The Existence of God: An Exposition and Application of Fregean Meta-Ontology 9783110245363, 9783110245356

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Stig Børsen Hansen The Existence of God

Quellen und Studien zur Philosophie Herausgegeben von Jens Halfwassen, Dominik Perler, Michael Quante

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The Existence of God An Exposition and Application of Fregean Meta-Ontology by

Stig Børsen Hansen

De Gruyter

ISBN 978-3-11-024535-6 e-ISBN 978-3-11-024536-3 ISSN 0344-8142 Library of Congress Cataloging-in-Publication Data Hansen, Stig Børsen. The existence of God : an exposition and application of Fregean meta-ontology / by Stig Børsen Hansen. p. cm. − (Quellen und Studien zur Philosophie, ISSN 0344-8142 ; Bd. 98) Includes bibliographical references (p. ) and index. ISBN 978-3-11-024535-6 (hardcover : alk. paper) 1. Frege, Gottlob, 1848−1925. 2. God (Christianity) 3. Ontology. I. Title. BT103.H36 2010 2311.042−dc22 2010027869

Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available in the Internet at http://dnb.d-nb.de. © 2010 Walter de Gruyter GmbH & Co. KG, Berlin/New York Printing and binding: Hubert & Co. GmbH & Co. KG, Göttingen ⬁ Printed on acid-free paper Printed in Germany www.degruyter.com

Preface Preface The question of the existence of God involves two questions. What does one mean by “existence” and what does one mean by the word “God”? While this study treats both questions, the emphasis is on the former. The use of the term “meta-ontology” is meant to designate the treatment of the meaning of “existence” quite generally. Since the 17th century, “ontology” has been used as a name for the Aristotelian study of things qua their existence. Since then, “ontology” has come to be used to designate a list of what exists, and there has been a tendency for the more systematic considerations, such as those introduced by Aristotle, to recede into the background. The recently introduced prefix, “meta”, indicates the reintroduction of the wider question of the nature of ontology. This study motivates the presentation of an explicit meta-ontology by surveying recent discussions of realism in two otherwise unconnected areas: philosophy of mathematics and philosophy of religion. What emerges from the survey is a widespread practice of insisting on differences in the meaning of different instances of “object” or different instances of “existence” and related terms. Such an insistence has recently been dubbed “quantifier variance” by Eli Hirsch. The position is also found in Wittgenstein’s later philosophy, and versions of it are presented and confronted in Aristotle’s Metaphysics. Aristotle rejected the view that the notion of “existence” varies across subjects. This study presents a standpoint to the same effect. The use of “Fregean” in the title of the study is likely to strike the reader as a very broad characterisation. My use of it echoes Fraser MacBride’s (2003) excellent study of neologicism. MacBride reserves the notion “neologicism” for the widely discussed position that arithmetic falls within the domain of logic. This position is of no consequence to what MacBride calls Fregeanism. This is a rather different and independent doctrine about language and reality, characterised by having linguistic categories be prior to ontological ones, while the question of truth is left for various sciences to settle. It is this aspect of Frege’s thought we shall focus on in what follows. Thus, as far as meta-ontology is concerned, the emphasis in this study will be on Frege as well as the young Wittgenstein who spoke of “the great works of Frege”. Throughout his authorship Wittgenstein would cite, with

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approval, versions of one of Frege’s fundamental principles, namely what was called by Michael Dummett the “context principle”. The principle has served in various capacities, but for more than two decades, it has been revived and defended as the main driving force behind a language-driven approach to ontology. I shall present the context principle – to ask for the meaning of a word only in the context of a proposition – as a guide to settling a question of what there is. The principle has largely been appealed to in connection with ontological questions regarding the existence of numbers or abstract objects generally, but nothing in the principle demands such a restriction. Thus, the overall approach of this study can be presented as follows. Had Frege, and those who have developed his approach to ontology, been interested in the existence of God rather than in numbers or abstract objects generally, what would their overall approach to this question be? In short, the chapters progress as follows. Chapters 1 and 2 motivate, present and defend the Fregean meta-ontology. Chapter 3 applies the metaontology to theology. The following two chapters outline and treat a problem with the Fregean approach to ontology that has been raised on Fregean grounds, but predominantly treated in the context of commentary on Wittgenstein’s Tractatus. In slightly more detail: Chapter 1 takes measure of the battlefield made up of the debate over realism in mathematics and theology. I locate what I take to be a crucial weakness in all camps: the lack of a clear concept of an object. The uses of “object” in these discussions nevertheless offer a set of desiderata for a meta-ontology with which chapter 1 concludes. In chapter 2 I take a stand and go on to defend and elaborate a concept of an object derived from Frege’s works. According to this position, the category of object is derivative of the syntactical category of singular term. I defend this position against a range of objections, both those already formulated and those one might reasonably imagine being put forward in response to the Fregean approach. By employing primarily inferential tests, I seek to restore and refine the criteria of singular terms, and I conclude by holding up the Fregean approach to ontology against the desiderata from chapter 1. A significant consequence of the Fregean meta-ontology, so clearly perceived in an early article of Dummett’s, is that a lot of traditional philosophical questioning is exposed as having little depth to it: questions of existence rarely are the proper domain of a philosopher. However, this is not to say philosophy, here in the shape of ontology, cannot provide significant clarity of a subject, and this is what is attempted in the following chapter. Chapter 3 makes for an application of the syntactic criteria to language about the Judeo-Christian god. Essentially, I show how the Fregean categories of predicate and proper name are of central importance

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in critical reflection on the ontology and wider nature of Christian theology. I shall engage in reflections on the structure of both Old and New Testament use of the relevant words with a view to make sense of the claim, found in the New Testament, that there are many gods. This claim remains oddly overlooked in much contemporary philosophy of religion that tends to understand itself as dealing with monotheistic religions. I explore how the concept “king” is central to an understanding of Christian theology, and I mount a defence of the meaningfulness, and indeed, the theological relevance of speaking of a true F – with “King” being a central example of predicates used about God. Rejection of such talk (i.e. “a true F”) has been made on the background of strands of thought from Wittgenstein’s later works. Speaking of a true F serves to confront another case of widespread insistence on “difference in meaning” as we see it in chapter 1. This insistence is frequently made in biblical studies, where one sees the claim that different religions merely inherit or borrow signs (such as “king”) from each other, while the meaning of these signs is utterly transformed in different contexts. It is the semantic underpinnings of this position that we shall confront. After treating a specific ontological question in a largely Fregean manner in chapter 3, chapter 4 returns to the theme of meta-ontology. Unlike the challenges posed in chapter 2, Fregean meta-ontology is now being challenged on Fregean grounds. The focus in the literature with respect to this essentially Fregean challenge is similar to the treatment of the liar paradox. The latter has concerned itself far more with the sentence that says of itself that it is false, rather than the equally problematic “truthteller”. In the case of Fregean meta-ontology, far more attention has been devoted to a paradox that arises from speaking about Fregean concepts (it is known as the paradox of the concept “horse”), while saying that something is an object has been largely left untouched. In Frege’s works, both the notion of an object and the notion of a concept are derived from syntactic features of propositions, and I show how the two notions are in fact equally problematic. Given the concept of object that I have defended, peculiarities arise when one tries to say that so-and-so is an object. Chapter 4 shows how these kinds of peculiarities feature in several ways in Frege’s writings. Having rejected some attempts at a solution, I argue that they should be understood in the context of what Frege called “a logical discussion”. Chapter 5 locates the idea of “a logical discussion” in the setting of Tractarian commentary. The purpose of introducing Wittgenstein’s Tractatus is not to provide an interpretation of this work. The introduction is made with the conviction that some Fregean strands of thought reach a conclusion in early Wittgenstein’s use of them. While those inspired by

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Frege in their meta-ontology arguably have been slow to acknowledge the problems with the concept of an object, Tractarian commentators have been very quick to deem sentences like “A is an object” nonsensical. If one makes nonsensical claims in a general defence of the priority of the syntactic over the ontological, as well as in attempts at describing particular, formal features of religious language, there remains the task of addressing the question of what point there might be in speaking this particular kind of nonsense – what communication might take place? This is a pressing question for Fregean meta-ontology. Answering this question is the task of the final chapter. The importance of answering this question is attenuated by the charge, made by Cora Diamond and others, that there is but one kind of nonsense, mere nonsense and that there is, therefore, no relevant difference between statements of the form “A is a singular term” or “A is an object” and “Piggly Wiggle”. The charge must be taken seriously, as it is motivated by the context principle: the very principle that drives the Fregean meta-ontology. Part of my defence against the charge consists in pointing to important differences between Frege’s and early Wittgenstein’s use of the concept “object”. While Frege most frequently used the term in a survey of what seems a restricted region of language (in his case, language that contains numerals), Wittgenstein employed the term with full generality, about any linguistic representation. I argue that the Fregean use is indeed useful, manages to communicate, but has a different purpose than early Wittgenstein’s. Thereby, an instructive role for the term “object” is reserved in face of the problems raised in chapters 4 and emphasised by Cora Diamond and others. This study does not attempt to settle the question of the existence of God. It presents a way of going about answering the question. This may strike the reader as unambitious, but the reader ought to be persuaded otherwise when taking into account the wide-spread insistence on “difference in meaning” found in discussions in ontology as well as in theology. Elizabeth Anscombe once wryly remarked: “Where we are tempted to speak of ‘different senses’ of a word which is clearly not equivocal, we may infer that we are in fact pretty much in the dark about the character of the concept which it represents” (Anscombe, 1963, p. 1). If philosophy can help us out of the dark, this remains a worthwhile task. Being an exploration of meta-ontology, the study has relevance for three areas: Firstly, those parts of philosophy that are engaged in discussions over the existence of any given kind of thing. Secondly, an analysis of key claims made in theology is provided, including an analysis of the logical forms of the sign “God” as both a name and a general term. Finally, the study provides a contribution to the discussion of meta-ontology in the context of Tractarian commentary. Given the breadth of topics that are

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treated, the study will quite naturally be incomplete on account of not answering all challenges to the Fregean meta-ontology, just as it will treat only a few, but nevertheless central, aspects of language about God. The hope is that the study will achieve more than to preach to the choir, whether in philosophy or theology, and succeed in displaying the Fregean approach to ontology as a genuinely useful way of attaining clarity on a given subject matter. Material from the book has been presented to audiences at The British Society for the Philosophy of Religion (Oxford, 2005), The Tyndale Philosophy Group (Cambridge, 2005), the Centre for Philosophy and Theology (Rome, 2008), The Centre for Philosophy and Religion (Glasgow, 2010) as well as on various occasions at the University of Leeds and the University of Southern Denmark. I am grateful for comments and suggestions made by the audience on these occasions. My greatest intellectual debt is to Roger White for all those informal and extremely rewarding talks and lessons over the years, the majority of which took place late at night in the corridors of the School of Philosophy at the University of Leeds. Thanks are also due to Peter Sullivan for letting me see unpublished material of his and for arranging a series of workshops on the Tractatus in Stirling. For a few years they were a continuing source of inspiration and learning. I am grateful to Jacob Busch, Angelo Cei, Sean Walton, Dawn Phillips, Anne-Marie Søndergaard Christensen, Lars Binderup, Søren Harnow Klausen, Joel Burnett and Jens André Pedersen Herbener for helpful comments on parts of the manuscript, and to John Mason and Lisa Sparling for meticulous and thoughtful linguistic revision of the manuscript. Finally, my wife Sonia was supportive as ever in the final stages of manuscript preparation. My research during the period of writing large parts of the material has been funded by The Danish Council for Independent Research (Humanities). I am grateful for its financial support.

Table of Contents Preface .............................................................................................................. v Abbreviations................................................................................................. xiii On All the Things There Are ............................................................................ 1 The Disambiguation Strategy........................................................................ 1 Criticisms of the Disambiguation Strategy ................................................... 6 Later Wittgenstein’s argument for the disambiguation strategy ................. 11 Conceptual Charity ..................................................................................... 13 Being Too Benevolent ................................................................................ 17 The Task Ahead .......................................................................................... 22 Fregean Meta-ontology ................................................................................... 27 Introduction: Reversing Ontology............................................................... 27 The Context Principle and Ontology: The Short Answer ........................... 28 Against Sufficiency I: Real, External Realism? .......................................... 34 Against Sufficiency II: Idealism?................................................................ 39 Sharpening the Linguistic Criteria .............................................................. 41 Against Sufficiency III: Epistemological Concerns .................................... 55 Against Sufficiency IV: Bogus objects? ..................................................... 58 Cases of Absent Sortals: Refining Frege’s Imperative................................ 65 Whither Ontology?...................................................................................... 75 Conclusion .................................................................................................. 80 The Logical Behaviour of “God”.................................................................... 83 Introduction: Criticism and clarification ..................................................... 83 Geach and Durrant on the Logical Status of “God” .................................... 88

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“God”, the Name......................................................................................... 93 “God”, the sortal: The centrality of kingship ............................................ 105 Analysis of 1. Cor 8:4 ff............................................................................ 117 Fregean meta-ontology and philosophy of religion: concluding remarks ............................................................................... 121 Trying to Take Care of Logic........................................................................ 125 The Concept Horse ................................................................................... 128 Some Responses to the Paradox of the Concept Horse............................. 130 The Disease Spreads: The Concept Object ............................................... 139 Diagnosis: Frege’s “Logical Discussion”.................................................. 145 Nonsense ....................................................................................................... 151 Ankle-biting philosophy?.......................................................................... 152 Austerity About Nonsense ........................................................................ 155 Philosophical Varieties of Nonsense? ....................................................... 158 Wittgenstein and Frege on Ascribing the Formal Concept Object............ 169 Bibliography ................................................................................................. 175 Index ............................................................................................................. 187

Abbreviations FA TLP NB NIV

Gottlob Frege The Foundations of Arithmetic. A logicomathematical enquiry into the concept of number. Second rev. edition. Transl. John L. Austin. Oxford: Basil Blackwell, 1884/1968. Ludwig Wittgenstein Tractatus Logico-Philosophicus. Transl. C. K. Ogden, London: Routledge & Kegan Paul, 1922. Ludwig Wittgenstein 1otebooks 1914–1916. G. H. von Wright and G. E. M. Anscombe (eds.), G. E. M. Anscombe (transl.). Oxford: Blackwell, 1961/1979. The Holy Bible: 1ew International Version. London: Hodder and Stoughton, 1980.

On All the Things There Are The Disambiguation Strategy When philosophers engage in debates over what exists, a dominant line of reasoning can be identified. What characterises it is the reluctance to engage head-on with the question of the existence of a given kind of thing. Instead, a reflective step is taken away from the debate that can initially look like a sideways shuffle: The use of key terms like “real”, “existence” and “object” is qualified. As a consequence of this line of thinking, a variety of realist positions have emerged. These positions all have in common that they are not describable as realist per se. Rather, those who defend the positions insist on a qualification of what is meant by “realism”. In the philosophy of religion some examples of this move are found in what has been called theological realism and christocentric realism. These terms have been coined to describe those who draw on argumentative strategies in the philosophy of science in contrast with those who draw on the witness and existence of Jesus Christ.1 The understanding is that both are realist positions, and that scientific realism for various reasons is improper when concerned with the reality of God. In the same way, positions known as moral realism and innocent realism have been called upon to differentiate realisms in the service of clarifying the reality of God.2 We can see, then, that there are at least four possible ways to be a realist about God. While the topic often remains untreated, we find within this line of thinking an explicit rejection of the idea that existence can be spoken of univocally across what is often called “different discourses” or “ways of speaking”. The uses of language in theology, in philosophy, in everyday parlance and in science are presented as more or less sharply demarcated ways of speaking about reality – about what exists, or as often phrased after Quine, about what there is. The contention – at times inspired by the attention to the differences between language games offered by Wittgenstein in his later writings – is that speaking of what is real amounts to different things in different discourses. We are told that neglecting or _____________ 1 2

See Moore (2003) for this distinction. See Byrne (2003). The notion of innocent realism is originally found in Haack (1996).

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obscuring these differences leads to confusion and makes for an unfaithful representation of the religious subject matter. Such a view has been championed in the writings of D.Z. Phillips, which in turn have exerted a widespread influence in the philosophy of religion. Randy Ramal, a recent defender of Phillips, suggests that the sentence “God exists” can be given two meanings: A philosophical one and a religious one, and Ramal maintains that we are making a mistake if we elevate one of the meanings as a standard for all kinds of discourse: The meaning of God’s reality – or the “fact” of his reality – is relative to the religious context in which the reality belongs. (Ramal, 2000, p. 39)

Phillips himself has obviously championed a version of this view, and Hilary Putnam has likewise suggested what amounts to a very similar conviction: We may also say that “corresponds to reality” has a wholly different meaning as applied to religious language… (Putnam, 1997, p. 410)

The overall contention is that to speak about existence outside any specific context – reality without any qualification – is an illegitimate move that wrongly assumes that we are in possession of a single notion of existence, universally applicable across different regions of discourse. This way of reasoning is by no means confined to thought about language about God. It seems to be at least as vigorously pursued in the different camps clashing in the ongoing discussions over the reality of mathematical objects. To impress upon the reader how widespread this strategy is, we will look at a few examples from different positions in the ongoing debate concerning the statements of mathematicians (and, at a more basic level, the rest of us). The strategy is clearly expressed in Henri Poincaré’s philosophy of mathematics: The word “existence” has not the same meaning when it refers to a mathematical entity as when it refers to a material object. A mathematical entity exists provided there is no contradiction implied in its definition, either in itself, or with the proposition previously admitted. (Poincaré, 1902/1952, p. 44)

This is the same kind of response to the question of what there is that was displayed in the philosophy of religion. A more recent example is found in Stewart Shapiro’s presentation of his structural realism in the philosophy of mathematics: Recall that a traditional platonist, or realist in ontology, holds that the subjectmatter of a given branch of mathematics, like arithmetic or real analysis, is a collection of objects that have some sort of ontological independence. Resnik (1980, p. 162) defines “ontological platonist” to be someone who holds that ordinary physical objects and numbers are “on par”. For such a philosopher, numbers are

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the same kind of thing – objects – as automobiles, only there are more numbers than automobiles and numbers are abstract and eternal.[…] Resnik and myself are realists in ontology, after a fashion. Our versions of structuralism have ramifications for basic notions like existence, object, and identity, at least as those items are used in mathematics. (Shapiro, 2000, p. 257. My emphasis, citation style altered)

Shapiro is aware of the choice between considering different kinds of objects as “objects on par” or merely as objects in different senses of that word, and he opts for the latter option that qualifies the basic notions. A more radical version of this strategy is appealed to in other commentators’ understanding of intuitionism in the philosophy of mathematics: At the root… is the very strong interpretation that the intuitionist gives to existential quantifications: In order for an existential statement to be correctly assertable, one must be able in principle to describe the entity that has the property in question. Of course, putting the matter this way is misleading. This is a “strong” interpretation only from the perspective of the classical mathematician. From the intuitionist’s point of view, this is just what an existential assertion means. The intuitionist views the classical interpretation of existential quantifier not as weaker, but instead unintelligible. (George and Velleman, 2002, p. 144f. My emphasis)

Charles Parsons, a structuralist about mathematical objects, pursues a similar strategy: So I do not see there is any vicious circularity in saying, for example, that the natural numbers are a domain of objects with a successor relation, satisfying the elementary Peano axioms as well as induction. The explanation, of course, is not sufficient to convince us that the natural numbers exist. (Parsons (2004), p. 73. Parsons’ emphasis.)

Parsons seems engaged in what has mockingly been referred to as doing philosophy with italics – where the mocking consists in the observation that typography alone is a poor means of communicating the relevant difference in meanings, or more generally, a poor way of doing philosophy. It is merely a typographical version of stamping the floor, thumping the table or speaking louder. As an addition to the tool box of this argumentative strategy, Parsons invokes a distinction between an object and an entity: The structuralist view of mathematical objects coheres with a rather “thin” conception of what an object is, that the most general concept of object derives from formal logic, that we are speaking of objects when we use the apparatus of singular terms, identity and quantification… Even to call it a concept of object is somewhat misleading, because this hardly suggests a distinction between objects and “entities” that are not objects. However, although in general I do not regard structuralism and platonism as opposed alternatives, there is at least traditionally associated with platonism the idea of a somewhat “thicker” existence for mathematical ob-

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jects, expressed for example in Gödel’s remark that the axioms of set theory describe a well determined reality. (Parsons, 2004, pp. 62, 75)

It remains unclear what the difference between an object and an entity is supposed to be. It seems to boil down to the now accepted philosophical notion of thickness. Numbers may be thin objects, but this offers us no good reason why thin objects should not belong to that category which Kurt Gödel called well-determined reality. Numbers may be a lot less interesting than full-blooded objects like people and trees, but their criteria of identity, and hence, their determination, are a lot clearer. Also, we may reasonably ask what function might be expected to be fulfilled by the distinction between a concept of an object derived from formal logic and the concept associated with a thicker existence.3 When doing logic, we may introduce singular terms that refer to thin objects or that we know to have no reference, but this surely does not mean that we are introducing a wholly new concept of an object, entirely distinct from that which we apply to thick ones. Parsons may well have answers to such quick objections. What matters at present is the prevalence of the move in itself. Several more examples could be given that point to differences in the basic vocabulary of ontology, but we will conclude with an example that, although it comes from the philosophy of mathematics, is nevertheless of particular relevance to numerous attempts at coming to an understanding of religious language. The suggestion is that in certain cases the existential quantifier should be construed metaphorically rather than literally, and this has found expression in a recent attempt of Stephen Yablo’s to come to an understanding of the ontology of number statements: There is a non-negligible chance that numbers do not exist… Someone who says that “twelve is the number of apostles” is not really concerned about that, however; they are taking numbers for granted in order to call attention to their real subject matter, viz. how many apostles there are. How can someone unconcerned about the existence of Xs maintain with full confidence that “So and so is the X which Fs” that is, that “there is at least one X which Fs and all such Xs are identical to so and

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Parsons’ distinctions may have more plausibility than we credit it with for now. As I will go on to elaborate and defend a concept of an object that largely derives from formal logic, we shall address the intuition that lies behind the urge to distinguish such “thick” and “thin” objects. Tyler Burge, in an attempt at coming to grips with Frege’s view on the reality of numbers, relies on another characterisation: “Although I think that Frege maintained a metaphysical view about numbers and other such entities, I do not believe that this view dominated his thinking. His is, for the most part, the relaxed Platonism of a mathematician who simply assumes that there are numbers, functions, and so on… […] Numbers, functions and thought contents are independent of thinkers in the same way that physical objects are” (Burge, 1992, p. 633).

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so?” The answer is that they are using the definite article “the”, or rather the existential quantifier it implicitly contains, non-literally. (Yablo, 2000, p. 222)

Yablo is in this case working within the broadly Quinean framework that takes indispensability to our best sciences as a guide to what there is, and Yablo points to the distinction between figurative and literal use of language as a possible way of countering such an argument for number realism: When using the quantifier literally, propositions such as “numbers exist” or “there are numbers” are false. However, it is suggested that there is a metaphorical quantifier alongside the literal one, and we may employ it to get our message across. By such means we can convey what we want to convey without committing ourselves to what a literal construal of the quantifier implies – that there are (in the literal sense) numbers. This understanding of metaphor is not without its own problems. As Donald Davidson cogently argued, if words take on a new meaning when they feature in the metaphorical use of language, we would have no account of how we understand metaphors, on the assumption that language exhibits compositionality in a metaphorical sentence as it does in any other.4 Words must retain their original meaning for the metaphorical effect to take place and for us to begin to explain how it takes place. Further, Yablo makes little effort to pin down the difference between the literal and metaphorical. His suggestion is that words about medium-sized physical objects are always used literally. However, John Donne’s “No man is an island”, fits Yablo’s bill, is true in both a literal and a metaphorical sense but is a typical example of non-literal use of language. Whatever problems may beset Yablo’s understanding of metaphor, the key point here remains that this essentially is another case of the disambiguation strategy being put to use in a discussion of what there is. In the next section, I offer a way of understanding the insistence on disambiguation that seems to flourish around the use of the words “object”, “existence” and “real” in the philosophy of religion and the philosophy of mathematics alike, with the result that both the formulation of the question and the provision of answer pursued by both disciplines are beset by lack of clarity.

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Davidson frequently insisted that for a language to be learnable, it must have a finite number of semantical primitives. For this point in connection with figurative language, see Davidson (1984, p. 247).

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Criticisms of the Disambiguation Strategy I suggest that the disambiguation response should be taken to emphasise that reference in the putative cases involves reference to God and to numbers respectively. Focusing for now on the discussions over language about God, the italicised word is meant to convey that there are features of God, so that speaking of him must mean something markedly different from speaking about objects like tables and chairs or objects with greater theoretical ballast like electrons. This line of argument is, in fact, a local version of the challenge that Aristotle posed to his own project of a universal science of being qua being: The challenge is that “being is said in many ways”.5 The Aristotelian intuition is that we use language to talk about an enormous variety of things – football matches, challenges, people, peoples, cars, tables, electrons, smiles and so much more. Scepticism regarding there being one sense in which all these are said to exist readily suggests itself. To form sentences that are about God and then sentences about electrons invites the thought that the sense in which such sentences can be said to be about something varies to the point of having little or nothing in common. This would mean that all the very different things there are effectively turn the existential quantifier and the concept of an object into a number of distinct quantifiers and concepts of an object. While Aristotle developed the conceptual means to overcome this scepticism, recent thought has not had the same confidence. Witness Moore’s comments on the question at the outset of his Realism and Christian Faith: “The question of how or whether one maintains some sort of realism… is central to much current theological debate.” Nevertheless, perhaps because of the historical and philosophical scope of the problems related to the debate about realism, very few theological works have recently been published focussing on realism in its own right. (Moore (2003, p. 7). Moore cites David Ford’s (1992) programmatic article.)

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See e.g. the opening of chapters ǽ and ī of Aristotle’s Metaphysics. Aristotle uses the dictum in connection with being in different categories, which also are derived from the structure of predication. The use I wish to point to here is the one that draws attention to the differences within the same category, substances: “Clearly then, the word ‘is’ is said in just as many ways; a thing is a threshold because it lies in such a such position, and its being means its lying in that position, while being ice means having been solidified in such and such a way. And the being of some things will be defined by all these qualities, because some parts of them are mixed, others are fused…” (1042b26 – 1043a11). In chapter four, we return to a modern version of the question of being in connection with different categories.

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Moore rightly recognises the absence of a general understanding of realism to be a lacuna in any particular defence of it, but the task of clarification is not undertaken by him or any other of the writers on the topic of realism and the Christian faith mentioned at the outset of this chapter. Rather, another sort of realism is offered – in Moore’s case, a christocentric one – while leaving it unclear what makes a position realist in the first place.6 In effect, this amounts to what I call a disambiguation strategy: If the reality of a certain (kind of) entity is in question, a possible defence will consist in offering a disambiguation of what it means to be real or to be an object or to exist. In essence, the line of defence would boil down to an exchange of the following kind: – “I do not believe x’s exist for reasons z and y” – “That is because you fail to appreciate that x’s exist1, they don’t exist.” The indexing is meant to indicate the different kinds of existences that are supposed to correspond to the different meanings of “exist” or alternatively, of “object”. It ought to convey clearly the air of futility this strategy lends to an argument regarding the existence of anything, be it numbers or God. The futility has two related sources. Firstly, it is not clear when to disambiguate and when not to. The Eleatic and later Butlerian “everything is what it is and not something else” suggests itself. The aphorism was something Wittgenstein at one point considered as the motto of his Philosophical Investigations, and he is reported to have taken the emphasis on differences to be of central importance to his classes.7 When voiced in the present context, the aphorism could be seen to endorse an unrestrained use of the disambiguation strategy. To emphasise the challenge and also to suggest the Aristotelian answer, we may consider another case where we apparently use the same word about quite different things. Consider the following pair of sentences: The Nile is a long river. They have enjoyed a long friendship. and another pair The body of Ben Johnson is healthy. The urine of Ben Johnson is healthy. _____________ 6 7

In fairness, it must be said that Moore subscribes to a view of language and reality inspired by Michael Devitt. As we shall see below, Devitt does little to address the concern raised here. See Monk (1990, p. 471). Earl of Kent’s “I will teach you differences” from King Lear was also under consideration as a motto for Wittgenstein’s Investigations.

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On All the Things There Are

Seldom are we led to suspect that the usage of “long” and “healthy” might be equivocal just as usage of “real” or “existence” is suggested to be. But according to the disambiguation strategy we ought to be so led, and for the very same reasons: Just as “existence” supposedly means different things in so far as it is employed about a huge variety of things, so is “long” here employed about very different things: friendships and rivers. We may note here how the Aristotelian observation regarding linguistic variety has not gone wholly unnoticed in contemporary thought on what there is. John Mayberry explicitly recognises the Aristotelian concern in his attempt at a set-theoretic foundation of mathematics: Indeed, one might say that the non-univocality of the word “being” is the first principle of his metaphysics. (Mayberry, 2000, p. 30)

Mayberry goes on to express the wish to “try somehow to prevent the perplexities and uncertainties occasioned by these metaphysical questions from infecting the foundations of mathematics” (ibid). The perplexities are in this case metaphysical in the Aristotelian sense, but they have their source in a general and pervasive linguistic phenomenon. To Aristotle, perceived non-univocality was only ever initially grounds for scepticism regarding a universal notion of existence – a scepticism he had to, and did, overcome. It is an initial and important observation rather than a first principle. Exploring systematic ambiguities was integral to much of Aristotle’s thinking, perhaps most prominently in his thought on being, justice and biology. More generally, and of relevance to our example of “long” and “healthy” above, we can be aided by the realisation that there are systematic relations between the tokens of “long” and “healthy”, which allow us to say what we intuitively want to say; that one type of word is being employed twice in each case, rather than two words that just so happen to share typographical criteria of identity.8 In the first of the two cases above, the analogous scheme “a:b :: c:d” is instantiated in the following way: “The length of the Nile is to the length of the average river as the length of their friendship is to the average length of friendships”, which helps us understand how we apply the same word _____________ 8

Of relevance here is Wittgenstein’s distinction between sign and symbol, to be explored in more details in the following chapters. By speaking of “typographical criteria” I speak of how Wittgenstein identified a sign. His notion was broader and would include, for example, phonological means of identification. This is why for now I call “long” a type of sign. Strictly, “long” and “long” are not the same signs, but tokens of the same type of sign. Wittgenstein’s cryptic contention that “‘A’ is the same sign as ‘A’” (TLP 3.302) belongs to the category of what cannot be said, but is shown. A defence of this claim would have us involved in a study of Wittgenstein’s treatment of identity, which lies beyond the scope of the present study. See e.g. White (1978) and Landini (2007).

Criticisms of the Disambiguation Strategy

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about very different things. In the second case, the relation is what G. E. L. Owen (1986) called focal meaning, where the existence of, epistemic access to, and understanding of the cases can be systematically explored: We may have epistemic access to the health of an organism through the health of its urine, but there would be no healthy urine were it not for the existence of healthy bodies (the focal meaning of “health”) – the former is ontologically dependent on the latter. The meaning of “healthy” as applied to “urine” is always with reference to a healthy body and the function it has there – either as a sign of health, or as some believe, its consumption being conducive to the health of an organism. Thus, there are systematically related uses of the relevant words and they do not just happen to use the same type of sign. This is not the place to develop a fully fledged Aristotelian response to a linguistic intuition that stems from the huge variety of things there are. Suffice it to say that the problem of the apparent equivocity of central words was clearly recognised in several areas of his thinking. A solution was necessary and one presented itself that relied on the analogically related uses of words. More recent thinkers who rely on disambiguation suffer from only telling half of the Aristotelian story. They do not have the resources to convince a critical mind why it should take the different uses of “exists” or “reality” to have anything in common. The insistence on different kinds of reality is left without the provision of an understanding of why the signs {“exist1”, “exist2”…,“existn”} should be understood as tokens of one type of sign – one word being used repeatedly. In the absence of such assurance, all there is in common is what the typesetter will tell us there is in common. The commonality here is no different from that between the signs we use for a river bank and the bank where you borrow money. It is mere coincidence that we use the same sign as a symbol for the river banks and financial institutions and the sameness is of no philosophical interest as soon as it is disambiguated. Whatever the writers try to convey by their insistence on differences between meanings of “existence” and “object” , I do not believe we should see their insistence to stretch as far as to be an insistence on the differences making for cases of random ambiguity. They surely intend to address a question about the existence of God that is supposed to have something or other in common with questions we may ask about the existence of other kinds of objects. They ought to, if they are realists, say that what is the case with phlogiston is not the case with God – not that the questions of the

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On All the Things There Are

existence of phlogiston and God have only a surface appearance of commonality.9 Moreover, if adhered to in a consistent manner, the insistence would require significant revisions in the kind of inferences – such as existential generalisation – we take to be valid: “God loves human kind; therefore, there is something which loves human-kind” would not be valid according to someone in the grip of disambiguating “existence”. The inference could be proved invalid on account of ambiguity, considering that the domains in the premise and the conclusion might differ to an extent that would leave the quantifier in the conclusion without any logical relation to the naming that is done in the premise. Of course, what are thought of as different logics have been developed in response to various features of natural and scientific language, such as vagueness, fiction and empty terms in general. None, however, have been developed in response to the Aristotelian intuition, and accepting the validity of the inference above is one among a number of reasons why developing logics is not the first avenue we should explore.10 Finally, the disambiguation strategy should not be wholly dismissed in so far as it gives expression to significant linguistic as well as theological intuitions or convictions. But silence on the subsequent questions that we raised above leaves the insistence on ambiguity open to the question of how exactly we are to understand the ambiguity. When no answers to this query are forthcoming, the idea of ambiguity invites abuse, as suggested by the mock dialogue above. In short, if there really are different kinds of existence or reality, reflected in the different meanings of “existence” and “real”, what, if anything, makes them one of a kind, and thereby, gives purchase to questions regarding the existence of any particular kind of thing?

_____________ 9

Of course, it is possible that someone who believes that God or numbers do not exist would want to insist on the disambiguation, but it is typically a strategy that is employed by those wanting to defend realism (of some sort). 10 Another problem in logic that the strategy touches on is that of unrestricted quantification – talking about absolutely everything. Using the universal quantifier to do this must equally become untenable on the disambiguation strategy. Here though, the stakes are less, as such language comes with its own set of problems. See Sullivan (2000) for a particularly Tractarian account of these, and Rayo and Uzquiano (2006) for various perspectives on the problem of unrestricted quantification.

Later Wittgenstein’s argument for the disambiguation strategy

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Later Wittgenstein’s argument for the disambiguation strategy I have already alluded to Wittgenstein’s later works and its attention to differences in language use. In addition to this heightened sensitivity, Wittgenstein also offered an argument for the disambiguation strategy which we shall briefly address. The argument and its conclusion have been, and remain, hugely influential in philosophy of religion and beyond, but I shall argue that it ultimately fails. Phillips makes a gesture towards the argument in the following remark: What Wittgenstein shows us in his remarks on religious belief is why there is good reason to note the different use which “belief” and “existence” have, and to resist the craving for generality. (Phillips, 1993, p. 63)

Wittgenstein’s notion of family resemblances is what he would put in place of what he presented as the craving for generality in his early work and its notion of the general form of proposition. In his later works, Wittgenstein took the notion of a game as being central to an account of language. After emphasising variety in language use, Wittgenstein responds to the challenge to give the essence of games and thereby of language: “Don’t say: ‘there must be something in common, or they would not be called “games”’ but look and see whether there is something common to all” (Wittgenstein, 1958, §66) What Wittgenstein went on to say about “game” was generalised by himself to central notions in philosophy such as the ones we are considering, and it is the supposed lesson of the meaning of “game” that has been so influential. The central claim is that when one considers the objects to which the word “game” applies, one will not find any one thing in common between all the objects. Rather, the objects will have in common a significant number of similarities with other objects to which “game” truly applies. Thus, when giving an account of the meaning of a word, all we can do is survey the objects to which the relevant word applies, and spell out the network of similarities. Thus, the motto that informs the whole approach: “Don’t think; look and see” (ibid.) and the notion of family resemblances.11 Wittgenstein rightly advises against a tendency to construct theories about language in disregard for its actual functioning. Less obvious is his advice to “look and see”. Firstly, as most philosophers of science will insist, you need to know what features to look at. As Wittgenstein otherwise was well aware, one looks on a background of assumptions and _____________ 11 In his commentary on Wittgenstein’s Philosophical Investigations David Stern accepts the argument and with full consistency, applies the train of thought in order to reject the idea of there being something general that underlies the notion of “Wittgenstein’s philosophy”. (Stern, 2004, p. 54).

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On All the Things There Are

knowledge. Secondly, even if notion of a completely innocent eye is granted Wittgenstein and the subject is taken as ignorant of the concept “game” and we also grant that she pronounces that there is nothing in common, Wittgenstein’s conclusion just doesn’t follow. To see this, consider doing the same exercise with the concept “antimacassar” – the word for pieces of cloth that protects chairs from being sullied by hair.12 No parade of specimens attended by looking will help acquiring the concept of an antimacassar. Just looking is likely to result in something along the lines of the utterly uninformative “bright-coloured pieces of rectangular cloth”. Though antimacassars can be lined up and inspected, what it takes to be one cannot be seen, and thus, cannot be grasped by Wittgenstein’s looking at a list of specimens. To get at the meaning of a word like “antimacassar”, we would want to know the point of them: maintaining a certain appeal of hotel furniture even though some guests have filthy hair. Similarly with “game”: we have no guarantee that the innocent onlooker will unearth anything of relevance to grasping the meaning of the word. There are virtually countless similarities between any two objects, and only a narrow subset matters to their being a game, an antimacassar or something else. Thus, when just looking, it appears there are more similarities between rugby and a pub brawl that between rugby and a game of cards, and some acts of tourism (such as taking pictures) will look very close to espionage. However, we are reluctant to call a pub brawl a game, and this reluctance has its roots in the fact that the features a pub brawl has in common with rugby are irrelevant. Such a claim, however, can only be made by someone who does more than “see”: mastery of the concept is needed to weed out irrelevant similarities, but an appeal to conceptrelevant similarities makes for an explanatory reversal of Wittgenstein’s proposal. A simpler and very effective criticism has been levelled against prototype theories of concepts. These theories are traced to Wittgenstein’s notion of family resemblance and Frank Keil comments: Unfortunately, it is often assumed in the psychological literature that the failure of subjects to list a set of essential properties for members of a kind does entail that no such properties for the kind in fact exist. (Keil, 1989, p. 27)

A sign that Wittgenstein is being misled by his own image of language is the odd description he offers of what we would do with someone who genuinely didn’t know the meaning of “game”. According to Wittgenstein, we would list particular examples to a point where we thought the other _____________ 12 I owe the attention to Wittgenstein’s argument and the example to Roger White.

Conceptual Charity

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could go on by herself. But surely we would attempt a definition, which would include the point of games, and we would illustrate with typical uses of the word – the philosophical practice that later Wittgenstein otherwise emphasised. Nevertheless, many philosophers of religion have taken on good faith the upshot of Wittgenstein’s unfortunate gloss on philosophical method in Philosophical Investigations §65–67, and have accepted the conclusions reached regarding firstly, “game” and secondly, a range of philosophically significant words, including “existence” and “object”. Nevertheless, no convincing argument against, say, there being a universal concept of an object emerges from this passage and its notion of family resemblances. Inspecting specimens only may or may not hide something general underlying them all. This, of course, is not an argument for there being a universal meaning of object. However, early Wittgenstein’s notion of a general form of proposition, and inter alia a universal notion of an object, was not merely (if at all) the result of a craving for generality, but the result of argument.13

Conceptual Charity The previous sections identified examples of the widespread insistence on differences in basic notions when discussing the existence of different kinds of objects or, put differently, which regions of our language should be taken to be involved in reference to objects. We suggested that such an insistence must take place against the background of an agreement on what, in general, is meant by “existence” or “object”. Shapiro seemed to suggest the existence of such an agreement when he speaks of a position where different objects are considered “on par” with respect to being objects. In the philosophy of religion, Moore likewise emphasised the need for an account of realism in its own right, against the background of which we would be able to conduct local, ontological explorations. Other discussions in the philosophy of mathematics similarly allude to a supposed background agreement in the meaning of the relevant words – the insistence is here on sameness rather than difference. One example is offered by Penelope Maddy’s defence of realism with respect to mathematics: Realism, then (at first approximation), is the view that mathematics is the science of numbers sets, functions, etc., just as physical science is the study of ordinary

_____________ 13 To explicate Wittgenstein’s argument in the TLP is beyond the task pursued here. A central strand of the argument relies on the need to account for the linguistic phenomenon of compositionality: that language apparently forms a system that can communicate a new sense with old words put together in a familiar way.

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On All the Things There Are

physical objects, astronomical bodies, subatomic particles, and so on. (Maddy, 1990, p. 2. My emphasis)

Steven Wagner is another who, in response to something like the disambiguation strategy in ontological discussions, insists on the sameness of meaning of basic notions: [T]he Platonist’s best response [to the multivocity thesis] is to make a case for abstract objects, then challenge opponents to explain why, if the arguments seem good at all, their existential conclusion should in any way be qualified. Pending such an explanation I will set the multivocity thesis aside. We are pursuing a straight forward question about the existence of abstract objects. (Wagner, 1996, p. 74f.)

So what is a straightforward question about the existence of anything, including God, abstract objects such as sets and the various kinds of numbers? What is the given background of agreement that the disambiguation strategy must rely on in the first place? Answering this means offering a meta-ontology. One might reasonably suggest that we should extend a fair amount of charity when language is being used in questions of existence. Emphasis on the need for this kind of charity was often made by Frege, along with some guidance on how exactly to extend this. An example of this advice is worth quoting at some length, as it bears directly on the quandary we now find ourselves in: In the first stages of any discipline we cannot avoid the use of ordinary words. But these words are, for the most part, not really appropriate for scientific purposes, because they are not precise enough and fluctuate in their use. Science needs technical terms that have precise and fixed meanings, and in order to come to an understanding about these meanings and exclude possible misunderstandings, we give examples illustrating their use. Of course, in doing so we have again to use ordinary words, and these may display similar defects to those which the examples are intended to remove. So it seems that we shall then have to say the same thing over again, providing new examples. Theoretically, one will never really achieve one’s goal in this way. In practice however, we do manage to come to an understanding about the meanings of words. Of course we have to be able to count on a meeting of minds, on others guessing what we have in mind. (Frege, 1979c, p. 207)

This stress on the need for charity was even more outspoken in Frege’s writings on geometry. He suggests that in science there has to be certain logically primitive elements that are subject not to definition but to what he calls “explication” or “elucidation”. The success of this relies on the cooperative understanding, goodwill and even guesswork of those involved. The success of elucidation is achieved when we are “sure that all who use them henceforth also associate the same sense with the elucidated word” (Frege, 1984, p. 302). Supposedly, should people do science in isolation,

Conceptual Charity

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there would be no need for elucidations – all that would remain was the requirement that scientists were in agreement with themselves in the use they make of certain signs. But once we entertain discussions, elucidations serve to make sure that we are on a level playing-field with respect to central concepts. As such, elucidations are not part of science proper, but preparatory for the practice of it. Indeed, elucidations might be needed for any systematic investigation that seeks to track the truth of any given matter, including the ontological questions that we are ultimately seeking to address here. Taking our clue from Frege, the only initial step that we can take in preparation for a discussion of what objects there are, is to provide examples that we can hope will suffice to suggest a common usage – a meeting of minds – in the philosophical discipline. Here, the characterisation of the philosopher of religion John Hick captures the kind of expressions – shared by many – that are supposed to suggest to us the question in its most general form: “If you are a realist, you think that the term in question ‘refers’ to an object that is “there” to be referred to” (Hick, 1989, p. 173). The formulation is accompanied by what seems a not uncommon sense of unease, indicated by his use of scare quotes. While Hick’s characterisation in itself is anything but clarificatory with respect to the concept of an object, it nevertheless uses language that is typical of philosophy and that comes with a history. Whereas the English use of “thing” originates in what we today would call a collection of things,14 the medieval Latin “obiectum” is closer to the German “Gegenstand” in so far as it is commonly translated as “thing put before the mind”. While we cannot provide anything like a full history of the use of the related words, we can offer some examples of prominent uses of the sign “object”: Understanding is, generally speaking, the faculty of cognitions. These consist in the determinate relation of given representations to an object. An object, however, is that in the concept of which the manifold of a given intuition is united. (Kant, 1997, B137.)

