclusion? For one, the following alternative interpretation deserves to be considered: imagination may be nothing else than the ability of our mind to mimic the perception of something. From such a perspective, one should rephrase (12.4) as (12.7): (12.7)

Meinong’s mind mimics the perception of a golden mountain.

This seems to be a rather plausible explanation of imagination, which does not require it to be about non-existent mountains. Instead, what is required is simply a sensory experience produced by Meinong’s mind that mimics the experience he would have if he saw a golden mountain. Notice, moreover, that one may very well say that something is such that Meinong imagines it to be a golden mountain (thus, we may provide a de re reading). However, it is not really the case that it is a golden mountain. In fact, it is just an imitation of it. The same strategy may be applied to intentional statements of desire. Crane (2013, 131–133) discusses the following example:3 (12.8)

I desire an inexpensive bottle of Burgundy.

Since we would all agree that inexpensive bottles of Burgundy do not exist, we would again have an argument that allows us to regard existence as a discriminating property of objects. Yet, again, this conclusion may be too hasty. Indeed, it seems plausible to interpret desires as mental states that need to be grounded in imagination or perception: I desire things that I

 3

What follows may also be easily applied to intentional statements about fear, where fear may be understood in an analogous way to desires: we fear things that trigger certain feelings when we imagine or perceive them. Examples of intentional statements involving the notion of fear are discussed by Routley (1980, 35–37).

Intentional Statements

163

imagine or perceive and which–while being imagined or perceived–are accompanied by pleasurable feelings. If, then, we apply the same interpretation of imagination that was sketched above, we see how statement (12.8) does not imply any relation to a non-existent inexpensive bottle of Burgundy. To the contrary, what (12.8) implies is merely a mental event that mimics the perception of an inexpensive bottle of Burgundy.

12.3 A Further Objectual Attitude Report Someone may object that this strategy, even if it may be effective in the case of imagination and desires, cannot be applied to other kinds of objectual attitude reports. It clearly cannot be applied to the following instance (I am considering a variation on this very common example, which does not suppose that Ponce de Leon searched for a definite object): (12.9)

Ponce de Leon searched for a fountain of youth.

This, and similar examples, however, I take to be rather unproblematic. Every time we search for something, we are simply trying to establish a truth about something: namely, where it is.4 And, of course, in order to ask ourselves where something is, we have to believe or at least assume this something to be such and such. To return to our example, (12.9) implies that the famous Spanish explorer believed or assumed that something had the property of being a fountain of youth and that he was simply trying to figure out the truth about another statement; namely, the statement about its exact location. And since both the belief and the assumption that something is a fountain of youth are false, there is no reason to give a de re reading of (12.9). Thus, as far as intentional statements such as (12.9) are concerned, we should not be misled by the superficial analogy with, for instance, the statement “John kicks a ball.” Instead, we should pay attention to what we mean by the verb “to search.” I would like to stress that in the present chapter I have not argued for a specific account of imagination, desiring, searching and so forth. What I have tried to point out is simply how certain interpretations are prima facie plausible and allow us to uphold the deflationist view of existence. At the same time, it is crucial to highlight how the above given analyses of intentional statements do not rely on (PP) and thus (a) do not fall together



4 This approach follows a suggestion by Montague (1969, 175), who regards “to seek” as abbreviating “trying to find.”

164

Chapter Twelve

with a Fregean approach and (b) are not question-begging with respect to Neo-Meinongianism.

CHAPTER THIRTEEN SINGULAR EXISTENTIAL STATEMENTS

After having presented a deflationist approach to general existential statements, the time has now come to address the challenge of singular existential ones. As it happens, one might object that, since the argument of the previous paragraphs relied solely on quantified statements, it was itself question-begging, at least with respect to Neo-Meinongianism: the case for deeming existence a property of objects usually relies upon a specific kind of singular statements, i.e., statements involving proper names. This is especially the case since it is prima facie more impervious to apply the deflationist view to singular statements: does this approach not oblige us to reduce every name to a statement? Many philosophers would probably prefer to go Fregean or Neo-Meinongian instead of following such a path. However, before addressing the issue of singular statements, I would like to stress how the question about existence can and must be raised in the first place with respect to a theoretical language without singular statements, since a) such a language is conceivable, b) we may already go to a great length without relying on any singular statement, as sciences such as physics, chemistry and biology show us. This approach, moreover, also has a clear methodological advantage: namely it enables us to distinguish among the arguments about the status of existence that are independent of, or essentially linked to the presence of singular statements within a language. Having said that, I cannot avoid addressing the following question: can singular existential statements be accommodated by the deflationist view?

13.1 The Raw Intuition, again The first and most obvious kind of singular existential statements are statements with proper names in the subject position. As already addressed, this is the kind of singular statement invoked by NeoMeinongian philosophers to press their stance, so that in the present context we may confine our analysis to them. Thus, let us see whether we can re-establish the same difference in behavior between existential and

166

Chapter Thirteen

non-existential statements, as in the case of general existential statements. First, a pair of singular existential statements: (13.1)

Nessie does not exist.

(13.2)

It is not the case that Nessie exists.

Then, a couple of very similar, yet non-existential statements (let us assume we are Socrates’ contemporaries): (13.3)

Socrates is not a writer of tragedies.

(13.4)

It is not the case that Socrates is a writer of tragedies.

What is striking is that, this time round, there seems to be no difference in the behavior of the two pairs of statements: (13.3) and (13.4) mutually imply one another, as do (13.1) and (13.2). In other words, internal negation and external negation seem to be interchangeable, no matter whether we are dealing with existential or non-existential statements. How can it occur that the intuitive difference discussed in the previous chapters vanishes in thin air once singular statements are considered? More precisely, the question we should ask ourselves runs as follows: Why do (13.3) and (13.4) mutually imply one another, whilst (10.3) and (10.4) did not? Thus, the first challenge is to provide an explanation accounting for these differences.