Whatever else Kant took “object” to mean, and whatever he may have thought about the reality of objects, his use of “object” is clearly intended to serve as part of a discussion about what we call language and world at the most general level. Later, Frege would pit his understanding of statements of number specifically against that of Kant’s, and so Frege replaced his own, more varied use of “(Einzel)-Ding” with Kantian terminology: _____________ 14 “Ting” is still used in Scandinavian languages to mean a collection of animate objects, as in the name of what possibly was the first parliament, Isøre-tinget, or the current “folke-tinget”: the people’s “ting”.

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On All the Things There Are

Thus even although our idea often fails entirely to coincide with what we want, we still make judgments about an object such as the Earth with considerable certainty, even where its size is in point… Not every object has a place. (FA, §60–61.)15

The fact that Frege was contrasting his position with that of Kant and used the notion of an object in discussions about language and reality should make us question in what way – if at all – we should accept Dummett’s contention that Frege’s notion of an object provided a “clean break with the tradition that had prevailed in philosophy up to his time” (Dummett, 1981, p. 471). Surely – as will be explored in chapter 2 – much was new in Frege’s notion of an object, but the sign “object” was employed in a discussion with a far longer history.16 The use of “object” remains prevalent in philosophy. We have seen it used in the philosophy of religion, and examples are legion from the recent philosophy of mathematics. Witness Colyvan’s formulation: “So I take Platonism to be the view that mathematical objects exist…” (Colyvan, 2001, p. 3), which is repeated practically word for word by Charles Chihara (2004, p. 6) and is generally prevalent in the more recent literature on nominalistic and Platonist positions in the philosophy of mathematics. On a more comical, yet instructive note, it has entered meta-ethical debate. If you want to be a moral realist, you might have to believe in the existence of moral objects called morons.17 John Mackie (1977) found it hard to be a moral realist on account of the perceived queerness of moral properties or objects, while Putnam (2004) in his treatment of ethics unsurprisingly insists on disambiguating “object”. While the further determinations and usage of the concept of an object vary significantly between these cases, they all use tokens of the sign “object” in their reflection on the nature of what our cognition is about – constituents of reality. While Kant and others have invoked a contrast between “Gegenstand”, “Ding” and “Objekt”, I shall be using “thing”, “object”, “entity” and “particular” interchangeably. By now it should be clear (and unsurprising) that a large number of thinkers have used the _____________ 15 See also FA §89. 16 It was the Aristotelian heritage – including most significantly its equivalent of a concept of an object – that Heidegger took as his point of departure for the criticism of Western philosophy in Being and Time. In the programmatic lecture entitled “Phänomenologische Interpretationen zur Aristoteles” (1922/1985), Heidegger pointed out that both a certain way of speaking and a concern with a certain kind of question are what provide continuity in this – to his mind regrettable – philosophical tradition. In chapter 2 some of the Aristotelian heritage resurfaces in our characterisation of a singular term, from which we derive the concept of an object. 17 See Dworkin (1996). Though he speaks of moral properties, not objects, he compares morons with particles, which would generally count as objects in a logical categorisation.

Being Too Benevolent

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concept of an object in their general discussion of language and reality, or locally in the discussion about the existence of a certain kind of object. The quotes above from the philosophy of religion as well as the philosophy of mathematics might suggest that there is after all a meeting of minds when we try to conduct discussions about what there is, and, more specifically, that the usage of “object” is well suited to its purpose of communicating. However, in the next section, I make the case that not all is as it seems. More specifically, I will suggest that the common use of a sign, “object”, conceals a conceptual lacuna in discussions of realism.

Being Too Benevolent Frege perceptively remarked regarding proper names specifically, and words more generally: One need only use a word or symbol often enough, and the impression will be produced that this proper name designates something; and this impression will grow so strong in the course of time that in the end hardly anybody has any doubt about the matter. (Frege, 1903/1997, §142)

More recently, and in a more belligerent tone, Williamson (2006) has lamented the lack of methodological consideration in analytical philosophy, pouring scorn on partakers in debates over realism for wanting to come to what he calls “the sexy bits” (typically, a position that denies or accepts the reality of a given kind of object) too soon. While having wider concerns than that of reaching clarity regarding the use of basic vocabulary, his concerns regarding lack of conceptual clarity at the outset of discussions of realism seem to me pertinent.18 As he puts it, “When law and order break down, the result is not freedom or anarchy but the capricious tyranny of petty feuding warlords” (Williamson, 2006, p. 290). In this case, the disorder is as much conceptual as it is methodological. The warning issued by Frege and Williamson is called for. While the word “object” plays a crucial role in different discussions about realism, the philosophers surveyed above that are devoted to discussions of realism – whether in the philosophy of religion or mathematics – have not shown _____________ 18 Williamson, in his paper entitled “Must do better”, is concerned amongst other things with the ease with which classical logic is given up in defence of antirealism with respect to the past. This chapter locates two crucial tenets that are given up. The first lies in the suggestion that basic inferences such as existential generalisation may have to be relinquished on the disambiguation approach, and the second, offered by Hartry Field below, is the assertion that mathematical sentences purport to refer to numbers but are false because they fail in doing so.

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On All the Things There Are

themselves as models of clarity: Objects can be thick or thin, where only the former are part of the well-determined reality we call “the world”. In short, the world consists of thick objects, not thin ones. Something may be an object, but does not for that reason exist (Parsons). Meanwhile, if you are a Platonist, you do believe that mathematical objects exist (Colyvan). However, if you consult Colyvan for a general account of what realism amounts to, you are referred to works other than Colyvan’s. Finally, as in Burge’s characterisation of Frege, we may be relaxed Platonists when it comes to numbers. In addition to all this, there have been a variety of ways in which attempts have been made to disambiguate the word “existence”. In such an intellectual landscape, the insistence on clarity coming from Devitt, Wagner (cited above) and others carries little force: The distinctive thing about what has been called “realism” until recently has been a view about the nature of the world, not about the nature of language or thought. […] Existence is a fundamental and intuitively clear notion that stands in no need of explanation. (Devitt, 1997, pp. 40, 53)

The relevant words have been used to such an extent that the illusion has been created that we are all in the know about what they mean. When they are used by participants who see no need to disambiguate, little work is done to clarify the relevant meanings. Realism is simply the view that there are objects of certain kinds. When we look for explications of what an object is, there is often precious little on offer, which makes it hard to determine whether various positions effectively disagree or whether they in fact speak past each other. Frege suggested that we overcome such a hurdle by offering examples that illustrate the use of the relevant scientific terms. This appears to have been done in more prominent cases, where the meaning of “object” is provided – a meaning that is presumed focal or otherwise in some way paradigmatic – by pointing to medium-sized physical objects like tables and chairs and accompanying the gesture with exclamations like “These are objects – this is what I mean”. W.v.O. Quine seemed to provide just this kind of illustration at a late stage in his thinking: “Bodies are assumed, yes; they are the things, first and foremost. Beyond them there is a succession of swindling analogies” (Quine, 1981, §2). Michael Dummett at one point expresses himself in similar fashion as he introduces demonstrative reference as a paradigm case of reference, and then goes on to suggest a breakdown in the analogy with singular terms referring to a certain class of abstract terms.19 Yablo (1998), cited above, offered a similar priority to medium-sized, physical objects, while Maddy (1990) bases her defence of _____________ 19 See e.g. Dummett (1981, chapter 14).

Being Too Benevolent

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realism in relation to mathematical entities on the existence of sets of physical things. Maddy took one of the main strengths of her position to consist in the fact that sets of medium-sized, physical objects can fall within the field of vision and as such be causally efficacious in generating beliefs. As we saw, Frege also used the example of a big chunk of matter – the Earth – when wanting to impart to his readers an example of an object, the objecthood of which few would contend. The crucial difference is that while Frege relied on this merely as an heuristic device while working with a somewhat sharper concept of an object (one we shall explicate and refine in chapter 2), some of these more recent thinkers have come to rely heavily on a picture that is by no means exhaustive and, in itself, of little clarificatory value. In sum, when applying the charity that Frege recommended, it would seem that writers rely on a material and spatial picture of what an object is – a view of objects also suggested by the frequently used expression “objects, out there”. Let us consider a specific case of this conjuring trick – Hartry Field’s – one that can be seen to smuggle into a given discussion a certain concept of an object. To appreciate his position, reflect on the following sentences: – There is a prime number that is larger than 17. – There is a car that is bigger than the Mascot Mini. – There is a planet that is bigger than the Earth. The sentences appear structurally identical, we take them to be true, and consequently – ceteris paribus – they should all be taken to be sentences that are true of objects and say of them that they stand in a certain relation. For instance, the existence of the number 23, a Range Rover and the planet Saturn make the three sentences true. However, many are reluctant to accept the first statement as making a claim about anything that is properly considered real. But then, why favour the two latter sentences and in this way allow the existence of cars and planets, while saying that the number 23 and prime numbers in general do not exist? This burden of explanation – alongside the nominalist’s motivation to carry it – received a clear formulation in a classic article by Paul Benacerraf: Two quite distinct kinds of concerns have separately motivated accounts of the nature of mathematical truth: (1) the concern for having a homogenous semantical theory in which semantics for the propositions of mathematics parallel the semantics for the rest of the language, and (2) the concern that the account of mathematical truth mesh with a reasonable epistemology. (Benacerraf, 1973/1983, p. 403)

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The nominalist’s motivation typically has its source in emphasising the latter demand.20 Like Plato’s notion of a form, Platonism about numbers is taken to be suspect in so far as numbers are regarded as somewhat otherworldly. They are abstract and so do not causally interact with the single, supposedly all-embracing, spatiotemporal system.21 While the challenge was originally posed as a matter of giving a causal account of reference to, and knowledge of numbers, the alleged demise of causal theories of reference22 has resulted in a rephrasing of the challenge by Field: Benacerraf’s challenge – or at least, the challenge which his paper suggests to me – is to provide an account of the mechanisms that explain how our beliefs about these remote entities can so well reflect the facts about them. […] The idea is that if it appears in principle impossible to explain this, then that tends to undermine the belief in mathematical entities (Field, 1989, p. 26. My emphasis)23

The challenge has become one of being accountable to the reliabilist account of our knowledge of numbers. When working mathematicians accept a statement as true, it is very likely to be true – how is that if not because of the existence of mathematical objects that are being tracked by the mathematician? As Field (see Field 1989, p. 239) places the challenge: How are we to give an account of mathematicians’ capability of tracking supposed mathematical facts so well? To avoid having to say that there indeed are trackable facts of the matter – facts that we here take Field to hold would include the existence of objects – Field tries to rephrase parts of mathematics in terms of space-time points, while taking it that the sentence “there is a prime number between 10 and 20” is, in fact, false on account of its failing to refer to anything. In dispensing with numbers in this way, he confronts the one argument for realism about numbers that he takes seriously: the suggestion that, because they are indispensable to our best scientific theories, they should be counted as real. Here follows one way of _____________ 20 Considerations of ontological parsimony are another widespread motivation for wishing to deny the existence of various abstract objects. 21 See e.g. Armstrong (1997, pp. 4–9) for an example of this line of reasoning. 22 Alvin Goldman originally endorsed the causal theory as a response to Gettier-style challenges to the analysis of knowledge as true, justified belief. He largely abandoned it in the mid-seventies in favour of reliabilism. When Steiner (1975) attacked Benacerraf’s challenge by means of an attack on various causal theories of knowledge, Hart, in a review of Steiner, replied that we should not be too hung up on “superficial worries about the intellectual hygiene of the causal theory of knowledge when the real problem is that of naturalizing the epistemology of mathematics” (1977, p. 125f.). 23 Frege, in describing numbers as reason’s nearest kin, put the spatial analogy to quite different use than Field does, when he describes numbers etc. as remote.

Being Too Benevolent

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formulating central features of Field’s line of argument, as found in Field (1989, p. 230f.): 1) Mathematicians make true propositions that represent facts. 2) As a consequence of (1), there are mathematical objects, such as the number two. 3) Given our best understanding of epistemology and the nature of the supposed mathematical objects, there can be no access to such objects, and thus, we lack justification in speaking about them. 4) With no justification forthcoming, we should take (2) to be false. 5) Given that (2) is false, mathematical propositions are false across the board, and so, (1) is false. This kind of account begins with what is taken to be a purely ontological notion, often formulated with the typical spatial connotation that ultimately helps mystify the existence of abstract objects: “Let us assume that there are some objects, out there, independently existing”. Then the explanation proceeds to explain the meaning of words and sentences in terms of these objects: “When the mathematician says the things he does, he is speaking about the objects, the existence of which we just assumed”. Finally, the account concludes with an epistemologically based, stark challenge: “Given what we know about reference and knowledge, how can we explain what we have just assumed – that mathematicians refer to abstract, mathematical objects?” Supposedly, we can’t, and consequently, they don’t exist. If that is the way that we are thought to progress – and the frequent mention of ordinary physical objects in the writings in philosophy of mathematics suggests this – more problems immediately present themselves. One of them arises from simply questioning the generalisation of the epistemological constraints as they pertain to the object of the type I can bump into when I am in my office or detect with various scientific instruments. Accepting these constraints amounts to giving the game away before it has even started: If this is what we mean by “object”, no one would ever have thought that there are numbers or gods – except, of course, the kind of gods that are made of wood, stone and other such materials. It is certainly worthwhile to question the generalisation of a certain kind of epistemology and its concomitant intuitions and convictions regarding what there is.24 Likewise, we should question the Quinean and Dummettian view that an analogy between “object” used about physical _____________ 24 This has played a major role in recent defences of Fregean number-theoretic Platonism. See for instance Wright and Hale (2001, chap. 7) as well as Øystein Linnebo (2006).

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objects and other uses “dwindles” and ultimately “breaks” at a certain point. Even if such dwindling took place, language about numbers would be on a surer footing than, say, people. As borderline cases in applied ethics suggests, people have less precise criteria of identity than the natural numbers, and numerals frequently feature in paradigmatic examples of truths. While we shall have recourse to probing these themes in the chapter that follows, the crucial conjuring trick is found in the first and second step of the argument. Here, the apparently innocent word “object” is relied upon and allowed to import assumptions about what kinds of things there are. These assumptions then conflict with other demands one may make in order to call something real. This lack of clarity and the lack of elucidation of the key concepts at stake should lead us to restrict the charity that Frege thought necessary at the beginning of any investigation – be it geometrical, arithmetical, or in this case, ontological. There simply isn’t enough elucidation going on for there to be a general agreement that can serve as a basis of a meaningful discussion. For this to take place, one needs to conduct a meta-ontological discussion. That is, one needs to agree on what is meant by “object” in the first place.

The Task Ahead Let us sum up what should emerge from this chapter. We have located a common question in two different areas of enquiry that can be phrased “Is there an x?” or “are there x’s?” or “is x real?”. We recognised that for this, and indeed any enquiry to proceed, there must be some agreement on the language that is being employed. When there is something we cannot or have not explicated, we must rely on a meeting of minds. While charity is usually a good method, we have found reason to question any meeting of minds in the two areas under scrutiny when it comes to the central notion of an object or that of existence. While we found confirmation – perhaps most succinctly with Poincaré – of the Aristotelian intuition regarding the variety of what exists, and consequently the possible variety of the meaning of “existence”, “object” and “real”, there has been too little effort to say what this variety is a variety of. That is, if numbers or God exist in some different sense of that word, we are entitled to ask what the relation is between these different senses. Emphasising the differences was dubbed the “disambiguation strategy”, and I suggested that, while faithful to certain linguistic intuitions about the variety of the things our language purports to be about, the strategy renders a debate about realism futile on the grounds that it generates endless fragmentation. If all we do to explain

The Task Ahead

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the reference of a word is to say that there is an object in the world that corresponds to it, we should accept Wittgenstein’s laconic characterisation of the exercise: “‘A reality corresponds to the word “two”’. – Should we say this? It might mean almost anything” (Wittgenstein, 1976, XXVI). Let us for now observe that the concern that has been raised here is not without precedents both in logic and theology. The concern finds expression in TLP: We may not first introduce [primitive ideas of logic] for one class of cases and then for another, for it would then remain doubtful whether its meaning in the two cases was the same, and there would be no reason to use the same way of symbolizing in the two cases. (In short, what Frege (“Grundgesetze der Arithmetik”) has said about the introduction of signs by definition holds, mutatis mutandis, for the introduction of primitive signs also.) (TLP 5.451)

Wittgenstein is likely to have had in mind Bertrand Russell’s and Alfred N. Whitehead’s practice of introducing the operators “and” and “or” more than once, at the cost of the unity of logic. One introduction would have been made in connection with quantificational logic, another for propositional logic. Frege was concerned with the practice of piecemeal definition of symbols for different kinds of numbers, leaving the mutual relations between the symbols unaccounted for. These concerns very much mirror the ones I have raised here about attempts at a piecemeal understanding of the expressions “there is”, “object” and “existence”, which are often understood to be a primitive and basic notion in logic. We saw how Parsons and Devitt explicitly subscribe in their different ways to the view that the relevant terms are basic, and Putnam has explicitly described these terms in ways reminiscent of the Tractarian complaint: “[T]he logical primitives themselves, and in particular the notion of object and existence, have a multitude of different uses rather than one absolute ‘meaning’” (Putnam, 1990, p. 71). Frege took the piecemeal definition of a sign as an indication that it was halfway known, halfway unknown. He compared such a use of the sign to operating in a kind of twilight zone with the goal of making a conjuring trick – and he did not consider this trick to be possible purely when seeking to define “equality”.25 His concern was that one sign was being used for what were in effect different symbols, and he in fact encouraged the introduction of new signs as an aid to clarify the mutual _____________ 25 See Frege (1893/1997, §67). In Philosophical Investigations, Wittgenstein used Frege’s analogy, where the decisive moment in the conjuring trick consisted in making basic assumptions about mental states that might lead us to deny their existence.

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On All the Things There Are

relation of the symbols.26 Introducing different signs is only the first and philosophically insignificant part of the job. The importance lies in giving an account of the newly introduced sign, including its relation to the meaning of other relevant signs. While the history of philosophy and theology is littered with examples of attempts to insist that language, including the use of “existence”, is of a certain and different nature when applied to God, we should also note how this view was confronted in the writings of theologian Karl Barth: We are speaking of the human knowledge of God on the basis of this revelation [of the knowledge of God] and therefore of an event which formally and technically cannot be distinguished from what we call knowledge in other connections, from human cognition. (Barth, 2004, II/1 §27)

Karl Barth is unlikely to have had in mind exactly the kind of problem we have outlined in the present chapter. Nevertheless, it is significant that in theology we see the same insistence on a level playing-field – here called human cognition as such – when it comes to language about God, and we may for present purposes take the formality and technicality that Barth mentioned to include the basic kind of logical vocabulary that we have surveyed here. In short, the language with which we speak about God is logically no different from the language with which we speak about tables, electrons, football matches and all the rest. This chapter leaves us with the need for a clear concept of an object – a meta-ontology – with the following desiderata: 1) The concept should be global and so not restricted to any particular region of language, characterised by being about a particular (kind of) object. Restricting your notion of realism to the kind of object you are interested in will make your position irrelevant to others. 2) The concept of an object must leave cases out – the concept must in this way be informative. Ideally, the concept and its implications should be amenable to an account of the different philosophical intuitions and convictions that we have surveyed. They are: _____________ 26 “Too great a horror of new signs, leading to the old ones being made to carry more meanings than they can bear, is far more damaging than an overfertile delight in invention, since anything superfluous soon disappears of its own accord, leaving what is of value behind” (Frege, 1979a, p. 27). This is a piece of advice that could appear to have been followed by, for example, Chihara (1990) and his notion of a constructability quantifier.

The Task Ahead

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3) The Aristotelian suggestions that “existence” comes with different meanings as applied to different kinds of objects. 4) Insistence on ordinary, physical objects having a paradigmatic status as instances of objects. 5) In addition to (2), the concept of an object does not result in a wildly counterintuitive ontology. I will conclude by flagging what I take to be Frege’s and also Wittgenstein’s answer to the tendency to disambiguate basic notions, while substantiation of this solution must await the treatment of the topics the solution includes. The answer is short and lies in the proclamation that “We cannot give a sign the wrong sense” (TLP 5.4732). As such, that may seem like an unjustified statement of what we could call linguistic luck, but it features as an essential part of Wittgenstein’s early philosophy as well as Frege’s remarks on problems he encountered in his discussion of logic. In TLP, Wittgenstein holds that “[logical syntax] must admit of being established without mention thereby being made of the meaning of a sign” (TLP 3.33). The general theme is that of trying to speak about the meaningful parts of our language, and possibly laying down rules for their use. Wittgenstein’s observations are of relevance to the present chapter, in so far as we see the continued attempt to prescribe meanings for “object”, “there is” etc. The insight that Wittgenstein took to be of fundamental and profound importance found its first expression in a letter to Russell, where Wittgenstein suggests that “a correct theory of symbolism must render all theories of types superfluous”. What Wittgenstein proposed in the place of a theory of types were the early “caretaker slogans”: that propositions of colloquial language are logically completely in order; that logic must take care of itself and we only need to recognise how language takes care of itself – we cannot make mistakes in logic.27 However, such remarks introduce notions of logic, syntax and symbolising that are alien to the discussions we have been surveying in the present chapter. The following chapters will attempt to make clear the relevance of Wittgenstein’s fundamental insights about logic and language, and in this case, their source in Frege’s meta-ontology. In the next chapter, I will fill the void that has been suggested in this chapter by introducing and defending a relatively clear-cut notion of what to understand by the word “object” _____________ 27 The conclusion of this paragraph compounds formulations from parts of TLP 5.5563, NB 2 / TLP 5.473 and NB 43. The letter to Russell of 16.1.1913 can be found in NB 121 f.. I take one predecessor of the caretaker slogans to be Frege’s remark: “I do not want to say that it is false to say concerning object what is said here concerning a concept; I want to say it is impossible, senseless, to do so” (Frege, 1892/1997a, p. 200).

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On All the Things There Are

as used in a discussion of what there is. This account will be informed by Frege’s context principle, which in turn influenced much of Wittgenstein’s thinking about logic, syntax and symbolising – the topics of subsequent chapters.

Fregean Meta-ontology Introduction: Reversing Ontology Gödel is frequently considered a prime example of someone who, like Frege, had fallen prey to a philosophically untenable position: Platonism. He believed that speaking about the existence of a realm of abstract objects was a good way of characterising what his mathematical practice was involved in. Anachronistically, he is then taken to have responded to the challenge of offering an account of our epistemological access to numbers by suggesting a certain kind of intuition – which he understood as being analogous to perception – that explains our cognitive contact with such objects. The existence of such a faculty is then easily questioned and rejected. Consequently, the case is made that Gödel has after all given us no good justification for believing in the existence of mathematical objects.1 However, a reading of Gödel (1947/1983) suggests that things were the other way around: Gödel believed in the existence of a realm of mathematical objects for mathematical reasons. He wanted to pursue the question of the continuum hypothesis independently of its undecidability on the basis of the standard axioms. He did not first assume that there are – or make a tentative posit of – objects and then go on to justify this assumption by reflecting on epistemological issues of access to such things. Rather, he had relevant and in this case scientific reasons for thinking that the question was after all decidable and could be solved. These reasons related to ways of extending the standard axiom system in a reasonable manner, along with an appeal to the notion of a set and its fruitfulness in mathematics and in physics. In other words, the dog of scientific reasoning and linguistic practice was wagging the tail of ontology. Though Gödel expressed views on epistemology, he arguably did so naively and ultimately his view of such matters had little relevance to the realism he defended. What came first in Gödel’s work and in his philosophical understanding of it was not the existence of mathematical objects, but the use of mathematical language and reasoning to solve various problems. This direction of thinking in _____________ 1

See e.g. Chihara (1982), or Shapiro (2000), for this understanding and criticism of Gödel.

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matters of ontology, taking its start in the relevant language rather than in the world, sits well with the overall drift of a method in ontology that is based on Frege’s context principle. In what follows, we will elaborate the relevance of the context principle for ontological enquiry in general. Though the setting in which we explore this principle for the most part remains the philosophy of mathematics, chapter one has made clear how it is essential that our approach should in no way be thus restricted. That it is not so limited is something that both Frege and his defenders, such as Bob Hale and Crispin Wright, have emphasised. The principle was intended and employed by Frege as an absolutely general principle regarding language and world. In fact, it was essential to Frege’s argumentative strategy that the concept of object should not be restricted but should have universal application, in so far as he argued by means of comparison with otherwise quite distinct regions of language.2 After the introductory presentation of the context principle below, the present chapter will to a great extent proceed by means reminiscent of a scholastic disputatio, albeit in reverse order: I shall begin by offering what I take to be the right answer regarding the concept of an object, and then go on to consider a range of sed contra. By confronting various criticisms of the principle and the intuitions and convictions that bear on the questions it addresses and the answers it suggests, we should gain an understanding of what the context principle does and does not entail with respect to metaontology. Such an exploration touches on topics in modality, conceptions of identity and other central areas in philosophy. As a consequence, the present chapter can only serve to make plausible and workable the overall approach, while some holes must wait to be filled on later occasions. Nevertheless, we should at least engage certain prominent ways of thinking that run counter to some of the consequences of employing the context principle as a method in ontology. By providing a universal concept of an object, we satisfy the first desideratum that was put forward in chapter 1. We shall then have to explore how it meets the further desiderata, such as non-vacuity and preservation of various intuitions.

The Context Principle and Ontology: The Short Answer Unlike Frege’s argument that numbers are logical objects, his argument for taking them to be objects is at first sight extremely simple. At the most _____________ 2

Frege stresses this in the following introductory remark: “[t]hought is in essentials the same everywhere: it is not true that there are different kinds of laws of thought to suit the different kinds of objects thought about” (FA, p. III).

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general level, the argument is in its nature no different from our methods of establishing that there are other kinds of objects. The reasons why we should take it that there are mathematical objects are as follows: Mathematical sentences appear to refer to mathematical objects. These sentences are subject to norms of correctness, taken to be equivalent to the concept of truth.3 In short, some of these sentences are true. Hence, there are mathematical objects. Anticipating the account of the relevant syntactic criteria that are offered in sections below, the relevant logical appearance of sentences is captured in sentences like these: “Peter is the same as the tennis player who hates himself for being dumber than his older brother”. In similar fashion, we might say something like “7 is a prime number larger than 3 and when multiplied by itself it equals 49”. Words that appear to be about numbers behave syntactically much like words that appear to be about other kinds of objects. In the two cases above, the relevant words – “Peter” and “7” – function in a way that allow them to have predicates ascribed to them, to enter into relations, to feature in statements of identity and to be used with a reflexive pronoun. Number words can be both attributive (as in “there are five horses”) and substantive (as in “the number of horses is five”). While the latter sounds strange to the modern ear, what mattered to Frege at the time of writing Foundations of Arithmetic was that the substantive use was possible across the board while the attributive use “can always be gotten round” (FA §57).4 The latter form is correct for some numbers in Arabic and biblical Hebrew and is preserved in most translations of the shema in Deuteronomy 6:4.5 Frege’s logicism included two separable strands, each supported by its own distinct set of arguments. Firstly, that numbers are objects and, secondly, that they are logical objects. The second strand has given rise to extensive debate: According to a widely shared understanding of the nature of logic, it is not supposed to tell us anything about what there is in the world. The much discussed equivalence relations that Frege introduced to _____________ 3 4

5

Typically, the slightly stronger claim is made that some sentences actually are true. Even if we only uttered false sentences regarding certain objects, we would still be able to infer truths from these, and so this position is only very slightly stronger. At a late stage of his career, Frege became dissatisfied, not with his emphasis on syntactic criteria but with the analogy he had suggested between language about objects like planets and language about numbers. See his somewhat dismaying diary entries for March 1924 in Frege (1979b). “Hear, O Israel: The LORD our God, the LORD is one”. (Deut 6:4, NIV). While thinkers like Maimonides and Aquinas took the shema to mean that God is absolutely simple, we shall in the following explore how it was uttered in a context where equivalents of the sign “God” were used as a general term, a sortal.

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give an account of how numbers were given to us by merely logical means, appear to use logical principles to generate referring terms in true sentences. The general principle that Frege employed in connection with the first of the two elements was that syntactic categories should have primacy over ontological ones. According to this approach, we can determine that, for example, numbers are objects – whether logical or not – by having the notions of object and concept be derivative of the syntactic notions of singular term and predicate. While the Fregean defences of the two strands are often conflated, it is important to separate them. Frege clearly did, as in the presentation he offered in FA he used syntactic criteria to reach the standpoint that numbers are objects before he suggested the equivalence relation as a way of clarifying how these objects are given to us in a way relying only on notions that he considered to belong to logic. The context principle is Frege’s second basic principle in FA: “[N]ever to ask for the meaning of a word in isolation, but only in the context of a proposition” (FA, p. X). This is repeated in, among other places, §46, §60, §62 and §106 of the same work. As such, this is an injunction of a very general and unspecific character, and Frege was not the first thinker to be somehow guided by it. He took it to be of crucial importance in avoiding both psychologism and physicalism in the philosophy of mathematics, and in its first mention in the body of FA Frege emphasises that its application is in no way restricted to arithmetic. Before him, George Berkeley had mentioned the principle when confronted with problems he encountered when trying to think about the mind. Something that on the surface is very similar to Frege’s context principle is formulated in Jeremy Bentham: “By anything less than an entire proposition, i.e. the import of an entire proposition, no communication can take place” (Bentham,1843, p. 188). Needless to say, the principle has served to shed light on quite different matters in the hands of different thinkers. Looking forward in time, the context principle crucially informed the entirety of Wittgenstein’s authorship.6 Versions of it are repeated in TLP, and while Frege was intent on de-psychologising arithmetic, much of Wittgenstein’s later writings have been seen, following Stanley Cavell, as a de-psychologising of psychology, in so far as he explored the wider context of psychological language in order to combat various misconceptions regarding the nature and knowledge of mental states. At the most general level, this understanding of Wittgenstein’s later writings is to some extent borne out by his reference to Frege’s context principle in Philoso_____________ 6

For a helpful survey of this, see Reck (1997), instructively entitled “Frege’s Influence in Wittgenstein: Reversing Metaphysics via the Context Principle”.

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phical Investigations §49 in connection with his introductory confrontation with the Augustinian view of language. The confusion we explored in the previous chapter can be seen to arise against the background of Augustinian thinking. Integral to Wittgenstein’s Augustine was that the meaning of words and their corresponding objects was taken to be a matter of connecting single words and objects, respectively considered apart from their setting in propositions and their worldly correlate, states of affairs. While such a view might have an initial plausibility with respect to medium-sized physical objects, it will make much of our linguistic practice appear mysterious, in so far as the objects it apparently refers to are very unlike material objects. The Fregean inspiration is also suggested by Wittgenstein’s concluding comparison between his own Philosophical Investigations and an investigation that “might deserve the name of an investigation of the ‘foundations of mathematics’” (Wittgenstein, 1958, p. XIV). Wittgenstein suggested that such an investigation should not contain actual computations, but clear up conceptual confusions. The comparison is puzzling, in so far as there is no explicit recognition of the Fregean debt with respect to method or the use of the title of Frege’s most philosophical and least logico-mathematical work – the work that offered the context principle fundamental importance. In FA, the context principle was introduced to safeguard against psychologistic theories of meaning, while the body of the same work clearly employed the principle as suggested above: as a guide for establishing what objects there are in the world and, not least, for clarifying why we say so. As in so many cases of trying to understand Frege’s theoretical vocabulary, there is disagreement. In this case, commentators have laboured over the fact that Frege in FA used “Bedeutung” both before and after the introduction of his famous bifurcation of conceptual content into sense and reference.7 For present purposes, all we need is to be able to refute, for example, Skorupski (1984, p. 241) when he claims that Frege could never have meant “reference” when using “Bedeutung” in FA. Skorupski’s standpoint is motivated by epistemological concerns such as those mentioned at the outset of the present chapter. The epistemological challenge in its present form was not one that seems to have concerned Frege a great deal. Contrary to Skorupski, I take it as given that Frege intended to employ linguistic criteria to help establish that numbers are _____________ 7

Ernst Tugendhat (1970) was one of the first to raise the problem about the meaning of “Bedeutung”. The translators of Frege’s 1achlass, Peter Long and White (1980) had an exchange with David Bell (1980) over the proper translation, while the problem more recently has received attention in an exchange between Hale (2001) and Potter and Smiley (2001) concerning the ontological implications of Frege’s employment of equivalence relations.

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what he calls self-subsistent objects, and there are a number of passages that clearly suggest this use: In connection with a rough characterisation of linguistic criteria for singular term-hood, Frege insists that “The word ‘one’, as the proper name of an object of mathematical inquiry, does not admit of a plural” (FA, §45) while in FA §61 he mentions the Earth as an example of an object. As Frege points out, this is surely a different kind of object than the number one, but both are objects nonetheless. These remarks are all intertwined with formulations of the context principle, and I consider it beyond doubt that whatever other roles the context principle play in Frege’s thinking about meaning, it certainly plays a role with respect to reference.8 We get a clearer picture of the drift of the context principle and its relevance to ontology from some of Michael Dummett’s early work. He was the one to give the context principle its name and gave a clear exposition of one of its significant implications: But the [context principle] is meant to have relevance to philosophical, not to everyday discussions of whether a given word has reference… We ask whether “the number 28” stands for an object, but we are not concerned with “28” rather than “29”. But what then are we asking? We are on the verge of introducing a philosophical sense of “exists” which is distinct from the ordinary application of “there is…”. Admittedly we do not ordinarily say that there is such a number as 28; but we do say that there is a perfect number between 10 and 30 and that that number is 28. But all the same, we want to add, the number 28 does not exist (in the philosophical sense). One of the consequences of [the context principle] is the repudiation of this philosophical existence. If a word functions as a proper name, then it is a proper name. If we have fixed the sense of sentences in which it occurs, then we have done all that there is to be done towards fixing the sense of the word. If its syntactical function is that of a proper name, then we have fixed the sense, and with it the reference, of a proper name. If we can find a true statement of identity in which the identity sign stands between the name and a phrase of the form “the x such that Fx”, then we can determine whether the name has a reference by finding out, in the ordinary way, the truth-value of the corresponding sentence of the form “There is one and only one x such that Fx.” There is no further philosophical question whether the name – i.e. every name of that kind – really stands for something or not. (Dummett, 1978, p. 40f. Dummett’s emphasis)9

Dummett’s reference to the ordinary in the passage quoted above mirrors the suggestion in FA §46 that we should “…consider number in the context of a judgment which brings out its basic use”. Immediately before the passage quoted above, Dummett appears to express his embarrassment on behalf of much philosophy, in so far as the principle reduces a range of _____________ 8 9

See also FA p. VII and §45. We shall return to the epistemological concerns below. See Dummett (1981, p. 496f.) for very similar formulations.

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traditional, “deep” philosophical questions to the ordinary and sometimes banal. To the extent that he rejects the suggestion that there is a meaning of “there is” that differs from the quite ordinary one, so the answers to a range of philosophical questions become similarly ordinary: – Do prime numbers exist? – Yes they do. For instance, there are four of them between 10 and 20. TLP was fundamentally informed by the context principle, and awkwardness similar to that expressed by Dummett is suggested in Wittgenstein’s concluding remarks on philosophical method despite the fact that they concluded a philosophical engagement with more questions than are addressed here.10 Wittgenstein did not expect that sticking with the propositions of science, as (at a very basic level) we did above, would satisfy someone attempting to engage in what Wittgenstein disparagingly refers to as metaphysics. What Dummett is aware of is that when we ask questions in ontology we are not supposed to be satisfied with, say, simple arithmetical assertions or for that matter, the message and apparent ontological implications of a sermon. We are after something deeper and more significant. Put in this simple way, the argument for taking numbers to be objects offends a number of intuitions and convictions and against more elaborate argumentative strategies in debates about realism that we shall address in what follows. It might seem that there are indeed convincing reasons why we should not accept the ontological consequences that the context principle suggests. Moreover, empirical linguistic evidence has often been taken to suggest that we should not accept the context principle itself. This linguistic evidence continues to exert a great influence in debates regarding the context principle and ontology and will be considered below. Since Dummett’s early presentation, the approach to questions of what there is that this meta-ontology embodies has been at the receiving end of a considerable amount of name-calling. Thus, it has been dubbed “deflationary” and has been described as being in the business of providing a “short answer” (see Arthur Collins (1998)). Field (1989) thinks this is “Platonism for Cheap”, and Steven Reynolds adjusts his own position on realism to avoid what he calls a “far too quick dismissal of antirealism” (2006, p. _____________ 10 “The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other – he would not have the feeling that we were teaching him philosophy – but it would be the only strictly correct method” (TLP 6.53). We shall return to this passage in chapter 5.

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485). Cian Dorr (2008) thinks the approach is superficial and takes the Dummettian point to be a case of “principled incomprehension” of his own “fundamental” approach to ontology. Such characterisations reflect a certain dissatisfaction with the implications of the context principle. However, as I set out to argue in this chapter, the short or deflationary answer is in its essentials right, though the answers to philosophical questions that are raised in response to the ontological implications of the context principle are not necessarily quite so brief. If Frege and others informed by the context principle are right, significant parts of our philosophical questioning cannot not have this certain kind of “philosophical” depth to them that somehow reaches deeper than our ordinary or scientific language. Of course, the belief that there is after all a further, deep question to be asked has not ceased to be influential-al. Accordingly, we shall continue our exposition of the context principle by looking at one recent attempt at giving expression to a distinction that is supposed to capture what those disappointed metaphysicians are after: that some kind of meaningful question about the (real) existence of numbers remains after we have established that there is a prime number between 10 and 20. In other words, that settling the mathematical and linguistic question is somehow insufficient for settling the ontological question.

Against Sufficiency I: Real, External Realism? The short answer runs counter to an essentially Kantian conviction. This has shed its original epistemological garb and found expression with regard to ontology in the writings of, amongst others, Hilary Putnam. While his views have changed considerably over the years, he did for a period defend a position called internal realism. Besides giving expression to the quantifier variance view – that there are different meanings of “object” and “exists” – that we also saw expressed in connection with Putnam’s writings on the philosophy of religion, the position gives expression to the view that, even though a range of singular terms under scrutiny seem to be in perfect working order and feature in sentences that are taken to be true, an intelligible question remains as to whether the singular term really refers to something. To paraphrase Kant, the question would be whether the singular term does anything beyond naming a thing-for-us, while the thingin-itself would remain elusive. This latter idea of a thing-in-itself is supposed to be put to use in raising the external question. After having settled that a certain range of things are real in the sense of being at the referring end of singular terms, the external question remains that gains its

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meaning from something different than the reality we ascribe to a thing that is named in true sentences.11 Putnam characterises a position he calls externalism – or external realism – by outlining a view according to which the world consists of a fixed totality of objects existing independently of any mind. According to this position, the world is describable in one way only, and this description would take place by making words correspond with things and sets of things. In contrast with this position, he poses his own internal realist position. What is most relevant to our concern is that, according to Putnam’s internalism, “what objects the world consists of is a question that it only makes sense to ask within a theory or description” (Putnam, 1981, p. 41, my emphasis). With this formulation of the Kantian intuition Putnam is committed to offering an explanation of the idea of remaining within a theory. When we consider Putnam’s use of language in formulating his position and what he takes to be its counter-position, we will at the same time have the opportunity to consider at least one expression of the Kantian idea in its linguistic clothing. In formulating the distinction, Putnam maintains: … [o]bjects do not exist independently of conceptual schemes. We cut up the world into objects when we introduce one or another scheme of description. Since the objects and the signs are alike internal to the scheme of description, it is possible to say what matches what. (Putnam, 1981, p. 52)

Meanwhile, Putnam insists that there is no external, language-independent view of the world available to us. Two criticisms should be levelled against the formulation of this distinction. Firstly, we should ask in what the likeness between sign and object consists? The word “rabbit” does not look or sound in any way remotely like a rabbit. Plato’s Cratylus discusses whether word meanings are based on convention or nature. According to the latter view, words have their meaning from a certain likeness with what they signify – they are fundamentally onomatopoeic. “Splash” is an example, and words for animal noises are similarly suited. Such phenomena may be of relevance for studies of the evolution of language. However, there is no such likeness in the case of the word “rabbit”, so this can surely not be the likeness that Putnam suggests. By saying that two things are alike, we require a respect in which we can compare them, and it is not clear from Putnam’s writings what could serve as a useful concept for this role. _____________ 11 The reader might think that Carnap’s distinction between external and internal questions should have received attention. It is arguably more influential, but as it has received suitable treatment in Hale (1987), I refer the reader to his writings.

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The second criticism I take to be the more damaging. Remember that, in order to be able to formulate and employ Putnam’s distinction between internal and external realism, we must be able to answer the following question: “how does one stay within a scheme of description and ensure the possibility of stating the required match between word and world?” This is the question that is most pertinent to our present concern, as an answer to this question would amount to a formulation of the Kantianinspired idea that there is some kind of further question to be asked after having provided the short answer to the question of the existence of numbers, sets, God or whatever our interest is. Putnam’s answer is suggested in the following passage: Indeed, it is trivial to say what any word refers to within the language the words belong to, by using the word itself. What does “rabbit” refer to? Why, to rabbits of course! What does “extraterrestrial” refer to? To extraterrestrials (if there are any). (Putnam, 1981, p. 52)

According to Putnam, the way to stay within a language is to use a sign. One might add, uncontroversially, that this is done in accordance with the conventions found in a particular community of other language users and so is subject to the constraints this community presents with respect to the correct use of the sign. Supposedly, within these confinements, we can say that a sign corresponds to an object. However, Putnam does not remain faithful to his own suggestion. The appearance of instances of the signs “rabbit” and “extraterrestrial” in his own reasoning does not suggest that they are being used in any ordinary, conventional way. Rather, the inverted commas suggest various kinds of appearance of the signs, none of which is available to Putnam if he is to remain true to his own suggestion regarding the use of a sign: One suggestion is that Putnam lets the sign “rabbit” feature in a setting that relies on a distinction between languages, as when one attempts to work out a truthconditional theory of meaning along Davidsonian lines. The distinction is typically that between an object-language and a meta-language. However, such uses taken from the hinterland of various theories of meaning and truth immediately run counter to Putnam’s intention of remaining within a language. Alternatively, the suggestion might be that language is being used to mention a part of that very language. But this only means that the bit of language in question is exactly what is not being used. Rather, it is typically being considered qua its appearance as a sign. That Putnam is unfaithful to his own suggestion about use of words is clear from the fact that, strictly speaking, his sentences are not well-formed. If the sign “rabbit” was used as it ordinarily is, the string:

Against Sufficiency I: Real, External Realism?

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Rabbit refers to rabbits would simply be ill-formed, unless the first occurrence of “rabbit” is understood to be the proper name of a specific rodent, caught in the act of pulling off a remarkable linguistic feat for such a creature. Whether rabbits refer to rabbits is – in the first instance – a question for the linguistically oriented zoologist, not the philosopher. We have seen how Putnam wanted to rely on the use of a sign to effect a distinction between internal and external realism, but then went on to employ the sign in a way that does not accord with the common usage he otherwise emphasised. To say that “‘Rabbit’ refers to rabbits” simply does not amount to the suggested ordinary usage of the first sign in that sentence. This common usage, in turn, was to serve as an explication of the difference between an external and internal perspective. If in this way no clear meaning has been given to the idea of remaining within a language, the opposite position suffers equally, and we should conclude that at least this attempt at formulating the supposed deep, Kantian-inspired philosophical question is compromised. We might add that all that remains is the ordinary use of words, with which we can quite successfully speak about different kinds of things. It would be premature to conclude on grounds of this section that any attempt at giving expression to the Kantian intuition about two different meanings of “existence” or “object” are doomed to fail. As suggested by the concluding remarks of TLP 6.53, all we should do is give careful consideration to the signs used in attempted metaphysics. The suggestion is that, when we do so, it will become clear that the signs cannot perform as the “metaphysicians” think they can. This method appears to have faithfully delivered in our treatment of Putnam. Following Dummett, we suggested that any sentence like “but are there really numbers?” only appears to make sense while in fact being somehow defective. This would be too strong, as other things than the linguistic version of Kant’s view may be expressed by the phrase “really”. To bring out the difference between Dummett’s target and possible collateral damage, we can contrast two settings in which the question can be put. In the first setting, we can imagine a school child being told the following: There is a prime number between 10 and 20. Not having the full grasp of the concept of a prime number or sufficient computational skills, the child asks: But is there really such a number between 10 and 20? In such a context, given reasonable assumptions about the school child, what is being asked is a mathematical question, and a mathematical answer

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with its background reasoning should ultimately suffice. The second context is that of a philosopher with a sufficient grasp of the relevant concepts as well as sufficient computational skills and otherwise under ideal cognitive conditions asking the same question. Whatever question he is asking, it will not be answerable to his satisfaction by mathematical methods. Given the somewhat censorious view of philosophy that is suggested by Dummett, he is not asking a philosophical one either. For now, presenting the view of philosophy with the edge that Dummett often does, the philosopher is in such cases not deserving of any other answer than the one we give the school child. Finally, we should note how instances of the signs “real” and “really” do have different, quite legitimate meanings in various contexts. As in the example above, “real” will serve as an epistemological marker of uncertainty on behalf of the listener. In the case of prime numbers, it might be used as part of a request to redo a calculation. With a much more difficult computation than the one suggested above, such a usage could easily be imagined. It is more frequently used in empirical matters, and Dummett’s contention that such a question is not a philosophical one is clearer here: Whether there really are polar bears in Scotland is a question of existence settled by entirely non-philosophical methods. Further, the marker is used when describing a matter of judgment between different representations of the same subject matter, where advances in our interpretation of representations will lead us to say something about how the world really is. An example is this: “The lines in the Müller-Lyer illusion are really of the same length”. Again, being settled by simple methods from geometry, this is not in the first instance a philosophical question. The idea that “real” frequently functions as an epistemological marker, is more general and can encompass the suggestion offered by Reynolds (2006), according to whose analysis, “real” primarily signifies a switch between reporting other people’s representations and reporting one’s own. Finally, we shall encounter yet another suggested usage of “real” in our treatment of analysis below. We need not commit ourselves to there being one sense of “real” in so far as it finds use outside discussions of ontology. Other uses of “real” are close in meaning to “genuine”, both in “a piece of genuine gold” and “I really meant what I said – I wasn’t joking”. None of these legitimate uses are of relevance in the present context.

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Against Sufficiency II: Idealism? In an encounter with Fregean meta-ontology and its thesis of syntactic primacy over ontology, Tennant (1987) levels a criticism that is often directed at varieties of antirealism that in various ways impose restrictions on what there is that are largely based on epistemological limitations. In short, the objection amounts to an accusation of endorsing a version of idealism. The objection is simple and convincing, but in the present case, it misses its target.12 Tennant has found the thesis of syntactic primacy to be equivalent to a kind of linguistic idealism. In a treatment of Fregean meta-ontology, he formulates this criticism in the following way: Our nominalist anti-realist might further hold an evolutionary account of mind and graspable meanings that recognizes many kinds of natural objects as existing before any language with names for them did them the dubious honour of confirming them in their existence, or indeed bring them into existence. As I said earlier, names wed language to the world, but they do not beget it. Linguistic idealism, like any form of idealism, is unacceptable to the scientifically minded. (Tennant, 1987, p. 41)

Tennant is ambiguous in the way he describes exactly what the primacy of the syntactic over the ontological amounts to. There is a significant difference between confirming something and making it come about. The difference is important, as it comes to suggest at least one of the ways we might formulate what the difference between realism and idealism is supposed to be. In any case, I take it that the target of his argument is a position according to which objects are there as a cause of – or for that matter, as Tennant describes it, begotten by – names in our language. What is targeted is a kind of spray-paint view of language (the spray) and world, and Tennant draws our attention to its strongly counterintuitive consequences. A general scientific – or common sense for that matter – viewpoint will have it that lots of objects were there before any language-using minds came about to give them a name. To maintain that our syntax should enjoy some kind of primacy over those objects can only invite an incredulous stare. _____________ 12 Besides having been suggested by Neil Tennant, seeing Frege’s view of numbers as of an idealist persuasion has been suggested by Resnik (1979). Resnik ignored Frege’s in this case crucial distinction, introduced in FA §26, between what is “actual” and what is “objective”. What is ascribed “actuality” is, broadly speaking, a matter of causing our sense apparatus to react in some way (see e.g. FA §85 and Frege (1918/1997, p. 76–78).) To Frege, this category does not exhaust what there is.

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This gloss on the thesis of syntactic primacy – that our language should bring rocks and planets into existence – is indeed incredible, and fortunately it is not something a Fregean ontologist has to commit to. He will survey the relevant language in its use and notice that in some cases it does not make sense to speak about coming into and out of existence, while in others it does. Numerals provide a well-rehearsed example. It would simply be a misapplication of number words to perform on them a temporal indexation that was supposed to distinguish them – much like the idea of putting an event into a hole. Put differently, having such a use of number words (e.g. “two yesterday divided by four an hour ago”) would amount to using names that we would be unwilling to equate with our ordinary, a-temporal use of number words. In a similar vein, we might notice cases where words are used specifically in temporal contexts. The Roman Empire rose and fell, and this will again be reflected in contexts where this name is commonly used in true sentences. I take it that where the name is used rightly, it is implicitly indexed to a certain period. This could be made explicit by a survey of what inferences a competent language user would be willing to make from sentences involving “the Roman Empire”. Similarly, the use of some names (e.g. in zoology) will be implicitly indexed to a time when no human language existed. Finally, we might discover that some objects do fit Tennant’s bill. The meaning of names in fiction is arguably determined by a specific language user. One can imagine this dependence being made explicit in cases where the use of a fictional name is being adopted after a period of discontinuation or change of authorship. If I was to write a pastiche featuring Sherlock Holmes, people might ask whether this Sherlock Holmes was the same as the one they read about when Conan Doyle was writing about his great detective. The answer to this question would undoubtedly involve a declaration of my intentions in writing and whether I could answer questions about Holmes in a fashion generally coherent with the original usage of that name. In short, the language-dependency of Sherlock Holmes would be established by criteria by means of which we decide whether we have referred to the same character. These questions regarding different language-dependent objects undoubtedly require a more complex answer than I suggest here.13 However, I am not committed to giving a full account of the nature of fictional discourse. Enough should have been said to make the case that what syntactic primacy comes down to is not some kind of linguistic idealism as _____________ 13 Fictional objects are likely to be a subset of objects whose existence depend on the existence of human minds and linguistic practices. See e.g. Thomasson (1999) for a treatment of fictional objects.

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Tennant imagines it. The fact that human beings over the course of time have developed a conceptual apparatus, by means of which they describe the world truly and falsely,14 does not mean that those sentences would not be true nor false had no humans existed. Of course, there would be no sentences were it not for human beings, but even so it is the world, not humans, that makes these sentences true or false. We offer conditions for being true by means of sentences, and the world responds to these. In Tennant’s parlance, there are many things that we only confirm in their existence, while there are others that we bring into existence. If we did not describe the world, it would still be ready to answer anyone or anything that tried to do so.

Sharpening the Linguistic Criteria While not concerned with the question of whether numbers are objects of a logical kind, we are concerned with Frege’s concept of an object, which in his hands became logical. That is, the Fregean concept of an object that we shall explicate and defend relies centrally on the validity of certain inferential patterns, supported by syntactic markers. Ideally, these are jointly sufficient to establish the presence of a singular term. Frege’s demand for his Concept Script was, in essence, that signs should overtly display their combinatorial possibilities in order to disallow confusion over different instances of the same type of sign. He suggested that… …signs are used only as they were intended to be used in introducing them, i.e. proper names as proper names, names of first-level functions with one argument as names of such functions, and so on, so that the argument places are always filled by appropriate names or marks. (Frege, 1903/1997, §28)

In Frege’s Concept Script, the appearance of a sign would be an excellent indicator to its way of symbolising. But the language we are analysing is not an artificial concept script, but natural language which is subject to potential confusion stemming from divergent uses of the same sign. We must therefore turn to an explication of the criteria of being a singular term. This sharpening of the criteria serves a dual role. Firstly and most importantly, if the direction from language to world in meta-ontology is consistently held, we cannot identify singular terms as those pieces of language that refer to objects. That would imply subscribing to the idea _____________ 14 A focus on such development and at times, radical change in our conceptual apparatus, may well be the motivating force behind Putnam’s internal realism.

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that we can have the linguistic scales fall from our eyes and so attain an unimpeded view of objects in the world with which we could compare our linguistic practice. Rather, some other criteria than those relying on a notion of object are needed. Secondly, the sharpening of these criteria also serves to meet two of the desiderata that we suggested should be met by any concept of an object, namely that it should be informative (criterion 2), and rule out cases that we intuitively would want our concept of an object to rule out (criterion 5). In short, we need to be able to sort the linguistic wheat from the chaff, in order to detect genuine singular terms. Frege did not elaborate the linguistic criteria to any great extent. He did not systematically distinguish proper names from definite descriptions more generally, and we shall include both in the broader notion “singular term”. In connection with the suggestion that the notion of a unit is key to an understanding of number statements, Frege pointed out that in contrast with the word “unit”, “the word ‘one’ as the proper name of an object of mathematical inquiry, does not admit of a plural” (FA §45). Further, in commenting on Ernst Schröder’s distinction between a concept word and a proper name, Frege suggests that “only when conjoined with the definite article or a demonstrative pronoun can [the general concept word] function as a proper name of a thing, but in that case it ceases to count as a concept word” (FA §51). Similarly, in “On Sense and Reference” Frege held that “the concept (as I understand the word) is predicative. On the other hand, a name of an object, a proper name is quite incapable of being used as a grammatical predicate” (Frege, 1892/1997b, p. 193) whereby he mirrored Aristotle’s criteria of the category of substance as that which is not predicable of anything. In Fregean terminology, the worldly correlate of a predicate, a concept, is characterised as a boundary-drawer to either side of which any object falls. That is, either it or its contrary will apply to the object, while no such thing takes place in the case of singular terms: While Peter can be a non-smoker, he cannot be a non-Peter. That we at times appear to use a name as a concept, as in “Blair is no Churchill”, will be treated in the analysis of language about God in chapter 3. The further task involves excluding certain cases that appear to be able to serve as singular terms and so slip through the fairly broad-meshed net that Frege left behind in FA. Here we begin by noting Peter Geach’s (1980), and later, Evans’ (1985) emphasis on another criterion for recognising proper names, namely that reflexive pronouns only make for a stylistic change when they refer back to genuine singular terms. Such pronouns are also known as pronouns of laziness, and they are indicative of the presence of a singular term, which is revealed by the logical behaviour of the pronoun. Using “himself” in Someone killed himself.

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cannot be a “lazy” way of saying Someone killed someone. as the two propositions clearly do not have the same truth conditions. This contrasts with “himself” in: Cato killed Cato and Cato killed himself. where the pronoun, given assumptions of non-ambiguity in naming on the given occasion, effectively refers to the object named at the beginning of the proposition. According to Geach, this test is able to rule out quantifier phrases from the class of singular terms on pain of the absurdity that arises if we treat them like a singular term. So, “he” functions as a pronoun of laziness in If Smith owns a donkey, he beats it. This is shown by the fact that replacing “he” with “Smith” provides only a stylistic change to the content, while the analogous change in: If any man owns a donkey, he beats it. would make for a proposition with different truth conditions altogether. Again, the differences in the contribution “he” makes in the different contexts tell us something about the different logical structures that the sign exhibits on the given occasion. Even though an expression in question has a single referent, it need not be able to take a pronoun of laziness. In Only Satan pities Satan the latter instance of the sign “Satan” would not be replaceable with “himself” salva veritate. The explanation is that “only” together with a name forms a quantifier, and the pronoun helps us detect this. Accordingly, and contrary to its superficial grammatical appearance, Geach characterises the pronoun of laziness as an expression that fills two places in a two-place predicate but nevertheless leaves something to be settled. That is, it is itself incomplete and stands in need of an antecedent. By filling in “himself” in the second of the vacant slots in ___ killed ___

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we would have determined what can satisfy argument and result in a truth in a different way from when the name below turns a two place predicate into a one-place predicate ___ killed Cato In this way, the distinct behaviour of the reflexive pronoun adds to Frege’s battery of tests to detect and confirm the presence of singular terms. To further characterise singular terms, we will firstly survey tests that further exclude expressions of generality and then elaborate the idea that singular terms come with sortals that serve to identify the object in question. Expressions of Generality Other criteria that serve to exclude terms of generality have been elaborated by, amongst others, Dummett and Hale. A concern has been to avoid having quantifiers like “something/someone” and “everything/everyone” count as singular terms. Generality is expressed by means of phrases such as these. They can, in many cases, take the place of a proper name salva congruitate. In so far as they play a significantly different semantic role than proper names, a method not based purely on grammaticality is needed for weeding the former out. Inferential tests serve this role, and to rule out the singular term contender “everything”, Dummett points to fact that the inference from x (A(x) › B(x)) to x A(x) › x B(x) is invalid. A singular term in place of the quantifier would give us a valid inference. An example in the vernacular should help to convince. While we can infer from Mr. Smith voted for or against the proposal. that Mr. Smith voted against the proposal or Mr. Smith voted for the proposal we cannot make the apparent identical inference from Everyone voted for or against the proposal. to

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Everyone voted against the proposal or everyone voted for the proposal. In this way, it should be clear that “everything” and “everyone” and similar expressions do not play a role in the sentences comparable to that of a singular term like “Mr. Smith” – their contribution to the truth-conditions of sentences where they feature differs radically from that of a singular term. Another test for being a genuine singular term employs existential generalisation. This tool would have been of great help to Polyphemos and his fellow cyclops, in so far as Odysseus relied on a trick use of the quantifier “nobody” in his escape from the creature’s cave. The change from the use of “nobody” as a singular term and as a quantifier could have been detected by Polyphemos’ friends, had they asked him if they could infer from his cry for help that there was someone who was trying to rid him of his life.15 While we clearly cannot from ™ x Kx infer x Kx we can from Ka infer x Kx which helps us detect the presence of a singular term. When introducing such tests that rely on existential generalisation, it becomes clear that a problem arises from the fact that “something” can express generality of different levels. Only if it is of the first level should we think that the test has detected a singular term that picks out an object and not a concept. So further tests are needed to reveal what linguistic function has occurred by reproducing that type of sign. Dummett originally _____________ 15 More recent use of trick singular terms is found with Lewis Carroll’s character in Alice in Wonderland, The White King. He apparently speaks about a person – “nobody” – that Alice saw and walked faster than. Commentator on Wittgenstein’s TLP, Denis McManus (2006, p. 53f.), uses this as part of a study in Tractarian nonsense. Calling it nonsense is clearly too strong a characterisation of the trick: using a sign that is typically used as a quantifier as a singular term still leaves us with a well-formed sentence with a singular term, though others may not catch on to our novel use of a sign straight away. Pacé MacManus, ambiguity of logical form does not amount to absence of it.

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suggested a specification test as the proper measure. The test works in the following way: Consider a variant of Frege’s example in On Concept and Object (1892/1997a, p. 196): The whale is big. The presence of the definite article as well as the fact that we can infer that there is something that is big together suggests that we have named an object. To sharpen the criteria, we take into consideration what questions we can legitimately go on to ask. If the question “Which?”, though grammatically in order, does not warrant an answer but can be rejected as illegitimate (Dummett, 1981, p. 68), we then conclude that it is not the case that an object has been named by a singular term and fallen under a concept. Rather, a concept has been what Frege called subordinated under another concept. Naming might take place while visiting an aquarium. Here The whale is big. would not warrant a rejection of the question. Rather, the request for specification would typically be met by means of descriptive material or a pointing to the whale in question, perhaps accompanied or substituted by the use of a proper name where possible. The same applies to the specification test applied to the quantifier expression “something”. The sign can express both first and higher level generality, depending on its setting. If I say: There is something Barack Obama is and I am not. And someone answers A president. Asking “which?” can be rejected as betraying a misunderstanding of the signs used in the original statement. Contrast this with There is something noisy in the room next door. where the answer A president. does not make the query “Which?” ineligible – if, for instance, the setting is that of a G8 summit. From this we infer that the sign “something” was here introduced to identify an object. As Hale rightly submits, this test is not infallible and will wrongly exclude cases where “something” must be understood to be of first level. One example is the use of mass rather than count nouns, where the character of

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the specification test will have to take on a different form. Hale (1987, p. 16) presents another case where the test appears to fail us. This arises from posing the question “who?” to the sentence: Someone committed a terrible crime last night at the harbour. which might prompt the answer A man with strong arms. while any further specification would typically not be warranted by the initial statement, given that the crime is unsolved. However, the rejection is here based on a matter of what we know and do not know, and so, it is of no relevance in the present context, where we are trying to detect logical form. The rejection does not have its basis in the structure of the original sentence, but in epistemological features pertaining to it. “Someone” does here serve to range over objects, though only an indefinite description can be gathered from its use in this example. Several cases of the tests giving us a false negative can be distinguished, and there is a corresponding variety of criteria that are employed to avoid the test offering results we otherwise think it shouldn’t. The type we initially used simply ruled out the specification question because it did not make sense to inquire about any object in the given case. In our next example, the specification question was deemed to make sense but could be rejected for broadly epistemological reasons. Finally, we can distinguish a group of cases where the specification test offers a false negative on account of something like conversational implications of a statement. Here the specification must be taken to have been already offered. This distinction has been introduced by Hale in answer to the following apparent counter-example, offered by Wetzel (1990). When saying: There is someone who is unduly fond of gin. where The man who proposed to Margaret. is an answer to the question of who that was that seems to resist the further question: Which man who proposed to Margaret? Given the assumption that this is the first marriage, we take the question to have been already answered by the first reply or alternatively, we go on to specify which of the suitors was mentioned. Consequently, we do not, in fact, have a case of our test having wrongly characterised a first-level expression as a second level.

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Another example, due to Wetzel (1990), of the kind of problem that has to be dealt with to avoid the singular term tests giving us what we take to be the wrong results is the following: If I am told “There is something my neighbour has learned to use”, I may in response to my specification request be told “a lawn mower”. The further specification question is, pacé Wetzel, not a clear case of a misunderstanding of the original statement. Rather, it reveals ambiguity in the original statement. According to one disambiguation of the original statements, a specification might be offered along the following lines: “The one he bought in Homebase three years back” However, we may, as Wetzel does, reject the specification test as a misunderstanding of the original statement, given that it was meant to speak of a kind of thing and not of an object. Frege notices a similar ambiguity in “The horse is a four-legged animal”.16 As in all other cases of ambiguity, the actual setting and functioning of the sign – not the sign itself – is the key to understanding how the given sign symbolises. Conceptual Debt The criteria that we have outlined have the consequence that the context principle properly formulated must regard a number of propositions rather than just one. This also surfaces in one of the expressions of the context principle in the TLP: “An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions. […] An expression has meaning only in a proposition”. (TLP 3.311, 3.314). We need a range of propositions and their inferential relation in order to detect logical form – predicates, singular terms, logical operators and more. Further tests can be devised for separating expressions of first and higher order. Wright and Hale (2001, pp. 41–46) display considerable technical ingenuity in devising tests that weed out substantival phrases that they are reluctant to acknowledge function as a singular term. Hale offers the hope that performing the various tests in the right progression will render the tests near sufficient. Meanwhile, Linda Wetzel refers to the failure of the tests that are to detect “singular terms of English” (Wetzel, 1990, p. 252), and similarly to the failure of the tests to rule out contenders that they should or should not rule out (p. 249). What I wish to address now is the fact that both parties have to rely on their knowledge of English when devising tests and providing counterexamples to argue their failure. Frege, in his treatment of the notions of object and concept, appealed to “the general feeling for the German language” (Frege, _____________ 16 See Frege (1892/1997a, p. 196).

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1892/1997a, p. 195). Frege’s and Wetzel’s appeal to knowledge of language raises a more fundamental problem with the task of devising criteria for singular terms. In short, such a notion of sufficiency must have its source in the knowledge of the language we speak, with all its grammatical and syntactic subtleties. Indeed, this is the background of both Hale’s and Wetzel’s normative standard for whether the tests perform as they should. Relying on such a normative standard points to an avenue of criticism of Fregean meta-ontology that has been pursued by Rumfitt (2003) as well as by Wetzel (1990). To appreciate Wetzel’s criticism, we may initially compare it with Chisholm’s problem of the criterion: we have neither the extension of “object” (a list of everything there is) nor the necessary and sufficient criteria of being an object. Consequently, we find ourselves in a situation where we have to adjust either the extension of the concept “object” or the proposed analysis of the given concept. In this case, this would mean adjusting which terms we take to be genuine singular terms in true sentences. The previous sections have seen appeals to inferences and singular terms that we all accept. That is, appeals to supposedly unproblematic cases of objects (such as the Earth and people), detected by supposedly equally agreed-upon inferences. A crucial part of the Fregean strategy relies on an application of the linguistic criteria to cases where some need convincing that something should be called an object (in Frege’s case, the natural numbers). In FA, Frege essentially tried to confer a kind of respectability from language that we agree is in good working order and straightforwardly involved in reference to objects, to cases that are argued to be identical in terms of truth and logico-syntactic features. But then, Wetzel’s argument is that the reasoning might as well go the other way. We may just as well adjust criteria for being a singular term in the face of “unacceptable” objects, and according to Wetzel, what we may ultimately hope for is a reflective equilibrium between general criteria of being a singular term and particular instances of what we call an object. Rumfitt levels a similar criticism against a meta-ontology that relies on sufficiency of our criteria for detecting singular terms. Here is his objection, quoted at some length: It seems to me, though, that the Dummettian tests do not accomplish even the “modest goal” of distinguishing genuine singular terms from other substantival expressions. To show this, however, we need first to consider what can be meant, in the context of these tests, by saying that the inference from a set of English sentences X to a single sentence A is valid. I do not think that we can gloss this as meaning that A is a logical consequence of X, if this is understood in any Tarskian way or Bolzanian way namely, as adverting to different possible interpretations of, or admissible substitutions for the non-logical expressions in X and A. For we can decide which interpretations of an expression are possible, or decide which sub-

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stituents for it are admissible, after we have determined its logical classification, whereas the Dummettian tests need to be applied before the sentences in question have been articulated into their logically relevant parts. (Rumfitt, 2003, p. 203)

Both Rumfitt’s and Wetzel’s worry is that we incur what we may call a conceptual debt that is too great when we apply the inferential tests to detect what behaves as a singular term.17 In so far as Wetzel criticises local applications (e.g. to arithmetical language) of the context principle, the debt is incurred to the language it is compared to. In Rumfitt’s case, the debt is more general: we have to be already in the know about logicosyntactic classification for us to deem the inferences valid. We need to either translate our natural language into a formalised language or apply the calculus to our natural language directly. Either presupposes a grasp of what the logically significant parts of English are, and so, could never serve to independently identify the logically relevant parts, which is what we are after. Rumfitt is right to point this out, but wrong in his suggestion that this makes the whole idea of assigning primacy to syntactic categories methodologically compromised. As Frege can be seen to admit in his appeal to the general feeling for the German language, we do indeed not approach the task empty-handed. Assuming some knowledge of the language to which the tests are applied is not asking too much, when considering that we are after all reading and understanding the sentences that are meant to convey the tests. For that reason we are in the right when we assume that the reader can parse the relevant language, English, into logically significant parts. In short, the tests are necessarily relativised to a language that is understood. We should recall that the overall approach we are advocating takes as a guide to ontology the quite general injunction to “…consider [words] in the context of a judgment that brings out [their] ordinary use” (FA §46). Rather than approaching the task empty-handed, we have an anchorage in model cases of logical form that provides material for a ruling in cases where we need to draw attention to an identical logical form. The model cases are, as we have explored, instances of use of proper names and the simple inferences they support. To Frege, this use of language – e.g. existential generalisation from use of a proper name – is so fundamental that a questioning of its validity can only be answered by providing further instances.18 Nothing more fundamental can underpin the understanding we _____________ 17 I owe the notion of a conceptual debt in local application of the context principle to Peter Sullivan (2001). 18 In short, this was Frege’s view on someone who wished to advance something like a “new” logic – it amounted to a new kind of madness. (See e.g. (Frege, 1893/1997, p. XVI ff.) As we will explore in chapter 5, this view set Wittgenstein’s TLP apart from Frege. In the TLP, the nature of logic was at centre stage,

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have when we are able to recognise the significant logical parts of wellformed sentences and the inferences they warrant. Nevertheless, Wetzel (1990) concludes with a characterisation of our dialectical position, which, as suggested, is reminiscent of the one we find ourselves in, according to Chisholm’s problem of the criterion in the analysis of “knowledge”. We do not know what singular terms there are, nor do we have an unproblematic general characterisation of them based on criteria of singular terms. According to Wetzel, actual cases of singular terms and our general notion of a logical form will have to mutually adjust to each other, so that they at some point reach a reflective equilibrium. This, however, is a poor comparison with the dialectical situation that actually faces us. The knowledge that we have of logical form – that is, the knowledge we display when we parse natural language – is of a far more intimate and simple character than is the general analysis of “knowledge”. While an analysis of “knowledge” involves some understanding of truth, justification and, arguably, the human mind, a characterisation of singular terms is far more basic and so less demanding.19 The context principle as a guide to ontology will simply have us survey language and, by means of more or less sophisticated tests, detect and clarify what natural language may conceal from us. This, rather than a totally language-independent characterisation of singular terms, is essentially what the Fregean thesis of syntactic primacy over the ontological amounts to. Sortals – to be is to be an F The passage in Wittgenstein’s Investigations that mentions Frege’s context principle is immediately preceded by the observation that after pointing and uttering, say, the words “the Nile”, “[w]e may say: nothing has so far been done, when a thing has been named” (Wittgenstein, 1958, §49). To Wittgenstein naming is not a move in the language game – and does not, we may add, say anything true or false. For naming truly to be what we call naming, we must be in possession of a concept that allows us to say what it is we name. When saying what it is we name, we are using the subset of predicate expressions that are generally known as sortals or count nouns. Frege _____________ and hence the context principle is presented with full generality, rather than being applied to a given region of language, such as that containing numerals. 19 We shall return to a further characterisation of epistemological issues regarding logical form in chapter 5.

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clearly recognised their significance and made use of them to establish a distinction between counting companies of men and men or between counting decks of cards and cards. This distinction is effected with a view to establish the Fregean view that number predications are relative to a sortal.20 Meanwhile, he did not distinguish sortals in his notation, though they do display a distinct logical feature: while negating a predicate results in a predicate, this is not the case with a sortal. “Man” is considered a sortal, while “red” does not have this status for the reason that we cannot effectively count red things in a room, whereas we can count men in a room. Saying of something that it is non-red still does not allow us to count but otherwise works fine, while being a non-man provides no criteria by means of which we can count. Consider a proposition of the form “there is something such that it is an F”. Up until now we have confronted one instance of what we might call a “noncommittal” or “internal” construal of the expression “there is”, also expressed by the existential quantifier. We have then by means of tests tried to weed out the cases where such a proposition must be taken to quantify over or name concepts and not objects. Now it emerges clearly that for a sign to be rightly treated as a singular term, it is a necessary condition that it is associated with a general expression. So, for instance, if all I am being told at a given time and place is that it is right to say “This is the Nile”, (accompanied by pointing or such tools for demonstrative reference) and I am left with no inkling about what kind of thing – what F – is being pointed out to me, then I have no reason to take it that an object was named by the utterance. For all I know, “the Nile” might as well be an aesthetic exclamation, some predicate or the sign for a kind of thing, as in “the whale” in “the whale is scarce”. Only explication, some of which would take place by varieties of the test for singular terms above, would help me determine which is the case. And only answers from the referrer will justify us in assuming that anything has been named. So pacé Wittgenstein, if a thing has truly been named, something has been done linguistically: the sign has been introduced as a sign that warrants certain inferences and identification relative to the kind of thing it is. Sortals offer us a way to begin identifying objects. They offer a set of criteria for answering the question that Frege insists on: “Same what?”. To refer to an object is to refer an F – to refer to something of any given kind. To those defending Frege’s realism about numbers, it becomes central that “natural number” serves as a sortal that allows identification of the relevant _____________ 20 “While looking at one and the same external phenomenon, I can say with equal truth both ‘it is a copse’ and ‘it is five trees.”’ (FA §46).

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objects.21 We still leave quite a bit to be settled in terms of further characterisation of sortals. We can, like Frege, offer examples such as the linguistic fact that “a red” offers us no way of counting (see FA §54), where as “a philosopher” does. We have already noted that unlike predicates, the negation of a sortal does not result in another sortal. We can easily count tables, but unambiguously counting non-tables in a room proves impossible. A sortal tells us what any given thing is, as opposed to what it is like or what it is doing. But, as regards anything beyond such examples and such relatively crude characteristics, we remain agnostic regarding any further general criteria that tell us which predicate expressions are also sortals, and we shall leave to one side the attempts at categorising among sortals the one that are more fundamental than others.22 In short, we will for present purposes repeat Wright’s insistence that “…whether or not it is ultimately rigorously explicable, the intuitive notion of a sortal concept is clear enough for our immediate purpose” (Wright, 1983, p. 4). Finally, the proper treatment of mass terms is not broached here. We would intuitively want gold and water to be something we can refer to and in that way be on the list of what exists, but offering the relevant sortal for such materials requires further refinement.23 We conclude by noting how Frege’s meta-ontology is expressed with his claim that “…[a]ffirmation of existence is in fact nothing but the denial of the number nought” (FA §53). The number nought is here understood to be the number of a given kind of thing, such as a playing-card or a deck of cards. Frege’s meta-ontology has been taken to mean that for an object to exist is for it to instantiate a property, and on this background, objections to Frege’s meta-ontology fall into at least two categories: one category questions the notion of a property, or in Frege’s terminology, concepts. Do they themselves exist? If not, we seem to be talking about nonexistent entities (i.e. the property) in our account of existence. If they do exist, they would, according to the doctrine, instantiate a property, and a regress ensues.24 Another category makes use of the concept of a “bare” object, i.e., an object that is not described as being any kind of thing, but just a thing. Such use of “object” is also found in Colin McGinn in his criticism of the Fregean understanding of questions of existence: _____________ 21 See Wright (1983, p. 3f). 22 See e.g. Wright and Hale (2001, p. 387 ff.). Part of the notion of an Aristotelian substance is that it would cease to exist if it were not that kind of thing. These sortals are called pure sortals: I can stop being a philosopher (“philosopher” being an impure sortal) and continue existing, but presumably not stop being a person and yet continue to exist. 23 See e.g. Durrant (2001) for an account of the workings of mass terms. 24 See e.g. Colin McGinn (2000, p. 24 f.) for this line of objection.

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The doctrine is that for something to exist is for there to be objects that are instances of some suitable predicate. Here are some objects, and they are instances of F. But that can only mean that these objects exist, so that we are saying that there exist instances of F, for some F… But how is that use of “exists” to be analysed? […] The instances have to be existent objects, so we are presupposing the notion of an existent object in our account of what an instance of a predicate is. (McGinn, 2000, p. 21)

The two categories of objection are connected in that they employ and question the Fregean ontological categories of “object” and “concept”. As we shall explore in chapter 4, the notions were connected and deeply troublesome to Frege himself. Our focus will be on questions regarding the concept of an object. In essence, we shall question and reject formulations, such as McGinn’s, that rely on the use of “object” as a sortal on par with “chair”. Without beginning the treatment here, we shall reject that we can infer that “here are some objects” from “here are some chairs”. Thereby we question the language that McGinn employs as well as language use in much ontology, and we shall have to accommodate the inclination on behalf of McGinn and many others to nevertheless use the notion of an object and make exactly this inference. This would also seem to question our own, Fregean concept of an object, and in what way this contention regarding the use of “object” affects Fregean meta-ontology will be the topic of chapter 5. However, before we get that far, there are more objections to the Fregean meta-ontology that must be met. Finally, sortalism has been recognised in the literature on causal accounts of reference. This line of study of reference abounds with cases of radically mistaken sortals being associated with presumed cases of successful reference, and thus seems to go against the grain of sortalism on empirical grounds. For example, Devitt and Sterelny (1999, p. 79) suggest that we should grant that a given speaker has referred successfully, even though the chain may fail to transmit a sortal, such as “a university”. Another example is due to Miller (1992) and his treatment and rejection of Devitt’s and Sterelny’s (e.g. 1999) hybrid (i.e. causal and descriptivist) theory of reference. What Miller calls the “qua problem” or “the generality of the referential relation” (p. 425f.) is equivalent to our insistence on the need for a sortal when referring to an object. Miller’s challenge to this thesis relies on one of Putnam’s thought experiments. Miller insists: If kangaroos had turned out not to be animals at all but rather Putnam’s Martian robots then, on the current hypothesis, “kangaroo” couldn’t refer to kangaroos since kangaroos turned out not to be a species. But of course we do refer to kangaroos whether or not they turn out to be animals. Moreover, laymen have little grasp of the subtleties of taxonomy and surely could not specify the particular level in the classificatory system this beast represented. (Miller, 1992, p. 427)

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The argument, in short, is as follows. Assume that only if you are in possession of a relevant sortal do you successfully refer to a given kind of object. However, there are successful cases of reference with radically mistaken sortals. Hence, we should reject the necessary condition for reference that is implied by sortalism. What we question in the argument is the truth of the second premise, that we could rightly be said to refer to kangaroos should they turn out not to be animals. Though I have not expressed clearly which pure sortals any given kangaroo would be associated with, “animal” would be a plausible candidate. What that means is that I would expect that people talking about kangaroos would assent, if prompted, to the proposition that they were talking about an animal. Should they respond with something like “no, I am talking about little robots”, my reaction would be to conclude that we clearly weren’t referring to the same things. I am certainly ignorant about what Miller calls subtleties of taxonomy, but his example does not make for a very subtle case in taxonomy at all. Should this happen quite generally, i.e., that all the Australian animals with extraordinary jumping capabilities that I had so far called “kangaroos” turned out to be robots from Mars, there would be a strong case for saying that there never were any kangaroos – that in fact we were radically mistaken. When we thought we were talking about kangaroos, we were talking about something entirely different. We conclude by simply noting that the requirement for a sortal, when applied to the empirical questions raised in the causal theory of reference, will place some restrictions on the licence for calling something a successful transmission of reference.

Against Sufficiency III: Epistemological Concerns As already indicated, concerns regarding the appeal to the context principle in ontology have been raised against the background of perceived epistemological constraints on reference. As a response to the kind of epistemological challenge that emphasises a causal relation as a necessary condition of reference, we note that such affectation of the referrer may only be at work in some of the cases where I make some recognition statement about an object. Being causally affected is in some cases a means of clarifying reference, but reference always relies more fundamentally on the implicit or explicit use of a sortal. The minimal criteria for the identification of objects by means of sortals do not necessarily stand in need of being supplemented by an account of how our sensory apparatus is affected when

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we refer. Such an account may be relevant in some cases – such as when one seeks to account for various referential puzzles. As my focus has not been the vindication of reference to abstract objects in particular, a confrontation with epistemological concerns has not featured as prominently as it would have, had my concerns been more in tune with the use that the context principle is often put to. In the language of those working within the framework offered by the causal theory of reference ascribed to Kripke, the present concern has mainly been with establishing a subset of the conditions for the grounding of reference25 and not for the transmission of reference between language users. Though those speaking about God will appeal to a rather different kind of grounding when compared with talk about numbers, we should welcome the methodological strategy that has been employed in discussions over reference to causally inert, abstract objects. In essence the strategy is as follows.26 The dilemma suggested by Benacerraf’s seminal article on mathematical truth, presented in chapter 1, is only apparent. If our account of mathematical truth fails to mesh with a “reasonable epistemology” (Benacerraf, 1973/1983, p. 403), this simply means that our epistemology is not in this case reasonable – regardless of whether this epistemology relies on a notion of causality or, more recently, on significant reliability in tracking the facts of the matter. Both approaches carry with them constraints on what we call “knowledge” that in some cases are alien to the scientific practice they are being applied to. For instance, even if we insist on a scientific explanation of the high reliability of claims to mathematical knowledge, we might still be thinking of a science that relies on perception aided by instruments and laboratories – that is, we might be physicalists and think that mathematical objects have a poor fit with our world view. However, appeal to the means of acquiring knowledge in physics will be of little use in offering an account for the reliability of mathematicians when it comes to mathematical truths. A systematic study of knowledge should certainly impose restraints on what we call knowledge, but in the event of an epistemologist encountering widely accepted truths such as those of mathematics, it is the epistemology that will have to give way. As suggested in the introductory reference to Gödel’s realism, it is the practice of the science of mathematics that does _____________ 25 We can of course have a sortal without having a grounded name. The notion of grounding is typically taken to include successful reference. Sortals only give us some of the descriptive content in the name, leaving it to the world together with our best relevant methods, to settle whether it is true that there is an x that is F. – i.e. whether the name is grounded. 26 This strategy has been pursued by Wright and Hale (2001) as well as Linnebo (2006). See also Divers and Miller (1999).

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the justifying of reference to its objects, not epistemology. The existence of the universally accepted truths of a set of statements like those of mathematics makes for an obvious difference with that of theological statements – the latter enjoy no such universal assent, and the meaning of the statements are in most cases far more fluid and less agreed on. This fact, however, is only an issue when one wants to engage in an actual ontological investigation as suggested by the question “does God exist?”. It is of no relevance for meta-ontology. Moreover, while I argue that objections to, say, an ontology of abstract objects such as numbers and sets that are based on epistemological concerns typically carry little weight as objections to the ontology, the objections might well serve as a call to clarify the relevant methods of attaining knowledge in the various sciences, such as methods of proving various theorems. This line of reply is essentially the one offered by Rosen and Burgess (2000) in their treatment of nominalism in the philosophy of mathematics. Linnebo (2006) dubs this approach “the internal explanation”. In this case, causality is the external, and hence illegitimate, demand to place on the justificatory practice of mathematics and by extension, on the claims to knowledge made by mathematicians. Linnebo agrees with Hartry Field that such an internal answer to the epistemological concern is uninformative: To see this, assume the scientific status of some discipline is contested and that someone therefore demands an explanation of the associated reliability claim. An internal explanation of this reliability claim will do nothing to reassure us. For this explanation simply assumes that the practitioners of the discipline are justified in what they do and uses this to establish that it is not just an accident that the reliability claim is true… Internal explanations are therefore deeply dissatisfying. (Linnebo, 2006, p. 562)

Linnebo, however, agrees that it is a position that remains undefeated, as it remains hard to formulate what else should be asked of the mathematician without putting him unreasonably at a disadvantage in his imagined defence of realism regarding numbers. We should agree and add that things will be less clear cut in other cases. For example, to what extent history as a discipline is external to theology appears as an open question. Barth’s study of Anselm is supposed to have deeply influenced Barth’s subsequent work. Also here we see reflections on something like the external and internal explanations, considered more generally: Anselm’s Proof works on the assumption that there is a solidarity between the theologian and the worldling which has not come about because the theologian has become one of the crowd, or one voice in a universal debating chamber, but because he is determined to address the worldling as one with whom he has at least this in common: theology. (Barth 1960 p. 68)

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As an interpretation of Anselm Proslogion, this is interesting in its own right, but what we also see is a remarkable reluctance to make theology accountable in matters of explanation and justification to what goes on outside the church walls. As we conclude chapter 3, we will encounter some reasons for such a stance on Christian theology.

Against Sufficiency IV: Bogus objects? We turn now to the fifth desideratum for the concept of an object: conformity with intuitions and convictions of various kinds. Russell insisted on “that feeling for reality which ought to be preserved even in the most abstract studies” (Russell, 1919, p. 169) as a motivation for his theory which avoided furnishing the world with an object such as “the present king of France”. Such feelings still play a role in ontological considerations. E. J. Lowe has expressed similar concerns regarding Fregean metaontology, by him called the semantic view of objects: However, if a sentence containing a singular term is true, then, on the present account, that term does indeed denote an object. […] But this threatens to produce a grossly overinflated ontology, with a world populated by many more species of objects than common sense would suggest. (Lowe, 2001, p. 34 f.)

Lowe goes on to make the charge of ontological extravagance, and it is to such hazy but recognisable intuitions that we shall now turn. We should start by noting the fact that the criteria presented so far do weed out some of the examples that have dominated literature on objects that many are reluctant to include on their list of what there is. Rephrased in our favoured terminology, these are words that appear to display the right kind of syntactic behaviour in order to indicate that they name objects but in so doing name objects that are somehow metaphysically bogus or unacceptable for other reasons. Thus, a number of writers such as van Inwagen (1990), Mackie (1993), Melia (1995), Heck (2000) and Yablo (2000) seem to agree in their reluctance to accept that the truth of a sentence like: The typical father has two children. should commit them to the object apparently named by what looks like a singular term. Our approach to ontology based on demarcating real from apparent singular terms has two strengths in the present debate. Firstly, it is able to weed out some of the contenders that have been used in the literature that broadly centres on natural language and ontology. All we need to do is reflect that

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The typical father hates himself. does not amount to the same as The typical father hates the typical father. This reveals that “the typical father” falls short of satisfying our criteria. Should someone insist on existential generalisation from these sentences (“there is someone who hates the typical father”), he is best convinced by being shown alternative construals of the hidden generality (the expression “typical father” gains its meaning from the existence of a set of fathers) in the sentence as well as by contrasting the sentence with superficially quite similar sentences where we do allow existential generalisation. The second and related advantage of Fregean meta-ontology is that it provides clear reasons as to why we accept or reject the various contenders for being a singular term and so allow or disallow objects in our ontology. The phenomenon of unclarity with regard to the concept of an object that was highlighted in the previous chapter is also found in the literature on natural language and ontology. Consequently, the reasons for accepting or rejecting the existence of objects will vary to the extent that they are clearly formulated. At times they will have to do with causal efficacy, but other kinds of reasons are also found. In the present context I can only offer the working assumption that a sufficient number of other examples can be dealt with satisfactorily by the criteria for singular termhood and immediately note what I explore in this section: That it is by no means clear that we ought to be able to rule out all objects that consensus intuitions would have ruled out. While the Fregean approach has some success with respect to examples from recent debates, it still suggests the existence of a plethora of objects, many of them abstract. If we intend to satisfy the common-sense intuitions regarding what there is, we should not celebrate too soon. The meta-ontology will in many cases suggest an ontology that is likely to be too inclusive for the intuitions of many, as suggested by Lowe. We understand ourselves to have all sorts of dealings with abstract objects, and natural language makes no distinction between abstract and concrete ones. We read books about the French revolution, understand languages such as German and English, live in a state, play games, we might read a review of works27 such as the Foundations of Arithmetic and we occasionally inquire about someone’s marital status or their whereabouts. Philosophers are prone to speak about validity, _____________ 27 Thus, Wiggins can preface his second edition of Sameness and Substance with expressions of doubt as to whether the new edition is the same work as the first edition: Identifying an object as the same as another one is in the case of works a somewhat vague matter.

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for example, in terms of models. In short, the way we speak seems to suggest that reality contains games, models, works and the likes that are not correctly identifiable with any concrete instantiations of them.28 What are we to say in response to the proliferation of these “bogus” objects, to borrow Hale’s helpful coinage? The ontological proliferation could simply be taken as a reductio ad absurdum of the thesis of linguistic priority over ontology that Fregean meta-ontology contains. The reductio has at least one precedent in Quine’s quip about the aesthetic qualities of desert landscapes, although he was targeting Meinongian ontology.29 However, such contentions should, particularly against the background of the linguistic uncertainty that was explored in chapter 1, not be afforded too much weight. The intuitions of the typical philosopher are not hard-and-fast data that we can rely on when attempting to achieve a clear understanding of what there is. That is, rather than present the inflated, bogus universe as a stark challenge to the reversal of ontology, we should see it as a call to confront our intuitions about what objects there are. Such a confrontation is not without Fregean precedent. I take the following exchange of words between Wittgenstein and Frege to be suggestive of such hunch swapping: The last time I saw Frege, as we were waiting at the station for my train, I said to him “Don’t you ever find any difficulty in your theory that numbers are objects?” He replied “Sometimes I seem to see a difficulty, but then again, I don’t see it.” (Geach and Anscombe, 1963, p. 130)

From Frege’s way of formulating himself, it seems that what he had in mind was precisely the rejection of appearance and reality when dealing with singular terms that were otherwise considered to be clear cases of such. In the late twenties, as Wittgenstein found greater freedom from the _____________ 28 An example of this reluctance to accept an ontology that includes abstract objects is found in Hawley’s discussion of two people on opposite sides of the world reading the same book and wearing the same outfit: “The Australian is reading a book whose type is identical to the type of the book being read by the Scot, and she is wearing an outfit of the type identical to the type of outfit worn by the Scot. But this interpretation is problematic, since it supposes that our talk of outfits commits us to the existence of abstract outfit types” (Hawley, 2002, p. 63). 1ew laws are similarly not identifiable with anything concrete. In the case of laws, I side with Amie Thomasson (2003) in accepting the existence of what she calls abstract institutional entities. In all of the above cases, what might drive the reluctance to accept the existence of abstract objects is the fact that concrete instances are epistemologically prior: we typically learn about certain kinds of outfits through acquintance with instances of them. 29 Found in Quine’s “On what there is” (1953/1980) along with a quick mention of the idea of disambiguating existence that was elaborated in the previous chapter.