13.2 Vindicating the Raw Intuition Let us start by addressing the implication from (13.3) to (13.4). The answer as to why (13.3) implicates (13.4), whereas (10.3) does not implicate (10.4) lies at hand. It is because we are talking of a unique object, and not simply of an object that happens to instantiate certain properties–of which there might be more than one–that we may infer (13.4) from (13.3). In other words, by ‘Socrates’ we do not simply mean something akin to ‘a man born in Athens in 469 BC’ (let us assume this was his actual birth year), because then it may very well be the case both that Socrates is not a writer of tragedies and that Socrates is a writer of tragedies (some writer of tragedies may very well be born in Athens in 469 BC). This is simply not what proper names are about. What about the second path of implication from (13.4) to (13.3)? First, let us recall why it is that we cannot infer that something red is not round (i.e. 10.3) from the fact that it is not the case that something red is round (i.e. 10.4): it may very well be the case that nothing is red. Once this

Singular Existential Statements

167

consideration is brought to bear, it is not difficult to see that we should revise the previous remark: it is not really the case that from (13.4) we may infer (13.3), for the very same reason that it may be the case that nothing is Socrates. On afterthought, then the difference between (10.1) to (10.4) and (13.1) to (13.4) is less dramatic than expected. Only the implication from (13.3) to (13.4) is surprising. But this can be explained through the uniqueness of the reference of proper names. Without this premise of uniqueness, (13.3) would not imply (13.4) exactly as (10.3) does not imply (10.4). All the other implications, on the other hand, are granted without further ado.

13.3 The Trilemma about Singular Existential Statements If the constellation of implications in our set of statements is the same as before, this means–once again–that there is something peculiar about existential statements, and that, moreover, there are three different approaches to explain this peculiarity: the Fregean, Neo-Meinongian, and deflationist one. Now, from a Fregean perspective (13.1), if taken literally, is non-sense. (13.1) is a contradictory statement for the very simple reason that from (13.1), if it is true, we may infer by generalization (13.5): (13.5)

Something does not exist.

However, as we saw in the relevant chapter, Frege concocted a way to make sense of statements such as (13.1), namely by reinterpreting them as in (13.6): (13.6)

The expression ‘Nessie’ does not refer.

Given this reinterpretation, a statement such as (13.1) may be deemed true while at the same time blocking the inference to (13.5). The price to be paid, if one were to follow the Fregean approach, is thus either yet another amputation of our language, or an asymmetry between how we should interpret general and singular existential statements. The Neo-Meinongian approach, on the other hand, presents the advantage that it comes to the rescue of (13.1), thus avoiding both the amputation and the introduction of an asymmetry in how we interpret existential statements. In fact, the strength of Neo-Meinongianism really comes to the fore in the case of singular existential statements. The reason is that a Neo-Meinongian philosopher does not need to stretch (13.1),

168

Chapter Thirteen

since the problematic inference from (13.1) to (13.2) must be preliminarily granted, owing to the nature of proper names. Thus, the only price we have to pay here if we are to follow the Neo-Meinongian approach is the stretching of language at the level of general existential statements, together with the introduction of the metaphysical epicycles discussed in Chapter 6. Let us now turn to the deflationist approach to existence. The first obstacle here is the following: Which is the statement we should extract from the proper name “Nessie” in order to apply (NES) to it? As they were formulated, neither (NES) nor (EES) can be applied to singular existential statements with proper names, for a proper name is not a nominal expression with a particular quantification. However, we may very well drop this condition from our understanding of (NES) and (EES), so that they apply to nominal expressions in general. Then we may say that the statement which is extracted from every proper name is “something is N,” where “N” stands for any possible proper name. Thus, by (NES) we obtain (13.7) from (13.1): (13.7)

Nessie does not exist if and only if it is not the case that something is Nessie.

This, however, cannot be the end of the story. Indeed, a possible understanding of the statement “it is not the case that something is Nessie” is as follows: (13.8) It is not the case that something is identical with Nessie. Now, if it is not the case that Nessie is identical with something, what is Nessie? Are we not obliged to consider her a non-existent object? This objection forces the deflationist approach to existence to take one additional and somewhat daring step.

13.4 Proper Names and Individuating Properties Let me start with an epistemological remark on identity statements such as (13.8). The identity in question is patently not something which may be given us directly through something akin to a Cartesian light of nature. Instead, what we have to rely upon are some properties which identify Nessie. What we need are individuating properties. More precisely, we must introduce a premise of the following form:

Singular Existential Statements

(13.9)

169

Something is identical with Nessie if and only if something is such and such.

Further below, I will say something about the question of how individuating properties may be established. For the time being, I would just like to point out how this is a requirement for making sense of an identity statement such as (13.8): only if we have a statement of the form of (13.9) may we then proceed to check whether (13.8) is the case. We may thus infer (13.10) from (13.8) together with (13.9): (13.10) It is not the case that something is such and such. It is worth stressing how the same strategy should be applied to affirmative existential statements as well. For instance, (13.2) leads us, via (EES) to (13.11): (13.11) Socrates exists if and only if it is the case that something is Socrates. In turn, because of the epistemological consideration just introduced, we may infer (13.11) from (13.12): (13.12) Socrates exists if and only if it is the case that something is such and such. Again, I am more than ready to concede how this additional step is rather a daring one. The reason is that Donnellan (1972) and Kripke (1972/1980) are often considered as having provided a definitive refutation of the reduction of proper names to descriptions–i.e., what is usually labeled as descriptivism. And, clearly, the view just advocated is a kind of descriptivism. However, I would simply like to point out that, as long as we persist in rejecting the view that we can assess the truth of an identity statement immediately through a mysterious light of nature, there simply is no way around a premise such as (13.10) to assess the truth of a statement such as (13.8). As for the Donnellan and Kripkean objections to descriptivism, a thorough discussion thereof would clearly not be possible in the present study. Instead, what I can do is refer to Dummett’s (1973, 110-151) criticism of these objections. What I would like to stress, however, is that by “individuating properties” we should not understand metaphysically necessary properties. To frame descriptivism as a kind of essentialism is an easy way to make a straw man out of it. At most, we might consider the individuating properties to be epistemically necessary properties:

170

Chapter Thirteen

according to what we (think we) know or presuppose, things cannot be otherwise.1 The latter point may be clarified by going back to a familiar example, namely the question about the existence of God. What the deflationist approach to existence (when applied to singular statements with proper names) is committed to is nothing more than the rather uncontroversial position that the only way we can even make sense of the question whether God exists is by relying on some individuating properties of God Himself. The usual candidates here are, of course, the properties of being omnipotent and supremely good. But this does not mean that these properties have to be essential to God, in the sense that it is metaphysically impossible for God to be to a certain extent mischievous or limited in powers. The only kind of necessity at stake is an epistemic necessity: according to what we presuppose, God must be omnipotent and supremely good. The same line of reasoning applies to the case of Nessie. It is only because we agree to presuppose that such and such properties are the individuating properties of Nessie (in the first place, a monster which inhabits the waters of Loch Ness), that we can make sense of the question whether or not she exists. And in both the cases of God and of Nessie there is only one way to sort out the right individuating properties: namely, by relying on given accounts of God or Nessie.