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direct intellectual influence of Frege, he commented with regard to the Fregean concept of an object: The [Fregean theory of number] explains the concept of number for the idioms of everyday speech. Of course, Frege would have said (I remember a conversation we had) that the simultaneous occurrence of an eclipse of the moon and a court case was an object. And what is wrong with that? Only that we in that case use the word “object” ambiguously, and so throw the results of the analysis into disarray. (Wittgenstein, 1975, §115)

Wittgenstein is levelling the same criticism that I made in the previous chapter with respect to contemporary discussions of what there is. In Wittgenstein’s case, however, no evidence is provided in support of the claim regarding equivocity, and in the previous chapter, we confronted his argument for equivocity as it would emerge in Philosophical Investigations. For that reason, the claim that “object” is in fact used ambiguously carries little conviction. If it were, Wittgenstein would be right about the ensuing disarray, but somewhat surprisingly, it appears that Wittgenstein is mistaking the quite inclusive Fregean concept of an object for not being one concept at all, but a case of randomly ambiguous words. Recall that the Fregean understanding of an object is universal, relatively clear and does exclude some cases, as we would expect a useful definition to do. Although he did not do so in any systematic fashion, Frege did offer criteria along with instances of what he took to be objects. Richard Heck, while otherwise sympathetic to Fregean meta-ontology, has raised a similar concern about bogus objects, which in his case are sets that he calls “duds” and “daps”. Duds and daps contain apparently random objects in contrast to sets, whose members all have some “standard” predicate that are applicable to them: The problem would be that, on [the view of the Fregean ontologist], the notion of an object, and the conception of what it is for an object to exist, would be so thin that the resulting view would not deserve the title “Platonism”. Such abstract objects as books…would be said to “exist” alright, but in no more robust sense than alleged abstract objects like duds and daps are said to “exist”. (Heck, 2000, p. 146, Heck’s emphasis)

The objection behind the notion of thin-ness should charitably30 be taken to be this: The list of what there is should not be subject to inflation by means of language. Frege’s event, as reported by Wittgenstein above, as well the _____________ 30 This is possibly misguided charity and thus a poor construal of what Heck has in mind as Heck lumps these odd object with books. Whatever we say of their existence, they are not as easily and readily conjured into existence by language users as duds and daps (if only they were), and their criteria of identity are very different.

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proliferation of sets, seem to be cases of exactly such inflation. Hence, subscription to the Fregean approach to ontology supposedly lands us in a bizarre universe that reduces the approach to absurdity. The response to this specific objection is simply this: The conditions for the existence of these sets are given in virtue of firstly, the existence of the members of the set and secondly, conceptual work in forming the sets. It is simply a case of inferring the existence of states of affairs on the basis of states of affairs we already accept as obtaining. Mathematical practice happens to be quite uneconomical when it comes to the existence of sets and other mathematical entities, but the example generalises. If I accept the existence of a set of things, then I should accept the existence of things that I can infer the existence of, or otherwise rightly speak of, purely on the grounds of the first-mentioned set of things. Given assumptions about agreement in the use of the concept of a car, there are many things whose existence I may infer purely on the basis of the truth of a sentence like “There is at least one car in the world”. Examples would be “There are at least three wheels in the world”, “There is at least one steering wheel in the world” etc.. Some of these inferences (and the conceptual work) are instructive and worthwhile, some appear more spurious. Consequently, the objects they introduce may well inherit the same qualities. Objects they are nonetheless. Regarding duds and daps, we note that most of us are after all primarily interested in sets whose members fall under a frequently used concept, which is why duds and daps appear odd.31 Having confronted the idea of defining things into existence, more considerations can be brought to bear on suspicions of the dubious character of the ontology that Fregean meta-ontology seems to result in. Firstly and most importantly, there is Frege’s emphasis in the introduction to FA that what matters is not the naturalness of the position that numbers are objects, but “whether they go to the heart of the matter and are logically unobjectionable” (FA, p. X). Whatever Frege meant by “logic” here, it seems clear that such considerations should have more weight than whatever intuitions about naturalness we have become equipped with. Being rationally inclined, we must give more weight to the simple, inferential patterns, accepted truths and other relatively simple uses of language that we have explored. Secondly, there is something we can do to ease the concerns of anyone regarding the Fregean ontology as strongly counterintuitive or “bogus”, in _____________ 31 The same reply will apply in the discussion, introduced by Hirsch, of incars. These are objects that exist when a car is in a garage. The Fregean should maintain that there surely are such things (there is frequently one outside my house), but also note that our (linguistic) practices do not afford them much attention.

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addition to it being “uneconomical”. Using Frege’s example, if we find it hard to convince someone that the Equator is an object (perhaps it sits poorly with their preferred understanding of cognition or reference), what we can do is make clear to them the kind of context in which “the Equator” features. Such an informal analysis should explain that speaking about the Equator depends on the Earth having poles and spinning around an axis. This ought to make clear to our objector the problem in thinking about the Equator as a material object, only without the causal powers that material objects are taken to have. It should instead be seen as a different kind of object, one we can identify by outlining the truth-conditions of sentences in which the term features. Given this geographical exercise, the existence of the Equator ought to be demystified and taken as granted. In the event of reluctance to do this, our only recourse is to abandon the objector to selfcongratulation on putting up resistance to Platonist superstition.32 In sum, the perceived oddity of bogus objects ought to be lessened when we reflect on how we speak about various objects – and the conditions under which we can say something true about them.33 Through these kinds of exercises we also begin to satisfy desideratum (3), an account of what we called the Aristotelian intuition regarding the meaning of “existence”. The sortals we employ for identifying planets, their equators, sets, radio programmes, people, smiles, numbers etc. really are diverse. However, we should not conclude from this that the logical form from which the concept of an object derives is similarly diverse. Thirdly, we may note that a lot of the objects that have been suggested in the literature as being somehow counterintuitive are typically objects that are ontologically dependent on other, related kinds of objects. We have already seen incars, duds and daps as examples of such objects. Whatever we make of these kinds of objects, they clearly would not exist were it not for, for example, cars. That is, their existence depends on the existence of other objects. Likewise, train tickets are objects that are dependent on railways and trains for their existence. These tickets nevertheless exist, but their dependency may mesh with convictions that objects proper should in _____________ 32 This is Dummett’s (1991, p. 182) disparaging characterisation of the ultimate position of the objector to the consequences of Fregean meta-ontology in this geographical case. 33 This line of defence has been the starting point for Reck’s (1997) distinction between traditional and contextualist Platonism, where only the former characterises the kind of Augustinian thinking our nominalist might be in the grip of. Frege and his defenders make no such distinction, and just as Wright, for example, is happy to call his own “contextual Platonism” Platonism, and as it is not always clear that the nominalists commits themselves to Augustinian thinking about reference, so will I stick with my usage of “realism”.

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some sense exist independently, not just from the beliefs that human minds entertain, but from anything particular at all. Indeed, we may here have located another, non-epistemological use of “real”: that which an ultimate and complete analysis would reveal not to rely on anything else for its existence.34 Fourthly, drawing attention to what Wittgenstein at one point calls “deep words” is of relevance in this connection. In NB, Wittgenstein describes words as the film on deep water, but he also ascribes depth to words: The older, the deeper (see NB 52 and 39f.). The tension between the two descriptions is resolved by considering the two comments as a synchronic and diachronic view of words respectively. Though words are uttered here and now, they carry with them a history. A word like “king” is a clear example of a case where the history of a word becomes present when trying to apply it. When asked if Norway has retained the monarchy, we could make a case for an answer in the affirmative as well the negative. A Viking or knight from times long gone would be inclined to answer in the negative, while they would also have reasons to answer in the affirmative (probably to do with lineage, residence and constitutional formalities). Thus, the history of a concept is brought to life when we apply it – Wittgenstein also speaks of its spirit – and it can make us reflect on its proper application. A prominent understanding of the paradox of vagueness would situate its roots in the Fregean view of concepts as complete boundary-drawers. The logical demands of concepts and the (historical) character of language are thus at odds and something needs to be said about the relationship between the two.35 To an even greater extent, words such as “object” and “substance” are deep, vague words that bring up a long history of philosophical and scientific use. We can speculate that reluctance to accept the ontological consequences of the context principle is, at its root, a result of our inherently vague natural language being a depository for a large number of conceptions of object-hood, which raise their heads when we are faced with the clear-cut concept of an object. In considering this, we can take some courage here from the fact that at the most general level, Frege’s and Aristotle’s use of “object” and “substance” are the result of linguistic analysis rather than, say, preoccupation with a particular range of objects, such as those explored by physics. _____________ 34 Fully fledged Aristotelian substances like human beings need matter for their existence, but no particular parcel of matter is needed. Aristotle’s Metaphysics levels arguments against taking some kind of atom to instantiate the primary meaning of “being”. The primary meaning remains exemplified by complex organic substances like trees and human beings. 35 See for instance Wittgenstein (1982, §206–211).

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Together, these considerations should serve to ease the challenge that “the feeling for reality” may pose to accepting the consequences of Fregean meta-ontology. Moreover, I have at least indicated how these intuitions may arise in the first place, and, by attempting both an analysis and accommodation (despite undoubtedly failing with respect to the latter in many cases), it has been my aim to be more forthcoming than Frege and Wittgenstein ever were on this topic.

Cases of Absent Sortals: Refining Frege’s Imperative Some moral psychology suggests that the very existence of prohibitions gives rise to an inclination to violate them. Presenting the context principle as something that should not be violated has its source in Frege’s own presentation of it in FA. More recently, Dummett (1994) and Stainton (2006) have spoken, respectively, of violations of and of obedience towards the principle in connection with coming to an understanding of subsentential expressions. Perhaps spurred on by such inclinations, several commentators have objected that we can indeed disobey the principle and ask for the reference of a name outside its typical or, indeed, outside any linguistic context. Moreover, this insistence has formed the backbone of an objection to the approach to Fregean meta-ontology. As a consequence, we will have to clarify the intent and nature of the prohibition in order to assess these objections. In order to do this, we shall introduce ideas from the TLP that lie in extension of Frege’s context principle. It seems that widespread linguistic evidence would render the context principle a non-starter. We quite often refer to things without uttering anything that has the complexity of a fully fledged sentence, which for present purposes we take to be an expression that contains a singular term and a predicate. Indeed, the opening sections of Philosophical Investigations have builders referring and making things happen with single words like “slab” and “beam”. Much earlier, probably pondering the military codes that were in use in WW1, Wittgenstein writes in his notebooks: The proposition is a picture only in so far as logically articulated. (A simple – nonarticulated – sign can neither be true nor false.) […] But in that case, how is it possible for “kilo” in a code to mean “I’m all right?” Here surely a simple sign does assert something and is used to give information to others. – For can’t the word “kilo”, with that meaning, be true or false? At any rate, it is certainly possible to correlate a simple sign with the sense of a sentence. – […] But how CAN a single word be true or false? (NB 8 f. Wittgenstein’s emphasis)

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A large quantity of empirical linguistic evidence of the use of single words to refer successfully to objects and state facts very much suggests that enquiring about the referent of the word only in the context of a proposition is a poorly-founded requirement. Our answer to this objection essentially questions the assumption that the word “kilo” is the same kind of thing when contributing to a sentence and when used above, as code, correlated with a sentence. The conventions behind these two uses of signs are very different. So far, our focus has been dedicated to what we may call the “positive” aspect of the context principle, which essentially centres on questioning and at times rejecting a distinction between appearance and reality with respect to syntactic behaviour of certain pieces of language. In short, if words appear to refer to, say, abstract objects, then we should take it that they really do so refer. This aspect – that logico-syntactic appearance is sufficient to ascribe reference – is captured in Wittgenstein’s claim that “if everything in the symbolism works as though a sign had meaning [Bedeutung], then it has meaning” (TLP 3.328). The present objection and the exposition below centre on the corresponding aspect of the context principle that emphasises a necessary condition for reference, namely that it is only in the context of a proposition, and nowhere else, that words have reference. This aspect of the context principle is equally defended in TLP. While the principle pervades its theory of the proposition, it is perhaps most succinctly expressed in saying that “[i]t is impossible for words to occur in two different ways, alone and in the proposition”, which has the corresponding ontological thesis that “[i]t is essential to a thing that it can be a constituent of an atomic fact” (TLP 2.0122; 2.011). The present section aims to flesh out the idea that it is essential to our thinking about words, and singular terms specifically, that they are considered qua contributors to sentences. The objection regarding use of single words to refer to objects has found its way into the literature about the context principle through the following macabre thought experiment, devised by Herbert Hochberg and directed against the use of the context principle in meta-ontology. If someone were to say “Socrates” and then die midsentence, we would be very much inclined to say that the unfortunate person did refer by making the utterance, only we might be unsure as to exactly what or who the intended referent was.36 A similar kind of evidence features centrally in Mayberry’s dismissal of the use of the context principle that I am currently defending: It is clear that in Frege’s eyes the principle has only limited application. For once he has disclosed, or rather has laid down, what the numbers are, there is nothing to

_____________ 36 See Hochberg (2003, p. 42 ff.)

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prevent our asking what “five” means outside the context of any proposition whatsoever…(Mayberry, 2000, p. 26f.)

The argument made by Hochberg and Mayberry is that the use of the context principle in meta-ontology fails to the extent that its general injunction regarding the meaning of words can be shown to be wrong. And, to repeat, linguistic evidence would strongly suggest this. We can render Hochberg’s and Mayberry’s objection in the following way. The one-word utterances that Wittgenstein’s builders make can be seen in two ways. We can see them either as elliptical for full sentences like “Bring me a slab”, or alternatively we can see them as the canonical way of giving expression to the lengthened “Bring me a slab”. I believe we are inclined to consider the first as the natural way of understanding the linguistic phenomenon. But then, I take the thrust of the argument of Hochberg and others to lie in the suggestion that there is no necessity to such linguistic intuitions. We could easily have the convention that “Slab” always means “bring me a slab”, and the suggestion is that our capacities in matters of reference would not for that reason be rendered void or otherwise impaired. Hence, we can refer to things by means of linguistic units that are simpler than sentences, and as a consequence, nothing should keep us from asking about the referent outside the context of sentences. In reply, we must set out by noting that whether we should or should not ask for the referent of a name outside the context of a sentence obviously depends on what we hope to achieve – Frege’s prohibition is by no means a categorical prohibition, nor even a general thesis about all aspects of language use. For instance, Dummett has made the quite general suggestion: A sentence is the smallest unit of language with which a linguistic act can be accomplished, with which a “move can be made in the language game”: so you cannot do anything with a word – cannot effect any conventional (linguistic) act by uttering it – save by uttering some sentence containing that word (save for the cases in which, as in the answer to some questions, the remainder of the sentence is understood from the context.) (Dummett, 1981, p. 194)

This is clearly too prohibitive. If we wish to study pragmatic features of language, there certainly are units smaller than a sentence that are interesting, besides the kind that Dummett mentions. We can clearly effect a move with a single word like “beer” without having asked a question. Nothing that Frege says about use and context ought to prohibit or somehow otherwise suggest that something is amiss with studies of the pragmatics of single word utterances. We may begin our explication of the intent of the prohibition by considering the Wittgensteinian builders more carefully. Why are we inclined to take the construal of “slab” as elliptical of the fully fledged sentence to

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be the right way of understanding what is going on? The answer is that the fully fledged sentence makes clear the logical form of the sign “slab”: While the builders could get on with the single word in their dramatically impoverished world with its accordingly diminished linguistic needs, we need to be able to ask for other things, or rather than ask (R) for slabs (s), we have the possibility of enquiring about their weight, praise them and many other things. Here, the fully fledged sentence makes transparent the combinatorial potential of the sign. Rather than have: P symbolising the request for a slab (s), the complexity of: Rs together with the possibility of the representations: Ws and Ps Makes it clear that the word “slab” can contribute uniformly to different linguistic contexts, where we praise (P) or weigh (W) the slabs. Similarly, we can ask for different things to be brought, like bottles of beer (b), which would lead us to new combinations such as Pb signifying the praising of a beer. In short, “A characteristic of a complex symbol: it has something in common with other symbols” (TLP 5.5261. Wittgenstein’s emphasis). As we can happily concede, we might decide to have P signify the request for a slab. However, with our language in our world in all its complexity, it is possible to ask for different things and perform different functions with these things. If we want to express this, we need a way of expressing ourselves that allows for suitable combinatorial possibilities. We might establish the convention that P should signify praise as I have suggested and so, the letter – but not the spirit – of Dummett’s contention is plainly wrong: We can make and do have numerous linguistic conventions that apply to single words and achieve the same effect as a fully fledged sentence. However, we could not use the same symbolism – relying on single words alone – to ask for other things or praise our slab. The expression simply does not have the necessary complexity. We can set

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up a convention like the one for P, but setting it up would require a symbolism with greater complexity. One might think that this is only a matter of our expressions, and that they should not be taken as a guide to the nature of what they are an expression of. However, the focus on such uses misses the methodological guidance that the context principle offers: to underscore the importance of combinatorial possibilities as what bestows meaning on utterances. To bring this to expression, we will explore elements of Wittgenstein’s reliance on the idea of picturing as a way of understanding the nature of propositions and their elements, signs. This should help us divert our focus away from pragmatics to the logical form, where “logical form” is here taken to mean the features of sentences that are captured by means of the predicate calculus and that make for our guide to ontology: That we name, negate, predicate, quantify over domains and join sentences by means of truth-conditional operators. Consider the following picture: XX X X X X

X X X X Fig. 1

Of their own accord, the marks can be taken to signify various things, or for that matter signify nothing at all. While creating a legend makes us rely on the functioning of another representational system, another way of showing what the signs represent will rely on clarifying the combinatorial possibilities. These possibilities allow the otherwise random signs to represent. Let us look at another picture: XXX XXX XXX XXX

Door

Fig. 2

As other elements of the states of affairs being pictured have entered the picture (in this case, we rely on a sign frequently used to designate doors), this might lead us to say that the x’s in fig. 1 are individual elements in the symbolism and that combined they symbolise the seating arrangements in a

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class room, rather than being, for example, a sign of less complexity signifying the potential presence of horses by means of an image of a horseshoe. It matters little to the point I am making that we might need more examples of seating arrangements to exclude other interpretations, and that a method of projection is assumed in order to have a certain picture of what arrangement the x’s picture. What matters to this interpretation is that there seems to be thirteen recognisable elements in the picture that can combine in certain ways – we would eventually have realised that it is not just a random mixture of x’s but articulated and structured in a certain way – paraphrasing TLP 3.14f.37 Only two dimensions in space are ordinarily relevant to the seating arrangements in a classroom and all that is ordinarily employed by a piece of paper. Using maps of cardboard that represent in three dimensions – as used in some popular cartography – along with a different height positioning of the x’s would lead one to look for an understanding of the picture that would have the x’s symbolise something entirely different than chairs in a room. Of course, we would only start looking in this way if there was a reasonable assumption that the difference in height – with its new combinatorial possibilities – was an element of the representational features of the picture. For all we know, the difference in height might be of no consequence for the representation. It might just be one of the accidental features of the representation, along with the colour and texture of the bumps on the map. Similarly, the colour of the print of this writing is a purely accidental feature of the representation, while according to bygone conventions, colours (red and black) in the symbolism used in accounting did have representational features. We have begun an exposition of Wittgenstein’s notion of the form of representation as it is introduced in the 2’s of TLP.38 While e.g. Proops (2000, p. 69) takes a notion of abstraction as key to the notion of logical form, I suggest that these kinds of considerations of combinatorial possibilities, grounded in Wittgenstein’s engineering background, are of key importance when coming to an understanding of Wittgenstein’s thinking _____________ 37 “The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way. The proposition is not a mixture of words (just as the musical theme is not a mixture of tones. The proposition is articulate”. 38 “What the picture must have in common with reality in order to be able to represent it after its manner – rightly or wrongly – is its form of representation” (TLP 2.17). Of course, chairs are likely to be radically different from the Tractarian objects that are represented by names that stand in for them. Tractarian objects are, after all, absolutely simple and common to all the ways the world might be. In the concluding section of chapter 5, we shall say more about the difference between Wittgenstein and Frege, when they speak of objects.

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about representation, including representation using words.39 While we shall devote greater attention to this in chapters 4 and 5, where we consider the question of propositional unity, we can now appreciate the idea that the most general and inclusive method of representation, our natural language, is subject to the same requirement as the x’s – qua representers or symbols – are in figs. (1) and (2). Neither the shape nor the colour of any single x matters: any of the x’s symbolises a chair only in so far as it is capable of combining with other elements and so contribute to a picture. While the x in: X Fig. 3

might symbolise a chair, it only does so in so far as it is considered as a potential contributor to depictions of seating arrangements such as fig. 1 and fig 2. When we find the same type of sign in Xenophobia is rarely encountered in New York Fig. 4

we do not suggest that the sign symbolised chairs as in figs. 1 and 2, because it here displays radically different possibilities of combination in this symbolism, and thus, symbolises differently. This simple account of what makes a sign into a symbol that is able to refer leads us to appreciate an aspect of Wittgenstein’s comparison of pictures and propositions that is often overlooked: The distinction between an “Abbildung” and a “Darstellung”. Both are lumped together as “representation” in Ogden’s widely used translation. The distinction is a matter of there being two aspects of an ordinary picture, say of Socrates. Firstly, the picture is about this person and secondly, it presents this person in a certain way – running, standing, smiling, having just had a haircut or whatever. To the first aspect Wittgenstein uses “Abbildung”. What should emerge from the series of presentations above is that for something to symbolise (abbilden) something else at all, there must be combinatorial possibilities in common between elements in the picture and elements in what is being pictured. In so far as Abbildung takes place, we are representing something that is there to Abbilden. Given this combinatorial commonality as a key to what is being represented (abbildet), we can then go on to _____________ 39 See e.g. Henk Visser (1999), Nordmann (2002) and in particular, Hyder (2002) for accounts of the background in science and engineering on which the picture theory was developed.

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represent (darstellen) a possible state of affairs (for example, seating arrangements) rightly or wrongly, truly or falsely. In the example given here, this relates to a set of chairs in the room being positioned in the way the picture displays. Regardless of whether a picture represents (darstellt) something truly or falsely, it must already have representational features that make it capable of achieving an Abbildung of what is being darstellt truly or falsely. In this way, we have incorporated into an account of language-use one of its central features, one which so troubled Russell: That even when we use language to make false claims, there is nevertheless a certain relationship with the world – a false proposition of the world is still an Abbildung of the world. As TLP 2.0122 puts it enigmatically, the independence of objects is a form of dependence on the possibility of occurring in possible states of affairs.40 Of course, there are significant differences between the Tractarian setting in which we find Darstellung and Abbildung and the present defence of meta-ontology. For a start, Tractarian objects exist necessarily, while only a subset of the objects considered in this chapter can lay claim to this (although the natural numbers are among the significant contenders for this title.) In chapter 5 we shall return to the question of the context principle in Frege’s FA and Wittgenstein’s TLP. Nevertheless, the contention remains that the articulated sounds or inscriptions known as words are no different than the x’s in figures 1–4. The symbolising of words relies essentially on their being able to form a part of the picture we call a sentence. “What the signs conceal, their application declares” (TLP 3.262) or more elaborately: An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions. It is therefore represented by the general form of the propositions which it characterizes. (TLP 3.311f.)

Because of the far greater expressive powers of our natural language and the correlated greater complexity of reality, our example with the chairs becomes strained. The kinds of significant propositions in which we may find “chair” – the logical space mentioned in TLP 3.4 – outstrip the complexity of the two-dimensional representation of the pictures containing x’s above. That is, of chairs that they are located somewhere but also, for _____________ 40 Unfortunately, the Ogden translation of “Sachlage” in TLP 2.0122 is “atomic fact”, which muddles the idea outlined in this paragraph. It ought to be something like “states of affairs”, as the point is that objects can enter into representations that are the case or not. The independence from facts (Tatsachen) is described in TLP 4.06ff.: “Propositions can be true or false only by being pictures of reality. If one does not observe that propositions have a sense independent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights”.

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example, that they have a price. In this way, the representative powers of the spatial picture are less than that of the logical picture. But it is true of both picture and logical picture that they must have the form of reality for them to be pictures at all: “every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)” (TLP 2.182). The dependency suggested by TLP 3.311 can stand in need of clarification when one type of word-sign can symbolise in different ways, exactly like the x’s could. Wittgenstein’s example, “Green is green”, is a case where the combinatory possibilities of the signs send us in search of different ways in which the same type of sign can symbolise.41 The same phenomenon lies behind our caution above regarding the possibility of a characterisation of singular terms that is too far removed from the use of signs. As suggested by Frege and Wittgenstein in different ways, the proper representation of different symbols would be via an indication of the different combinatorial possibilities of the relevant signs.42 In “Green is green” we would have either “is green” replaced by a variable (Green I) or “Green” replaced by a variable, “x is green”. Accordingly, the correct presentation of either would then be “a variable whose values are the propositions which contain the expression” (TLP 3.313). The fact that our written symbolism has a convention of writing proper names with the capital gives at least part of the game away in the present case. The same example would be more effective in its spoken version. What happened to the x’s in the sentence about xenophobia (fig. 4) above as well as to the sign “Green” happens less frequently in our natural language due to its greater complexity, but the phenomenon of reliance on a number of combinatorial possibilities for referential success is in nature no different.43 To return to Hochberg’s example, the reason that we tend to say that the dying soul was referring to Socrates (s) is simply because we _____________ 41 “In the language of everyday life it very often happens that the same word signifies in two different ways – and therefore belongs to two different symbols – or that two words, which signify in different ways, are apparently applied in the same way in the proposition. Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak of something, but also of something happening. (In the proposition, “Green is green”, where the first word is a proper name and the last an adjective – these words have not merely different meanings but they are different symbols.)” (TLP 3.323). 42 See chapter 4 for Frege’s version of this, offered in his notation that displays predicates as unsaturated. 43 Unsurprisingly, Danish, with fewer words than English, provides better examples of this phenomenon: “Får får får”? (do sheep beget sheep?) is both a perfectly acceptable question and a perfectly well-formed and meaningful, albeit slightly incorrect, answer to the question.

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see the expression in the following way: “sI”. This makes it conspicuous that “Socrates” was always understood to be a sign that contributes in a certain way to a whole sentence – in this case as the name of an object we can predicate something of. Of course, for all we know there might have been a dog called Socrates that the person called out for, which would make for reference to a different kind of object. This change would not be a matter of well-formedness or syntax, but rather that of the kind of sortals associated with the object. This phenomenon is not philosophically interesting or relevant to our present concern, as we have a clear case of reference in both cases. What is important is the assumption that he was about to utter a well-formed proposition. Indeed, the reliance on a full sentence seems – unwittingly, I suspect – to be granted by Hochberg when he goes on to say that “we might never be able to figure out what she was going to say” (Hochberg, 2003, p. 42. My emphasis), thereby showing that he also understands that the important things about the sign was not its actual occurrence, but its disposition to be a part of something yet to be completed. If for none other than pedagogical reasons – never a great concern in Wittgenstein’s early writings – something needs to be said about our strong temptation to think that we effectively are able to quote words, and that we thereby quote the same as what we see at work in the proposition. In connection with the suggestion that the proper representation of expressions is by means of a variable, Wittgenstein suggests that failure to appreciate this gives rise to “the most fundamental confusions of which the whole of philosophy is full” (TLP 3.324, parenthesis omitted). While we must postpone this badly-needed therapy until we have treated propositional complexity in greater detail, we can for now note the occasion for confusion between name and proposition: For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word. Thus, it was possible for Frege to call the proposition a compounded name. (TLP 3.314)

We will explore Frege’s view of the proposition in chapter 4, but the point Wittgenstein is making also applies in our present context. On paper, it appears easy to extract the name from the proposition and present it independently, as in this setting both word and proposition have a very similar appearance whether written down or spoken. It is likely to be this fact that leads Hochberg and others to level their objection.44 However, as _____________ 44 A similar deception informs Lowe’s (1997) objection against the thesis of syntactic priority. The objection is that we seemingly name and quantify over propositions, which are otherwise supposed to be not at all like objects. He takes this linguistic phenomenon to have provided a reductio ad absurdum of the thesis. Rather, when

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we will explore in subsequent chapters, propositions and names are only superficially similar in that we write both down, while essentially different in virtue of their combinatorial possibilities. The considerations in this section allow us refine Frege’s constraint: “If you want to gain an understanding of the logical form of a sentence, you will do well to consider the parts of the proposition only in the context of a proposition, the inferences such a proposition warrants, and other propositions that the signs can contribute to”. The TLP in fact presents the context principle in a way that resembles this, where it resurfaces as the distinction between symbol and sign: “In order to recognize the symbol in the sign we must consider the significant use. The sign determines a logical form only together with its logical application” (TLP, 3.327 f.). The greater part of FA is a demonstration of how the failure to be guided by the context principle had led various thinkers on the foundations of arithmetic to misunderstand the nature of what they were talking about. They did not have to make these mistakes – they just did. Likewise, we need not get the logical form of the sign “Peter” wrong, but consideration of how this sign contributes to the truth-conditions of various propositions will guide us if need be.

Whither Ontology? We have spent considerable effort expanding what Collins (1998) called “the short answer” regarding the reality of numbers, not so much out of concern for mathematical objects in particular but for the sake of understanding the meta-ontology that Frege brought to bear on a particular question in ontology. I return now to the widespread impression that there is something unsatisfactory about the kind of philosophy that the context principle embodies – that we are offered an unphilosophical answer to a philosophical question. Recall the Aristotelian remark about the huge variety of things that language is answerable to – things are said to be in many ways. While there has been little conscious recognition and exploration of this observation in the ontological debates we surveyed in the previous chapter, we also noted how Mayberry (2000) makes for an exception. Nevertheless, he draws the wrong conclusions from Aristotle’s observation. In connection _____________ Wittgenstein held “that there are no such things as facts” (NB 123), he was exactly making a logico-syntactic point: that despite appearances, facts are essentially unlike objects. We shall see more of such attempts at describing the symbolism and its worldly correlate in chapter 4.

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with his comments on the many things – some of them abstract – we speak about, he says: The profusion of these examples [of various different kinds of objects] is discouraging and mocks any ambition we might have to order or to classify [the objects]… I have no such ambition here. On the contrary, I want merely to call attention to these facts so that we may reflect on the abyss of difficulties they disclose. It is, after all, no easy matter to determine what does and what does not exist… (Mayberry, 2000, p. 31)

It is indeed not easy. For instance, at the time of my writing this, engineers and physicists are engaged in exceedingly complex operations in order to find out if the Higgs particle exists. However, Mayberry blurs two questions that must be kept separate. One is what we have called metaontological: What does it mean that something exists / is an object? This question gives rise to the formulation of a concept of an object that I have elaborated in the present chapter, with the important proviso that we may not want to restrict our meta-ontology to be concerned with objects.45 Another related question is this: What exists? Naturalism has long been thought to form the basis of an adequate answer to this question. I take naturalism to be the idea that philosophy has no privileged, foundational position when it comes to answering this question but must take seriously the dominant language in our best, ongoing natural sciences. Mayberry seems to think that providing an answer to the first of these questions in effect means providing an answer to the second. It is often suggested that the working mathematician says things that he does not believe to be true – namely that there (really) are numbers, sets, functions and so on – and that he stands in need of some account that allows him to escape a kind of intellectual dishonesty: Presumably, his meta-ontological outlook would not allow for such abstract objects.46 _____________ 45 We have after all mentioned facts, and in chapter 4 we shall say a little about a subset of functions, predicates. They all have in common that they are derived from reflection on the nature of complete propositions. 46 Melia (2000) presents the issue this way. Horgan and Potrþ (2006) develop an account inspired by epistemological contextualism to accommodate the perceived doublethink. Here we have the declared philosophical use of “really” alluded to previously:“‘Are there corporations? Of course! Are there really corporations? No!’ This is a specific philosophical usage of ‘really’ – not the only one that might be appropriate in philosophical contexts, to be sure, and one that is different from most uses of ‘really’. This specific usage is employed to overtly signal a shift into

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At this point, it is worth noting that there is one possibility that gets little consideration, namely that the working scientist is largely ignorant with respect to the first of the two questions above – the question that concerns meta-ontology. The possibility is that he has crossed a boundary, the crossing or ignoring of which was spurred on by early writings of Putnam, between science and philosophy. The distinction that I wish to maintain can be formulated thus: The philosopher considers the significance of asking questions about existence and at the most general level, delineates the possibilities and general methods of answering them, while the various sciences do the job of accounting for and settling the truth of propositions within their area, thereby making good their claims about what exists. Hence, the existence of electrons is determined by the scientists, the existence of species by the biologist, the existence of business cycles by the economist, and the existence of God by the theologian. We should not be surprised if the truth-conditions for the claims made in the different sciences are going to look quite different in the different cases, but I have attempted to show how they can share a concept of an object, based on syntactic criteria that are recognisable across the board. This is not the suggestion of a “mind your own business” policy to be strictly adhered to by practitioners of any given science. Arguably, most leaps in science happen when people transcend the sometimes arbitrary academic categorisations. An exemplary case is Darwin’s use of concepts and ideas taken from Malthus’s thinking. Rather, the distinction is intended to acknowledge the difference between the two questions above. We have, rather unusually, set out by answering the first and more general of these questions, and have then pointed to different sciences for their various, systematically worked-out suggestions as to what there is. When ways of identifying cultural, social and “everyday objects” are sought after, we shall have to turn away from the natural scientists. Philosophers along with everyone else make claims to truth every day when navigating the world.47 An example may clarify the matter a bit. We can imagine approaching a working economist, researching the behaviour of business cycles. He will _____________ a mode of thought/discourse governed by direct-correspondence semantic standards” (Horgan and Potrþ, 2006, p. 144). We have already suggested that the ontological dependency of train tickets or spurious sets do not make them less real, but this use of “real” made by Horgan and Potrþ does point to a worthwhile distinction. In some ways, the TLP operates with something like this with the idea of absolutely specificity being a marker of an atomic proposition, which mirrors the world in virtue of names that stand in for (vertreten) objects. 47 Quine at times speaks as if our everyday reference to tables and chairs is a kind of theory – a tendency also found in contemporary theories of mind. That seems to me to make a mockery of our concept of a science and its theoretical endeavours, but for present purposes, nothing much hinges on our choice of words.

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tell you that business cycles have to do with trends in large-scale economic behaviour and give some reasons why we take them seriously in our decision-making etc.. So far so good. Now, if we ask him: But do business cycles really exist? we will presumably have gone from the second question to the first question, not being content with a short answer. The economist may or may not have views on this matter, but I think a reasonable economist would either repeat himself and say what he means when he says “business cycle” – offer truth-conditions of sentences containing the singular term or the sortal, to do with fluctuations in aggregate economical transactions – or, alternatively, shrug his shoulders and send us to another department for an answer to our question. While working scientists may have no clearly-explicated concept of an object, philosophers will simplify things, sometimes too gravely, when giving an account of our language about different kinds of objects. I can cite two examples of this. Firstly, while we can all agree that there are mountains, Barry Smith and David M. Mark (2003) convincingly take John Searle (1995) to task for taking Mount Everest to be a straightforward case of an object whose existence is entirely independent of human beliefs and practices. Secondly, tables are often taken to be objects whose existence can be accounted for purely by reference to a certain arrangement of matter. One example of this is John Heil (2005), who entertains a discussion of the reality of tables purely in such terms. Meanwhile, Amie Thomasson (2003) identifies tables as what she calls artifactual, and not natural, kinds. The upshot of such a characterisation is that the existence of tables is in some sense mind-dependent: for instance, the existence of certain human intentions and practices are necessary for being a table.48 Thus, when presenting the meaning of the sortal “table” – what it means to be a table – one is then involved in accounting for something more complex than an arrangement of matter. Further explanation of the nature of the dependency is the significant task for those who want to clarify that part of reality. While I side with Smith and Thomasson respectively in what I take to be their greater attention to scientific and everyday language, nothing in the Fregean meta-ontology defended here hinges on their analyses being right. I only mean to draw attention to the fact that even philosophers _____________ 48 I leave aside the question whether the notion of intention or the notion of practice will best serve to account for the reality of tables. It is interesting to observe how the causal theory of reference has placed alien constraints also on the nature of an account of artifactual objects. See Thomasson (2003, p. 593 ff.)

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disagree about apparently simple matters when they start thinking more carefully about our language and what it purports to be about. In this way, the short answer may have a long and often interesting continuation. In Frege’s case, he sought to remind his sometimes psychologistically inclined readers that the existence of numbers is independent of minds and intentions. By relocating the second of the two questions above to the various sciences along with more everyday claims to truth, we have given expression to the concern that we found expressed in the Aristotelian scepticism. There is surely a huge variety in the kinds of condition under which we can truly refer to electrons, to numbers, tables and football matches. Nevertheless, across these different subject areas there are general logical forms, such as those displayed in propositions containing singular terms and their accompanying sortals. It is the explication of this which we have attempted here – not a full defence of realism in any of the areas suggested above or in theology for that matter. The argumentative move in the chapter that follows can be summarised as follows. In theology, language is employed that logically mirrors the language we ordinarily use to effect reference to objects; and that language comes with certain sortals whose meaning is subject to explication. And, in essence, that explication of logical form and meaning takes place by repeating and clarifying what is said in theology. Hence, the task that will be undertaken in chapter 3 comes down to making clear whether “God” or “god” are singular terms and what nature of the associated sortal is. The reader will recall that this is only half the task for someone who wishes to settle a question of existence. The other would be to have “[t]he truth of the relevant existential statement determined by the methods proper to that realm of discourse” (Dummett, 1981, p. 497). As the present task falls short of a treatment of realism with respect to Christian theology, this is not a place to engage in giving reasons why we should take language about God to be true. Engaging in the relevant science would in this case mean bearing witness and preaching, which was never the task of philosophy.49 Frege, in so far as he was concerned with a question in ontology and not logicism, had an easier task as he could rely on accepted arithmetical truths and only had to draw attention to logico-syntactic features. As will be clear from chapter 3, the theologian has, in addition to the question of truth, an unclear account of the syntactic role of “God” to contend with. _____________ 49 Regarding the truth of language about God, here is a programmatic remark at the outset of Barth’s Church Dogmatics: “Talk about God has true content when it conforms to the being of the church, i.e. when it conforms to Jesus Christ” (2004, I/1, p. 12). My brief account of the science of theology is by no means uncontested.

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What one can do when doing ontology as Frege did it, is to explicate the logical form of signs in different regions of language, and this will be our task regarding variants of the sign “God” in the following chapter. While matters are not straightforward in the case of statements referring to numbers (for instance, that they can have both substantive and attributive uses has been a subject of some discussion), or as we have seen, to tables and mountains, they prove to be even less so with respect to “god” and “God”. Thus, though dissatisfying to some, there will be work for the Fregean ontologist to do. The case study that is undertaken in chapter 3 aims to substantiate such a claim.

Conclusion It is time to summarise how the Fregean meta-ontology based on the context principle performs with respect to the desiderata that were presented in chapter 1: 1) The concept is universal in that it is derived from the concept of a singular term. Singular terms and sortals are found throughout all use of language. 2) The concept leaves cases out. In some cases, contenders for the title “singular term” are ruled out by relatively simple inferential tests. 3) The Aristotelian impression that “existence” or “object” comes with different meanings is preserved in the shape of significantly differing sortals. Biological objects are functional wholes and consist of some matter or other, while natural numbers are identified by their place in a series. An analysis of the existence of chairs and tables will arguably require an account of human subjects and their intentions and social practices. 4) Ordinary objects have a paradigmatic status because their corresponding singular terms are well-grounded. The notion of grounding involves agreed upon ways of identifying a given kind of thing, as well as the world offering examples of the relevant object – a fully fledged realism. Hence, when philosophers want to give examples of what is real, such objects will offer broad resonance. In addition to what is mentioned in (3), this resonance in characterising realism will make thinkers about reference to other kinds of object insist on qualifying what is meant by “realism”. It is important to make clear that when Frege makes use of examples like “the Earth”, he does so to draw attention to the similarity between

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sets of linguistic facts. Meanwhile, he took for granted that some statements of pure arithmetic are true, as are statements to the effect that the Earth exists. To repeat, we have said next to nothing about the truth of the statements of any region of language. 5) To some extent, the ontology suggested by the context principle runs counter to various intuitions and convictions. However, several of these intuitions are of a meta-ontological nature rather than intuitions stemming from ordinary language use. More work remains to be done to address these various meta-ontological convictions. I hope at least to have indicated how such answers can be developed. I registered a certain kind of disappointment with the short answer to a question in ontology. In response to such disappointment, we should note that a lot of questions about what exists, as they are addressed by natural, social and other sciences, require both instrumental and conceptual ingenuity. However, the examples relied upon in discussions in meta-ontology, such as truths about tables or the existence of prime numbers, require less of such ingenuity. Consequently, in these cases a short answer is more appropriate and often correspondingly uninteresting.

The Logical Behaviour of “God” Introduction: Criticism and clarification This chapter sets out to employ Fregean meta-ontology to a particular case: the question of the existence of God. It seeks to elucidate the logical form of “God” as it is used in the Christian tradition, and the exposition will evolve around the standpoint that “God” first and foremost exhibits the syntactic behaviour of a proper name. The analysis will rely on our criteria for being a singular term, supported by inferential and other tests that were elaborated in chapter 2. This also means that we must consider the character of the relevant sortal that allows us to identify the object in question, and here the sign “god” will also emerge as a sortal we need to possess in order to be able to identify an object. The use of capital letters usually gives away the occurrence of a proper name. However, with the case of “god” and “God” we cannot, for reasons that will become clear, use this as a reliable indicator. I will suggest that the linguistic phenomenon where a sign that usually functions as a name in certain cases is used as a sortal is of key importance when seeking an understanding of the logical status of “god”. Saying of someone that “he is no Churchill” is an example of this pivotal phenomenon. Before we proceed, we shall make some introductory remarks on how the Fregean approach compares with other prominent ways of approaching the question of the existence of God. Language about God has been subject to much criticism in 20th century philosophy. Taking a critical stance towards the way we use elements of language is by no means a novelty in the intellectual landscape within which the present kind of philosophy is conducted. Indeed, TLP 4.0031 has it that all philosophy is critique of language.1 To appreciate the elements of such a critique, we should distinguish two different forms it might take. The first kind of critique is levelled against the background of some general account of how language works. Logical positivism would be a prime example of this line of criticism, and Ayer did not miss the opportunity to criticise language about God in frequently repeated terms: _____________ 1

See e.g. Nordmann (2005, chapter 2) and Savickey (1999, chapters 1–3) for illuminating accounts of the history of this contention.