13.5 The Trilemma, again Let us now go back to our trilemma and see whether we may apply it to existential statements with proper names. If the notion of existence is captured by quantification, then we must amputate (13.1) as contradictory. Alternatively, we must provide an essentially asymmetrical interpretation of the predicate “to exist” in general existential statements and in

 1

In this respect, I fully agree with Reicher’s (2005, 217–220) view that we should distinguish between definitory characterizations of objects and non-definitory ones. The properties we use to identify objects, i.e., the characterizations of such objects, are in most cases not definitory properties but, rather, properties we think we know the objects have (e.g., Aristotle’s characterization as the teacher of Alexander). Thus, we should not think of characterizations or descriptions of objects as yielding us necessary properties of objects but, in most cases, just epistemic necessary ones. The same result may be reached if we rely on Orilia’s (2010) contextual descriptivism, i.e., a strategy that highlights how the characterizations of objects do not have to be definitory ones, but may instead be simply contextual.

Singular Existential Statements

171

statements with proper names, so that the real meaning of (13.1) becomes something like (13.6). If, on the other hand, the notion of existence is a discriminating property, we may take (13.1) at face value. Furthermore, the reader may notice that within this setting no stretching of our language is required, since the implication from (13.1) to (13.2) is no longer an issue. This approach, however, still requires that very same stretching of our language with respect to general existential statements, as well as the introduction of dubious metaphysical principles. Finally, if the notion of existence is a redundant one, entirely captured by (EES) and (NES), then we need neither amputate nor stretch our language. However, we must assume that proper names may be interpreted away: the statement that Nessie does not exist is explained via the statement that it is not the case that something is such and such. Now, a Neo-Meinongian philosopher may very well argue that, in this case, the trilemma speaks in favor of his approach. But, abstracting from the stretching of language which is still necessary with respect to general existential statements and the introduction of dubious metaphysical principles, we should consider the following. How can a Neo-Meinongian answer the epistemological question as to how we come to confidently state (say) that Nessie does not exist? It seems that a Neo-Meinongian philosopher, too, would have to rely on some identifying properties in order to distinguish the non-existing Nessie from all other existing objects. But once we are obliged to introduce identifying properties, we may as well do without the distinction between existent and non-existent objects and endorse the deflationist view. A final remark should address singular existential statements in modal and intentional contexts. Given the line of reasoning of the present chapter, nothing needs to be added to the previous discussions in Chapter 11 and 12: proper names–i.e., the only kind of singular statements upon which I focus in the present study–may be interpreted away so that alleged singular statements yield us general ones.

CONCLUDING REMARKS

The first two parts of this study were aporetic. I have presented a survey of different approaches to existence that stretched from David Hume to Graham Priest, and have tried to highlight both their advantages and drawbacks. Part One addressed those theories that have argued against the property-view of existence. Not surprisingly, the most convincing approach to existence as something other than a property was the Fregean one. The view of existence as quantification defended by Frege has in fact become the orthodoxy within contemporary–one should perhaps add analytic–philosophy. Part Two addressed the heretic view according to which existence is (almost) a plain property of objects, i.e., something that may divide the domain of objects into two classes. Here, the most convincing approach was the one developed by Richard Routley, usually labeled as Nuclear Neo-Meinongianism. The problem this study was confronted with, however, was that neither Fregeanism nor Nuclear NeoMeinongianism could be declared to have the upper hand in the debate on existence: the choice between the two approaches seemed to rest on mere intuitions. If one were to favor what Russell labeled as the robust sense of reality, he would lean towards Fregeanism; if not, he would lean towards Nuclear Neo-Meinongianism. This conclusion was left untouched by the discussion of free logics in the Interlude between the second and third part of this study. Finally, in Part Three, I have tried to break this stalemate. More precisely, my suggestion was that a third option had as yet not been taken into due consideration: existence is neither something akin to a plain property of objects, nor something that is captured by quantification; rather, it should be deemed a redundant notion which may always be interpreted away by means of what I have labeled the Existence and the Non-Existence Equivalence Schema. Just as the well-known truth (and falsity) equivalence schema yields us a deflationist, anti-metaphysical approach to truth, so the existence (and non-existence) equivalence schema yields us a deflationist, anti-metaphysical approach to existence. I am confident that this theory can stand on its own feet: it is not just because it fares better than the competitor theories that we should endorse it. Nevertheless, as noted at several reprises in Part Three, a crucial advantage of this theory is that it allows us to strike a middle path. Both the Fregean intuition that, paradoxically speaking, there are no non-

A Study on Existence: Two Approaches and a Deflationist Compromise 173

existent objects and the Neo-Meinongian intuition that it is not contradictory to say of something that it does not exist are upheld. The problem with these two arch-enemies, however, was that reliance on their intuitions led them too far: the latter by declaring existence to be an almost ordinary property of objects, the former by interpreting the notion of existence as captured by the notion of quantification. As is often the case, it takes two to argue. From the vantage point of the deflationist approach to existence, it may also be interesting to reconsider the approaches developed by Hume, Kant and Brentano, which were discussed in Part One. Is Hume’s claim that existence makes no addition to our ideas not already hinting towards a kind of deflationism? Can we not say the same about Kant’s view, i.e., that existence is not a real but merely a logical predicate, and about Brentano’s view, i.e. that to say that something exists is simply to (correctly) accept that something? In a sense, yes. Indeed, the fact that at least Hume and Kant may be enrolled in the deflationist camp was already noted by Thomasson (2014, 191). However, I would like to stress that these authors–if they did move towards deflationism–were not radical enough. On the one hand, Hume should not have said that existence makes no addition to our ideas, but, rather, that we simply have no idea of existence. Kant and Brentano, on the other, should have refrained from providing a subjectivist interpretation of the notion of existence: the notion of (correct) acceptance and the notion of perception do not bring us any step closer to understanding the notion of existence. And this for the very simple fact that–if the deflationism defended here is true–we simply do not have any (substantial) notion of existence. To conclude, I would like to draw attention one last time to the fact that the deflationist approach to existence remains neutral with respect to ontological debates as to whether or not objects of a specific kind exist. If someone is convinced that numbers, propositions, possible worlds, fictional characters, etc., exist, he is welcome to phrase this position within the deflationist approach to existence.1 He would then simply have to accept that the statement “some xs exist” in question is explained by the statement “something is x” (i.e., the Existence Equivalence Schema). The same is true for those who believe, for instance, that ordinary physical objects, the external world or even individuals as such do not exist (i.e., the position labeled as “ontological nihilism”). These philosophers would simply have to accept that the statement “some xs do not exist” in question

 1

Obviously, if realism about fictional characters were true, the number of true negative existential statements would be drastically reduced. For instance, the statement “Sherlock Holmes does not exist” would turn out to be false.

174

Concluding Remarks

is explained by the statement “it is not the case that something is x” (i.e., the Non-Existence Equivalence Schema). In this respect, this study is truly a work in meta-ontology, which, as such, does not predecide any ontological debate. At least to this extent, I agree with the Gattopardo: “For things to remain the same, everything must change.”

BIBLIOGRAPHY

Abaci, Uygar. 2008. “Kant’s Theses on Existence.” British Journal for the History of Philosophy 16/3: 559–593 Albertazzi, Liliana, Massimo Libardi, and Roberto Poli, eds. 1996. The School of Franz Brentano. Dordrecht: Kluwer. Albertazzi, Liliana, Dale Jacquette, and Roberto Poli, eds. 2001, The School of Alexius Meinong. Aldershot: Ashgate. Antonelli, Mauro. 2000. “Franz Brentano und die Neuentdeckung der Intentionalität.” Grazer Philosophischen Studien 58: 93–117. —. 2001. Seiendes, Bewußtsein, Intentionalität im Frühwerk von Franz Brentano. Freiburg and München: Alber. Beaney, Michael, ed. 1997. The Frege Reader. Oxford: Blackwell. Bencivenga, Ermanno. 1986. “Free Logics.” In Handbook of Philosophical Logic. Volume 3: Alternatives to Classical Logic, edited by Dov M. Gabbay and Franz Guenthner, 373–426. Dordrecht: D. Reidel. Bennett, Jonathan. 1974. Kant’s Dialectic. Cambridge: Cambridge University Press. Berto, Francesco. 2013. Existence as a Real Property: the Ontology of Meinongianism. Dordrecht: Springer. Brandl, Johannes. 2005. “What Is Wrong with the Immanence Theory of Intentionality?” In Phenomenology and Philosophy of Mind, edited by Amie L. Thomasson and David. W. Smith, 167–182. Oxford: Clarendon Press. —. 2014. “Brentano’s Theory of Judgement.” The Stanford Encyclopedia of Philosophy (Summer 2010 Edition), edited by Edward N. Zalta, URL = . Branquinho, Joao. 2012. “What is Existence.” Disputatio 34/4: 575–590. Brentano, Franz. 1874. Psychologie vom empirischen Standpunkt. Leipzig: Dunker. English translation in Brentano (1994) (references to the English translation in square brackets). —. 1889. Vom Ursprung sittlicher Erkenntnis. Leipzig: Dunker & Humblot.

176

Bibliography

—. 1911. Von der Klassifikation der psychischen Phänomene, (Psychologie vom empirischen Standpunkt, vol. 2). Leipzig: Duncker und Humblot. English translation in Brentano (1994) (references to the English translation in square brackets). —. 1930. Wahrheit und Evidenz, edited by Oskar Kraus. Hamburg: Meiner. English translation in Brentano (1966) (references to the English translation in square brackets). —. 1966. The True and the Evident, edited by Roderick M. Chisholm. London: Routledge & Kegan. —. 1982. Deskriptive Psychologie, edited by Roderick M. Chisholm and Willhelm Baumgartner. Hamburg: Meiner. —. 1994. Psychology from an Empirical Standpoint, edited by Linda L. McAlister. London and New York: Routledge. Bricke, John. 1991. “Hume’s Argument Concerning the Idea of Existence.” Hume Studies 17/2: 161–166. Byrd, Michael. 1986. “Review of Zalta’s Abstract Objects.” Journal of Symbolic Logic 51: 246–248. Carnap, Rudolf. 1950. “Empiricism, Semantics, and Ontology.” Revue International de Philosophie 4: 20–40. Reprinted in Meaning and Necessity, 2nd ed., 205–221. Chicago: University of Chicago Press, 1956. Castañeda, Hector-Neri. 1974. “Thinking and the Structure of the World.” Philosophia 4: 3–40. Chakrabarti, Arindam. 1997. Denying Existence. The Logic, Epistemology and Pragmatics of Negative Existentials and Fictional Discourse. Dordrecht: Kluwer. Chisholm, Roderick M. 1972. “Beyond Being and Nonbeing.” In Haller (1972, 245–255). —. 1982. “Brentano’s Theory of Judgement.” In Brentano and Meinong Studies, 17–36. Amsterdam: Rodopi. Chrudzimski, Arkadiusz. 2001. Intentionalitätstheorie beim frühen Brentano. Dordrecht, Kluwer —. 2004. Die Ontologie Franz Brentanos. Dordrecht: Kluwer. —. 2007. Gegenstandstheorie und Theorie der Intentionalität bei Alexius Meinong. Dordrecht: Kluwer. Chrudzimski, Arkadiusz and Barry Smith. 2004. “Brentano’s Ontology: from Conceptualism to Reism.” In: Jacquette (2004, 197–220). Crane, Tim. 2013. The Objects of Thought. Oxford: Oxford University Press. Cummins, Phillip. 1991, “Hume on the Idea of Existence.” Hume Studies 17/1: 61–82.