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Theism is so confused and the sentences in which “God” appears so incoherent and so incapable of verifiability or falsifiability that to speak of belief or unbelief, faith or unfaith, is logically impossible. (Ayer, 1936/1974, p. 152)

Below, I attend to a version of the first of the criticisms that Ayer and others have levelled. The charge of meaninglessness in the use of “God” is by no means wedded to a general acceptance of the verificationist credo. A recent repetition of the charge of nonsense, although expressed with some moderation, is found in Rundle (2004, p. 11 ff.). While Rundle maintains that issues of verifiability still present devastating problems for language about God, he is aware of the demise of this approach to semantics and maintains that “…it is important to stress that a failure in definition is more devastating than a failure to be verifiable” (Rundle, 2004, p. 23). He is right, and it is the more devastating kind of criticism we shall be concerned with in what follows. In addition to variants of logical positivism, Quine’s thesis of the inscrutability of reference is similarly posed against the background of certain views of meaning as rooted in the stimulus of an organism, while Putnam’s arguably most sophisticated challenge to realism is of modeltheoretic character. More relevant to the current theme, the notion of causality is often taken as a general key to an account of reference, and criticism of reference to God has been undertaken from this general, meaning-theoretic platform. These are all cases where the questioning and critique of language use is carried out against the background of an account of meaning that is itself questionable. Of course, I would like to think that my own criticisms and analysis carry more weight in virtue of the Fregean-inspired view of reference is more convincing. This convincingness ought to be gained by relying on general and basic, syntactic and logical features of our use of language. Furthermore, the approach should have appeal in virtue of it not being biased towards ascribing mind-independent reality to a certain, restricted range of objects, such as physical or biological objects. But ultimately, the Fregean concept of an object should only convince someone who is already broadly in agreement with the Fregean understanding of syntactic categories and of their importance for questions in ontology. The second kind of critique of language does not rely on a general account of language. Rather, it suggests that in some way certain parts of language have degenerated through systematic misuse. In a rather informal way, Karl Kraus’ aphorism that “[m]y language is the universal whore whom I must make into a virgin” aptly characterises this other approach to

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criticism of language.2 Meaning and use are intimately connected, and so are meaning and misuse. In a religious setting, Søren Kierkegaard would express a very similar contention at the outset of his career: Every Christian concept has become so volatized, so completely dissolved in a mass of fog, that it is beyond all recognition. To the concepts of faith, incarnation, tradition, inspiration, which in the particularly Christian sphere are to refer to a particular historical fact, the philosophers have chosen to give an entirely different, ordinary meaning… We would also wish that powerfully equipped men might emerge who would restore the lost power and meaning of words. (Kierkegaard, 1967–1978, p. 5181)3

This often more informal line of criticism tends to focus on how individual words are used and the setting in which they are usually found. Examples would be G. E. M. Anscombe’s criticism of the prevalent use of the concept of “law” in ethics without there being any law-giver. A similar line of criticism is found in Alasdair MacIntyre’s After Virtue (1985). His work makes the case that our moral language is a jumbled and incoherent mixture that unsuccessfully tries to reconcile different strands of thought, remnants of which are all preserved in the moral language of our time. This chapter will present a position similar to Macintyre’s: much contemporary use of “God” is unfaithful to how the sign is rightly used both as a name and a sortal, and it is often unfaithful to key content of this sortal. Thus, an integral part of the second kind of criticism consists in a clarification of our thinking. While the notion of criticism is often strongly associated with the notion of legitimacy, I will largely restrict myself to criticism in the sense of clarification. With this in place, the present chapter offers a clarification of contemporary use of “God” in theology and discussions thereof. The clarification has two strands, reflecting the two kinds of criticism outlined above. The first and most fundamental kind seeks to clarify what kind of symbol “God” is, that is, its logico-syntactic application. This first kind of clarification relies on the general, Fregean categories in ontology. The clarification will make use of the distinctions between a singular term, a predicate and a sortal that was explored in the previous chapter.4 The attempt at clarification will be guided by the thesis _____________ 2

3 4

Somewhat reminiscent of Frege’s insistence on looking at number statements in their quite ordinary use, Kraus finds a purity of language which is “akin in its vital force to the simple forms of speech used by unspoilt people” (Cited in Savickey (1999, p. 20). Frege had his own fights. In “Thought” (1918/1997, p. 334) he famously speaks of being compelled to fight against language, though language is not his concern. The otherwise detailed study by Sobel, Logic and Theism (2004), records the difference between “God” as a name and as a general term, but does little to explicate it.

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that what takes place when the word “god” is used in the Christian tradition is frequently a case of a sortal having grown capital letters and thus behaving like a proper name. The phrase is borrowed from Peter Strawson: The capital letters are a sign of that extra-logical selectivity in their referring use, which is characteristic of pure names. Such phrases are found in print or in writing when one member of some class of events or things is of quite outstanding interest in a certain society. These phrases are embryonic names. (Strawson, 1950, p. 341)

Strawson spoke of substantival phrases such as “The Glorious Revolution” growing capital letters. When the background conditions for such a transformation of the character of a sign vanish or are significantly altered, as I will argue they frequently are in the Christian case, the significance of the linguistic phenomenon can and has to a great extent become opaque to its users in theology and philosophy of religion, which makes the proper use and discussion of the sign and the symbol difficult and potentially confused. The second strand of clarification will present and elaborate one of the most relevant sortals when seeking to name God, namely “king”. Against objections from Wittgenstein and from some of his commentators, I shall defend the meaningfulness, but not the truth, of the claim that in the Christian god we have an instance of true kingship. The two attempts at clarification have the potential to clear some of the conceptual fog that Kierkegaard and others have found in Christian language about God. We shall seek to make good the clarity thus achieved by concluding the chapter with an analysis of a New Testament passage, the meaning of which often remains either neglected or elusive. One of later Wittgenstein’s remarks on religion promises much by suggesting a survey of the kind of things believers say, with a view to clarifying the logical status of “God”: How are we taught the word “God” (its use that is)? I cannot give an exhaustive systematic description. But I can as it were make contributions toward the description; I can say something about it and perhaps in time assemble a sort of collection of examples. (Wittgenstein, 1980, p. 94)

However, Wittgenstein never offered anything close to a description of the word “God”, and his interest in religion was mainly focused on the religious practices of primitive peoples and elements of his Jewish heritage. When he treats of issues in Christian theology, the remarks are quite tentative, at times they have character of confession and they tend to treat far more complex issues than we wish to throw light on here. Meanwhile, his remark does raise a relevant question. With what claims shall we begin our analysis? An obvious point of departure might be the sentences that believers utter qua believers in God. However, the

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history of the Judeo-Christian religion is itself a long history of quarrels over, and adjustments to, what was considered the right use of the word “god”. Recall from chapter 1 Frege’s comments on elucidations offered at the outset of a science. We use words (e.g. “line”) in certain simple and fundamental sentences to get across what we mean and so to ensure that we are speaking about the same things. In FA, Frege had to direct our attention to the use of number words in quite ordinary contexts to make us appreciate logical features of arithmetical language. Where shall we direct our attention when attempting to achieve an overview of logical features of language about God? In this connection we emphasise the method in theology that Barth took from his reading of Anselm. Theology has to start with what is given to it, namely the threefold revelation of the word of God, and then proceed from there. To appeal to any other (linguistic) authority in order to confirm the importance of this form of address and ways of speaking – the phrases we must focus on – would imply a reversal of the priority between theology as a science and reflections on it. Should anyone want to claim that to appeal to linguistic authority in matters of language about God is to give too much of the game away, we should reflect how other sciences qua linguistic practices will generally do the same. If questioning regions of language – say the existence of business cycles – we suggested that the first step of an economist would be to provide elucidatory examples from his science, in order to clarify what it means to say that business cycles exist, and then, using the relevant methods, make the case that the cycles exist. The overall message of chapter 2 was that this essentially is the right answer to an external criticism of existence claims, while we sought to allow some conceptual space for a genuine external engagement with any given science.5 Finally, we must remember that we are not addressing the truth of religious language, but the logical form and meaning of it. The signs that display a logical form are an integral condition for saying something true or false. For example, when, in the manner of Field, someone insists that language about God is false across the board because there is no God, he will at least have to know what it means to say that God exists – the conditions that have to obtain. What lies behind and motivates Field’s objection to the existence of numbers is precisely an agreement on the logical structure of language about numbers as well as a grasp of the relevant sortals, coupled with the view that mathematical statements are truth-apt and often true. Together, these claims suggest the existence of _____________ 5

For present purposes, we leave the much discussed relation of theology to e.g. the sciences of history or biology as an open question.

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mathematical objects, which is his key motivation for Field’s reformulation of parts of mathematics. Presently, it is the more modest goal of an agreement on logical form of “god” that we are working towards, not a fully fledged defence of the claim that God exists. In trying to achieve the modest goal, we will in the main rely on what, according to Barth, is one of the threefold manifestation of the word of God, namely the Christian scripture.

Geach and Durrant on the Logical Status of “God” Michael Durrant and Peter Geach, both heavily inspired by Frege in their approach to philosophy, have approached the question of language about god in a way that has strong affinities with Fregean meta-ontology. On this basis, Durrant defends the position that Ayer suggested: When one actually makes this linguistic survey, it emerges… that any attempt to set out a scheme in which “God” has a singly logical status such that a coherent and consistent account of the form of proposition expressed by sentences [of the form “God is F”] can be offered, is doomed to failure. No such scheme can cope with the manifold and inconsistent logic of “God”. (Durrant, 1973, p. x f.)

Durrant makes significant efforts to argue against the position that “God” exhibits the behaviour of a proper name. Since both Geach and Durrant are arguing against the position I defend, I shall engage in a point by point rebuttal and accommodation of Durrant’s and Geach’s arguments. As it will emerge, much of their argument is carried out within the framework of Roman Catholic theology and, more particularly, within the framework of Aquinas’ writings. To what extent they are true to the letter and spirit of Aquinas’ thought is a question far beyond the task pursued here. I will restrict myself to confronting the various arguments and to attempting to show how Durrant and Geach display a lack of sensitivity to actual language use that leads the former in particular to conclude that there are logico-syntactic grounds for saying that there is something fundamentally wrong with language about God. I will proceed by showing firstly how the reasons that Geach and Durrant provide against taking “God” to be a proper name are based on recognisable linguistic phenomena that do not lend themselves to the conclusions that Durrant and Geach wish to draw. I will then begin to offer my own account of the logical form of “God”. This exposition will address and accommodate some further arguments that Geach and Durrant have offered in support of their view.

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Transliteration Before we follow Durrant and Geach in their analysis of the logical form of sentences containing instances of the sign “god”, there is one simpler argument that both Geach (1963, p. 109) and Durrant (1973, p. 18) claim as linguistic evidence against the position that “god” functions as a proper name. While we tend to translate other words, our tendency with proper names is to transliterate them. For example, when relocating from one country to another, it comes as no surprise that words that appear to have a familiar function sound quite different. Nevertheless, when you move, you tend to take your name with you as it is. If that name does not make for a good phonetic fit with the relevant language or if it employs different letters, you either maintain it in some form anyway or represent it in the closest corresponding letters in the language that the name is transliterated into. The English name “Roger” is, if pronounced in Danish, phonetically equivalent to the Danish word for beet. Typically, the name would either be changed somehow or be retained in English pronunciation, but in any case it would be recognisable as a part of the language of its “owner”. This makes for a contrast with “God”. The variants of the Teutonic “Gott” are relatively new inventions and were never used in any of the Judaeo-Christian scripture manuscripts whose creation involved, amongst other languages, Hebrew, Aramaic and Greek. The sign just quoted has little in common with the Greek “Theos”, the Latin “Deus”, the Aramaic “Alaahaa”, the Hebrew “elohim” or “YHWH”, the Rwandese and Kirundi “imana” or Arabic “Allah” to mention but a few signs used in connection with the Christian god. The argument is that the sign used to speak about God thus lacks a central feature of proper names. Supposedly, “God” has been translated, not transliterated, and thereby does not display the behaviour typical of proper names when being used in different languages. In consequence, it isn’t a proper name. All we need to do for now is to note that the linguistic evidence simply does not support this conclusion. Durrant and Geach are involved in a case of a genetic fallacy: You cannot phonetically trace a piece of language to an origin that has the character of a proper name. Therefore, that piece of language does not behave as a proper name. To offer a counter-example, consider the degrees of phonetic change between various languages. One slight change would be from, say, “The Queen’s English” to Scottish English. Use of names will undergo a change, but should be easily recognisable. Next we can again envisage a change from English to Danish, where some names will not work very well, while others are smoothly integrated, with respect to spelling and with respect to phonetics, into the

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new language.6 We can continue this process to the point where it is not clear that there are any letters or anything phonetically in common between the two languages. This often is the case with Chinese immigrants in many Western countries. The immigrants adopt names that are generally not thought to have much of relevance to a transliteration in common with their Chinese names. This phenomenon, however, does not make us say that their adopted names do not name them – that they do not function in the appropriate way. After sufficient training of their environment, this name will perform its function just as well as their previous name. Similarly, to say that there is a significant phonetic distance from ancient Hebrew to modern English is in itself not a reason for construing “god” in any of the ways suggested. God is a god The title of this section mirrors Wittgenstein’s example “Green is green” (TLP 3.323), as the next argument against taking “God” to function as a proper name relies on the kind of sign phenomenon that Wittgenstein drew attention to in this passage. Here, the same type of sign functions in different instances as different symbols. Our next argument against taking “God” to function as a proper name is found in Durrant (1973, p. 16) and Geach and Anscombe (1963, p. 109). The objection relies on Frege’s criteria of proper names in FA, §50–53: Proper names cannot be prefaced with “many”, “several” and “one”. However, this kind of prefixing of “God” or “Lord” takes place in scripture. Hence, “God” does not behave like a proper name. As our initial response to this argument, we should simply note two linguistic phenomena that speak against the inference that Geach and Durrant draw. A second, more elaborate response will be offered below, where I show how the distinction between the use of “god” as a sortal and as a name in fact serves a purpose in Judeo-Christian language about God. The first linguistic phenomenon that speaks against Geach’s and Durrant’s inference is the kind noted by Frege when considering sentences like “Trieste is no Vienna”. This makes for one of several cases where a sign that normally serves as a name becomes part of a predicate. The history of commercial products would furnish us with more examples. “Xerox” and _____________ 6

In 1920 the Danish State Police registered names phonetically as part of their effort to keep track of foreigners. Spelling of names was subject to change when the name-bearers “integrated” and thus the spelling of names was insufficient to identify people.

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“Hoover” are examples of names that have become sortals for apparatuses as well as activities. We should not and do not normally conclude from a proposition like “Tony Blair was no Churchill” that “Churchill” does not normally function like a proper name. The sentence conveys something that people with sufficient knowledge about Winston Churchill and Tony Blair easily understand and that they can reasonably – despite its significant vagueness – assign a truth value to. More generally yet, it is not uncommon that we rely on using a type of sign that usually performs one kind of logico-syntactic role in a way that makes the sign look out of place, and that we nevertheless manage to communicate in this way. Monroe Beardsley (1962) suggested this as a way of detecting uses of metaphor. The sentence “There are not many Churchills” is readily construed as a statement about the political environment, and arguably a harsh judgment about the blandness of its nature and players. This use of language, where a name is used as a sortal is dependent on there being a strongly established use and knowledge of the name in question – Strawson spoke of an outstanding interest in a given society. If there is not in some way something special about an individual, the effect cannot be achieved. If I say: “There are so few Smith’s” about a common, quite ordinary acquaintance, it would either warrant the question, “What is so special about Smith?” or alternatively be understood as a case of sarcasm, relying for its effect on the failure of “Smith” to function as a relevant category, since Smith belongs to no recognised special class. That is, we are not sure whether indeed the sign of a name here is sufficient in character for the category switch to take place, and in an act of interpretative charity we assume that what has been said is not a garbled verbal hash of independently recognisable linguistic units but is somehow significant in a way yet to be worked out from the way the parts contribute to the whole. The phenomenon is more familiar as a form of appraisal: “There are few John F. Kennedy’s” or “There has only been one Churchill”, which are taken to mean that there are few or no people around with a similar set of characteristics to these two statesmen. That is, the change from a sign featuring as a name to its functioning as part of a predicate is dependent on “Churchill” being used as a name in many other contexts. The naming of the Churchill antedated him getting a certain set of attributes attached to his name beyond the sortals (such as human being and, later, politician) that would allow us to identify him in the first place. When such attribution, in this case of a person, adds up to the description of someone outstanding or remarkable, it becomes possible to turn the name into a concept that relies on the set of attributes that over time have been attached to the name.

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This concludes the first linguistic observation that must be taken into account. A name that has attained a certain distinction – that names a sufficiently remarkable object – can become useable and convey information as part of a predicate. The second linguistic phenomenon is more straightforward. It simply consists in Wittgenstein’s observation that a name and a concept may share the same type of sign. “Green is green” and “God is a god” are perfectly well-formed. In both these cases, the name just so happens to share typographical criteria of identity with the sortal. That does not mean that both signs are not put to use in a normal and correct way. The latter example differs from the former only in it attempts to tells us what sort of thing “god” is, while on one disambiguation of the first sentence being green is not a sort of thing that Mr. Green can be – it is not a sortal. In conclusion, the first point to make is that the fact that we find instances of the sign “god” in places other than where we expect a proper name to go is no good reason to think that “god” cannot and does not behave as a proper name. Secondly, it is no reason to suggest that there cannot be good and meaningful uses of the sign “god” as part of a predicate together with “God” used as a name. The impression that such usage should result in a logically incoherent use of “God” is quickly dispelled, and, as I suggested, the impression essentially arises from taking a type of sign as an unproblematic guide to correctly identifying a symbol. The motivation for Geach’s and Durrant’s view is partly found in their view of questions of existence. Given their Fregean background, it is similar to the one we defended in chapter 2. In particular, they emphasise the need for a sortal and Durrant maintains: …it is only if “God” is construed as an “affirmatively predicable” term (Geach and Anscombe, 1963, p. 89) that it is possible to affirm that God exists, that there is a god. (Durrant, 1992, p. 72. Citation style altered)7

This sentence gets Durrant involved in linguistic confusion, stemming from the combination of the actual use of a type of sign set alongside conflicting directives for its use. Firstly, we are supposedly told something about the sign “God” and how it must function. However, Durrant then goes on to put the signs “God” and “god” to use in two different logical roles that, judging from the setting of the argument, are nevertheless supposed to be semantically equivalent – the second being a rephrase of the first. We are left wondering what we learn something about. The first _____________ 7

See also Geach (1969, p. 57) for a similar contention. For present purposes, we may replace Durrant’s and Geach’s notion of an “affirmatively predicable term” with the notion of a sortal.

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occurrence, “God”? Or the second, “god”? Judging from the use of the capital letter, we learn something about the former. However, on that assumption, the following problem arises. Durrant seems to suggest that these two occurrences of “God/god” are equivalent. If so, he can either say of both or none that they exist, but not one of them exclusively, as he seems to suggest. Durrant’s problematic use of language emerges clearly if we replace in the little piece of argument “God” with a sortal like “man”: …it is only if “Man” is construed as an “affirmatively predicable” term that it is possible to affirm that Man exists, that there is a man.

This way of speaking leaves us with two questions rather than one. One is whether some kind of abstraction from all human beings through history should be included in our ontology (in the same way we may discuss if there is such a thing as the spirit of the German people); another is a rather banal one, which warrants an affirmative answer: there are men. At any rate, these are two different questions, corresponding to two different uses of the sign “man”. Consequently, no unambiguous conclusion about the use of “God” or “god” emerges from Durrant’s passage. In the fashion that we described at the conclusion of chapter 1, he is trying to speak about the meanings of signs, and even as he tries to lay down rules for their proper use, transgresses those rules. Nevertheless, there is something right about Durrant’s initial contention, which is the fairly general idea that we explored in chapter 2: Only if we are in possession of a sortal can we use a name to refer to a thing – or the same contention in its ontological garb: to be is to be an F. However, the fact that the sign “God” is employed both as a name and as a sortal leads to confusion in the analysis of the logical status of the sign. In the following two sections, we shall therefore treat the name and the sortal respectively.

“God”, the Name We naturally assume that we know well enough how to speak about God, and that we inter alia have a firm grip on what kind of thing God is or God would be, should he exist. To challenge this idea, I offer the beginnings of the kind of catalogue of religious language that Wittgenstein suggested, but few, including him, have worked out in the context of philosophy of religion. However, in making such a challenge, I will typically be on the brink of transgressing against it. I use signs in a certain way, but I use the same type of signs as those with whom I wish to take issue. I shall have to

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elucidate the workings of a type of sign “God” before I am able to appeal to a symbol – the sign in its proper application – as a linchpin in my criticism. What I cannot do is appeal to or otherwise assume a common background agreement regarding the type of sign “God”, as I suggest that there is radical confusion about it. For my suggestion to gain force, I must engage in the making of a sort of catalogue that clearly elucidates how the relevant signs work. It is only on this basis that, in the manner of Frege’s criticisms of various construals of statements of number, I can take issue with certain uses of the sign “God” as being unfaithful to the theological equivalents of Frege’s reliance on quite ordinary uses of statements of number. In making this catalogue in order to clarify the use of the relevant signs, I will have to engage in areas of investigation that are far removed from mainstream analytical philosophy of religion. Particularly, I will have to engage with historical and philological studies of the relevant biblical sources. I cannot here settle any of the questions and standing debates concerning these sources and, more generally, the relevance of historical methods in offering an account of the history of Israel. The historical account is detailed relatively to the relevant, in this case logico-syntactic, features that I wish to draw out. My account may be, and is, I am sure, historically inaccurate in several respects. The catalogue takes as its starting point Christian-Judaic scripture and is aided by a number of commentators.8 To begin to grasp the logical behaviour of “God”, I will follow suit with the consensus that emphasises the centrality of the book of Exodus in coming to understand the language about the god of the Israelites. Before offering this account, we should note a contrast with the tradition of naming we are familiar with in our day. Our naming of infants is to a great extent a rather arbitrary process, bound by legal constraints9 and at _____________ 8

9

Most importantly, the book length studies of Mettinger (1988), Brettler (1989) Moberly (1992), Moor (1997), Burnett (2001), Lang (2002) and Lemaire (2007) as well as Seitz (1998/2004) and Thompson (1992, 1999). Given the great uncertainty regarding the historical facts and dispute over their relevance to theology, there is considerable disagreement between the writers on how to solve the historical puzzles that the bible throws up in relation to its cultural environment. Moreover, when claims are made that “It is not a good idea to believe in a god when he is a character in a story” (Thompson, 1999, p. 303) historical commentary becomes overtly “ideological” and compounds a range of questions, in this case at considerable expense of detail in regard to our present concern. Just as theophoric names serve as an indicator of the worship of various gods, so have various European governments sought to restrict name-giving – often with Jews in mind – for political and religious motives. The laws passed by the Nazi regime in 1938 regarding names of Jews is but one of several examples. Mean-

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times guided by the use of literature that offers information about the etymology of names and about some of their prominent bearers. Even against this background, it would seem that names are more or less random appendages. Not until the person’s history unfolds might we get a kind of linguistic feeling that there is something fitting about the name and what it names. The Old Testament displays a different naming tradition where the name is far more suggestive of what it names – of who we are or the significance of the place that is named. This was made possible in part by people adopting names other than their given names and partly by the fact that names could contain a degree of semantically significant compositionality, which could be parsed by the listener. Moses named his son according to the circumstances in which they both found themselves (Gershom, “a sojourner there”, referring to Moses’s escape from Egypt). Jacob – so named from circumstances surrounding his birth – inquired about the name of his divine wrestling opponent but in reply he was given a new name himself: Israel. This new name was suggestive of a radical change in who Jacob/Israel was. Thus, in the Old Testament, the opposite of superficiality and indifference is suggested when God tells Moses that “…I know you by name” (Exodus 33:17, NIV). In addition to this closeness between a proper name and its bearer, the pronouncing of names would be a central legal act in connection with the exchange of land and the general claim to property rights. It is in this light that we should understand Jeremiah’s exclamation that God’s name is named, or invoked, over Jeremiah’s name. The prophet is the property of God, and elsewhere in the OT, we see similar claims about the temple (1 Kings 8:43) and the people (Amos 9:12), and this connotation of a name survives into the New Testament, where James reminds his congregation that they are now considered the property of Jesus as his name has been called over them (James 2:7). Our account of the logical form of “God” begins with Moses, at a point in his life where he was living far away from his own people. The son of a Levite, he was raised by an Egyptian and named as one (Lemaire, 2007, p. 24). After avenging the mistreatment of one of his Hebrew kinsmen at the hands of an Egyptian official, he is estranged by his own people and by the Egyptians. The Pharaoh wants him dead. Not recognised by the Hebrews as one of their own (Exodus 2:14), he flees to Midian, where he is regarded as an Egyptian. He marries the daughter of a priest and raises a son. At this point, he cannot be assumed to be very knowledgeable about the god who _____________ while, Zionists would advise migrants to Palestine, and later, Israel, on naming in accordance with Hebrew tradition.

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was to call out the Hebrew people from Egypt and so play a key role in the forming of a nation. He is “an alien in an alien land” (Exodus 2:22, NIV). One day, he is presented with an elohim10 at a sacred place.11 Moses is informed that this elohim is the same as that which appeared to Moses’ ancestors and was the elohim of his father, the Levite (Exodus 3:6). The elohim intends to come to the rescue of those oppressed in Egypt. Moses is to worship this elohim on the mountain and be his spokesman before the Pharaoh. Moses, being an adopted child, not recognised by his kinsmen, does not recognise this elohim as his own or himself as a part of the people he is to call. In accordance with this, the elohim speaks of the people as being distinct from Moses. Consequently, Moses quite naturally asks “Who am I?” (Exodus 3:11, NIV) that he should address these people and expresses his concern: “Suppose I go to the Israelites and say to them ‘The God [elohim] of your fathers has sent me to you’ and they ask me ‘What is his name?’ Then what shall I tell them?” (Exodus 3:13, NIV). Given Moses’ estrangement from the people he is to address, displayed in Moses’ “your fathers” rather than “our”, and his lack of knowledge of this particular elohim, he is asking a very reasonable question. There would be many elohim, where YHWH (the four Hebrew letters “Yodh”, “He”, “Waw” and “He”) is only one among others such as El, Baal, Marduk and others. Naturally, the people he was sent to address would want to inquire which elohim Moses was sent by.12 Moses is in fact offered two answers to his question. We shall treat each in turn. We begin with the second answer. The second answer given to Moses is simply that he should let people know that “[YHWH]…has sent me to you” (Exodus 3:15, NIV). The uses of the Hebraic equivalent of the signs “elohim” and “YHWH” have led commentators to pursue and develop Wellhausen’s documentary hypothesis, suggesting that a number of writers _____________ 10 For more on the concept of an elohim, see the following section. It is a plural expression, but is frequently associated with the singular personal pronoun. While recognising the need for an explication of this sortal, we may for now simply follow Burnett’s (2001) suggestion and translate it as “deity” or “divinity”, or, as it is frequently used as a way of picking out an individual in a suitable context, “the deity”. 11 The sacred place is often described as a bush. In the Medianite dessert, the bush is the equivalent of the tree found in traditional sanctuaries dedicated to the god of the fathers (see below), along with a standing stone and an altar. Moses is probably found in the sanctuary over which his father in law presided as priest. 12 As Burnett (2001) points out, Moses’ ignorance about the elohim of his Hebrew ancestors may not have been complete, as he displays recognition and awe when being told that it is the patriarchal elohim of Abraham, Isaac and Jacob that is about to send him on a mission.

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have been at work in the first books of the bible, and that the signs could act as a guide to which source or redaction is found where. Contrary to this, Moberly (1992) suggests that rather than operate with the assumption of different sources or redactors of the first books of the Old Testament, we should see the use of “elohim” and “YHWH” as gently easing the reader into using the name “YHWH” by way of the sortal “elohim” as it is found in Genesis 1 and throughout. The suggestion is that rather than distinguish sources when seeing the signs “elohim” and “YHWH”, we should distinguish the perspective of a disloyal Egyptian noble, Moses, who is being introduced to YHWH, and the narrator/reader who is familiar with the people and its genealogy and history. The name of this particular god, YHWH, is first found in Gen 2:4 without any explanation as to how he got this name and how humans eventually came to use it.13 Genesis relates how people “began to call on the name of [YHWH]” (Genesis 4:26, NIV). The notion that the name of the elohim that was to go before Israel is introduced at this point will have to be squared with the account of the name being introduced in Exodus 3. Inspired by Moberly, Seitz (1998/2004, Chap. 17) has suggested that the repeated, latter introduction is a self-conscious anachronism on behalf of the narrator – an anachronism to which the writer and his contemporary readers would ascribe no deep theological significance. They shared knowledge of YHWH, and read about the introduction of the particular god by means of the sortal “elohim” which had also been used to identify the god of the patriarchs, Abraham, Isaac, and Jacob. So Burnett: …the general designation of this god [i.e. the ancestral deity] as “the patriarchal elohim” allows various and distinct traditions of ancestral gods to be included into a composite representation of this deity. In the terminology of family religion, the designation of a single ancestral ’Člǀhîm facilitates both the inclusion of various traditions and the amalgamation of these into the representation of a single deity. This is not to mention E’s [the redactor] designation of the patriarchal deity simply as ’Člǀhîm . The use of ’Člǀhîm serves not only the forging of a single “god of the fathers”, but also the identification of the patriarchal god with the national deity Yahweh, the god of the Exodus. (Burnett, 2001, p. 68)

_____________ 13 Mettinger (1988) and Lemaire (2007) defend the position that we should associate the geographical location of the burning bush theophany firstly with other biblical references to YHWH coming from the south (e.g. Deut. 33:2, Judges 5:4–5) and secondly with Nabataean uses of versions of “I Am” when addressing their god. In biblical Sinai (not an entirely well-defined area) the Nabataeans may well have had interactions with the Medianites whom Moses encountered. Finally, a god would frequently be known by the same name as a geographical region, and in the same breath as they speak of Bedouins, Egyptian sources mention a Yhw region/deity. The affiliation between the Hebrews and people of this region is affirmed in Exodus 18:12, where a common sacrifice is made. Cf. Moor (1997, p. 123 ff.).

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Burnett (2001) suggests that the main connotation of “elohim” is that of a patron deity which in turn is “any god who, by virtue of a unique association with a particular individual, social group, or place, was understood to act as its divine representative and to advance its welfare. In the Hebrew Bible reference is made to the patron deity by use of the general term ’Člǀhîm” (Burnett, 2001, p. 63f.). That is, gods are here individuated as x’s (an individual or a society) god, and the devotion and commitment is (mostly) mutual.14 Burnett goes on to suggest that this aspect was adopted in the description of YHWH, who becomes a patron of the nation as he had been of the patriarchs. In sum, the distinction between a name and a concept can and has contributed to answering the intricate source-critical question of whether and how “Yahwist” and “Elohist” redactors or composers are at work in the Pentateuch, where the idea is that redactors are characterised by the designation (“YHWH” or “elohim”) they use when speaking of the god of Israel. Burnett (2001, p. 121ff.) suggests that certain features go with the use of “elohim”: A certain ethical sensitivity, an emphasis on the deity being supernatural, particularly “international” contexts and close association between god and patriarch. As we shall continue to explore, both name and sortal can easily have been used by one writer in order to achieve certain effects. Indeed, particularly when offering an account of the introduction of something new, one will want to convey what kind of thing is being introduced, and here, a sortal is used. We have now considered the second answer Moses got when enquiring about the identity of the elohim. The first answer Moses receives is anything but plain and straightforward, and there is no strong consensus on any exact understanding of the answer. Nevertheless, the answer that the elohim initially offers has been ascribed a theological significance that has been accorded to few other passages, particularly in philosophical circles. Moses is apparently fobbed off with “’ehyeh ’asher ’ehyeh”, translated “I Am who I Am” or “I will be who I will be”.15 The Hebrew signs can be seen as a play on the initial assurance offered to Moses in verse 12 (“I will _____________ 14 See also the use of “god” (“elohim”) in Genesis 48:15f: “The god before whom my fathers Abraham and Isaac walked, the god who has been my shepherd all my life until this day, the (divine) messenger who has redeemed me from all harm”. Translation from Burnett (2001, p. 138)). A constant theme in the use of “elohim” is of the god “being with” the person in question. 15 In the traditional choice of the former translation several commentators have located what they take to be the infusion into scripture of an essentially Aristotelian metaphysics that degrades potentiality in favour of actuality. This perceived degrading was transmitted through Averroes’ commentaries and supposedly found clear expression in Aquinas’ view that God is pure actuality.

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be with you”). Accordingly, the account of the novel answer is as follows: Moses asks “Who am I?” (Exodus 3:11, NIV), and YHWH’s response reveals, for the first time, mutuality between Moses and the people he is to call: “I will be with you”, where the “you” is in the plural. According to this understanding, YHWH equipped Moses not just with what was sufficient to convince the Hebrews – knowledge of his name, “YHWH” – but also a hint that this god’s intentions and nature would be reflected in the unfolding events. Thus, at the beginning of one of the most famous of those events, the god pronounces that, “The Egyptians will know that I am [YHWH] when I gain glory through Pharaoh, his chariots and his horsemen” (Exodus 14:18, NIV). This knowledge is imparted again and again as the Egyptians have an increasingly hard time, ultimately faced by the sea (peoples) at the Sea of Reeds.16 Events unfold in order that, as we are repeatedly told, “they may know that I am YHWH”. The theophany is taken to be an account of how God introduced himself to Moses in order to teach a whole generation to address this elohim. If something new is revealed – as it is claimed in Exodus 6:3 – it is the extent to which this elohim lets his name gain currency through the spectacular rescue of the oppressed people in Egypt. These events came to define the group of people that gained their identity through the call of the elohim and the many events that followed. The narrative reaches a conclusion in the Decalogue, where we very clearly see the distinction between a name and sortal in the naming of God: “I am [YHWH], your [elohim], who brought you out of Egypt, out of the land of slavery” (Exodus 20:2) Other elohim _____________ 16 I have already alluded to the intricate question of the relation between the disciplines of theology and history. The parenthesis is made in recognition of Moor (1997, §4.6) and what he perceives to be an unnecessary “dehistorisation” of salvation history. Moor maintain that in other writings, the Israelites would equate “the sea” with “the peoples of the sea” (see. e.g. Psalm 68 and Habakkuk 3), and anyone who in faith sees divine deliverance in the events of the escape should be able to join in with this kind of speaking. Moor offers the following account of the relation between Israel (personified in Moses) and Egypt: The pharaoh was confronted with various sea-faring nations. This allowed a party in the previous power struggle in Egypt to escape the new ruler, Pharaoh Setnakhte. The escaping party had offered the silver and gold that they had laid hands on during their brief rule to a group of Canaanites in the hope of support. An extraordinary escape was made and Pharaoh Setnakhte was distracted from the crushing of this opposition by attacks from the sea peoples. While “Moses” receives no mention, “Baya” from the north does. Originally a royal scribe, he caused outrage by treating the Egyptian god, Amun-Re, as a man and not as a god. Baya has been depicted as standing while others are kneeling. He rose in the ranks through his association with the widow of the deceased Seti II, Pharaoh Tausret. While this does not amount to what we read in the book of Exodus, there are significant parallels.

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would try to win the allegiance of the Israelites, but the Israelites were to obey and worship YHWH only. What to Moses initially appeared to be a rebuff can be seen as a signal that the full meaning of this name is yet to be revealed. Much as knowledge of the name “YHWH” may have helped Moses and Aaron to convince the Hebrews (Exodus 4:29f.), it could have been their ability to explain the name as well as their knowledge of it that helped gain the trust of the Hebrews. We are not told what exactly did the trick, only that the Hebrews believed and worshipped on account of what Moses’ mouthpiece was conveying. The fact that little fuss is made of this linguistic transaction between Moses and the Hebrews would further suggest that, according to the narrative, there was nothing new – except to Moses – about the name of the elohim. As events unfolded, meaning was added to the name in the sense that the name was made distinct in a way that would make it suitable for use as a sortal in the same Strawsonian sense as “Trieste” and “Churchill”. In this sense, the Israelites (Exodus 11:7), the Egyptians (Exodus 7:5) and Pharaoh (Exodus 7:17), the other elohim (Exodus 8:10), the earth (Exodus 9:16) and the entire creation (Exodus 9:29) did not yet know the name “YHWH” (Exodus 6:3). Moses continues to lead the exodus, and his successor, Joshua (Yehoshua)17 has the first Yahwist name on record in the Old Testament. Through a number of conquests and treatises, he continues to give shape to Israel. What matters here is not whether the distinction between a name and a sortal will convincingly answer the hugely complex source-critical questions that arise throughout the Old Testament canon. What matters for our purposes is that throughout the Old Testament there is a use of “elohim” as a sortal, as well as a use of the “YHWH” as a proper name. That a sortal features as a central part of language about God also explains the quandary a number of writers (including Durrant, treated above) have expressed over the supposed translation, rather than transliteration”, of the name. Sortals and predicates are rarely transliterated, and such a general term features centrally in an account of the logical status of “God”. Perhaps one of the clearest examples of this crucial distinction is in the more “international” setting18 of the spectacular showdown on Mount _____________ 17 Its Greek transliteration coincided with the Greek version of “Jesus”. In Greek, both would be “Iesous”, and so, Paul would add “Christ” with the additional purpose of disambiguating the name. 18 Burnett (2001, p. 70ff.) gives a number of examples where the international or otherwise general setting makes the use of “elohim” far more prevalent than “YHWH” in connection with reference to a god, be it YHWH or others. Examples are the interaction between Jonah and the Ninevites, the agreement between Jacob

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Carmel between two of the elohim, YHWH and Baal, and their respective prophets. The confrontation described in 1 Kings 17–19 serves to settle the question who the elohim of Israel is. The choice is presented in a clear fashion: “If [YHWH] is [the elohim], follow him, but if Baal is [the elohim], follow him” (1 Kings 18: 21, NIV).19 Another clear example is the criticism levelled by the prophet Hosea, also keen to make the identity of Israel’s elohim clear in what he perceives to be their confusion of Baal and YHWH.20 Monotheism? The complex historical discussion over the evolution of Israelite monolatry – the worship of one god only – need not distract us much when offering an exposition of the logical status of “god”. YHWH is the particular god which elects and makes claims on a particular people, that responds in its own, at times disobedient, ways. We never in the Old Testament have a move towards something properly called monotheism – the belief in the existence of one god only – except what we might call “intramural monotheism” or with oriental philologist, Max Müller, henotheism. The monotheistic pronouncements of what is known as the Second Isaiah (that is, chapters 40–55 of Isaiah) are really an iteration of the first commandment. The statement “I am the first and I am the last; apart from me there is no God” (Isaiah 44:6, NIV) is YHWH’s assertion of exclusivity in the face of challenges from Bel and Nebo and their respective people, and it is prophesied that other nations will display the allegiance that the Israelites were commanded to pay (Isaiah 45:14). Both the Old and the New Testaments, though increasingly emphasising exclusivity, can and do speak freely of different gods. The recognition of an ever-latent polytheism survives in the New Testament and contrary to Durrant’s view, the uses of “god” as both a sortal and a name do not reduce the relevant parts of religious language to incoherence. In the New Testament, Paul used the distinction in his attempt at helping the potential _____________ and Laban (who each worshipped different gods) and the book of Ecclesiastes, which continues to speak clearly to many who are neither Jews nor Christians. 19 For the sake of simplicity, we are treating “Baal” as a straightforward proper name. It is in fact properly translated something like “the master” and has been used as a name for a different elohim. 20 See e.g. Hosea 12. Such a confusion is also suggested by the variants of “Baal” appearing in the names of the sons of Saul and David, and by YHWH frequently being ascribed powers and roles – mostly of a meteorological kind – that were typically ascribed to Baal.

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idolater. Paul is reported to have told the Artemis-worshipping Ephesians that “man-made gods are no gods at all” (Acts 19:26) and more elaborately to the church in Corinth: We know that an idol is nothing at all in the world, and there is no God but one. For even if there are so-called gods, whether in heaven or on earth (as indeed there are many “gods” and many “lords”), yet for us there is but one God, the Father… (1 Cor. 8:4b–6, NIV)

With the expression there is no God but one, Paul is in fact drawing on the Shema in the tradition of Moses.21 The idols were not and should not be lords to the Christian but could from time to time assume that role to believers and nonbelievers alike. In that sense, Paul would have agreed that there clearly are gods. The German expression “Abgott”, used in connection with other gods than the Christian, is for us useful in that it clearly indicates that there is something general that ties reference to the Christian god as well as other ones. What is often taken to be the monotheistic creed of the Christian is made against the background of the existence of a number of gods, but with an insistence on monolatry. At first sight, the drift of Paul’s teaching, to which we shall return in greater detail below, seems to be that the Father is a god but a different god from other gods, in the same sense as Churchill was a rather different politician than other ones. Though both the Old and New Testaments can and do speak of different gods, their mention becomes less frequent as time advances and a puritan tendency arises that seeks to do away even with their mention. But they form a part of the background against which YHWH asserts himself.22 Likewise Moberly (1999, 2004) suggests that the best understanding of the shema – traditionally taken to be about the “oneness of god” of Deuteronomy 6:4 ff.23 – has the shema to be very much like the exclamation we find said of the lover in Song of Songs 6:8f. In the passage from the Song of Songs, rather than use “one”, several translations use “unique” for the same expression in Hebrew as the expression, “ehad” (“one”), in the shema. It is the existence of both several women (queens, concubines and countless virgins) as well as the existence of several gods that lead to expressions of oneness or uniqueness. Rather than ascription of the number one, both the shema and the passage in Song of Songs are expressions of affection and _____________ 21 Paul’s exclamation is in fact closer to that of Moses in Deuteronomy 4:39 “You were shown these things so that you might know that the LORD is God; besides him there is no other” (NIV). The point, however, is the same. In Romans 3:29 ff. Paul alludes to the Shema when describing the universalisation of the covenant. 22 See e.g. the poem of Deuteronomy 32. See also Thompson (1999, p. 295ff.). 23 “Hear, O Israel: The LORD our God, the LORD is one” (Deut 6:4, NIV).

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exclusivity. The shema was originally expressed as the Israelites were to cross the Jordan and enter the land of Canaan. In this context, Moses wished to raise the issue of Israel’s covenant, offer reminders of YHWH’s past actions and his claim to undivided devotion to him as they entered a land where other elohim were worshipped. I have already alluded to the heavy metaphysical weather that Aquinas and others have made of the first of the two answers offered to Moses when he asked for the divine name. The shema is another case, and here the philosophical upshot is the doctrine of God’s simplicity, which by many is taken to be a key element of Aquinas’ theological system and subject of immense and continued philosophical debate. Aquinas (1989, I.11.3) makes reference to Deut. 6:4 in connection with the hugely influential doctrine of divine simplicity, and Eleanore Stump (2003) has attempted to get philosophical and theological mileage out of the doctrine of divine simplicity. This can, of course, be done without any foundation in scripture, but with no such foundation, the doctrine loses a significant part of its persuasiveness and immediate theological relevance. Mention of the divine name disappears As the group of people known by the name of Israel came to know the name – in the Strawsonian sense – of their elohim, they were commanded not to use his name in vain. The fittingness of the name and the referent was at the forefront of the Israelite mind in its address to its god. The name became revered to the extent where the Israelites start talking around it, rather than using the tetragrammaton as such. This was done by means of circumlocutions such as “the name”, “the eternal”, “lord” (“adonai”) and as we have already encountered it, “the god”. This linguistic usage had the clear intention of avoiding profaning the name and thereby profaning what the name names. In the Psalms it is frequently the “The name” that is praised, and with time, instantiations of the name itself are restricted to temple worship and to the scriptures, on pain of severe, possibly capital, punishment.24 Through the period when the New Testament is written, this linguistic temper is so widespread among the Israelites that apart from a possible _____________ 24 Moor makes the suggestion that the widespread apprehension with respect to the use of a holy proper name that was found in most neighbouring religions in the Israelite case resulted in a preference for elohistic designations (See Moor (1997, p. 246)). He suggests moreover that this phenomenon can account for the general preponderance of pre-Davidic tribal names with the theophoric element “El” rather than of variants of “YHWH” (Moor, 1997, p. 335).