A Study on Existence: Two Approaches and a Deflationist Compromise 177

Donnellan, Keith. 1972. “Proper Names and Identifying Descriptions.” In Semantics of Natural Language, edited by Donald Davidson and Gilbert Harman, 356–379. Dordrecht: Reidel. Dummett, Michael. 1973. Frege. The Philosophy of Language. London: Duckworth. Findlay, John. 1933. Meinong’s Theory of Objects. London: Oxford University Press. —. 1963. Meinong’s Theory of Objects and Values. Oxford: Clarendon Press (2nd, enlarged edition of Findlay 1933). Fitting, Melvin and Richard Mendelsohn. 1998. First-Order Modal Logic. Dordrecht: Kluwer. Fontaine, Matthieu and Juan Redmond. 2008. Logique dialogique: une Introduction. Volume I. Méthod de Dialogique: Règles et Exercises, volume 5 of Cahiers de Logique et d’Épistemologie. London: College Publications. —. 2012. “To Be Is to Be Chosen–A Dialogical Understanding of Ontological Commitment.” In Logic of Knowledge. Theory and Applications, edited by Cristina Barés Gomez, Sébastien Magnier and Francisco Salguero, 203–222. London: College Publication. Forgie, J. William. 2000. “Kant and Frege: Existence as a Second Level Property.” Kant-Studien 91: 165–177. Frege, Gottlob. 1879. Begriffschrift, eine der arithmetischen nachgebildeten Formelsprache des Reinen Denkens. Halle: Verlag L. Nebart. Preface and Part 1 translated in Beaney (1997, 47–78). —. 1883?. “Dialog mit Pünjer.” Unpublished during Frege’s lifetime. Reproduced in Hermes, Kambartel and Kaulbach (1969, 60–75). Reprinted in Gabriel (2001, 1–22). Translated by Peter Long and Roger White as “Dialogue with Pünjer on Existence.” In Hermes, Kambartel and Kaulbach (1979, 53–67) (references to the page numbers of the English translation in square brackets). —. 1884. Die Grundlagen der Arithmetik, eine Logisch-Mathematische Untersuchung über den Begriff der Zahl. Breslau: Verlag von Wilhelm Koebner. English translation by John L. Austin as The Foundations of Arithmetic: a Logico-Mathematical Enquiry into the Concept of Number. Oxford: Blackwell, 1959. —. 1892. “Über Sinn und Bedeutung.” Zeitschrift für Philosophie und philosophische Kritik 100: 25–50. Translated as “On Sinn and Bedeutung” in Beaney (1997, 151–171) (references to the page numbers of the English translation in square brackets).

178

Bibliography

—. 1976. Wissenschaftlicher Briefwechsel, edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel and Albert Veraart. Hamburg: Felix Meiner. Geach, Peter. 1965. “Assertion.” Philosophical Review 74 (4): 449–465. Grossmann, Reinhardt. 1974. “Meinong’s Doctrine of the Aussersein of the Pure Object.” Noûs 8/1: 67–82. Haaparanta, Leila. 1986. “On Frege’s Concept of Being.” In Knuuttila and Hintikka (1986, 269–290). Haller, Rudolf. 1972. Jenseits von Sein und Nichtsein. Graz: Akademische Druck- u. Verlagsanstalt. Hermes, Hans, Friedrich Kambartel and Friedrich Kaulbach, eds. 1969. Nachgelassene Schriften. Hamburg: Felix Meiner. —. eds. 1979. Posthumous Writings. Oxford: Blackwell. Hintikka, Jaakko. 1966. “On the Logic of Existence and Necessity I: Existence.” The Monist 50: 55–76. —. 1986. “Kant, Existence, Predication and the Ontological Argument.” In Knuuttila and Hintikka (1986, 249–268). Hume, David. 1947. Dialogues Concerning Natural Religion, edited by Norman Kemp Smith. Indianapolis and New York: The Bobbs-Merrill Company. —. 2000. A Treatise of Human Nature. Oxford: Oxford University Press (references to the volume, book, section and paragraph in square brackets). Jacquette, Dale. 1987. “Twardowski on Content and Object.” Conceptus 21 (53/54): 193–199. —. 1996. Meinongian Logic. The Semantics of Existence and Nonexistence. Berlin and New York: de Gruyter. —. 2004. The Cambridge Companion to Brentano. Cambridge: Cambridge University Press. Jorgensen, Andrew. 2002. “Meinong’s much Maligned Modal Momement.” Grazer Philosophische Studien 64/1: 95–118. Kant, Immanuel. 1998. Critique of Pure Reason, Cambridge: Cambridge University Press. Keiff, Laurent. 2009. “Dialogical Logic,” The Stanford Encyclopedia of Philosophy (Summer 2011 Edition), edited by Edward N. Zalta, URL = . Knuuttila, Simo and Jaakko Hintikka, eds. 1986. The Logic of Being. Dordrecht: Reidel. Kriegel, Uriah. 2015. “How to Speak of Existence: a Brentanian Approach to (Linguistic and Mental) Ontological Commitment.” Grazer Philosophische Studien 91: 81–106.

A Study on Existence: Two Approaches and a Deflationist Compromise 179

Kripke, Saul. 1972/1980. Naming and Necessity. Oxford: Blackwell. —. 1973. Reference and Existence (The John Locke Lectures). The Saul Kripke Center Archives, The CUNY Graduate Center. Kroon, Frederick. 2012. “Characterization and Existence in Modal Meinongianism.” Grazer Philosophische Studien 85: 23–34. Kroon, Frederick and Alberto Voltolini. 2011. “Fiction,” The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), edited by E. Zalta, URL = . Lambert, Karel. 1960. “The Definition of E(xistence) in Free Logic.” In Abstracts: International Congress for Logic, Methodology and the Philosophy of Science. Stanford: Stanford University Press. —. 1983. Meinong and the Principle of Independence. Its Place in Meinong’s Theory of Objects and Its Significance in Contemporary Philosophical Logic. Cambridge: Cambridge University Press. Leonard, Henry S. 1956. “The Logic of Existence.” Philosophical Studies 7/4:49–64. Lewis, David. 1970. “General Semantics.” Synthese 22: 18–67. —. 1986. On the Plurality of Worlds. Oxford: Blackwell Publishing. —. 1990. “Noneism or Allism?” Mind 99 (393): 23–31. Lycan, William G. 1979. “The Trouble with Possible Worlds.” In The Possible and the Actual, edited by Michael Loux, 274–316. Ithaca (NY): Cornell University Press. MacColl, Hugh. 1902. “Symbolic reasoning (IV).” Mind 11 (43): 352– 368. —. 1905a. “Symbolic reasoning (VI).” Mind 14 (53): 74–81. —. 1905b. “The existential import of propositions.” Mind 14 (56): 578– 580. —. 1906. “Symbolic Logic and its Applications.” London: Longmans, Green, Marek, Johannes. 2013. “Alexius Meinong.” The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), edited by E. Zalta, URL = . Martin, Wayne M. 2006. Theories of Judgement. Psychology, Logic, Phenomenology. Cambridge: Cambridge University Press. Marty, Anton. 1884. “Über subjectlose Sätze und das Verhältnis der Grammatik zu Logik und Psychologie I–III.” In Vierteljahresschrift für wissenschaftliche Philosophie 8: 56–94; 161–92; 292–340; Reprinted in Gesammelte Schriften. Bd. II/1, edited by Josef Eisenmeier, Alfred Kastil and Oskar Kraus, 1–35, 36–62, 62–101. Halle: Niemeyer, 1918. McGinn, Colin. 2001. Logical Properties. Oxford: Oxford University Press.

180

Bibliography

McLeod, Stephen, K. 2011. “First-Order Logic and Some Existential Sentences.” Disputatio 31/4: 255–70. Meinong, Alexius. 1877. “Hume Studien I: Zur Geschichte und Kritik des modernen Nominalismus.” Sitzungsberichte der philosophischhistorischen Klasse der Kaiserlichen Akademie der wissenschaften 87: 187–260. Reprinted in Gesamtausgabe Bd. I, 1–72. —. 1899. “Über Gegenstände höherer Ordnung und deren Verhältnis zur inneren Wahrnehmung.” Zeitschrift für Psychologie und Physiologie der Sinnesorgane 21: 182–272. Reprinted in Gesamtausgabe Bd. II, 377–480. —. 1901. Über Annahmen. Leipzig: Barth. —. 1904. “Über Gegenstandstheorie.” In Untersuchungen zur Gegenstandstheorie und Psychologie, edited by Alexius Meinong, 1– 50. Leipzig: Barth. Reprinted in Gesamtausgabe Bd. II, 481–535. English translation in Chisholm (1960, 76–117) (references to the page numbers of the English translation in square brackets). —. 1907. Über die Stellung der Gegenstandstheorie im System der Wissenschaften. Leipzig: Voigtländer. Reprinted in Gesamtausgabe Bd. V, 197–366. —. 1910. Über Annahmen (2nd edition). Leipzig: Barth. Reprinted in Gesamtausgabe Bd. IV. English translation by James Heanue, On Assumptions, Berkeley: University of California Press, 1983 (references to the page numbers of the English translation in square brackets). —. 1915. Über Möglichkeit und Wahrscheinlichkeit. Beiträge zur Gegenstandstheorie und Erkenntnistheorie. Leipzig: Barth. Reprinted in Gesamtausgabe Bd. VI. —. 1969–1978. Gesamtausgabe, edited by Rudolf Haller and Rudolf Kindinger. Graz: Akademische Druck- und Verlagsanstalt. Mendelsohn, Richard L. 2005. The Philosophy of Gottlob Frege. Cambridge: Cambridge University Press. Menzel, Christopher. 1992. “Review of Intentional Logic and the Metaphysics of Intentionality by Edward Zalta.” The Journal of Symbolic Logic 57/3: 1146–1150. —. 2014. “Actualism.” The Stanford Encyclopedia of Philosophy (Summer 2014 Edition), Edward N. Zalta (ed.), URL = . Miller, Barry. 1975. “In Defence of the Predicate ‘Exists’.” Mind 84 (335): 338–354. —. 1986. “‘Exists’ and Existence.” The Review of Metaphysics 40/2: 237– 270.

A Study on Existence: Two Approaches and a Deflationist Compromise 181

Montague, Richard. 1969. “On the Nature of Certain Philosophical Entities.” The Monist 53/2: 159–194. Reprinted in Formal Philosophy. Selected Papers of Richard Montague, edited by Richmond Thomason, 148–187. New Heaven and London: Yale University Press, 1974. Morscher, Edgar and Peter Simons. 2001. “Meinong’s Theory of Meaning.” In Albertazzi et al. (2001, 427–455). Münch, Dieter. 1993. Intention und Zeichen. Untersuchungen zu Franz Brentano und Edmund Husserls Frühwerk. Frankfurt am M.: Suhrkamp. Nelson, Michael. 2012. “Existence.” The Stanford Encyclopedia of Philosophy (Winter 2012 Edition), edited by Edward N. Zalta, URL = . Nolan, Daniel. 2008. “Properties and Paradox in Graham Priest’s Towards Non-Being.” Philosophy and Phenomenological Research 76/1: 191– 198. Orilia, Francesco. 2002. Ulisse, il quadrato rotondo e l’attuale re di Francia. Pisa: Edizioni ETS. —. 2010. Singular Reference: a Descriptivist Perspective. Dordrecht: Springer. Owen, David. 2003. “Locke and Hume on Belief, Judgment and Assent.” Topoi 22: 15–28. Parsons, Terence. 1980. Nonexistent Objects. New Haven and London: Yale University Press. Pelletier, Francis J., and Bernard Linsky. 2009. “Russell vs. Frege on Definite Descriptions as Singular Terms.” In Russell vs. Meinong: The Legacy of “On Denoting,” edited by Nicholas Griffin and Dale Jacquette, 40–64. London: Routledge, 2009. Perszyk, Kenneth. 1993. Nonexistent Objects: Meinong and Contemporary Philosophy. Dordrecht: Springer. Poli, Roberto. 2001. “General Thesis of the Theory of Objects.” In Albertazzi et al. (2001, 341–367). Priest, Graham. 2005. Towards Non-Being: the Logic and Metaphysics of Intentionality. Oxford: Clarendon Press. —. 2008a. “The Closing of the Mind: How the Particular Quantifier Became Existentially Loaded Behind Our Backs.” The Review of Symbolic Logic 1/1: 42–55. —. 2008b. An Introduction to Non-Classical Logic: From If to Is. 2nd edition, Cambridge: Cambridge University Press. Quine, Willard v. O. 1948. “On What There Is.” Review of Metaphysics, 2: 21–38. Reprinted in From a Logical Point of View, 1–19. Cambridge, MA: Harvard University Press, 1953.