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reference to the “I am” in John 8:58 and various allusions on Paul’s part, the tetragrammaton is presupposed rather than directly expressed.25 While most frequently designated “kyrios” (lord) by Paul,26 it is YHWH that we, like his son, are to approach with the epithet “heavenly father”, and many of the ways of speaking about the god of Israel are applied to Jesus, most significantly “lord”. They seem to come together in a passage such as Romans 10:13: “Everyone who calls on the name of the Lord will be saved”. (NIV) This is a reappropriation of a prophetic promise of delivery that was originally backed by YHWH and that Paul thought had now been made good. Calling on the name would typically be associated with a cultic activity in the Old Testament, and it was an activity that set Israel apart from neighbouring religions. Now, “at the name of Jesus every knee should bow” (Phil. 2:10, NIV, relying on Isaiah 45:23) – a name that he has been given by YHWH (John 17:11–12). In the gospels the Johannine account in particular underscores Jesus’ close relation to the name of God. In what appears as a continuation of the notion of making a name known, Jesus makes the name of the elohim known to his disciples (John 17:26). He comes and acts in his name (John 5:43; 10:25), and Jesus asks that his father’s name may be glorified (John 12:28). Finally, Richard Bauckham (1998, p. 34) argues that the Christology of Hebrews 1:427 simply lets Jesus inherit the name of YHWH with all that would signify to an Israelite. The avoidance of quoting a name despite knowing it well is also a recognisable linguistic phenomenon. Even though they may have few royalist sympathies, subjects of a monarch will often bow to a certain sense of propriety in addressing their king or queen, which would (in most cases) be contravened by addressing, say, the Danish Queen, by her first name only. We are supposed to say something along the lines of “Your Royal Highness”. A biblical equivalent is the concept of a master: “…just as a person usually addresses the king ‘my master, the king’ so one polite form of addressing God is ‘my master, Yahweh’” (Brettler, 1989, p. 43). Aquinas simply called Aristotle “The Philosopher”. The former Canadian president, Jean Chretien, is supposed to have been addressed “Mr. President” by his wife on the morning following his election. To Mary, Jesus was “the teacher” (John 20:16). In such ways, we quite frequently let signs more _____________ 25 In addition to our previous treatment of the argument regarding the lack of transliteration of “god”, we should note that “YHWH” was, in fact, transliterated as “ ǿǹȍ”, possibly pronounced “Yaho”, in some early Greek manuscripts. See Capes (2004). 26 Like YHWH was also “the god“, so Jesus is sometimes referred to by Paul as simply “the lord”. (Romans 14:6, 8; 16:2, 8, 11–13, Cor 3:5; 4:45) 27 "So he became as much superior to the angels as the name he has inherited is superior to theirs” (Hebrews 1:4, NIV).

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generally used to symbolise in the capacity of flaccid designators grow capital letters and become proper names. This is typically done with the purpose of expressing awe, respect and endearment. Such use of descriptive material is parasitical on the linguistic context being sufficient to help identify the individual in question. “The Philosopher”, used to speak about Aristotle, would only work in the sufficiently restricted medieval philosophical milieu. With a clear, shared background, it is possible for signs that normally symbolise in a flaccid manner to become rigid designators. Here we have located the proper understanding of the linguistic phenomenon that Durrant points to as another argument against taking the category of a proper name as central in speaking about the god of Israel. The argument is found in Aquinas and is here repeated by Durrant: If “God” were the proper name of some entity, then it would not be pertinent to ask for the name of an already named object. But this question is asked and answered in Holy scripture, viz. “‘Almighty’ is his name” (Exodus 15:3, Cf. Summa Theologica Ia, q13, a3). (Durrant, 1973, p. 18)

Predicating something of a name is not the same as using it to name. And we may want to name a name for a number of reasons. “Is a funny name” is a straightforward predicate that says something about the sign for a name when completed by the right kind of sign. In the case that Durrant mentions, the ascription of a predicate to a name takes place on the basis of linguistic intuitions to do with reverence and awe and should not in the least detract from saying that “YHWH” functions as a proper name, or that “God” functions in this way today, even though it also functions as a sortal.

“God”, the sortal: The centrality of kingship So far we have learned that there is an elohim named “YHWH”, and that it is one among a number of elohim known by different names. While the notion of monotheism is now widespread, in the previous chapter we argued that we still need to rely on a general expression, a sortal, with which we can count the relevant objects, if genuine naming is to take place – counting to one is still counting. What we have so far said about the sort of thing that is named by the name “YHWH” is aptly captured in Luther’s insistence on a god being tied to human intentionality, whether collective or individual.28 A concise _____________ 28 The notion of collective intentionality is widely discussed in social ontology. It is beyond the task pursued here to treat it, but such an exploration will have theological relevance.

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expression of the view can be found in his exposition of the first commandment in his Greater Catechism: A god is that to which we look for all good and in which we find refuge in every time of need. To have a god is nothing else than to trust and believe him with our whole heart. As I have often said, the trust and faith of the heart alone make both God and an idol [Abgott]. If your faith and trust are right then your god is the true God… For these two belong together, faith and God. That to which your heart clings and entrusts itself is, I say, really your God. (Luther, 1959, p. 9)

In seeking confidence in one’s strength, moral goodness, a political system, money, intelligence and so on, we can, according to this understanding, be taken to have a god, and rightly claim that a god exists in a theologically relevant sense. However, to describe what we rightly put our trust in, according to the Christian religion, one would need to qualify this concept of a god based on notions of trust and belief. That is, we shall have to say something about the further content of the sortal “elohim” or “god” in the Christian tradition that we are exploring. Further, we shall have recourse to explore Luther’s appeal to the notion of “a true god”, where we in the first instance will replace “god” with “king”. At the most general level, an elohim is spoken about analogously to a human being, with a similar emotional life, will and so on. While there is significant variety in use of the concept “god”, there is general agreement among those seeking to explicate the concept to give prominence to the concept of a king: To be a god is to be a king. Mettinger emphasises this importance in the following: When the prophet Isaiah experiences his prophetic call, he finds himself in the presence of one whom he must acknowledge as king: “for my eyes have seen the King, the Lord of hosts” (Isa 6:5). When the biblical psalmists sing hymns, it is the royal majesty of God they single out for praise. When they address themselves to God in prayer, they often do so presupposing that God is king. The Psalter and Isaiah are profoundly influenced by this understanding of God. Nor would it be an exaggeration to claim that this understanding links two testaments together: “Thy kingdom come!” is, of course, a prayer which presupposes someone who bears the royal title. (Mettinger, 1988, p. 92)29

_____________ 29 Moor (1997), Mettinger (1988) and Brettler (1989) all in different ways emphasise the centrality of kingship in explicating the concept of a god. Lang (2002), in his reliance on Georges Dumézil’s tripartite analysis of Indo-European religion, takes the concept of a king to be what unifies the three gifts we would hope for and perhaps expect of a god and of a king in various societies: wisdom, victory and life. Whether this interpretive scheme is satisfactory or not in the case of the Old and New Testaments, its suggestion does serve to underscore the centrality of kingship for the god of Israel as well as for neighbouring religions.

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The religious use of the sortal “king” in connection with the sortal “god” is by no means restricted to the Judeo-Christian tradition. The uses would blend in Egyptian traditions, while Canaanite tablets discovered at Ugarit describe how Baal would defeat various opponents, whereupon he would be pronounced King amongst the gods. It has been shown how, in general, more than half of the terms used to describe YHWH are also found, and may originate, in Canaanite religion.30 Levinson (2001) offers one among many comparative studies of some near-Eastern and Israelite concepts of kingship and finds strong parallels in related notions such as divine adoption (Psalm 89: 27), judicial insight (a famous instance is Solomon’s request in 1. Kings 3), the administering of justice (the biblical presentation emphasises that a king is someone who brings justice. See e.g. psalm 72:4), re-establishing temples (e.g. 1 Kings 1 ff.), economic relief and the commanding of armies – hence the indictment of David (2. Sam 11:1–2) before the ill-fated affair with Bathsheba. In accordance with his understanding that YHWH is the king, 1. Samuel reports apprehension when faced with the idea of an earthly kingship in Israel. As expressed to Samuel, the request for an earthly king amounted to a rejection of YHWH as king (1. Sam 8), and only with this reservation is Israelite monarchy established. As later Rabbinic commentary has it: “Just as in the world the ass grows up in the wilderness and has no fear of man, so too I planned that you should have no fear of kings” (Deuteronomy Rabbah 5:8 cited in Blidstein (1982, p. 18)). Wittgenstein and Disambiguation Again: The Concept of Kingship We have emphasised the commonality as well as centrality in the use of “king” among different nations’ understanding of what kind of a thing their god is. From this observation however, we cannot easily conclude anything about commonality or ancestry regarding different gods. Kings notoriously usurp or succeed one another, and the use of the concept of kingship in connection with the Israelite god might have been a protest or demonstration against foreign gods. More significantly, it has to many appeared as if the meaning of the sortal “king” is significantly altered by the JudeoChristian tradition. Hence the title of Levison’s (2001) contribution to the study of biblical language: “The reconceptualization of kingship in Deuteronomy”. Even if we just consider the Old Testament, it seems that the most significant of the six widespread features of kingship mentioned above – judicial authority – is severely reduced or denied by the law of _____________ 30 See Korpel (1990, p. 621ff.) and Moor (1997, §4.3).

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kingship in Deuteronomy. Whatever account will ultimately prevail of this apparent discrepancy between the charter of the king in Deuteronomy 17ff. and the descriptions of kingship in what is generally considered as Deuteronomistic history (Deuteronomy to 2. Kings), it would seem clear that the concept of kingship is being negotiated and altered in a number of ways in the Old Testament. This perceived linguistic phenomenon – i.e. that the same type of sign gets a new meaning in a new religious context – is widely appealed to in biblical studies. Anthony C. Thiselton (1973) simply calls it a redefinition; John D. Moores (1995) relies on Umberto Eco’s (1976) notion of “codeswitching” while Chiara Peri (2005), in an attempted overview of the evolution of the idea of monotheism in the bible, speaks of an intellectual process of what he calls “desemantization”. According to Peri, old words were used with a new meaning and this “implied a deep transformation of the data” (Peri, 2005, p. 141). In order to maintain a tradition, the same signs would be used, but with a radically transformed meaning. The understanding is that little or nothing of semantic significance would remain in such a transition – all that would be left would be the signs. In what follows, we shall confront this widespread understanding of the behaviour of the relevant sortal. In effect, what we confront is the reliance on another version of the disambiguation strategy that we confronted in chapter 1, and the strategy seems to gain credence when one considers the use of “king” across the Old and New Testaments. As noted by Mettinger, the notion of kingship remains central in the New Testament, even though the sortal “father” also becomes central. To Mettinger’s reference to “thy kingdom come” of the Lord’s prayer, we may add the temptation of Jesus, when he is offered “all the kingdoms of the world and their splendour” (Matthew 4:8, NIV). The offer to assume this kingship is rejected. Though kings appear to be depicted as servants of Satan by Jesus, the offer may also include the favourable depiction of kings offered by the Deuteronomistic historian, namely as a power that offers justice and protection, for all the severe cost explained by 1 Sam 8:11ff. The account of Jesus’ ministry ends with Jesus’ apparent humiliation and degradation, and yet, Pilate insists on Jesus’ kingship despite the complaints of the Jews: The chief priests of the Jews protested to Pilate, “Do not write ‘The King of the Jews,’ but that this man claimed to be king of the Jews” (John 19:21, NIV)

For whatever reasons, Pilate lets the sign remain in place as a characterisation of Jesus’ work and character at his crucifixion. During his ministry, about half of the parables would concern the Kingdom of God, while Luke

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reports that the risen Christ would continue to speak of the Kingdom (Acts 1:3). The writers mentioned above, who all see a transformation of the concept of “kingship” and related concepts in the Old Testament, are likely to now see an extreme perversion of the concept – a use of a sign that in fact gives it an entirely different meaning. The thought that this is simply a different religion and a different god is an inviting one. Along such lines, Judaic scholar Jacob Neusner can claim the following: …Christianity and Judaism each took over the inherited symbolic structure of Israel’s religion. Each, in fact, did work with the same categories as the other. But in the hands of each, the available and encompassing classification system found wholly new meaning. The upshot was two religions out of one, each speaking within precisely the same categories but so radically redefining the substance of these categories that conversation with the other became impossible. (Neusner, 1991, p. 5)

In line with Peri above, Neusner speaks of “redefinition” as well as “infusion of new meaning” (ibid, p. 13) in connection with the Christian King-Messiah. Meanwhile a commentator of Christian persuasion, Larry Hurtado, describes how Jesus would “…(re)define and reveal what messiahship really means” while he also emphasises “…that Mark describes the redefinition of royal messiahship in Jesus…” (Hurtado, 2003, p. 289. My emphasis). That “king” along with other things said of YWHW appears to be used in different ways is a well-attested linguistic phenomenon. The character of the relation between these different uses is a theological as well as a philosophical matter. The claim of Christian theology is that Jesus makes for an instance of true Kingship. The philosophical claim is that the very notion of a true F must be done away with. Below we treat each in turn. The theological claim is that, when we see “kingship” applied to Jesus, we see true or real kingship and not just a different kind of kingship or a redefinition of the word. While we focus on “kingship” below, this claim is made with respect to several words. We are told that the true meaning of fatherhood is taught through our encounter with the father of Jesus rather than the other way around. This I take to be the drift of the Pauline variation in Ephesians 3:15 on Jesus’ teaching (Matt 23:9) about only calling our father in heaven “father”. Regarding another predicate, goodness, Jesus emphasises that we are to use that word primarily and even exclusively about God (Mark 10:18). Similar contentions are made regarding “teacher” (Matt 23:8 ff.) and in Paul’s discussion of wisdom: We do, however, speak a message of wisdom among the mature, but not the wisdom of this age or of the rulers of this age, who are coming to nothing. No, we

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speak of God’s secret wisdom, a wisdom that has been hidden and that God destined for our glory before time began. (1. Cor 2:6–7, NIV)

Returning to the concept of kingship, we see semantically significant interactions between Jesus and his disciples, who found it hard to reconcile his role as the Messiah with his fate on the cross (being a Messiah would among other things involve kingship).31 To Peter, Jesus’ mission was a thorough perversion of the concept of a Messiah, but his voicing of that concern was sharply rebuked by Jesus (see Mark 8:32 ff.).While William Wrede (1971) in an influential work took such interactions along with saying of Jesus as a sign that the kingship of Jesus was not something proclaimed by himself, we should see the sharp interactions between Jesus and Peter regarding Jesus’ mission as lessons in the true meaning of kingship. Rather than seeing the gospels as an account of how Jesus was a Messiah in spite of the lack of central features of kingship, it is in effect a sophisticated theological narrative that offers an account of how the true meaning of kingship was displayed in Jesus’ ministry and only dimly perceived by the disciples. As we read in the Johannine account, it was a puzzle to Pilate that Jesus, upon Pilate’s enquiry, should accept the title of king: “My kingdom is not of this world. If it were, my servants would fight to prevent my arrest by the Jews. But now my kingdom is from another place.” “You are a king, then!” said Pilate. Jesus answered, “You are right in saying I am a king. In fact, for this reason I was born, and for this I came into the world, to testify to the truth”. (John 18: 36-37, NIV)

This represents a puzzle to most of us, who “see but a poor reflection as in a mirror”,“know only in part” and “speak like children” (1 Cor 13: 9 ff., NIV), not fully cognisant of the true meaning of the words we utter. Like Pilate in the ensuing exchange, the theological claim is that we do not fully know the true meaning of associated concepts of power and might, and most of the time we do not have ears that hear, that we might understand what the true meaning of these concepts – sortals as well as predicates more generally – are. So far I have tried to give a very rough outline of what remains a theological task of immense importance. It is in such a framework that we should understand Karl Barth’s repeated insistence that we do not truly know what F is (love, freedom, man, goodness, wisdom etc.) in his treatment of the divine perfections in Church Dogmatics II/1. However, the _____________ 31 For the treatment of “true kingship”, I rely on the excellent discussion in White (1982).

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basic theological claim and its more detailed realisation faces a philosophical challenge that is widely attested by the several commentators who see different concepts of kingship – rather than true instantiations of the same concept – in play in different religions and within the canon of the Christian religion. Like the insistence on difference of meaning of “object” explored in chapter 1, the present claim regarding the sortal “king” serves to trivialise and ultimately obfuscate a cardinal theological tenet. Hurtado made the claim that the real meaning of “messiahship” was expressed by Jesus, but he also spoke of a redefinition of the same sign. It is the former claim that must be defended if Christian theology is not to be disambiguated into irrelevance. This leads us to philosophical matter that was mentioned above. It has the shape of a general objection to the very idea of a speaking of a true F, in distinction to ordinary uses of F in connection with cases of an F. In our example, the F is the sortal “king”. It had obviously been used prior to Jesus, but the theological claim is that a true instance of kingship was seen in Jesus. The philosophical objection has one recent origin not in theological predicates and sortals but in the concept “white”, and is found in Wittgenstein’s Remarks on Colour: Lichtenberg says that very few people have ever seen pure white. So do most people use the word wrongly then? And how did he learn the right use?– He constructed an ideal use from the ordinary one. And that doesn’t mean a better one, but one refined along certain lines and in which something has been carried to extremes. And of course such a construction may for its part tell something about the way we actually use the word. If I say a piece of paper is true white, and if snow were placed next to it and it then looked grey, I would still be right in calling it white and not light in its normal surroundings. It might be that I use a more refined concept of white, in a laboratory, say (where e.g. I also use a more refined concept of exact time measurement). (Wittgenstein, 1977, §3 ff.)

Although dealing with a very different topic, we have here the beginnings of an argument against the intelligibility of speaking of a true F as an element of the meaning of the ordinary and everyday uses of F. Again, we see in Wittgenstein talk of a different predicate being employed when one uses the epithet “true”, rather than use of the epithet being part of the meaning of one predicate. Marie McGinn has sided with Wittgenstein’s apparent attack on Lichtenberg and lumps this passage with other criticisms of idealisations of everyday language, a criticism found in the more well-known Wittgen-

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steinian corpus.32 In the case of the predicate “white”, McGinn’s criticism seeks to reject the idea of there being a meaningful use of a predicate that is reserved for an ideal or eminent application in addition to the quite ordinary application of the predicate. Someone of a broadly Fregean persuasion would see an intimate connection between the meaning of a predicate and its extension, and the suggestion that we can speak of “a true F” opens the possibility of severing this close tie. This I take to be the drift of Wittgenstein’s criticism when he appeals to ordinary white as the basis upon which we may construct another concept, albeit one that has no “everyday” use. Likewise with “kingship”. Wittgenstein would here question the theological claim that the vast majority (in fact, everyone except God) are using one and the same sortal without having learnt “the ideal use”, i.e. what it is to be truly king, where the latter claim makes use of the same “everyday” and “non-ideal” sortal. Regarding the use of “white”, we shall side with White (1982) against McGinn. There is indeed a use of “true white” as well as “pure white” in our ordinary, “nonconstructed” use of “white”. As White (1982, p. 203 ff.) points out, under the influence of the more incisive discussion of colourwords found in Wittgenstein’s Philosophical Remarks (1975), we do in fact use the epithet “true” of colours, albeit only the primary colours and white and black. We also compare different whites without being implicated in use of a new concept with the idea of “pure white”, and we correctly apply “white” twice when the colour samples, for example as found on a shirt and a piece of snow, are not placed next to one another. The everyday uses of “true white” in washing commercials have not changed since White wrote. Finally, what have been called opponent colours do not admit of shades, which suggests they are points of reference for describing other colours, and they are also part of everyday idiom in exactly this way – “orange lies between red and yellow”. In extension of this, Wittgenstein makes a contrast between colours that are comparable to points and those that are comparable to lines. Those comparable to points work as points of reference for others. The lesson to be learnt from this very simple and brief overview of colour words is that actual instances of our predicates, including sortals, _____________ 32 Marie McGinn cites the passage as part of a criticism of what she perceives to be wrong-headed idealisations in accounts of our everyday use of colour words: “What we need is to forget our idealisations and come to a clearer view of the grammar of this ordinary language-game, as it is revealed in our everyday use of colour terms” (McGinn, 1991, p. 446) Both she and her adversary, Peter Hacker, seem to be able to agree about the illusory character of the “quest for a description of reality in terms of true concepts…” (Hacker (1986) cited in (McGinn, 1991, p. 441)).

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may not exhaust the account we give of their meaning. Should pointing to samples suffice and nothing else be possible when asked for an account of the meaning of “white”, we should have no account of the significant uses of the predicate that involves the epithet “true”. In the case of colours, we have the primary case, (pure) white etc., used for making distinctions between colour surfaces, and we have the name for coloured objects such as the table in front of me and the mug that is placed on it. Thus, we are in fundamental disagreement with Wittgenstein when he says “When we’re asked ‘what do “red”, “blue”, “black”, “white” mean?’ we can, of course, immediately point to things which have these colours – but that is all we can do: our ability to explain their meaning goes no further” (Wittgenstein, 1977, III, 102). Wittgenstein’s position seems to be informed by the methodology that we criticised in our treatment of family resemblances in chapter 1. How does this discussion bear on the theological discussion? Firstly, we have warded off a general criticism of speaking about true kingship (or other relevant sortals and predicates) as part of an account of the meaning of one and the same sortal. When the utterances detailed in the New Testament were made, they would make use of notions of kingship in the region, and it is generally this usage that informs a large number of biblical studies (perhaps most eminently Brettler (1989), though his study is restricted to the Old Testament). Nevertheless, the concept of kingship can contain both the things we normally predicate as “king” and an ideal instance as part of that usage, that shows us what kingship truly amounts to. And this is possible without having to say that we simply have a case of different and unrelated concepts of kingship. There are relevant differences between the colour predicates and divine sortals and predicates such as “king”, “wise” and ultimately “God”. I shall point to two important differences for an investigation of the range of sortals employed to describe the Christian god and Jesus. The first difference regards the comparatively higher complexity of the sortal “king” when compared with the colour-predicates. Someone with whom we have a radical disagreement about the extension of “white” would not be ascribed mastery of the concept. We would simply take that person to be radically confused about the concept, dishonest or somehow physiologically impaired. However, in the Christian theological case, we do have a case of insistence on a shared concept of kingship or fatherhood, paired with radical disagreement on one of the instances. Jesus does not, after all, tell us that his kingship has nothing to do with what those around him call kingship. As we have seen, the Johannine account has Jesus insist that he is king. And responses to this insistence that appeal to conceptual confusion,

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dishonesty and cognitive impairment are, unlike the case of colour words, by no means as exhaustive. This difference is in part made possible by the far greater complexity of concepts like “king” compared with colour concepts. The former involves, amongst others, the values of dignity, power and its preconditions, establishing (true) peace, and so on, which allow us to reason with someone in a way it is hard to imagine in the case of colour words. As a modest beginning of such a theological exercise, White (1982) invites us to consider carefully the power exercised by Pilate and Caiaphas in their respective offices in the events leading to the crucifixion. Caiaphas – also a chairman of the high court – is dominated by considerations of Realpolitik rather than justice and seeks to avoid a religious upheaval that would attract the attention of the mighty Roman war machine. Meanwhile, Pilate, the local representative of this very machine, in spite of being somewhat reluctant and spooked at the prospect of being involved in the death of Jesus, can do nothing when faced with the Jewish leadership and ultimately acts against his conscience. It is against the background of such a spectacle of impotence in Caiaphas and Pilate that we may begin to see in the man Jesus true freedom, power and dignity. This theological exercise is furthered by White’s study of portrayals of kings that were excellent benefactors to their nation but at the cost of their own humanity. Ivan the Terrible, in filmmaker Sergei Eisenstein’s portrayal, serves the Russian people outstandingly but at the expense of his personal moral habitus. To serve as king, he must be brutal, remorseless – “tyrannical towards himself and others” (White, 1982, p. 213). On the background of the study of Ivan the Terrible and Caesar, White comments on the passage from 1 Samuel that warns against having any other than YHWH serve as King of the Israelites. White suggests: The issue, God or Saul, is not only an issue of who shall be their king, but in what sense of the word ‘king’ they shall have a king to rule over them. If the constraints and conditions of this sinful and fallen world are taken as absolute, then the good king becomes the man who uses violence and Realpolitik to make the best accommodation with those conditions and constraints, and so inevitably becomes one of the long line of ambiguous figures sketched by Saul: from Saul to David, to Caiaphas and Pilate, to Octavius and Ivan. (White, 1982, p. 217)

In this passage White appeals to different senses of “king” at stake in the choice of kingship. In so doing, it might seem that he sides after all with the strand of commentary that simply sees different meanings of signs, the most extreme exponent being Peri in his construal of linguistic development. However, the senses he speaks of are “primary” and “secondary”

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senses of one predicate, senses that are systematically related.33 He models the development on concepts like “beauty” and “wisdom”. With a concept such as “beauty”, most of us undergo significant changes over time in what we are willing to call beautiful, and we might have deep disagreements with each other over what these concepts apply to, but, says White, “to make true sense of what is going on here, we have to say that the word ‘beautiful’ is used in the same sense throughout; if we criticise someone for finding Swinburne’s poetry beautiful, this has no sense at all if all what we are criticising him for is using the word ‘beautiful’ with a different sense from our own. And similarly for the other words at stake in the doctrine of the divine perfections” (White, 1982, p. 207). I believe this overstates the case one may have against those who disambiguate. We have nothing like a reductio ad absurdum argument against Neusner, Peri and others who see absolutely no commonality – apart from use of a certain sign – when old words are adopted in what they take to be new religions. The closest we get to such a reductio is that they will have difficulty accounting for the meaning of statements of generality that contain the sign in question. “Of all the kingdoms in the first millennium, the Chinese was the best organised” is by all appearances a meaningful, albeit vague, statement. Such very common expressions of generality will also have to go by the board if we adopt the sociologically motivated disambiguation strategy. Lowering our aims a bit, we may follow Barth in his suggestion that a significant difference is whether one decides to disambiguate or not. A decision and willingness suggested by Barth in passages like these: And although in all this He is concealed from us in so far as these words are our words and not His own Word about Himself, yet it remains true that we are invited and authorized by His revelation to name Him with these words of ours in the confidence that in this way we are moving in the sphere of truth and not of falsehood so long as we are willing to allow Him to be Himself interpreter of these human words which He has placed upon our lips. (Barth, 2004, II/1 p. 336)

It does make some kind of sense to disambiguate and speak of “desemantisation” etc., but it is a poor representation of the, admittedly extraordinary, claims made by the Christian canon and by its focal point, Jesus. We can surely disagree about whether we see true power, kingship, dignity etc. in Jesus and his father, but we have encountered no convincing philosophical reasons why we should reject such a claim. This points to the second difference between the relevant divine sortals and predicates and other sortals and predicates where we use the epithet _____________ 33 These notions are at home in theories of analogy. White (2010) provides a thorough treatment of analogy in the writings of Aristotle, Barth and Aquinas.

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“true”. We underlined how we, in the case of religious language, have to allow for differences in the extension of a sortal that we wouldn’t allow in the case of “white”. As we have maintained, if one wishes to settle a question about anything, be it the equator, business cycles or the Christian god, one needs to know what kind of thing one is talking about. A very reasonable assumption is that one can attain this linguistic knowledge of one’s own effort. The first time one hears of business cycles and wishes to enquire if they are real, one can easily learn that the existence of such things has to do with certain fluctuations in aggregate economical activity, and given mastery of statistical methods, one can settle whether there indeed are these cycles. This in essence was the short, Fregean answer to a question in ontology. In the case of theology, the assumption regarding linguistic knowledge has been challenged on theological grounds, i.e. on grounds that we called internal to the relevant science. While we read about the linguistic uncertainty on behalf of Pilate as well as the disciples, theologians are in no better condition. They themselves speak a language that, for theological reasons, is in and of itself deemed insufficient to speak about God. In a sense, we do not use words correctly, although there is an everyday and well established use of them. What we call wise is not what God calls wise (cf. 1. Cor 1). When we use the word “father”, it is derived from the primary use when applied to God. As Barth expressed this phenomenon in the quote above, as long we use our “everyday”, creaturely words without knowledge of their true instance, we are not really talking about God – he remains concealed from us. In the opposite direction – concerning ordinary usage of sortals and predicates from the point of view of awareness of their true instance, Barth claimed that “… [w]e use our words improperly and pictorially – as we can now say, looking back from our divine revelation – when we apply them within the confines of what is appropriate to us as creatures” (Barth, 2004, II/1 p. 229). Such a position is far stronger than the case of “white”, where the true instance and “everyday” cases are both properly called “white”. That is, there is not such a clear divergence between everyday usage and the case of a true instance. If this divergence strikes the reader as a completely untenable position for the theologian, we should reflect that there are other cases we are willing to accept such divergence. Semantic externalism – the doctrine that a certain range of words ultimately get their meaning not primarily from general usage, but from the way the world is – suggests just this in certain cases. As long as there have been economies of a certain magnitude, government officials may have attempted to describe business cycles long before they were properly understood by the discipline of economics. If we go on to say that such officials were in fact speaking about business cycles,

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though they were unaware that that is what they were speaking about, we would subscribe to a version of semantic externalism.34 What is being proposed is a theological, semantic externalism, where the true meaning of words are discovered not by the economist or the natural scientist, but are given by God to whom he reveals it.35 As already suggested, in the case of “king” and other relevant sortals, it is a more radical kind of externalism than externalism about natural kinds: With natural kinds, the appearance of, say water, is a useful guide to those who do not or did not know the true meaning of “water”, given by its microphysical composition. Not so with theological language. If Barth is right, when we look back from revelation, we see error in natural language use. Further, with natural kind terms, we do take the meaning to be discoverable in principle by our means, namely our best sciences. Meanwhile, according to Barth, “it certainly does not lie in our power to return our words to their proper use” (Barth, 2004, II/1 p. 230). While one may share Kierkegaard’s pious “…wish that powerfully equipped men might emerge who would restore the lost power and meaning of words” (Kierkegaard, 1967–1978, p. 5181), according to Barth, such a task is ultimately beyond human strength and capability. Left to our own devices, we remain in the dark whether we disambiguate or not.36

Analysis of 1. Cor 8:4 ff. Karl Barth’s account of language about God does not stand uncontested, and we have only scratched the surface of a fuller account of the nature of language used to describe the Christian god. As we suggested in the introduction to this chapter, Christian theologians disagree about the means of correctly identifying their god. Some Roman Catholic theology, with its Aquinian insistence on the possibility of natural theology, will maintain _____________ 34 Typically, semantic externalism has concerned natural kind terms such as “gold” and “water”, where the true meaning is given by scientific analysis, which for a long time remained unknown to language users. 35 I have arrived at the comparison of Barth’s thinking about sortals and predicates said about God with semantic externalism independently of White, but based on his earlier writings. In his book-length study of analogy and religious language, White (2010) defends and explores the comparison in far more detail, both with respect to its theological background as well as issues in philosophy of language. 36 We have concluded the treatment of the relevant religious sortals – prerequisites for raising and answering questions of existence – in a way that to many will seem to render language about God untenable. It certainly leaves us with poor prospects for natural theology – our attempt to say whether God exists, independently of God’s revelation. As a Barthian account of language about God, our presentation stands in need being supplemented by other theological doctrines.

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that there are other means of identifying the Christian god than those explored above – means that are accessible to us without revelation. Fregean meta-ontology as such does not suffer from disagreement within the discipline of theology and below, we seek to show the relevance of the Fregean approach to ontology by providing a logico-syntactic clarification of “God” that all parties should be able to subscribe to. Chapter 2 presented the categories of singular terms and sortals as essential to ontological investigations. In the present chapter, we have confronted the contention that, by appeal to these categories, the Christian canon can somehow be shown to be illogical or incoherent. This confrontation, and if successful, rejection, does not amount to a fully fledged defence of realism with respect to Christian theology. It is only a defence against what would be the most categorical and successful attack on language about God, such as those mentioned at the introduction of this chapter. Neither does it exonerate language about the Christian god from all charges of being nonsensical. Nevertheless, we do have the outline of a general strategy: When attempts are made to challenge or somehow dismiss language about God with reference to problems with a concept of, for example, omnipotence, an attempt should be made to retrieve the true meaning of the concepts. Having also argued for the necessity of an associated sortal in the use of names to name objects, we could approach the task of clarifying the logical status of “god” with something like a priori support of the existence of a relevant sortal. The sortal “elohim” serves in this capacity, allowing us to begin to individuate what “YHWH” names. In much of the language being used in the present philosophical discussion, the same sign is used for the sortal and the name, which makes for potential confusion. The best way of summarising the findings regarding the logical status of “god” would be to attempt to clarify a piece of commentary on a New Testament passage where the different symbols are run together by using the same type of sign. As we saw, Paul told the strong faction in the Corinthian church: We know that an idol is nothing at all in the world, and there is no God but one. For even if there are so-called gods, whether in heaven or on earth (as indeed there are many “gods” and many “lords”), yet for us there is but one God, the Father… (1. Cor 8:4b-6, NIV)

Thiselton gives the following explanation in his detailed commentary on the passage from Paul’s letter to the Corinthians: The “strong” at Corinth asserted an ontological and existential monotheism in which the so-called (Greek) gods were nonexistent nothings. Paul endorses their ontological monotheism. Even if these “so-called gods” have power over people’s

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lives, they are not gods or God. Only God is God. (Thiselton, 2000, p. 633, Thiselton’s emphasis)

If read in isolation and with little charity, some of Thiselton’s language appears nonsensical. It concludes by attempting to tell us something by means of typography – a usage that often relies on knowledge that is already present in the reader. In chapter 1 I made unfavourable mention of the notion of doing philosophy with italics. Doing theology in this way fares no better. However, we should be able to perceive the structure of Thiselton’s claim by making clear the different functions of the sign “God”. It is often remarked that “god” is an ambiguous word, and below I offer an attempt at a disambiguation of the Christian usage. After performing a disambiguation, we shall return to Thiselton’s commentary. “God1” serves as a sortal that individuates objects with reference to people’s intentional life, such as we saw it described by Luther. It is close to the “international concept” of an elohim that was shared between different religions, and as such it does not judge whether the object in question could be individuated by other criteria that makes no reference to minds. Thiselton suitably calls this an “existential theism”, where “existential” is used to designate aspects of our mental and personal life. Another New Testament scholar, Wolfgang Schrage, suggest something very similar in his commentary on Paul’s admonition: These are only so-called gods and lords. From this, however, Paul does not infer in a psychologising or belittling manner that they (gods and lords) are mere fantasies or constructions or that they exist only in the mind of the worshippers; what is more, he does not even say that they owe their real power only to their followers, who grant it to them. Certainly, there are no metaphysical or ontological judgments being passed on them but this does not mean that gods become gods merely by being worshipped as such. (Schrage, 1991–2001, p. 239, vol. III. My translation)

In short, this concept leaves open the question of further characterisation of the God1. I can put my trust in objects that depend on my mind for their existence as well objects that do not. Further, there are social phenomena that can exist and influence people without there being any minds that are aware of them – racism and inflation being two examples. It is frequently in the sense “God1” that both the Old and the New Testament writers define their religion against others and can be said to be polytheistic. Moreover, the sign “God1” is, in fact, itself ambiguous. As we have seen, gods1 are individuated both according to intentional lives and commitments of individuals and according to peoples, nations or other such grouping of individuals. The relation between these two disambiguations is in itself a significant theological task. “God2” is a sortal that will appeal to individuating factors beyond being the “god of x” where “x” is a human subject or a group of such. In so

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far as clarifying the existence of a god2 does not appeal to human minds or collections of human subjects, gods2 will typically be the subject of most discussion. I believe Thiselton’s use of “theism” – a word often used in connection with philosophical discussion – is a sign of this. We have explored one such feature, kingship, which will clearly be one amongst many relevant sortals and predicates in Christian theology. Interventions in human affairs, acts of creation and much else serve to individuate gods2. The implication, pointed to by Luther, is that there can be a discrepancy between a god1 and a god2 , in that the correct identification of a god2 will not be a matter of our intentions. “God3” is a sign that in effect functions as a proper name. In this case, the background for this function is the tetragrammaton. It is mirrored by Thiselton’s use of the capital letter in opposition to “god2”. We may see it as a case of a sign for a name being replaced with another sign for religious reasons to do with awe and reverence. Though the sign that serves as a replacement is often a sign that will be flaccid in other contexts, in the right setting it functions as a rigid, singular term. Thus, “Allah” is used to name the father of Jesus in some contexts, while it is most often used as a name in a different religion that appears to deny central features of Jesus’ claims. The sortal associated with this name will be “god1” and “god2”, with the addition of the Christians’ claim that their god offers true instantiations of a range of relevant sortals and predicates. “God4” is a case of a sortal that can emerge on the basis of the extraordinariness of the bearer of a name. It denotes a kind of thing that has such significance within its class that it can be made into a concept. It is this sortal that allows Paul to say that “for us there is but one God”, like one can imagine Aquinas saying “For us there is but one philosopher”. The reader will recall this phenomenon from the use of “Churchill” and “Vienna”. Had anyone said “Only Churchill is (a) Churchill” before Winston Churchill had performed the extraordinary feats of leadership for which he is known, the utterance would not have had the semantic content that it has today. The concept “is a Churchill” only does what it does for us today because Churchill, the politician, did what he did. In a manner of speaking, he supplied us with a sortal by means of which we are able to recognise someone of a similar stature. In essentially the same way, we have seen a similar linguistic development from the book of Exodus to the letter to the Church in Corinth. The father of Jesus introduces himself as a god amongst others, called YHWH. “God3” distinguishes himself from other gods1 and gods2 by his covenant and salvific actions, culminating in the death and resurrection of Jesus. To the Christian, God has distinguished himself to an extent that the concept of a god, with its related descriptive material, has seen a true instance. This makes the Christian say that other

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gods1 and gods2 are not really gods4, but only gods4 in a derived, deficient sense. This ambiguity was captured by Moberly’s analysis of the shema, according to which there surely are more gods1 and gods2, while one of them, “God3”, stands out. A god1 and a god2 was always going to be someone from whom you expected protection and various favours and that you found worthy of worship. However, as suggested, the true character of salvation, kingship, gifts and life means that the sortal “god2”, that allows us to recognise YHWH, was offered a true instance that makes more commentators inclined to say that God3 is something different from what the other gods are. Understanding this difference by means of human concepts is a matter of constant work and striving to see that God is truly god, his kingship truly kingship, that Jesus was truly man etc. With this disambiguation in place, we can rewrite Thiselton’s commentary as follows. The “strong” at Corinth asserted an ontological and existential monotheism in which the so-called (Greek) gods1 were nonexistent nothings. Paul endorses their ontological monotheism2 [indexing the implicit claim: “only one God2 exists”] Even if these “so-called gods1” have power over people’s lives, they are not gods2 or God3. Only God3 is God4. (Thiselton, 2000, p. 633, Thiselton’s emphasis. My indexation)

One might question the concluding indexation (God4) on account of the missing indefinite article, “a”. However, I believe we should take this omission on Thiselton’s part to stem from a wish to stress that God3 is very different from other gods1 as well as any other gods2 there may be. This he does by omitting expression of the generality otherwise contained in a sortal. After all, the sentence “Blair is not Churchill, only Churchill is Churchill” is not best understood as statements expressing identity and non-identity.

Fregean meta-ontology and philosophy of religion: concluding remarks Apart from mention of later Wittgenstein and Aquinas, this chapter has not sought to compare the Fregean approach to a question in ontology with more mainstream philosophy of religion to the extent that it addresses the question of the existence of God. A typical approach to the question is here expressed in the context of Richard Swinburne’s natural theology: Could there be more than one God? [Title] I understand by a God a person necessarily necessary, eternal, essentially bodiless, omnipresent, creator and sustainer of

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any world there may be, perfectly free, omnipotent, perfectly good, and a source of moral obligation. […] [B]y and large, those who have worshipped one being during the last two thousand years have had some similar understandings of what he is like captured (with all their possibilities for diversity of interpretation) by these predicates. (Swinburne, 1988, p. 359)

What is frequently being discussed is identified by means of a definite description that contains some subset of Swinburne’s impressive list of predicates. So what is the answer to the questions of a Swinburne? Regarding god1, we can clearly answer his question with an affirmation. But despite its theological significance, that is not what the typical philosopher is interested in. Much philosophy is concerned with settling whether anything fits the rather large bill that Swinburne goes on to present, and our Fregean approach to ontology has pointed to two related challenges to such an approach. Firstly, we noticed that the Fregean approach to a question would largely leave it to the relevant sciences to settle questions of existence. Michael Dummett provided a particularly clear expression of this when he claims that existence is a matter of there being genuine singular terms, where “[t]he truth of the relevant existential statement [is] determined by the methods proper to that realm of discourse” (Dummett, 1981, p. 497). In this case, this means, in the first instance, that we should carefully consider the claims made in any given region of language, in order not to impose on them claims that they do not make. Then, when having made clear what existential claims are in fact being made, whether the claims are true or not turns on employing the methods of that realm of discourse. Not writing a piece of theology, we have not thoroughly addressed the “proper methods” of attempting to settle the existential claim. We have pointed to an understanding of theology according to which it is not something we alone can settle. Secondly, pointing to a limited “realm of discourse” seems quite feasible in the case of addressing the question of the existence of business cycles. There are after all clearly identifiable means of settling the truth of statements regarding business cycles, and we are genuinely ready to defer to experts regarding the meaning of the sign “business cycle”, as the sign finds limited application in branches of economics. This makes for a contrast with Christian religious language, when one moves beyond the sign “god”: when explicating the meaning of this sign, we are after all relying on language that unlike “business cycle” is used universally: “king”, “father”, “good”, “power”, “wise” “ear”, “hand” and many more are all predicates and sortals that feature in the biblical description of the Christian god. Because of the familiarity of such words are we – whether philosophers or not – less ready to defer to others on the assumption that

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we do not know the true meaning of these words. In a radical way, this appears to be what the Christian theologian asks of us.

Trying to Take Care of Logic Trying to Take Care of Logic We return now to the theme of meta-ontology. After having motivated, defended and applied Fregean meta-ontology, we return to a defence of it. Contrary to the various objections that were faced in chapter 2, the issue we shall explore in the two concluding chapters arises from Frege’s context principle. The principle was subscribed to in the TLP, and I will seek to show how the problems with Fregean meta-ontology to be explored in the present chapter find an answer in Wittgenstein’s early thinking. Much recent commentary on the TLP has centered on the status of the work as a whole in the light of its concluding judgment on its contents. As the work concludes by saying that it lacks sense, a pressing question has become what to make of the work – what is it about? In contrast with the present focus on the concept of an object, the concluding remarks of the TLP are the result of several intertwined strands of argument on different topics, such as the nature of the proposition, modality, unrestricted quantification and the nature of logic, to name but some of the central areas being treated in the work. Some peripheral topics are God, mysticism and value, but we might add that there is no universal agreement on what is peripheral and central in the TLP. These facts alone should make us refrain from a characterisation of the achievement of the work at too general a level, even though such a judgment is invited by its conclusion. Even Wittgenstein himself is not necessarily the best guide to the overall achievement of the TLP: we are, after all, not always famed or recognised for the things we would like to be recognised for.1 One of strands of the TLP has to do with logical form and ontology as we have characterised it up till now. Indeed, the main contention of chapter 2 regarding necessary and sufficient conditions for being a singular term, is captured in TLP 3.326ff. Paraphrasing the passage: we must consider the syntactical use of a sign to determine the way it symbolises, and if every_____________ 1

I have in mind the oft-quoted letter to a potential publisher of the TLP, Ludwig von Ficker, where Wittgenstein maintains that “the sense of the book is ethical […] My work consists of two parts: of one presented here and of all that I have not written. And it is precisely this second part that is the important one” (Quoted in Engelmann (1967, p. 144)).

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thing seems as if a sign symbolises in the manner of a name, then the sign is a name. Names and singular terms more generally are what serve to pick out objects, and with respect to “object”, it has become commonly accepted among several Tractarian commentators that it is a consequence of the thoughts presented in the TLP that statements like “A is an object” are nonsense.2 However, this contention has not played any role in delivering a substantial criticism or renewed appreciation of recent cases of appeal to Fregean meta-ontology, in spite of the centrality of statements such as these. Neither have the defenders of Fregean meta-ontology, such as Wright and Hale, seized on the remarks and tried to formulate a criticism or renewed understanding of their overall argument that numbers are objects or that the existence of abstract objects more generally should be accepted. The reader is reminded of the title of Crispin Wright’s first, sustained defence of Frege’s logicism, Frege’s Conception of 1umbers as Objects, where a key claim is that the expression “natural number” functions as a sortal. The apparent lack of cross-fertilisation between two branches of philosophy that take seriously the context principle as a guide to ontology may have several sources. I suggest they should be seen as a result of two instances of neglect. On one hand, while defenders of Frege’s realism and his use of the context principle have been very effective in homing in on Frege’s insight of ascribing primacy to the complete proposition, a consideration that must go hand in hand with this has not received due attention. This would be a consideration of the nature of the complexes that are considered as proper candidates for being true and containing singular terms. I will suggest how such considerations ought to lead to a questioning of the status of the conclusions reached by Hale and Wright. On the other hand, it seems that much commentary on the TLP is not actually prepared to engage in the kind of philosophy that Wittgenstein envisaged: To minutely and critically engage with the ways that signs are put to use when “metaphysicians” or in this case, Fregean ontologists, do their work. This Wittgenstein simply called the activity of philosophy.3 In an attempt at engaging in such activity, this chapter outlines the consequences of the former neglect. Considering the understanding of the nature of the propositions that Frege and his defenders put forward, I argue that, given other things these defenders are committed to in virtue of their _____________ 2 3

See e.g. the very influential Diamond (1988/1991) and Hacker (1986) as well as Eli Friedlander (2001) and Matthew Ostrow (2002). “The object of philosophy is the logical clarification of thoughts. Philosophy is not a theory but an activity” (TLP 4.112).