182

Bibliography

Rahman, Shahid. 2001. “On Frege’s Nightmare: Ways to Combine Paraconsistent and Intuitionistic Free Logic.” In Essays in NonClassical Logic, edited by Heinrich Wansing, 64–85. London: World Scientific. —. 2011. “Some Remarks on Hugh MacColl’s Notion of Symbolic Existence.” Philosophia Scientiae 15/1: 149–161. Rahman, Shahid, Helge Rückert and Matthias Fishermann. 1997. “On Dialogues and Ontology. The Dialogical Approach to Free Logic.” Logique et Analyse 160: 357–374. Rahman, Shahid and Laurent Keiff. 2005. “On How to Be a Dialogician.” In Logic, Thought and Action, edited by Daniel Vanderken, 359–408. Dordrecht: Springer. Rapaport, William. 1978. “Meinongian Theories and a Russellian Paradox.” Noûs 12: 153–180. —. 1984. “To Be and Not to Be.” Noûs 19/2: 255–271. Reed, Delbert. 2007. The Origins of Analytic Philosophy: Kant and Frege. London: Continuum. Reicher, Maria. 2005. Referenz, Quantifikation und ontologische Festlegung. Frankfurt: Ontos Verlag. —. 2014. “Nonexistent Objects.” The Stanford Encyclopedia of Philosophy (Summer 2014 Edition), URL = . Rosefeldt, Tobias. 2006. Was es nicht gibt: Eine Untersuchung des Begriffes der Existenz. Habilationsschrift an der Philosophischen Fakultät der Ruprecht-Karls-Universität Heidelberg. —. 2011. “Frege, Pünjer, and Kant on Existence.” Grazer Philosophische Studien 82/1: 329–351. Routley, Richard. 1980. Exploring Meinong’s Jungle and Beyond, Canberra: Research School of the Social Sciences. Russell, Bertrand. 1903. The Principles of Mathematics. Cambridge: At the University Press. —. 1904. “On Denoting.” Mind 14 (56): 479–493. —. 1905. “Review of A. Meinong’s Untersuchungen zur Gegenstandstheorie und Psychologie.” Mind 14: 530–538. —. 1918/1919. “The Philosophy of Logical Atomism,” Monist 28: 495– 527; 29: 32–63, 190–222, 345–380. Reprinted in Logic and Knowledge: Essays 1905-1950, edited by Robert C. Marsh, 177–281. London: Allen and Unwin, 1956. —. 1973. Essays in Analysis. London: George Allen and Unwin. Ryle, Gilbert. 1972. “Intentionality-Theory and the Nature of Thinking.” In Haller (1972, 7–14).

A Study on Existence: Two Approaches and a Deflationist Compromise 183

Salmon, Nathan. 1987. “Existence.” In Philosophical Perspectives 1, edited by James Tomberlin, 49–108. Atascadero: Ridgeview Press. —. 1998. “Nonexistence.” Noûs 32: 277–319. Salmon, Nathan and George Nakhnikian. 1957. ““Exists” as a Predicate.” Philosophical Review 66: 535–542. Sauer, Werner. 2006. “Die Einheit der Intentionalitätskonzeption bei Brentano.” Grazer Philosophischen Studien 26: 1–26. Simons, Peter. 1992. Philosophy and Logic in Central Europe from Bolzano to Tarski. Dordrecht, Boston and London: Kluwer Academic Publishers. —. 1992a. “Brentano’s Reform of Logic.” In Simons (1992, 41–69). —. 1992b. “A Brentanian Basis for Le’sniewskian logic.” In Simons (1992, 259–269). —. 1992c. “On what there isn’t.” In Simons (1992, 159–193). —. 1995. “Meinong’s Theory of Sense and Reference.” Grazer Philosophische Studien 50: 171–186. —. 1994. Introduction to Psychology from an Empirical Standpoint, by Franz Brentano, xiii–xxii. London and New York: Routledge. —. 1996. “Logic in the Brentano School.” In Albertazzi et al. (1996, 305– 321). —. 2004. “Judging Correctly: Brentano and the Reform of Elementary Logic.” In Jacquette (2004, 45–65). Sluga, Hans D. 1980. Gottlob Frege. London: Routledge. Sullivan, David. 1991. “Frege on Existential Propositions.” Grazer Philosophischen Studien 41: 127–149. Thomasson, Amie. 2014. “Deflationism in Semantics and Metaphysics.” In Metasemantics. New Essays on the Foundations of Meaning, edited by Alexis Burgess and Brett Shermann, 185–213. Oxford: Oxford University Press. Twardowski, Kasimir. 1894. Zur Lehre vom Inhalt und Gegenstand der Vorstellungen. Eine psychologische Untersuchung. Wien: Hölder. Translated in Twardowski (1977) (references to the page numbers of the translation in square brackets). —. 1977. On the Content and Object of Presentations, edited by Reinhardt Grossmann. The Hague: M. Nijhof. Tweyman, Stanley. 1992. “Some Reflections on Hume and Existence.” Hume Studies 18/2: 137–150. Vallicella, William F. 2001. “Brentano on Existence.” History of Philosophy Quarterly 18/3: 311–327. van Inwagen, Peter. 2008. “McGinn on Existence.” The Philosophical Quarterly 58 (230): 36–358.

184

Bibliography

Voltolini, Alberto. 2012. “All the Existences there are.” Disputatio 32: 361–383. Williams, Christopher J. F. 1988. What is Existence. New York: The Clarendon Press. Williamson, Timothy. 1998. “Bare Possibilia.” Erkenntnis 48: 257–273. —. 2013. Modal Logic as Metaphysics. Oxford: Oxford University Press. Zalta, Edward. 1988. Intensional Logic and the Metaphysics of Intentionality. Cambridge: MIT Press.