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Fregean approach, their thesis is compromised. By “compromised” I do not mean that it is false, and nominalism or psychologism regarding numbers is true. Rather, I mean that it is nonsense. To what extent this is damaging to Fregean meta-ontology will be the topic of chapter 5. The present chapter sets out to show that the preferred way of engaging in ontology is blocked, or at least, must be understood in a fashion that is significantly different from that Wright, Hale and others display in their writings, or notably, that has been displayed in the previous chapters of this study. This chapter will explore how Frege’s notion of a “logical discussion” is best understood as the attempt to make symbols the subject of propositions, and how this attempt leads to the Tractarian view that we cannot make mistakes in logic. We will support this contention by way of addressing a problem that arises with the counterpart of the Fregean notion of an object, namely the notion of a concept. However precisely we characterise them, concepts make for an integral part of Frege’s logicism. It is, after all, equivalence relations between them that are supposed to account for the status of numbers as being purely logical. This is likely to be one important reason why the notion of a concept, and not that of an object, has played an overwhelming role in the treatment of Frege. His main concern, after all, was with our ability to account for number statements by purely logical means and not with an approach to ontology. A great deal of Frege’s contribution to our understanding of language was in the novel use of the notion of a function. The notion was widened so that predicates were simply considered a specific case of functions that can take all kinds of names of objects, rather than just names of numbers, as their argument. To Frege, the worldly counterpart of a such a function is a concept. The centrality of functions in Frege’s philosophy notwithstanding, the notion both of an object and of a concept are derived from the logical form of pieces of language in complete propositions. Hence, it should come as little surprise that we can generalise the problem known as the paradox of the concept horse4 to include its counterpart: the concept of an object. In the same way as the paradoxical liar sentence has received far more attention than the equally problematic truth-teller, problems associated with concepts have received more attention than attempts to ascribe the concept “object” – to say that this or that is an object. This chapter will show how this focus on the notion of a concept is unwarranted in the case of meta-ontology. However, as by far the most attention has been offered Frege’s notion of a concept, we will present our criticism of the Fregean concept of an “object” via a detour through _____________ 4

By italicising “horse”, I follow Frege’s typographical practice.

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discussions of the attempt at speaking about Fregean concepts. This detour serves a dual purpose: Firstly, it ultimately reveals a reliance on the Fregean concept of an object, which is our main concern. Secondly, the detour serves to emphasise the importance of the context principle when one tries to entertain discussions in meta-ontology. Whether we are concerned with the concept of an object or a concept, a treatment of the latter will expose a shared problem: the attempt at making symbols – signs in their logico-syntactic application – the subject of propositions. This attempt, in turn, is central when one tries to take care of logic.

The Concept Horse The paradox of the concept horse is best understood as a problem that arises from a universal, consistent application of the context principle. This principle deemed certain syntactic behaviours jointly sufficient to establish the presence of a singular term, from which Frege derived the notion of an object. The context principle throws up problems, as it seemingly confers object-status on what we on various occasions may want to describe as a concept – to Frege, the worldly correlate of an incomplete, functional expression of a given level. This conferral takes place because our language appears to have the means of turning a concept into an object when we construct the name for a concept. By way of example, if asked what it is that is predicated of Shergar in 1) Shergar is a horse our answer is likely to be that 2) The concept horse is what is predicated of Shergar Surely, the onus for an explanation would be on someone denying that (2) is a true statement about the concept horse as it is expressed in (1). After all, and as Frege suggests, such a denial flies in the face of the fact that we take apparently very similar sentences to be true, and true in virtue of their meaning only: “The car Toyota is a car” and “The city Berlin is a city”. What we do in the latter sentence is to explicate the sortal we have argued is associated with the naming of an object. What we essentially do in what follows is to question the appearance of “concept” and “object” as sortals. Use of the latter would supposedly allow us to name an object qua an object (a “bare” object), and not as a car, a book or some third kind of thing.

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Frege’s problem with an account of the semantics of predicates is addressed in Frege’s “On Concept and Object” (1892/1997a), where, to retain consistency in criteria of objecthood, he has to countenance sentences like 3) The concept horse is not a concept as the instance of the signs “The concept horse” in (3) apparently plays the role of filling the gap in the predicate “___ is not a concept” and hence functions as a singular term. The predicate, “___ is a horse”, is what is left when the name in the sentence is replaced by a variable. This way of viewing what takes place is a consequence of the primacy Frege ascribes to the whole proposition in distinguishing parts of it, coupled with his functional analysis of the proposition. Given the thesis of the primacy of syntax over ontology, we cannot say that “the concept horse” stands for a concept but must say things like “the concept horse is not a concept”, as the expression that completes the predicate names an object – the contention that was defended in chapter 2. Moreover, Frege will not be able to consistently express fundamental tenets of his, for example that predicates are unsaturated, or that no firstlevel concept is an object. The first tenet would be expressed by saying that “the concept horse is unsaturated”, and here, the first three words will have to be a complete, saturated expression (the opposite of a predicate) in order to be able to saturate the incomplete function. The problem is that we have what must be a complete expression referring to one that is otherwise understood to be incomplete and, as it stands, seemingly leaves us incapable of stating what any predicate stands for, as we will inadvertently end up performing a naming from which the notion of an object, not a concept, derives. This difficulty led Frege to his oftrepeated complaint: I mention an object, when what I intend is a concept. I fully realize that in such cases I was relying upon a reader who would be ready to meet me halfway – who does not begrudge me a pinch of salt. (Frege, 1892/1997a, p. 193)

What has become known as the paradox of the concept horse relies on the Fregean understanding that predicates are functional expressions, whereas other theoretical settings would not generate a similar paradox. Frege’s notion of a concept was – along with advances in logic – closely tied up with an attempt at understanding the proposition. To Frege, predicates and names are complementary notions that serve to give account of propositional unity. His answer to the question of propositional unity is a recurring theme throughout his writings. Frege‘s Concept Script (1879/1967, §9), though not addressing the question directly, speaks of a whole that is split up into function and argument along with the idea that we can only identify

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the former in the context of a proposition. Later, in Frege (1891/1997), an understanding of the wholeness that characterises the proposition is taken to be a motivating factor in the idea of the function as an incomplete expression. More forcefully, Frege (1892/1997a) maintains that we cannot dodge the paradox of the concept horse, as we have to subscribe to some version of his notion of subsentential completeness and incompleteness in order to understand the unity of propositions. In short, Frege’s notion of an object, derived from that of a singular term, served two purposes. Firstly, it was put to use in an ontological investigation regarding number statements. Secondly, as the worldly counterpart of an argument, it served as part of the conceptual apparatus used for understanding propositional unity. Though encountering problems when trying to speak consistently about his fundamental categories, Frege justified his continued practice of doing just that with reference to the lacuna that having no account of propositional unity would leave.

Some Responses to the Paradox of the Concept Horse About a century later in Jena, with elements of Fregean meta-ontology having fallen out of favour, Hans Julius Schneider could expect his views to have widespread resonance when he opened a discussion of the paradox at a Frege colloquium with the following: I assume that a number of readers before me have had the feeling that Frege got himself entangled in a fake problem [Scheinproblem], even though no agreed-upon way of doing away with the problem has emerged either from Frege or from posterity. (Schneider, 1995, p. 165. Own translation).

Schneider is right about the lack of agreement.5 The various reactions to the paradox of the concept horse can be divided into two broad categories. The first category is characterised at a general level by a reluctance to take seriously the fact that ontological categories should be derived from syntactic ones. Hence, writers in this category fail to see any deep problem in the paradox. Lowe (2001, p. 40 f.) does see a problem, but simply takes it to be another nail in what he takes to be the coffin of Fregean metaontology. Commentators in the other category are more firmly committed to the Fregean approach to ontology. Hence, to them the problem is real and demands a solution. In this latter category, we find, apart from Frege himself, Geach, Dummett and Crispin Wright. I will argue that, if we wish _____________ 5

For an overview, see Proops (2009). Unfortunately, the very thorough treatment of the issue found in Sullivan (1989) remains unpublished.

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to come to grips with the issue, the distinction between a sign and a symbol and the possibility of mistaking one for the other, are of key importance. This was a theme that was introduced in connection with the Tractarian version of the context principle, and we shall return to it in chapter 5, where I confront what I take to be an excessive emphasis on signs being mere signs when they do not symbolise in a well-formed proposition. For now, I will show that non-Fregean commentators on Frege’s paradox err on the other side by equating a sign and a symbol, which gives the appearance that we can quote and speak about a symbol. An “un-Fregean” response to the Paradox We set out by addressing what I call an “un-Fregean” response to the paradox. It is un-Fregean in that the starting point for the solution to the paradox is the fact that we seem perfectly able to name functions. If we successfully do that, it means we can relinquish the overall Fregean contention that we need to take the nature of symbols (name, singular term, etc.) as a guide to ontology. In defending what he calls cross-categorical quantification against Fregean-based objections against the possibility of unrestricted quantification over different Fregean categories, Peter Simons has offered the kind of formulations that would render ascription of the predicate “___is a concept” innocuous. Simons suggests: Ordinary language according to Frege allows logically inept things here: the only expressions apt for designating functions are functional expressions, and names are not functional expressions. […] Frege’s point is the most extreme manifestation of his view that ontological categories are correlated with logico-linguistic categories, in a pre-established harmony of expression classes and logical types. But ordinary language is within its rights and with sufficient care and delicate handling we can use transcategorical names without running foul of either Frege’s paradox or others. How then might a name do an alien job, the job normally and most transparently done by a predicate or functor? In general, a named function, predicate referent, etc. is being caught out in the open, not doing its normal and most characteristic job. When we say “sin(ʌ) = 0” the expression for the sine function is incomplete and is doing its proper job, here being completed by the name “ʌ” to yield a complex name of the number 0. When we say “the sine function has period 2ʌ on the reals” the expression “the sine function” as it were catches the function on holiday, away from its day job of taking arguments (whether names or bound variables). (Simons, 2003, p. 244f.)

Simons is clearly right. Something is recognised when we see the expression “the sine function”. Taking a simpler case: We are inclined to say that by writing down “+” we have written down the symbol of a function – that we “have caught it out in the open” as Simons has it. Accordingly, we say

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we know that “+” is the function at work in “2+3” and “6+8”, and very naturally take it that the “+” that was written down in the three quotes is the same symbol. Simons gives expression to this line of thought when he takes the fact that we know the meaning of the expression “the sine function” and can rephrase it in a way where the sign “sine” functions by taking arguments and symbolises, as a clear indicator that nothing is amiss with the first expression. By all appearances, it names the function. Simons remains convinced that the function is named by a singular term, while the sign used for the function does something other than functioning by taking arguments and giving a value. When a Fregean ontologist claims otherwise, he is clearly left with the challenge of giving an account of the linguistic phenomenon – the appearance – that Simons appeals to. We meet the challenge from Simons through an exposition of Wittgenstein’s treatment of Russell’s use of indices. The relevance of the notion of an index for an understanding of the function is pointed to in TLP 5.02 and has been explored by Peter Long (1969) and Sullivan (1989). Wittgenstein originally targeted Russell for having added the subscript “c” to the sign for cardinal addition, thinking that he thereby had managed to characterise the symbol in any way that wasn’t already clear from the use of the sign. He wrongly thought that the index was part of the expression just as a function that is completed by an argument is. This attempt at indexing is identical with our own example from chapter 1 of the suggested indexing of different kinds of existence. Ultimately, both attempts at indexing are unnecessary, and given that “…unnecessary elements in a symbolism mean nothing” (TLP 5.47321) they perform no role that is not already performed by the functioning signs. In his exposition of the notion of an index, Sullivan sets out by pointing to a difference between two instances of two expressions of the same function: There is plainly no part common to ‘Brutus killed Brutus’ and ‘Cato killed Cato’ which indicates that the same thing is predicated of Cato in the second as is predicated of Brutus in the first; but there is such a part in ‘Brutus killed himself’ and ‘Cato killed himself’. But this quotable lump is only the index of a function… (Sullivan, 1989, p. 51)

The latter expression of the function contains a sign that, off its own bat, indicates to us what function is being used, while the latter does not aid us in that way. Only in the former case can we make the formulations that Simons makes, because here there is the appearance of a quotable sign with which we name a function. Returning to an arithmetical example, we will see how the index is no fail-safe guide to identifying the function, which further questions Simons’ contention that a function has been named. Even if we think we know that “+” symbolises the same function in “2+3” and

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“3+4”, we cannot by means of this quotable sign recognise the different function in “3+3” and “4+4”, although it is expressed by means of the same type of sign. To recognise a function, whether it has an index or not, is to recognise a range of settings where a functional expression such as “+” contributes uniformly to producing a value when completed by one or more arguments. To further illustrate the notion of an index,6 imagine that “a b” and “a is bigger than b” both express the same relation between “a” and “b” – we can imagine having added the latter sign to our language for ease of expression. Instead of writing “My car is red and yours is green and my car is bigger than your car” we would write “my car is red and yours is green”. That one of the propositional expressions is the one we prefer is a matter of fact that the number of possible relations between the objects outstrips the number of possible spatial relations in our symbolism, as well as being a matter of convention and convenience. Nevertheless, both propositional signs essentially relate two signs, “a” and “b”. In our more convenient symbolism with no super- and subscript, this relation is indicated by the quotable index “bigger than”. We then ask what the difference is between the two propositional signs, respectively employing only super- and subscript and those using “bigger than” as well. The obvious answer is that the latter contains a sign for the relation whereas the former does not. This sign can serve as a reminder of the way “a” and “b” can be related and how the objects are presented as being related when we write “a b”. The fact that we have indices, however, does not speak against thinking of the predicate as incomplete and the proposition as essentially a matter of relations between signs, while having a sign for any specific relation or predicate is of accidental significance. In the first case, the fact that “a” is placed above “b” says that “a is bigger than b”. In the second case, the fact that “a” stands to the left of “is bigger than” which stands to the left of “b” says that “a is bigger than b”.7 Given that “What is essential in a proposition is what is common to all propositions that can express the same sense” (TLP 3.3341), the difference between the two expressions can only be an accidental one. _____________ 6 7

For this and the following three paragraphs, cf. Anscombe (1967), p. 100 ff. and Sullivan (1989) chapter 5. We have now reached Wittgenstein’s understanding that propositions themselves are facts, facts about the signs that are present in the proposition. In this way, he offered a new take on the question of propositional unity. The proposition already has the relevant unity, as a characterisation of it is a fact about the signs it contains, and thus not exhausted by quoting the signs. With Wittgenstein, the metaphor of incompleteness now becomes that of links in a chain, where the linking takes place when the links stand in a certain relation to each other and so form a chain.

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The difference lies in the fact that while they both express meaning by using relations between signs, the latter does so by containing an index of this relation. Instead of relating signs in a certain way, we introduce a sign for a certain way of relating signs. This is how we should understand the transition from “a b” to “a is bigger than b”. The signs “is bigger than” serve as an index of the relation in the propositional fact “a b”. Russell’s index for cardinal addition and other indices are wholly dependent on the class of propositions where the relevant signs in fact function as they do. And so, by employing the index, we do not say anything about a symbol. Rather, we “jog the memory” (Sullivan, 2001, p. 77) of the combinatorial possibilities, and hence the symbolising of “a” and “b”. We have made this case with functional, incomplete expressions, but quite generally, “to make explicit our recognition of what kind of thing an expression must be as a bearer of meaning, we should present an expression as a propositional variable “whose values are the propositions which contain the expression. (3.313)” (Sullivan, 2001, p. 76). The quotable sign indicates or alludes to these propositions – and in this consists the knowledge – but it does not symbolise. In chapter 5, we shall further explore the fact that a sign, looked at as a word, ordinarily alludes to a range of propositions where it can contribute to a proposition that is true or false and thereby symbolise. It is on such an allusion that Simons relies when he seems to catch the functor on holiday, not doing what it normally does. This is essentially the knowledge that Simons relies on. But there is a difference between naming an object and drawing attention to linguistic knowledge already present with the hearer. We do, of course, have ways of expressing functions in a way that correctly identifies them. In the mathematical case, by writing down: 2 × x2 + x we have managed to express a function. However, this is an incomplete expression as Fregean orthodoxy has it, and what we have written down is manifestly not present in 2 × 52 + 5 as the latter expression contains no “x”. Geach (1963, 1976) called the former a pattern for deriving a value, and patterns are not the kind of thing that can form part of anything quotable. They emerge as a property of a range of expressions. At the root of the objection levelled by Simons is the very natural tendency we have to take quotable signs to be individually identifiable parts of the meaningful proposition where they symbolise. Part and parcel of this tendency is the idea that we can extract symbols from a written proposition

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and equate them with the signs that on paper make up the proposition. What clearly speaks in favour of this natural tendency are considerations of compositionality and the fact that signs – or, simply, words – appear like individually identifiable units. As Wittgenstein puts it, “…in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word” (TLP 3.14). However, his own suggestion that we are disabused of this tendency when we think of the propositional sign as made up of spatial objects (such as tables, chairs and books) instead of signs (See TLP 4.1431) is of itself incapable of changing this natural tendency. Such objects, after all, would seem easily identifiable on their own rather than in concatenation with other objects. While we have only been concerned with functions and predicates in this section, we are again pointed in the direction of Wittgenstein’s general and on the surface, cryptic, contention that “It is impossible for words to occur in two different ways, alone and in the proposition” (TLP 2.0122). This was explored in chapter 2 when we confronted the objection that we seemingly refer with the use of one word only, and we shall return to the theme in chapter 5. Frege’s Response to the Paradox The paradox of the concept horse must be taken seriously by anyone who relies on Frege’s logico-syntactic categories in their approach to ontology. As Dummett insists, maintaining that the concept horse is not a concept ((3) above) “would be a reductio ad absurdum of Frege’s logical doctrines” (Dummett, 1981, p. 212). Frege did take it seriously himself. His answer to the problem changed over the years, probably as a consequence of becoming aware of the antinomy in his conception of concepts as extensions. As speaking about a range of objects – extensions – got Frege involved in another paradox (Russell’s), he abandoned the position he had previously defended in Frege (1892/1997a): that a particular kind of object acts as a proxy for concepts in sentences like (3). However, for some time this seemed to be his preferred solution. In connection with commenting on the oddity of sentences like (2) and (3) above, Frege insists: In logical discussions one quite often needs to say something about a concept, and to express this in the form usual for such predication – viz. to make what is said about the concept into the content of grammatical predicate. Consequently, one would expect that the reference [Bedeutung] of the grammatical subject would be the concept; but the concept as such cannot play this part, in view of its predicative nature; it must first be converted into an object, or more precisely, an object must go proxy for it. We designate this object by prefixing the words “the concept”… (Frege, 1892/1997a, p. 197)

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In favour of this construal, Frege (ibid. p. 199) adduces that we should not be surprised to see the same sentence conceived as an assertion about a concept and also as an assertion about an object. He offers the following example of what he takes to be two sentences that express the same thought: 4) There is at least one square root of 4 which is a statement about a concept: that it is not empty, but has objects falling under it. Frege takes it that the same thought is expressed by 5) The concept square root of 4 is realised Here, the first six words form the name of an object, and Frege takes it that something is said about it: that it is realised. Frege says little about why the two sentences express the same thought. They are, after all, about different things, objects and concepts, which usually would suggest to us that different thoughts are expressed. In saying that (4) and (5) express the same thought, Frege is likely to have had in mind the idea of cutting up the same content differently. This idea was first introduced – uncontroversially – in Frege’s Concept Script (1879/1967, §9) in connection with functions and then somewhat problematically extended to other contexts such as the equivalence relations of FA §62ff. where much discussion has taken place over what to make of “sameness of content” in that context. Straightforwardly, “Hydrogen is lighter than carbon dioxide” can be split up in different ways, such as “___ is lighter than carbon dioxide” or “Hydrogen is lighter than___”. In this way, the same thought can be split up as an assertion about something being lighter than carbon dioxide or about something that hydrogen is lighter than. The thought might have been that the equivalence between (4) and (5) is a straightforward case of such different analyses of the same content. It remains unclear why we should think so. For one thing, the signs contained are markedly different.8 More importantly, if Frege thinks that (5) has the logical form of naming an object, a form no different from that of “Socrates is funny”, he is committed to replacing “The concept square root of 4” by a variable that can take other names as argument. He accepts this commitment, and goes on to say that, although such a sentence with “Julius Caesar” as the argument of the variable will have a sense, it is in fact false. The reason for this anomaly is “…that so-and-so is realised (as the word is _____________ 8

As we saw in the previous section, this can, of course, be no knockdown argument. The sign “suicide” is not found in “x killed x”, but an analysis of the latter might well make use of the sign “suicide”.

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being taken here) is something that can be truly said only concerning a quite special kind of object, viz. such as can be designated by proper names of the form ‘the concept F’” (Frege, 1892/1997a, p. 201). A problem with this solution is that whatever we think “Julius Caesar is realised” means there has to be something wrong about declaring it false no matter what. Given that “Julius Caesar is realised” is false, it must be false in virtue of what it means. And, given that this does not at all appear to be a truth of logic, we would have to consult the world to see if it is true or false. Frege’s suggestion effectively is that it is false because of the way the object is spoken about. Now the way an object is introduced becomes a central feature of how it contributes to contexts in which it is found, rather than maintaining that the same object can be given in different ways. As Frege himself thought9, and anyone indeed ought to think, there would be something odd about not recognising the referent of “22” as the same as that of “4” because we have introduced the referent they share in a certain way. This solution of Frege’s thus remains unconvincing. Geach’s Fregean Response A number of responses to the paradox have been offered. Some commentators have found a solution in Frege’s Comments on Sinn und Bedeutung (1892–95/1997), where the notions of sense and reference are discussed specifically with respect to predicates. The solution is at first sight analogous to the advice a tongue-in-cheek medical doctor might offer her patient with an arm that aches when moved: “Don’t move it!” Thus, Frege (1892–95/1997) suggests: Indeed, we should really outlaw the expression “The reference [Bedeutung] of the concept word A”, because the definite article before “reference [Bedeutung]” points to an object and belies the predicative nature of a concept. (Frege, 1892– 95/1997, p. 133)

Geach suggests that “[Frege] would have allowed such expressions as “what the French word ‘cheval’ stands for”; but this must not be used as a singular term…” (1963, p. 156). While outlawing speaking in certain ways would seem to solve the problem with immediate effect, there is something unsatisfactory about the answer. Our body has the capacity to move in certain ways, and our problem arises when we rightly exercise that capacity for various purposes. The logical problem, of course, is that the relevant predicate in (3) apparently can be used as a predicate, just like “what the _____________ 9

See e.g. Frege (1980a, §10).

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French word “cheval” stands for” apparently can be used as a singular term. In addition to this possibility, chapters 2 and 3 in the present study suggested a rightful purpose and use for speaking about sortals (a predicative, incomplete expression) and singular terms. Both Geach and Dummett have suggested that we should replace expressions beginning with variants of “the concept” with something less problematic. Geach’s (1972) original diagnosis consisted of the comparison with another case in which logical analysis dispels the impression that surface grammar leaves us with: we should not infer from the fact that “some man” does not stand for a definite man, that it stands for an indefinite man. Neither, holds Geach, should Frege take the fact that apparently well-formed expressions beginning with “The concept” do not stand for a concept to mean that they stand for an object. As the expression of generality will fail the singular term tests outlined earlier, Geach (1972) suggests that correct analysis will reveal a sentence like (5) to be constructed from the second level predicate: 6) The concept ___ is realised and the argument “man”. Geach maintains that another way of formulating the second level predicate would be 7) Something is a ___ Geach holds that expressions that are not so translatable – that is, where we cannot readily do without expressions like “the concept man” – are to be rejected as nonsensical (see Geach, 1972, pp. 221, 230). Apart from being unhelpful in cases where we may not be able to construct a suitable predicate, there is something more fundamentally wrong with this suggestion. What is, in effect, suggested is that we can outlaw a certain kind of expression in some cases, while in other cases instances it can be translated into a more innocent way of speaking. A problem is that even if a rendering is offered that leaves out the problematical expressions, then if the meaning of the original problematical sentence is preserved (and surely, that must be the idea), our new sentence would seem to straightforwardly imply the problematical one. In other words, there is no good reason to prefer one of the renderings. My point is a version of the one originally made by William P. Alston (1958). Alston’s point had to do with ontological commitment and paraphrase, while the present, stronger case is that of translatability into and from something that is somehow illegitimate. Whatever we make of this idea, it surely sits poorly with any reasonable understanding of what translation or paraphrase does. If I say of my friend’s stammering or unclear speech that I will translate it for you, I take it that I am really saying that I will say

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something that my friend in fact didn’t manage to do, but that he feasibly can be taken to have wanted to say – he did not have in mind something syntactically malformed. However, it is deeply problematic to say that a kind of sentence that we wish to rule out for broadly logico-syntactic reasons can be rendered in a way where its meaning is clear and unproblematic. “Walks sleeps at night” is a kind of sentence that we should rule out on account of it being nonsense, but I have no idea how to begin to translate or paraphrase this into a string of signs that are well-formed and convey meaning.

The Disease Spreads: The Concept Object Tarski compared paradox to a symptom of a disease in our thinking. We return now to the focus of our investigation, the Fregean concept of an object, and we shall argue that the symptoms we have pointed to spread to this concept. We do this by noticing another attempted solution to Frege’s paradox. The solution has been suggested by Geach (1963) and Dummett (1981) and relies on a different kind of boxing clever: Instead of using phrases like “concept”, we are to use the phrase “kind of thing”. The suggestion is that instead of problematically saying 8) The concept dragon is a concept under which no object falls we get 9) Dragons are a kind of thing, but no object is that kind of thing The burden is thus shifted to the concept of an object or a thing, with the assumption that such expressions are somehow a safer haven. This assumption is clearly expressed by Crispin Wright’s characterisation of Fregean meta-ontology, here in connection with his treatment of the paradox of the concept horse: [N]o parallel incoherence has been disclosed in the use of the common noun, “object”… [W]hat was wanted was, in effect, a predicate which could be truly appended to all and only expressions referring within the domain of concepts (if I may so speak), just as “is an object” may be appended, for Frege, to all and only referring singular terms. […] The general notion of an object remains: referent of a (possible) singular term, and nothing occurs to compromise the grounds of the Platonism of Grundlagen, understood in the way that I myself would favour. (Wright and Hale, 2001, pp. 77, 79 and 90)

However, when we consider the sentences that Wright otherwise puts forward in his defence of Frege’s Platonism, peculiarities about the way he speaks do occur. Though not immediately giving rise to statements of

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paradox and incoherence like (3), analogous problems strike at the very heart of the Platonism that Wright has set out to defend for more than two decades. In short, something does occur to compromise his (and our) Fregean grounds of Platonism, and the problems arise with the use of “object”. If we use the logico-syntactic criteria that Wright employed to establish his fundamental tenet that “natural numbers do indeed constitute a unique domain of objects of a special kind” (Wright, 1983, p. xvii), in opposition to the view ascribed to Benacerraf that “…there are no special objects: the natural numbers” (ibid.), it would seem that Wright cannot be wrong, given that “___ is a domain of objects” here appears to feature as a predicate that takes names referring to a kind of object as its argument. Presently, nothing hinges on Wright’s use of “domain” in the predicate. He is clearly committed to defend the truth of sentences like “The number five is an object”, while obviously not being concerned about any number in particular. That this is the intention behind Wright’s way of speaking can be gathered from his claim above that “___ is an object” appears and behaves like any other common noun, or as we have called them, sortal. Wright takes it that he is in possession of a predicate that enables him to pick out the words that refer to objects, and that the formulation of Wright’s Fregean inspired realism has a kind of propositional complexity that is no different in kind from standard combinations of predicates and singular terms: supposedly, just as “Jesus was a man” in Fregean parlance maps an object onto the True, so “Five is an object” does the same, if Frege and Wright’s argument are successful. An important part of the reason why it does this is formulated by means of sentences like “‘5’ is a singular term”. However there is a crucial discrepancy between the two pieces of language. To bring into focus this discrepancy, we will rely on Russell’s suggestion, made in the introduction to the TLP, that “[n]otational irregularities are often the first sign of philosophical error” (TLP, p. 18). By formalising claims made in ontology and noticing irregularities, the error will become clearer. While we can make good sense of a sentence like 10) Jesus was a man The supposedly analogous 11) The number five is an object is only a structurally identical sentence construction by appearance. While the former draws a line among a given domain of objects, the latter attempts to draw a line between all objects and other ontological categories – what Wright, for instance tentatively called a domain of concepts in his

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treatment of (3). This, however, cannot be the task of a predicate within the Fregean framework. Predicates are extracted from the proposition and were characterised as what does the mapping of anything onto one of the two truth values. The concept of an object plays a central role in any textbook presentation (including, of course, some of Frege’s own) of predicate logic. If it is granted that “thing”, “object” and “entity” can be used interchangeably, use of the predicate is omnipresent. “Object” is used to speak about the widest domain of quantification possible.10 If we explain the meaning of “xFx”, where “F” means “___ is a president”, we might want to say that the variable is restricted to, say, human beings. This is supposed to contrast with cases where there is not such restriction – where we are considering all the objects such as human beings, nations, statues and much else – all the things there are. Here is Williamson’s characterisation of equivalents of “object”: My remarks will constitute no attempt to define “every” and “thing” in terms that are more basic. Definitions must come to an end somewhere […] In some obvious ways, natural languages differ in their apparatus of generality from languages with x and x. Natural languages have determiners such as “every”, “some”, and “no” which combine with singular or plural nouns. . . to form explicitly restricted quantifiers (“every donkey”, “a brown donkey”, “no donkey that I have ever seen”.) Even “everything”, “something” and “nothing” decompose into “every thing”, “some thing” and “no thing”. (Williamson, 2003, p. 416, 419)

This last contention seems to be a particularly clear exposition of the apparent logical form of “object” as it is found in ontological debates, including those relying on Fregean meta-ontology. Williamson is making the suggestion that we can treat “nothing” as a composition of “no” and “thing”, and seems to think that the latter has the same logical form as “___ is a donkey”, “___ is a table” and other humdrum sortals. However, what Russell is likely to have referred to as notational irregularities come out when we treat “___ is an object” as a predicate (O) that is logically on a par with “___ is a donkey”. Consider the two contra_____________ 10 Witness Williamson’s elucidation of “thing” in his treatment of unrestricted quantification: “In case it is not already obvious, let me emphasize that one can never defend the claim that everything Fs against a purported counterexample by admitting that it does not F but denying that it is a thing. If the word ‘it’ there refers at all, it refers to a thing in the relevant sense; if ‘it’ does not refer, nothing has been denied to be a thing. Whatever is is a thing. If there were any non-things, they too would be things: so there are no non-things. In any sense of ‘exist’ in which there are non-existents, they are things just as much as existents are. Any natural or unnatural kind or substance is a thing; so too is any member of the kind or sample of the substance. Whatever is abstract or concrete or neither is a thing. Whatever is basic or derived, simple or complex, is a thing” (Williamson, 2003, p. 420).

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positions below, involving mundane predicates like being a book (B), being expensive (E) and, less mundane, being made by God (G) 12) All books are expensive: x (Bx o Ex) { x (™Ex o ™Bx) That the two formalised expressions are equivalent ought to be uncontroversial. That all books are expensive comes to the same as saying that anything that is not expensive is not a book. Compare this with: 13) All objects are made by God: x (Ox o Gx) { x (™Gx o ™Ox) The problematic nature of our apparent sortal “___ is an object” is suggested by the consequent of our second contraposition. The variable is taken to range unrestrictedly over all objects. However, the consequent now aspires to range over a wider domain than the unrestricted domain otherwise introduced by the variable in the quantifier expression. The natural language rendering of the contraposition should illustrate the problem: “For all objects, if it is not made by God, then it is not an object”. Speaking of objects that are not objects is obviously problematic, contrary to speaking of objects that are not books. They might after all be music albums or tickets for hot-air balloon rides or bottles of water.11 Let me counter two misunderstandings of the lesson of (13). Firstly, I should stress that (13) does not commit me to any views regarding the status of God, i.e. whether he is an object or whether he is a necessary existing object. All that is being questioned is the meaningfulness of the use of “object” to speak about everything there is or for that matter, some of what there is, as when Wright uses it in formulation of number-theoretic Platonism. What these usages share is that they treat “object” as a sortal. Secondly, the sentence might be perceived to be in good standing, but in fact be a claim that is true or false by necessity. Against such a view, we note that it would seem very odd that claims like “the number five is an object” or “all objects are made by God” should be necessarily true or false, for reasons that can immediately be detected by means of reflection on logical form. _____________ 11 Hyder (2002), in his study of Wittgenstein’s and Russell’s account of propositional complexity reaches, as we shall see, a position similar to the one defended here. Hyder’s interest is in what he calls “riders” such as “a is an individual”, which are supposed to demarcate either ontological types (a relation, an individual) or linguistic ones (a name, a predicate etc.) for purposes of formulating a theory of the proposition. He finds that “[t]hese riders overstep the very strictures on significance that they were supposed to establish”. (Hyder, 2002, p. 70), While we are not presently seeking to establish strictures on significance, we do find ourselves in a position where strictures on significance in fact seem overstepped by the use of “object”.

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We seem to have revealed the inconsistency that Wright claimed had not been found in the “cousin” of the concept “___ is a concept”. If we cannot make simple and fundamental operations like contraposition with our apparent sortal, “___ is an object”, without running into inconsistent statements, we should question and reject the perceived logical form of the the sign used as a sortal. Whatever its logical structure, it cannot have the logical form of other predicates, and the shift from “everything” to “every thing” is anything but innocent. The process of moving from less and less restricted concepts to an unrestricted one is described in Frege’s dialogue on existence with the theologian Pünjer: If one wants to do the thing quite generally [subordinating concepts under more general ones] one needs to look for a concept superordinate to all concepts. Such a concept, if one wishes to give it that name, can no longer have any content at all since its extension will be unlimited; for any content can only consist in a certain delimitation of the extension. (Frege, 1884/1979, p. 63)12

What Frege is describing is the same predicate as Wright employs in his formulation of realism about numbers, and that we might employ when somehow trying to restrict a domain of objects from “things that are not objects”. Frege, however, makes a contrast between concepts as boundary drawers amongst objects and concepts like this that look as though they are not proper concepts at all – that is, they are without content. Such a distinction is clearly not maintained by Wright when he formulates his conclusion that numbers are objects. His use suggests that the role of the concept is to draw boundaries and defend a true claim in opposition to the claims of, say, a nominalist. This point is in effect reiterated when we reflect that whatever can rightly fill the gap in “___ is an object” must be a singular term.13 The role of singular terms is to refer to objects, and as a consequence, the proposition to which the singular term contributes would be true simply in virtue of its logical form. Whereas Frege intended a concept but mentioned an object, Wright intends an object and can do nothing but mention an object, given the account of propositional complexity he is committed to. That numbers are objects becomes either true by virtue of being stated in a wellformed manner or is simply not a proposition that is constructed in a way similar to those that refer to numbers. Russell, in later correspondence with Frege, drew exactly this conclusion, but did so with respect to formal _____________ 12 Compare Frege’s comments on use of “unity” in treatment of statements of number in FA §29. 13 It could admittedly be construed as a second-order concept, in which case it would necessarily be false.

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features of language rather than reality. The difference matters little as long we take syntax as a guide to ontology: For “[ can never take the place of a proper name” is a false proposition if [ is a proper name. But otherwise it is not a proposition at all. If there can be something which is not an object, then this fact cannot be stated without contradiction; for in the statement, the something in question becomes an object. It therefore seems to me doubtful whether the M in Mx can be regarded as anything at all. But at this point we are plunging into philosophical logic. (Russell, 1980)

This is the point Russell makes in Principles of Mathematics (1903/1937, §47) regarding his notion of a “term”, and later, in §487, in discussion of Frege. To Russell, a term is that which may be made subject of a proposition – things being that subclass that can only occur as a subject. No further leeway is made in matters of philosophical logic or unity of the proposition. When Russell takes it that a proposition is made of a list of individually identifiable items, he is in need of an account of their unity. Here his notion of the verb supposedly embodies the unity of the proposition, but, as regards its characterisation, he “does not know how to give a clear account of [its] precise nature” (Russell, 1903/1937, §55). It seems we are lumbered with the uncomfortable choice between having to say that Wright with claims like “the number five is an object”, or my own varieties of “‘God’ is a name”, are either necessary truths or simply not sentences that are in any way constructed like normal, truth-apt sentences.14 When we say that the proposition is true in some cases, meaningless in others, Frege would have it that we have been slightly imprecise. According to Frege, the predicate is essentially extracted from the complete proposition and the sign for the predicate therefore comes with limitations on what it can unite with and still be a predicate – still be the same symbol.15 _____________ 14 Some have argued that these expressions are not even sentences. This is the contention of those who profess a “strong” reading of the context principle and the related distinction between sign and symbol. We will return to this strong reading in chapter 5. 15 Frege at one point suggested that a proposition and its parts are somehow equiprimordial: “And so instead of putting a judgement together out of an individual subject and an already previously formed concept as predicate, we do the opposite and arrive at a concept by splitting up the content of possible judgment. Of course, if the expression of the content of possible judgement is to be analysable in this way, it must already be itself articulated. We may infer from this that at least the properties and relations that are not further analysable must have their own simple designations. But it does not follow from this that the ideas of these properties and relations are formed apart from objects: on the contrary, they arise simultaneously with the first judgement in which they are ascribed to things” (Frege, 1979a, p. 17).

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Diagnosis: Frege’s “Logical Discussion” The answer to our problems is that we wrongly treat “object” or “thing” as a sortal, and, in order for questions of existence to be meaningful, a sortal is required. This is essentially the Fregean-inspired dictum “to be is to be an F” that was surveyed in chapter 2. While “object” appears as a sortal, ordinary linguistic intuitions do support the contention that this appearance is misleading. If one was told that “there is something” or “that there is nothing”,16 this would usually warrant the question, “Something what?”, unless an answer to this could have been taken to be provided by the context of the utterance. The reply is precisely a request to be told what kind of thing we are talking about. With the differences between inferential patterns of “___ is an object” and sortals like “___ is a donkey” in place, we should also have aroused suspicion against the use of “object” as an answer to the question. In short, when offered closer attention, it seems to make little sense to say that objects can be just that – objects. Grammatically, “thing” and “object” by all means appear to be count nouns, and we find them used this way in ordinary language. Such uses are frequently what Amie Thomasson (2007) calls “covering uses”; by Wiggins (2001) called “dummy sortals”. In order to demonstrate such usage, contrast the following two statements: 14) How many things do I have in my garage? 15) According to Wittgenstein, there are more things in the world than we ordinarily think. When answering (14), the use of “thing” really is shorthand for a range of relevant sortals. I can go and count tools, machines, containers, shelves, old posters etc., and this is what I do when I try to answer (14). Of course, disagreements may arise if, say, I have taken the wheel off the bike in my shed. We may be in doubt whether we should count to two or to one when we see the bike and the wheel, and such disagreements are not due to empirical matters but to linguistic deficiency in the question – we are unsure about what to count. While there may be some deficiency in questions such as (14), in (15) the deficiency is complete. We may follow Thomasson and others in calling the quantification in (15) “bare” and note that it is frequently this kind that is found in what she, following Wright, teasingly refers to as the science of ontology. Whatever the appearance of _____________ 16 The themes we are surveying now has consequences for how we treat the expression “there might have been nothing” in theories of modality and philosophy of religion. See e.g. my Hansen (forthcoming) for a Tractarian assessment of cosmological arguments for the existence of God.

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statements made in sentences like (15), they simply fail to make sense. Of course, this is not to say that questions of existence are somehow problematic: “How many whales are there in the North Sea?” is, despite the vagueness of “The North Sea”, a meaningful question of existence. I started out by noting that ascription of “___ is a concept” has received far more attention in the literature than “___ is an object”. This is reflected in a significant impatience with the standpoint that “object” is deficient as a sortal that can be used in semantic and ontological discussion. This kind of impatience was displayed by Russell, who insisted on putting “___ is a blob of ink” on a par with “___ is an object”: [Wittgenstein] says that such a proposition as “there are more than three things in the world” is meaningless. When I was discussing the Tractatus with him at The Hague in 1919, I had before me a sheet of paper and I made on it three blobs of ink. I besought him to admit that, since there were these three blobs, there must be at least three things in the world; but he refused, resolutely. He would admit that there were three blobs on the page… (Russell, 1995, p. 86)

A similar impatience more recently received a clearer expression by van Inwagen. In discussing Tractarian-inspired objections to talking about “a number of objects”, which features the attempt to use “object” as a count noun, he suggests: The word “object” is so used that any substitution-instances of the following pair of formulae are equivalent: x (x is an object o Fx)

x (Fx)

And of the following pair: x (x is an object & Fx)

x (Fx) (van Inwagen, 2002, p. 180)

Finally, let the reader be reminded of Shapiro placing sortals like “___ is an automobile” on a par with “___ is an object” from the introductory presentation of ontological disagreements: “…numbers are the same kind of thing – objects – as automobiles, only there are more numbers than automobiles…” (Shapiro, 2000, p. 257). What we have so far said against the use of “object” makes for a strong anti-metaphysical thrust against “bare” questions of existence. Given how widespread such questions and answers are, what is being argued here should meet with significant resistance. Meanwhile, the upshot of the argument will be more palatable if we can offer some account of why, in light of the anti-metaphysical thrust, there remains a strong tendency to nevertheless use “object” as a sortal. Such an account is offered in the chapter that follows, were we explore how Wittgenstein in his discussion with Russell might helpfully have alluded to the Tractarian doctrine of saying and showing. It is here that we find one possible way to reconcile

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the two tendencies that have been surveyed up till now: Firstly, to want to secure a meaningful and legitimate use of the concept of an object – in different ways displayed by Wright and van Inwagen – and secondly, to insist that there is something deficient about the concept of an object we have defended up till now. Before pointing to the Tractarian account of the ailment we discovered in trying to use the pseudo-sortals “___ is a concept” or “___ is an object”, we should pause to ask why we wanted to apply them in the first place. As Frege suggested, there should be an awareness of what we are doing when we speak imprecisely. We saw how a commentator like Geach wanted to dispense with this way of speaking, but Frege in places displays a different attitude to such predicates. Let us revisit his initial characterisation of the quandary: In logical discussions one quite often needs to say something about a concept, and to express this in the form usual for such predication – viz. to make what is said about the concept into the content of grammatical predicate… (Frege, 1892/1997a, p. 197, my emphasis)

After making the point we have made about “object” as well as “concept”, Frege, in his correspondence with Russell, held that expressing himself in this imprecise manner was simply unavoidable. Here and elsewhere Frege expresses the view that “strictly” there are certain things we should not say, but on occasion, these very things need saying, and that we may do so as long as we are aware of what we are doing. Notice that to Frege there is a need for the kind of ascription that Geach would happily banish. It is true that banishing such statements would solve the problem in a way, but this solution would equally banish what Frege calls a “logical discussion”. The way Frege uses the notion of logic and the discussion thereof strongly suggests that Frege held these discussions to be a matter of trying to talk about symbols. That is, to discuss the functioning of signs. The theme of trying to draw boundaries that cannot be drawn – i.e. “whether something is an object” – is expressed in Wittgenstein’s early work: “We cannot therefore say in logic: This and this there is in the world, that there is not. For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world: that is, if it could consider these limits from the other side also” (TLP 5.61). To draw this kind of limit, we would have to say what we cannot say: “What we cannot think, we cannot think: we cannot therefore say what we cannot think” (ibid.). We have here located one of the senses in which we cannot make mistakes in logic: we cannot catch a symbol out in the open and give it the wrong designation, such as calling it a name when it really is a function. The reader will recall

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that chapter 1 flagged this as one of the key insights of the TLP that were relevant to the quandary that was pointed to in ontological discussion. Thinking that we can make symbols – contributors to proper propositions – the subjects of propositions will easily lead us to suspect that we can get the characterisation of symbols wrong. That we cannot make such a description by means of propositions also means that we cannot express it wrongly in a proposition. For the Tractarian viewpoint to gain force, we should say something about its conception of logic and compare it with the conception of logic Frege was using when he spoke of a logical discussion. We cannot here offer anything like an exhaustive treatment of the views on logic of Frege and Russell. In fact, such a task would be hugely complicated by what was in large part the motivation for writing the TLP: the perception on Wittgenstein’s behalf of the lack of a clear and correct notion of logic in Frege’s and Russell’s logicism. Thus, regarding Frege’s mention of the self-evidence of the supposedly logical axiom V, Wittgenstein can rightly say: …it is remarkable that so exact a thinker as Frege should have appealed to the degree of self-evidence as the criterion of a logical proposition. (TLP 6.1271)

What at one point was Russell’s criterion for a truth of logic – absolute generality – gets equally unfavourable mention in TLP 6.1231f.17 In the present context, we shall nevertheless notice a convergence between Frege, Russell and Wittgenstein towards the idea that a “logical discussion” is a discussion of the logical structure of propositions. After writing to Frege but before getting his new student, Wittgenstein, to pay Frege a visit, Russell does in fact equate logic with the general science of propositional structure. Wittgenstein, dissatisfied with previous conceptions of the domain of truths of logic, can say of his own work that “my whole task consists in explaining the nature of the proposition. That is to say, in giving the nature of all facts, whose picture the proposition is” (NB 39. Wittgenstein’s emphasis). Wittgenstein’s way of singling out truths of logic was their tautologousness – they say nothing. He singled them out in the most general fashion by way of saying something absolutely general about those cases where we do say something about the world, and locating tautologies as a certain degenerate kind of representation, which has something in common with propositions proper, but fails to describe the world being a certain way. Thus Wittgenstein can say that “…my work has extended from the foundations of logic to the nature of the _____________ 17 See Landini (2007, p. 19 ff.) for an account of the complex history of Russell’s development.