INDEX

Abaci, Uygar, 21, 27, 30 Antonelli, Mauro, 34 Aristotle, 3 Bencivenga, Ermanno, 118, 123, 124, 125, 130, 131, 132 Bennett, Jonathan, 20 Berkeley, George, 15 Berto, Francesco, 11, 86, 93, 100, 105, 107, 109, 111 Brandl, Johannes, 34, 39 Branquinho, Joao, 2 Brentano, Franz, 2, 3, 8, 18, 33, 34, 35, 36, 37, 38, 39, 40, 41, 44, 46, 47, 48, 66, 67, 69, 76, 80, 81, 173 Bricke, John, 11, 12 Byrd, Michael, 107 Carnap, Rudolf, 148 Castañeda, Hector-Neri, 103, 104 Chakrabarti, Arindam, 20, 27, 28, 29 Chisholm, Roderick, 34, 38, 71, 75 Chrudzimski, Arkadiusz, 34, 35, 36, 40, 45, 48, 67, 75 Crane, Tim, 63, 115, 162 Cummins, Phillip, 10, 11, 12 Donnellan, Keith, 63, 169 Dummett, Michael, 51, 169 Findlay, John, 73, 75, 90 Fischermann, Matthias, 125, 126 Fitting, Melvin, 15 Fontaine, Matthieu, 120, 123, 125, 126, 128, 129, 130, 132 Forgie, J. William, 20 Frege, Gottlob, 1, 2, 3, 4, 8, 20, 24, 25, 26, 27, 28, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 69, 70, 73, 80, 85, 87, 99, 100, 116, 118, 119,

120, 130, 131, 132, 136, 140, 167, 172 Geach, Peter, 38, 40, 47 Grossmann, Reinhardt, 43, 73, 75 Haaparanta, Leila, 20 Hintikka, Jaakko, 20, 118, 139 Hume, David, 2, 3, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 24, 27, 30, 32, 33, 35, 40, 41, 48, 66, 172, 173 Jacquette, Dale, 2, 4, 43, 75, 82, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 98, 99, 100, 102, 106, 107, 108, 109, 119, 116, 136, 141 Jorgensen, Andrew, 90, 91 Kant, Immanuel, 2, 3, 8, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 48, 58, 76, 173 Keiff, Laurent, 126 Kriegel, Uriah, 33, 47 Kripke, Saul, 61, 63, 113, 169 Kroon, Frederick, 100, 102, 109, 114, 115 Lambert, Karel, 75, 120 Leibniz, Gottfried, 96 Leonard, Henry, 120 Lewis, David, 9, 30, 31, 100, 140, 143 Linsky, Bernard, 60 Lycan, William, 100 MacColl, Hugh, 82, 83, 84, 85, 86, 87, 98, 99, 106, 107, 108 Mally, Ernst, 74, 90, 104 Marek, Johannes, 75 Martin, Wayne, 24 Marty, Anton, 37, 47, 63 McGinn,Colin, 14, 52, 63 McLeod, Stephen, 140

186 Meinong, Alexius, 2, 3, 4, 28, 33, 46, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 97, 98, 99, 100, 102, 103, 104, 106, 107, 108, 111, 112, 122, 142, 160, 161, 162 Mendelsohn, Richard, 2, 15, 20, 25, 50, 54, 55, 56, 57, 59, 61, 62, 63 Menzel, Christopher, 107, 151, 156 Miller, Barry, 2 Montague, Richard, 163 Morscher, Edgar, 67 Münch, Dieter, 34 Nakhnikian, George, 2, 57 Nelson, Michael, 3 Nolan, Daniel, 111 Orilia, Francesco, 73, 75, 103, 170 Owen, David, 41 Parmenides, 3 Parsons, Terence, 2, 4, 28, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 98, 99, 100, 102, 105, 106, 107, 108, 110, 141 Pelletier, Francis, 60 Perszyk, Kenneth, 85, 100 Plato, 3, 102 Poli, Roberto, 73, 75 Priest, Graham, 3, 4, 100, 109, 110, 111, 112, 113, 114, 115, 116, 122, 161, 172 Quine, Willard, 37, 49, 59, 61, 62, 63, 82, 85, 93, 94, 95, 96, 97, 111, 120 Rahman, Shahid, 83, 86, 125, 126, 132 Rapaport, William, 3, 4, 73, 75, 81, 102, 103, 104, 105, 106, 107, 108

Index Redmond, Juan, 120, 123, 125, 126, 128, 129, 130, 132 Reed, Delbert, 20 Reicher, Maria, 25, 75, 91, 105, 111, 170 Reid, Thomas, 3 Rosefeldt, Tobias, 20, 28, 29, 75 Routley, Richard, 2, 3, 4, 28, 30, 63, 76, 83, 85, 86, 87, 88, 89, 90, 92, 93, 94, 97, 98, 99, 100, 102, 106, 108, 109, 110, 113, 116, 122, 133, 136, 140, 141, 142, 162, 172 Rückert, Helge, 125, 126 Russell, Bertrand, 49, 52, 57, 59, 60, 61, 62, 63, 64, 68, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 93, 94, 95, 96, 98, 99, 100, 105, 106, 107, 108, 120, 131, 140, 172 Ryle, Gilbert, 71, 85 Salmon, Nathan, 2, 5, 57 Sauer, Werner, 34 Simons, Peter, 38, 40, 67, 75, 80 Sluga, Hans, 20 Smith, Barry, 34 Sullivan, David, 20 Thomasson, Amie, 4, 147, 148, 173 Twardowski, Kasimir, 33, 41, 42, 43, 44, 45, 46, 67, 76 Tweyman, Stanley, 9, 11, 12 Vallicella, William, 37 van Fraassen, Bas, 123, 124 van Inwagen, Peter, 100 Voltolini, Alberto, 2, 100, 102 Williams, Christopher, 16, 20 Williamson, Timothy, 2, 155 Wittgenstein, Ludwig, 100, 126 Zalta, Edward, 3, 4, 102, 104, 105, 106, 107, 108