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world” (NB 79). The nature of propositions and their logical form were of central importance to Russell, Frege and Wittgenstein when they addressed a question of logic. At the heart of a question of logic was the attempt to make symbols, not signs, the subject of propositions. The problems we have located in entertaining logical discussions become particularly pertinent to the tasks being attempted in chapter 3 as well as in the present chapter. This chapter has frequently attempted to do the kind of work that has finally been deemed impossible: To speak about formal properties of areas of language and world by means of using variants of “___ is an object” and “___ is concept”. Chapter 3 saw frequent attempts to catch a symbol out in the open and – in opposition to the views of Geach, Durrant and others – to place it n the right syntactic category. Even a cursory reading of chapter 3 would suggest that this writer thinks he is right and others are getting it wrong, when it comes to formal features of religious language making use of instances of the sign “god”. To all appearances I have defended the truth of certain claims in opposition to others, and this I have done exactly by trying to make the structure of propositions the subject of proposition – to describe logical form. In short, my work up till now is subject to the same criticism that has been levelled against the Fregean approach to ontology as pursued by Wright and others. It seems I must allocate my claims and the position they embody to a category of language different from the kind of language that I use in everyday language and, for that matter, in science. The move bears essential similarities to that made by Wittgenstein in TLP, though they are in many ways cruder and address fewer topics. Consequently, we must enter the minefield of Tractarian exegesis of the notion of “object” and the charge of nonsensicality. Apart from Tractarian concerns, the task becomes that of answering what point there might be – what might be achieved – by speaking nonsense of the particular kind I have done. I have already alluded to formal properties, the designation of which has been attempted by use of formal concepts. The latter notion is at home in a passage where Wittgenstein addresses the logical form of “object”: So the variable name “x” is the proper sign of the pseudo-concept object. Wherever the word “object” (“thing”, “entity”, etc.) is rightly used, it is expressed in logical symbolism by the variable name. […] Wherever it is used otherwise, i.e. as a proper concept word, there arise senseless pseudo-propositions. So one cannot, e.g. say “there are objects” as one says “there are books”. […] [The words “Complex”, “Fact”, “Function”, “Number” etc.] all signify formal concepts and are presented in logical symbolism by variables, not by functions or classes (as Frege and Russell thought). (TLP 4.1272)

Against this background our task, in short, will be as follows. Frege says we sometimes need to use “___ is an object” or “___ is a singular term”

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and the like, and we only need be aware of what we are doing for it to be acceptable. But what is the need exactly, and what are we doing? Our answer will have to negotiate the tendency to dispose utterly of such “senseless pseudo-propositions“ as we dispose of other, more blatant cases of nonsense, and the view, expressed by Frege, that they serve a worthwhile purpose in spite of their admitted deficiency. This lands us in the tension that also characterises Wittgenstein’s TLP, to which we now turn.

Nonsense While the previous chapter brought into focus that there are genuine problems with expressions that are central to Fregean meta-ontology, this chapter seeks to assess the severity of these problems. Without directly confronting recent so-called “new Wittgensteinians” in their reading of the TLP, this chapter treats some of the issues that have been the subject of extensive discussion as a result of certain key tenets of the new reading. I will show that while those working in the Fregean tradition have downplayed or overlooked the problems, the new Wittgensteinians err on the other side when they claim that we are misguided in seeing any philosophically relevant difference between expressions like “A is an object” and blatant nonsense like “Piggly Wiggle” and “Socrates is frabble”. I should stress that entering the discussion of the TLP is not done with the purpose of gaining an overview and understanding of this work as a whole. It is done on the assumption that Wittgenstein offered a solution to some of the problems that we encountered in chapter 4. Michael Morris (2008), a recent commentator on Wittgenstein’s TLP, nevertheless takes the Fregean paradox of the concept horse as central in his own preferred characterisation of the nature of Wittgenstein’s TLP and its notion of the unsayable. While I do not agree with this overall assessment of the TLP, Morris’ choice of interpretational key to central Tractarian doctrines supports the idea that a range of themes from the TLP are highly relevant to the issues in Fregean meta-ontology that we have surveyed. The present chapter sets out by commenting on the overall strategy of the previous chapters in the light of the method of philosophy suggested by TLP 6.53. We shall then confront two commentators in their disparaging view of this strategy but suggest that their queries nevertheless reveal a real problem in the strategy: it is committed to the idea of their being kinds of nonsense, such as religious, metaphysical or meta-ontological nonsense. One of the main contentions of the “new Wittgensteinians” is that such an idea must be done away with. The motivation for this contention has its source in Frege’s context principle and the related distinction between sign and symbol. I will show how one can share their commitment to the context principle and yet reject the view, integral to the new reading, that there only is one kind of nonsense: mere or austere nonsense. In contrasting Frege’s and Wittgenstein’s use of the concept object, as well as

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contrasting the background for Frege’s use with the background for the theological case study presented in chapter 3, I offer some concluding comments on the nature of Fregean meta-ontology.

Ankle-biting philosophy? The previous chapters have to a great extent been written in the spirit of the philosophical method outlined towards the end of the TLP: To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other – he would not have the feeling that we were teaching him philosophy – but it would be the only strictly correct method. (TLP 6.53)

That is, we have surveyed ontological debates over what (really) exists. This survey motivated the Fregean meta-ontology, which in turn suggested the Dummettian “deflationary” contention that a lot of the discussions in the local debates are rarely genuine philosophical problems. We saw how many debates in philosophy of religion and philosophy of mathematics, however charitably read, could not be taken to have offered a clear meaning to the sign “object”. It was suggested that recent Fregean logicists, Hale and Wright, were on firmer ground, as “object” here received a relatively clear use in line with Fregean meta-ontology. However, Wright took “object” to be a sign that is identical in logical form to a paradigmatic Fregean predicate, such as the sortal “___ is a donkey”, which landed him a version of the paradox of the concept horse. He was suggested to be engaged in speaking a kind of nonsense. Finally, while we have not been dealing in natural science, we have at least outlined the character and logical form of language about a particular god, while leaving the question of the truth of such language to one side. That is, we have not attempted to spell out the justification with which theologians and others speak about God, but sought to explicate the logical form of “God” – where logical form has been presented as something that is shared between otherwise quite different subject areas. Early Wittgenstein’s characterisation of the right method in doing philosophy has not been very well-received by commentators. Sullivan has characterised this kind of exercise as “…a kind of heckling from the sidelines, which wouldn’t itself try to do anything in philosophy”. The victims of such an exercise might not find it satisfying and might well take it to be a kind of “contemptible, ankle-biting pernicketiness associated with the worst kind of ‘ordinary language philosophy’” (Sullivan, 2002, p. 62 /

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footnote 28). From a somewhat different angle, Mary Midgley has described the Tractarian method suggested above as part and parcel of a belligerent intellectual milieu. She suggests that the method is likely to result in exactly the kind of state of affairs that characterised the local, ontological discussions regarding mathematics and theology at the outset of chapter 1 – they remain local. The legitimate and necessary process of outlining a particular topic for philosophical discussion expands here into a systematic avoidance of larger difficulties. (Midgley, 1988–1989, p. 25)

While Midgley goes on to point out the psychological effects of such a method and, in connection with that, its ramifications for the pursuit of learning in the kind of atomistic research environment it results in, Sullivan rightly points out that the main problem with the method is not its tendency to disappoint and discourage metaphysicians.1 Rather, according to Sullivan, the problem is that the method assumes a standpoint that is so atomistic that it cannot even begin to identify what it seeks to do away with: The main problem is that the method is founded on too atomistic a notion of the contrast between sense and nonsense: it presumes, wrongly, that a piece of nonsense can be immediately latched onto and exposed as nonsense without waiting to see how it pans out. (Sullivan, 2002, footnote 28)

In sports at least, hecklers are usually consumed by the game that in their own unappealing way they engage in. Tractarian hecklers – even on the atomistic construal – are surely a different breed of hecklers altogether, as their shouting is not motivated by the way a game is being played, nor by frustration over who is winning, but by the very fact that the game is being played. While archetypical hecklers see themselves on the pitch, making the right passes and winning the game, Tractarian hecklers are inclined to dig up the pitch. It is not at all clear why Sullivan takes the method outlined in TLP 6.53 as being committed to the idea that we can immediately latch on to a piece of nonsense without exploring how it pans out.2 Latching on to a _____________ 1

2

If that was the main thrust of the criticism, it would merely be a repeat of the essentially conservative contention that criticism is only legitimate if a better substitute for what is being criticised is immediately put forward for consideration. Clearly, providing a critique of a certain practice can, at least if successful, make us think creatively about where to redirect our intellectual efforts. I believe it is this kind of impatience that characterises Carnap’s quick rejection of Heideggarian sentences like “Das Nichts selbst nichtet” (“the nothing nothings”). We may have ascribed no meaning to the sign “nothing” as a verb, but that is not

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piece of nonsense and seeing how it pans out seems to be a good first shot at describing what takes place in the TLP, and so TLP 6.53 could feasibly be seen to characterise at least some of the important elements of the practice displayed in the work itself – such as the demonstration that no meaning has been given to certain signs in the formulation of e.g. Russell’s type-theoretic hierarchy or in Frege’s attempt at defining objects as anything that is not a function.3 That Wittgenstein uses “would be” in his characterisation of method suggests that he did not take this to be a characterisation of what had actually taken place in the TLP. Neither should he, in so far as the TLP is littered with use of signs that TLP 6.53 encourages us to do away with. The description of the method suggests that Wittgenstein had a predominantly destructive errand, which I take to be the motivation for Sullivan’s and Midgley’s complaints. Meanwhile, a good textual case can be made that in the TLP Wittgenstein was honestly involved in the constructive task of bringing to expression something like the essence of the world by way of the essence of representation.4 At the time of writing TLP 6.53, he may have taken himself to have successfully achieved this, and on that basis, to have pointed the way for future philosophy. Sullivan’s legitimate complaint is that the heckling cannot even get started, as the philosopher needs to be able to identify the proper sidelines – what we are to direct our heckling at. If all we are offered to help identify the lines is “he had given no meaning to certain signs in his propositions”, philosophy will become an extremely diffuse kind of enterprise. Nonsensical strings of signs are found in all sorts of places, and some of them we clearly do not take to be involved in anything we ordinarily call philosophy. As a toddler or under the influence of intoxicating substances, I have produced strings of signs to which no meaning could have been given in their context. In no such cases do we think that it would have been appropriate to call upon a philosopher to have me cured of some kind of confusion. Therefore, the passage on methodology naturally suggests that there is a special kind of nonsense that the metaphysician utters qua metaphysician _____________ 3 4

to say one couldn’t do that and that Heidegger hadn’t done just that in a way that could shed light on significant phenomena. Cf. TLP 5.4733. For this definition to work, the quantifier would have to – in an unfregean manner – range over different ontological categories. The beginning of such a case would refer to the passage regarding the centrality of an understanding of the proposition, quoted at the conclusion of the previous chapter. Wittgenstein says that in so far as the task consists in giving an account of the nature of the proposition, it consists “[i]n giving the nature of all being. And here Being does not mean existing – in that case it would be nonsensical” (NB 39).

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and not qua anything else. Wittgenstein was able to recognise such nonsense through a thorough engagement with Russell’s and Frege’s logicisms, and we are supposed – through a thorough and non-atomistic engagement – to be able to recognise similar kinds of nonsense. The demand of the train of thought just outlined – that there are kinds of nonsense – has been denied by a relatively influential strand of Fregean and Tractarian commentary. Cora Diamond and James Conant amongst others have rejected the idea that there are different kinds of nonsense. To them, there is only austere, plain nonsense, while they reject the idea that there is “deep”, metaphysically significant or otherwise philosophically significant nonsense. If that is the case, it clearly demands our attention, to the extent that previous chapters have regularly been engaged in speaking in ways that are now deemed nonsensical: apparently, nonsense has been located in various writers such as Wright (and of course, our own writing) and in addition, it has been used in further reasoning. If we are austere about that way of speaking, we are thereby austere about the cognitive efficacy of the meta-ontology that we have presented. In short, no illumination has been offered by the nonsense spoken, neither by others nor in my explication and use of the Fregean concept of an object.

Austerity About Nonsense According to Diamond, thinking that there might be, after all, a kind of nonsense that is philosophically illuminating amounts to chickening out.5 Being a chicken means not having the courage of your conviction that something is a piece of nonsense but wanting nevertheless to insist that your nonsense manages to make some kind of philosophically significant sense. We should start by characterising the position that is being targeted by the austere reading. It involves the Tractarian notion of showing, and the target has been formulated in different ways, either as the contention that nonsense is a kind of sense6, or alternatively, that something is shown by speaking nonsense. Nordmann also seems to speak in this latter way:

_____________ 5

6

I take austerity about nonsense to originate in points made in Diamond (1988/1991) some of which in turn can be traced to Geach (1976). Conant (1991/2000, 2002), Goldfarb (1997), Kremer (2001), and many more have in various ways tried to develop and explore this view. See e.g. Alfred Nordmann (2005) in the chapter entitled “The senses of sense”.

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“a is more beautiful than b” [does not] say that there are two things, it says nothing at all; but though it is nonsensical, it shows you what you want to express by saying “There are two things”. (Nordmann, 2005, p. 180. My emphasis)7

Rather than thinking that nonsense shows anything, Wittgenstein makes the claim that “every real proposition shews something, besides what it says, about the universe” NB (108) and insists that “What can be shown cannot be said” (TLP 4.1212). Ordinary, “real”, propositions that picture the world being a certain way show us something. What new Wittgensteinians have targeted is typically a variant of the following: the idea that in speaking nonsense, we are nevertheless able to point to what is shown by what Wittgenstein calls real propositions – that we, by speaking nonsense in that way, nevertheless can point to and communicate something about the world that is ordinarily shown. According to the austerity view of nonsense, there is only one kind of nonsense, that which Conant has called “austere nonsense”. In Wittgenstein’s preface to the TLP he describes parts of his strategy as follows: “therefore the limit can only be drawn in language, and what lies on the other side will simply be nonsense” (TLP, preface). However, both Conant and Diamond have suggested that what Wittgenstein wished to say is best rendered as “…will be plain/simple nonsense”.8 The view that there is nothing but austere nonsense is opposed to a view that it is possible to utter some kind of substantial nonsense: The substantial concept distinguishes between two different kinds of nonsense: mere nonsense and substantial nonsense. Mere nonsense is simply unintelligible – it expresses no thought. Substantial nonsense is composed of intelligible ingredients combined in an illegitimate way – it expresses a logically incoherent thought. According to the substantial conception, these two kinds of thought are logically distinct: the former is mere gibberish, whereas the latter involves (what commentators on the Tractatus are fond of calling) a “violation of logical syntax”. The austere conception, on the other hand, holds that mere nonsense is, from a logical point of view, the only kind of nonsense there is. (Conant, 1991/2000, p. 176 f.)

Austerity about nonsense is the view that we cannot distinguish between different kinds of nonsense and, consequently, that we cannot take an appreciation of the TLP as a whole to involve anything like an appreciation of a special kind of “deep”, metaphysically significant nonsense. As has _____________ 7

8

Nordmann relies on Wittgenstein’s letter to Russell of 19.8.19 regarding meaningful propositions. We can also locate the view that nonsense shows us something (on the Tractarian conception of showing, explored below) in Carruthers (1990, p. 5) and Fogelin (1976). Nonetheless, I take it to be clear from the sentences that what Wittgenstein is describing are features of his strategy (the distinction between sense and nonsense) rather than features of the nonsense that this strategy results in.

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been suggested, the reading takes very seriously Wittgenstein’s final characterisation of the TLP in its entirety, and it is not the case that parts of the TLP9 are spared its own general judgment that it is nonsense. In the words of Goldfarb (1997), thinking that such elements remain would be “irresolute”. Being shown or told nothing about the world or language, modality, simplicity etc., we are thereby left none the wiser by the picture theory, the general form of proposition, the distinction between sign and symbol, the distinction between saying and showing or any other distinguishable theoretical elements of the TLP. According to both Kremer (2001) and Conant (1991/2000), the saying-showing distinction is just one more piece of nonsense that will have to be discarded when we read the TLP in a consistent way. And so, it is not just the TLP that comes to be judged as mere nonsense here, but much of Frege’s writings as well, for instance his reliance on the ascription of the predicate“___ is an object” which, along with its complimentary, “___ is an concept” has been the focus of attention in previous chapters. Thus, Diamond makes the following specific comment about “___ is an object”: “A is an object” is no more than an innocently meaningless sentence like “Socrates is frabble”; it merely contains a word to which, in its use as a predicate noun, no meaning has been given. But we inflate it…we think of ourselves as meaning by it something which lies beyond what Wittgenstein allows to be sayable. We think it has to be rejected by him because of that. We think of there being a content for it which, according to his doctrines, no sentence can have. But this conception of what we cannot say is an illusion created by our taking the word “object”, which works in meaningful English sentences essentially as a variable, and putting it into other sentences where it has a wholly different grammatical function. (Diamond, 1988/1991, p. 197. Diamond’s emphasis)

Various formulations of this reading have successfully been shown by numerous commentators to be internally inconsistent as well as inconsistent with key tenets of the TLP and Wittgenstein’s subsequent grappling with them. In the sections below, I will only join in this stampede to pass judgment in so far as the new reading is of relevance to the argumentative structure and tenets of the previous chapters.10 _____________ 9

For now, we can charitably take that to mean “philosophically significant parts” as we otherwise make the position out to be more unreasonable than necessary. It clearly is not nonsense to say, for example, that “Calculation is not an experiment” TLP (6.2331) or to quote what Frege said about some topic. 10 For a comprehensive overview of the development of the austerity view of nonsense, see Proops (2001b). For further criticisms, see Sullivan (2002, 2003, 2004), Hacker (2000, 2003) and White (unpublished, 2006). The New Wittgensteinians are a moving target and a broad church, so I will make no claim to have presented the development and details of their take on the TLP with great accuracy.

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A large part of the criticism of the new Wittgensteinians consists in criticisms of the suggestion that there are well-formed “frames” in the TLP that are supposed to guide attempts to spell out a different – therapeutic or ironic – account of the TLP. As such, these readings fall prey to Sullivan’s criticism above. For such a reading that relies on frames to be effective, it would need to latch on to significantly bigger portions of the work than those parts that typically make out the suggested frames. This idea sits poorly both with actual characterisations of the frame, and with the view that nonsense is austere, and as such, we should be able to latch on to it and see it somehow implode or degenerate, leaving us with nothing of any cognitive worth, apart from our own psychological states. As White aptly comments on Diamond’s example of nonsense, to which she wants to reduce the nonsense of the TLP: “‘piggly wiggle’ does not dissolve into incoherence no matter how hard you push it” (White, unpublished , p. 31). This line of criticism is of a piece with the conviction that significant thinking about language and confrontation with, and use of, the writings of Frege and Russell does take place in the TLP. This makes it very strained to see “the entire body of the Tractatus [as forming] a continuous train of nonsense” (Conant, 1993, p. 223) while insisting on austerity regarding nonsense.

Philosophical Varieties of Nonsense? The resolute, “brave” reading of the TLP is intimately connected with austerity about nonsense. When new Wittgensteinians insist on being austere about nonsense, they do so on grounds that have played a key role in previous chapters, namely that a necessary condition for a sign to be a symbol, and for it to be one symbol rather than another, is the existence of certain combinatorial possibilities. The overall drift of the context principle was that signs only attain their philosophically interesting qualities in certain concatenations. Otherwise, they are not symbols and make no meaningful contribution to the context in which they feature – at the peril of their own symbolising qualities, and typically, at the peril of realising the symbolising potential of the other signs with which they have been put together. Formulated in Wittgenstein’s chess analogy, moving a pawn in a bishop-like manner does not just make it cease to be a pawn. Instead it ruins the setting in which it is found – a game of chess. Such reflections run like a leitmotiv through the writings of Conant and Diamond. Thus, Conant in the passage above: “Substantial nonsense is composed of intelligible ingredients combined in an illegitimate way – it expresses a logically incoherent thought” (Conant, 1991/2000, p. 176 f.)

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and Diamond speaks of and rejects a “kind of positive nonsense [that would be] nonsense on account of what the terms composing it mean” (Diamond, 1981/1991, p. 106). It is not a far cry from such developments of the context principle to the view that signs that fail to be symbols are mere signs. They just stand there, and no philosophically interesting distinction is to be made between them. Such signs cannot be made out to be of more or less worth because of the work they do elsewhere – thinking that that matters is, in fact, failing to appreciate the main point of the context principle. Focusing for now on the sign “object”, the brave contention is this. We know a range of propositions where the sign is used as a verb, and we know a range of facts about the sign as part of a natural language rendering of a proposition of generality; however, if it is not used in one of these ways or used in some other way in which a clear meaning has been ascribed to it, no proposition or thought about objects or objections in general has been put forward.11 We cannot take ourselves to have been told anything by such a sentence, because it simply does not contain the symbol we are interested in and so does not say or show anything about it or what it symbolises. In short, such sentences are in no way about objects or objection, and this is so regardless of the intentions of the utterer. This line of reasoning is attractive as it supplies us with a sharp way of dissolving philosophical puzzles and offers clear answers. Moreover it takes seriously two of the three guidelines that Frege laid down in the introduction to FA, namely the essential setting of words in propositions and a sharp separation of the logical from the psychological; and so it appears faithful to the very foundation of much subsequent philosophy of language and logic. However, it also seems to fit the phenomena poorly. If we adhere unflinchingly to the line of reasoning in the way Diamond and Conant suggest, we are faced with a number of cases where we are naturally drawn to saying, for instance, that what we are dealing with is _____________ 11 Contrary to what Hacker (2000) maintains, physicists may well have ascribed a clear and legitimate meaning to “object” – different from the one defended here – if, for example, they say something like “wave fields are not objects”. We make a similar mistake in thinking that statements like “He thinks he is something” or the film title “The thing” are somehow rendered inadmissible by rules already in play for use of the quantifier. However, if we want to do the kind of thing that Russell and Simons are doing and try to speak of types of things to justify a symbolism, then “wherever the word “object”… is rightly used, it is expressed in logical symbolism by the variable name” (TLP 4.1272. My emphasis). Diamond (2005) devotes great efforts to making the first, straightforward point, while largely ignoring Wittgenstein’s actual target when he took a normative stance on use of the sign “object”. To violate rules and logical syntax more specifically, we must have a clear idea of what the rules are supposed to achieve – of what makes for success.

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nonsense but that it is nevertheless a nonsense sentence. On the austere view, not even this much can be granted, for the reasons outlined above, namely that the signs are not what they appear to be and, consequently, do not contribute to anything we may call a well-formed formula. That is, what they appear to contribute to is equally affected. Proops (2001a) is hard at work to dispel what he and Diamond recognise to be the natural conception of typical nonsense: A possibly controversial feature of my account – but one which I fully embrace – is that it commits Wittgenstein to denying the existence of syntactically wellformed nonsense. (Proops, 2001a, p. 10)12

This is what I earlier referred to as a strong reading of the context principle. Below, we explore how a development of one of later Wittgenstein’s examples will suggest how we may speak about different kinds of nonsense without being at odds with the context principle.13 We may accept that in a piece of nonsense, signs do not symbolise as part of a true or false sentence, and in that sense that there can be no substantial, philosophically illuminating nonsense. Nevertheless, as I will suggest, though not symbolising in their usual manner, signs can in certain settings serve as guides to how they can symbolise – and in that sense, at least, convey more substantial knowledge than “piggly wiggle” on most occasions manages to do. The move is to register something less than the logical distinction between the kinds of nonsense that Conant is emphatic cannot be made. We shall have to register differences finer than those visible from the “logical point of view”, where “logic” can here be taken to mean either the logical discussions of chapter 4, i.e. whether “something is an object or a concept”, or what we may infer from an utterance in virtue of its logical form and content. Given that inference is a matter of truth-preservation, we obviously cannot infer anything from nonsense, but we shall see how something less than inference can nevertheless be substantial. Consider the following string of signs: It is five o’clock smokes and Typically, this utterance will not be taken to say anything about timekeeping, about anyone smoking, or to be a conjunction. The signs are simply put together in a wrong way. “Smokes” usually symbolises in virtue of the fact that it stands to the right of a name or an expression of general_____________ 12 That Proops elsewhere takes sides against important strands of the new Wittgensteinian’s understanding of the TLP only goes to show the inadequacy of the polarised approach to a discussion of themes in TLP that characterises too much of the recent debate. 13 See Philosophical Investigation §350 for its original setting.

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ity, but “it is five o’clock” does not usually serve in any of those capacities. Hence, we happily reject the whole utterance as some kind of failed attempt or simply an odd word-hash. On one construal – the one Conant and Diamond are insistent on, the utterance It is five o’clock on the Sun. is nonsense for exactly the same reasons and in exactly the same way as “It is five o’clock smokes and”: “It is five o’clock” is either implicitly or explicitly indexed to places on the Earth. That is the meaning we have given to those signs, and it is that which determines how they can combine with other signs and symbolise. Our time-keeping is frequently done with reference to the location of places on the Earth as they move in a certain relation to the Sun. The reason why some of us may have to do a bit of thinking to recognise the nonsensicality is that the argument in the function “it is five o’ clock on ___” is in this case quite close in kind to substitutions that are legitimate, like “Greenland”. When I speak of closeness, I simply mean that they share a number of significant features. Though not both geo-graphical locations, they are locations, and “the Sun” and “Greenland” will frequently be able to complete the same predicate and thus make a proposition that is true or false (such as “___ is hot”). As an extension of this, the thinking becomes slightly harder when we replace “Greenland’ with “the North Pole”. In this instance of replacing parts of a sentence, the distance between success and failure in making sense is very short. If we abide in a legalistic way by the reasoning about context, sign and symbol that Diamond, Conant and Proops insist on, the sentences above are all nonsensical in the same way. We have put signs together in a way where we have ascribed no meaning to them in their context. Moreover, according to Proops, they are not even nonsensical sentences. While they are essentially right in their former contention, their understanding of nonsense is presented at too abstract a level. “Something failing to move” is a truthful characterisation of both a Ferrari and a Mini with an empty tank as well as of a bicycle with a missing front wheel. In most cases, we would feel cheated if no mention or distinction is made between the instances. As a consequence of the high level of generality with which Diamond and Proops present and apply the context principle, they would fail to register relevant differences in instances of nonsense such as the series of statements containing “five o’clock” above. While the first of the sentences

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is genuinely close to “piggly wiggle”14, the latter potentially manages to communicate something about the practice of, and symbolism at work in, time-keeping. The latter instances of nonsense can do this without regard for the intention of uttering them and, most importantly, they do this exactly because of the meanings the signs have when used legitimately – when the signs perform their role in their usual context. Contrary to the views of Diamond and Conant, they become interesting kinds of nonsense because of the symbols these signs are in their ordinary and rightful context. The compositionality of our language means that we try to somehow make sense of the signs we are faced with, based on facts already known to us, about their meaningful concatenation with other signs. As Wittgenstein suggests: The reason why, e.g., it seems as if “Plato Socrates” might have a meaning, while “Abacadabra Socrates” will never be suspected to have one, is because we know that “Plato” has one… (NB 116)

We can for present purposes substitute Wittgenstein’s “abacadabra” with Diamond’s “frabble” or “piggly wiggle”. Rather than taking this passage to be a flagrant rejection of the context-principle, we should take Wittgenstein to be effecting a contrast between signs that carry very little or no allusion to a range of meaningful propositions, and signs that are widely used in true or false propositions, and thus part of a propositional fact. Only with the latter group of signs do we make an effort in assigning a sense to the rest of the potential sentence. That the signs retain some of their symbolising features in “It is five o’clock on the North Pole” or “It is five o’clock on the moon” is suggested by the fact that though the signs in such sentences do not depict a possible state of affairs, we are quite ready to make arrangements for ascribing meaning to them. In such cases we could transfer elements of conventions for our keeping time to the moon – such conventions would probably be derivative of the current ones, and would largely have to do with the motions of various heavenly bodies. In that case, we would have a way of presenting a possible state of affairs by saying “It is five o’clock on the moon”. We can have no analogous ideas about what to do with “piggly wiggle” or how to ascribe a meaning to the fact that “It is five o’clock” stands to the left of “smokes and”. At the risk of furthering confusion by the introduction of more distinctions in our terminology, we characterise the position that Diamond, _____________ 14 Even here, there is an important difference. While instances of the sign “smokes” does suggest to us a range of propositional facts where it could symbolise, there are fewer, if any, such facts about instances of the signs “piggly wiggle”.

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Conant and Proops defend as one that ignores the existence of words – as unlikely as that may initially sound. In stressing the necessity of context for signs being symbols, they ignore the means by which our symbolism makes it practically possible to recognise symbols. A huge number of words, that, despite the legitimate complaint of confusions of the kind indicated by “Green is green” and, in Danish, “Får Får Får?”, do provide good guides to their combinatorial possibilities in so far as we are familiar with the language in which they feature. In short, when we see a word, we see a range of possibilities for combining that word with other words – a range of possible facts about signs that in concatenation represent the world rightly or wrongly. We still do not see a symbol, and we quite clearly do not have a fail-safe guide to the symbolising nature of a sign. But neither are we at a total loss: We do have what Conant referred to as intelligible ingredients combined in an illegitimate way. What Wittgenstein can be taken to say in the passage from his “Notes to Moore” above, is that “Plato” is a word, while we are reluctant to ascribe this status to “abacadabra” or “frabble”. As with words and sentences, a pawn still looks like a pawn when it is off the chessboard, and it looks like a pawn when it is used as a bishop and so, it is possible to break or alter the rules of chess without calling the game something else. After all, we try to make sense of the move as a move in chess, and it is in this respect that a rule is broken. When faced with a word, we do our best to try and make sense of its immediate setting amongst other signs. If no other signs are present, pragmatic features may guide us. When we fail to make sense of the sign in its setting and realise that we have not been presented with a possible state of affairs, we may well have been reminded of features of the range of possible states of affairs, to whose presentation the word may legitimately contribute. That is, we are reminded how the sign is properly used. Diamond’s and Conant’s neglect of words – in the sense introduced above – leads them to neglect what may be gathered about their proper use by way of their misuse. The simple notion of a word allows us to avoid the uncomfortable choice between saying that some nonsensical occurrences of a sign are either just a sign on a par with “frabble” or part of a “fully fledged” propositional fact with a sense that presents a way the world might be.15 The elements of a sentence – here understood as words – retain their meaning, without being part of a nonsense sentence with a sense that is nonsense. _____________ 15 A. W. Moore (2003, p. 187) outlines these uncomfortable choices in a clear fashion without committing firmly to any of them.

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With our current conventions for putting signs together, we do not present a possible state of affairs by making the statements such as those above about time-keeping on the sun. What then do we do? In this context, the general drift of Geach’s (1976) suggestion regarding Frege’s use of ontological concepts – such as “object” and “concept” – is appealing: While sentences using the concepts as though they were genuine may be nonsensical, such sentences can serve as heuristic tools when one seeks to acquire a better grasp of the proper functioning of a symbolism. The statements are nonsense and so do not show anything in the way that senseless as well as what Wittgenstein calls real, “bipolar” propositions do. In this case, they have not told us what time it might be. Consequently, if our perception of the sentences is that they are conveying knowledge to us by means of presenting a possible state of affairs, we are on the wrong track. Instead, as my reasoning about conditions for time-keeping as commonly practised suggested, nonsensical sentences are able to remind us of features of the ordinary use of time-keeping that we may not have been aware of, by making us aware of places where we cannot speak of it being “anything o’clock”. What general lessons about these cases of nonsense are to be learnt? Firstly, in contrast to the comparison with a breakdown of rules of the game of chess, we clearly have a case where we have violated rules for putting words together. It fits the phenomena poorly to say that by speaking about the time on the sun, we have in no way conveyed anything that has something to do with time-keeping. This is a rather unspecific contention, but we have to remember that austerity about nonsense, in its neglect of the allusion to propositional facts that meaningful signs (words) carry, entails the view that there are no features of the symbol – no meaning – left, when the sign finds itself in an improper context. Rather than seeing a mere word-hash, we are clearly inclined to construe this sentence as a misguided attempt at expressing a possible state of affairs regarding time, and this we do because of the strong similarity in combinatorial possibilities between “in Greenland” and “at the North Pole” when put forward as arguments for “it is five o’clock ___”. As mentioned, there is a wide range of legitimate cases where “Greenland” and “The North Pole” can be substituted for each other and still contribute to the expression of a possible state of affairs. Both will present a truth when being the argument of “It is cold on ___” and “___ is in the northern hemisphere”. These are the relevant features of what it is to be a symbol that are retained in the misapplication. Secondly, we should be inclined to say that “It is five o’clock on the Sun” can be helpful, convey knowledge and in that sense be substantial. Unless we immediately discard a piece of nonsense when we recognise it

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as such,16 we can, in the manner of reflection on time-keeping above, learn about conditions for using “o’clock” in a way that does make it contribute to presenting a possible state of affairs. This, broadly speaking, sits rather poorly with Diamond’s comparison of “frabble” and “object” above, but it sits quite well with Frege’s own view of his ascription of formal concepts: “I am well aware of having again expressed myself imprecisely. Sometimes this is just unavoidable. All that matters is that we know what we are doing and how it happens” (Frege, 1980b, p. 136). What Frege is calling imprecision is what we are calling nonsense, and there clearly is the implication that, if we are aware of the point of the ascription, it may be useful and convey knowledge in certain contexts. What needs to be clearly identified and rejected is the view that substantiality in the sense used above leads to knowledge that something is the case, in anything like the way that “it is 12 o’clock in Leeds” is the case as I write this.17 That is not how we can characterise the knowledge conveyed. However, as several commentators have suggested, this understanding very much appears to be what Diamond targets in her description of the spineless philosopher.18 Indeed, this is how one might initially present the Tractarian concept of an object and the concomitant notion of showing: namely by saying that there are objects is a nonsense statement, but that x is an object – here presented as if it was a possibly obtaining state of affairs – is shown by the workings of our language. Presenting both the cognitive efficacy and result of uttering nonsense in that way makes Wittgenstein’s thinking appear extremely crude and straight away incoherent. Fortunately, there are good reasons to reject the view that this is the best way of construing Wittgenstein’s notion of showing and the related notion of nonsense in that way in the TLP, or that we should put it that way in our reliance on “object” in our Fregean meta-ontology. “Substantial nonsense” can mean something other than what it does when we take it to be logically of a piece with normal propositions and thus warrant inferences that something or other is the case. A quick rehearsal of the Trac_____________ 16 I suspect this practice is what leads to the infertile intellectual milieu, targeted by Sullivan and Midgley above. The concern that something is nonsense, rather than why and in what way, becomes predominant. Indeed, Wittgenstein would later impress on us: “Don’t for heaven’s sake, be afraid of talking nonsense! But you must pay attention to your nonsense” (Wittgenstein, 1980, p. 56). 17 Or alternatively, as Diamond puts it, at the level of things, not states of affairs, in connection with reference to Wittgenstein’s topographical metaphor of setting limits to thought: “[it] very clearly suggests that there are two categories: things speakable about and things not speakable about” (Diamond, 1991/2000, p. 149). 18 See e.g. the exchange between A. W. Moore (2003) and Sullivan (2003) as well as Kremer (2001).

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tarian idea of showing something regarding objects in general will help us to begin to formulate wherein the substantiality of nonsense consists. A formulation that must not be open to the charge of immediate incoherence. Wittgenstein suggested that, while not being able to employ the formal concept “object” or “thing” like proper concepts and so being barred from a sortal by means of which we can speak about objects qua their formal features, what we must do away with is not necessarily the types, but the theory: “A THEORY of types is impossible” (NB p. 111). What the theory tries to say is shown when signs do in fact manage to picture possible states of affairs and thus symbolise. What we may say is that instances of the signs “R” do in certain cases form part of a proposition. Thereby we do not say anything about “R” qua symbol, but we say that there are facts about “R” that say certain things. What we may wish to say about the symbol is shown by a range of propositions. Here Wittgenstein explains with respect to our concept of an object: Thus a proposition “fa” shows that in its sense the object “a” occurs, two propositions “fa” and “ga” that they are both about the same object. (TLP 4.1211)

As Wittgenstein also maintains, propositions show the logical form of reality, and “that which expresses itself in language, we cannot express by language… What can be shown cannot be said” (TLP 4.121; 4.1212). But what is shown does go without saying. This strand of Tractarian nonsense is not directed towards nothing – there is that which “goes”. It is the attempted linguistic commenting on, or ensuring of, this “going” – by means of formal concepts employed in a Fregean “logical discussion” – that is nonsensical. Logical forms, understood in the Russellian way as a number of facts that make up the world, forms that we are acquainted with in virtue of understanding a proposition, do not exist in the sense that we have no sortal by means of which we can count them – “The logical forms are anumerical” (TLP 4.128). That a proposition is about an object is what Wittgenstein calls an internal property of a proposition. “The holding of such internal properties and relations cannot, however, be asserted by propositions, but it shows itself in the propositions, which present the facts and treat of the objects in question” (TLP 4.122). Wittgenstein goes on to make the comparison between the internal property of a fact and facial features. This comparison is helpful in coming to understand how we may speak of conveying knowledge about language, by means of language, without the knowledge consisting of the appreciation of a state of affairs with proper propositional structure. Further, it helps us account for the apparent impatience that we in chapter 4 registered with Russell and van Inwagen, directed against Wittgenstein’s reluctance to consider “object” as having the logical form of a sortal.

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Firstly, we are extremely familiar with facial features and can quickly recognise even minute differences.19 This suggests that in making the comparison, Wittgenstein wants to suggest a cognitive relation of an intimate and epistemologically basic kind. Secondly, faces have a certain structure in virtue of which the faces are easily recognised. On this background, we can agree with the drift of Devitt’s claim, cited in chapter 1, that “Existence is a fundamental and intuitively clear notion…” while nevertheless disagreeing with the further claim that “[it] stands in no need of explanation” (Devitt, 1997, p. 53). Moreover, what we are trying, and failing, to say in Wittgenstein’s simple examples is so clearly shown that we can understand why van Inwagen wanted to make it a matter of inference and why Russell had little patience with Wittgenstein’s rejection of the inference from “there are three blobs of ink” to “there are three objects”. Knowledge of logical form is so basic that Russell and van Inwagen equate it with analytical truths. Thirdly, though we are so very familiar with features of faces, our vocabulary for describing them is extremely limited. We just cannot describe the faces of our best friends the way we are able to describe, say, the interior of our favourite bookshop. We can gather the same conviction from Wittgenstein’s choice of words in his initial characterisation of objects: The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.) If I know [kennen] an object, then I also know all the possibilities of its occurrence in atomic facts. (TLP 2.0122 f.)

Wittgenstein wished to use an expression which can be used about kinds of knowledge of a primarily non-propositional character. Wittgenstein, in discussion with C.K. Ogden over the translation of “kennen” in TLP 2.0123, stressed that the word should imply that we could know the object without knowing anything about it.20 _____________ 19 A fact that is put to use in Chernoff faces. These faces are used when one wishes to represent statistical material with a limited number of variables. The representation is achieved by means of simple “smileys” with varying mouths, eyes, eye brows, ears etc. 20 See (Wittgenstein, 1973, p. 59). The Tractarian idea of the ladder that must be climbed and thrown away is found in Fritz Mauthner’s criticism of scepticism regarding knowledge of logic, and originally in Sextus Empiricus. See Black (1964, p. 377). Landini (2007, p. 244 f.) follows Russell in the objection to Wittgenstein that, if there is no science – i.e. true and false propositions – regarding logic and formal features of the proposition, then there is no epistemic access to it. Wittgenstein’s discussions with Ogden over possible translations of “kennen” suggests that

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In short, Wittgenstein’s vocabulary for the knowledge displayed in a basic command of language suggests that, in speaking nonsense, there is a real possibility that we point to knowledge that we possess about language when it functions conventionally, that we point by means of elements of language, but that the content of what is conveyed is not on a par with the content of propositions with which we present states of affairs. Putting such knowledge on a par with the knowledge we have when we know that states of affairs obtain would rightly be subject to the criticisms of Diamond and Conant, but that is a move we are resisting. Such resistance may come easier in the cases of ethics, aesthetics and theology, where the suggestion of insufficiency or irrelevance of propositional knowledge – if not downright ineffability – traditionally commands greater attention and adherence. In the circumstances of highly theoretical reflections such as those on logic and language that led Wittgenstein to his final judgment of the TLP, we are typically less willing to ascribe a central role to nonpropositional knowledge. How knowledge presented as states of affairs that obtain and knowledge of language conveyed by nonsense are closely intertwined and invite the conflation, comes out very clearly in Sullivan’s elegant comment on Diamond’s understanding of nonsense in connection with Frege’s Concept Script. Diamond suggests that we “…look at some of Frege’s logical work as providing replacements for certain parts of the philosophical vocabulary, in particular, predicates like “function”, “concept”, “relation”. These are replaced by features of a notation designed to make logical similarities and differences clear” (Diamond, 1988/1991, p. 183), to which Sullivan comments that something is made clear.21 At the heart of reflection on language lies that which we can’t express. And so, we should be careful about what not to do with the sentence “There is something that we cannot express but that is made clear”. Despite its surface appearance, when used in its Tractarian setting, the sentence cannot have said that something is the case.

_____________ he wished to counter such an objection. The slogan for Wittgenstein’s disagreement with Russell is summarised by Wittgenstein in TLP 4.0312: “My fundamental thought is that the ‘logical constants’ do not represent. That the logic of the facts cannot be represented”. In short, according to Wittgenstein’s view of logic, there is nothing a science of logic can be about in the sense that e.g. biology is about living entities. 21 See Sullivan (2002, p. 48). This is of a piece with Wittgenstein’s contention, cited above, that it is the theory of types that has to be done away with, rather than the types.

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Should we say that, in addition to being helpful and conveying a kind of knowledge, that truths may be conveyed by nonsense?22 Parts of Sullivan (2003) are dedicated to rejecting such ways of speaking and to clearing Anscombe (1967) of the charge of having done just that. There are good reasons to do with terminological consistency in the context of Tractarian commentary that speak in favour of Sullivan’s contention. In the context of Tractarian exegesis, he claims, speaking of true nonsense is better avoided, for the reason that truths are a result of genuine picturing, and we so immediately run into the charge of inconsistency emphasised by new Wittgensteinians. Nevertheless, I suggest we may speak of true nonsense in the following derived way. As speaking about the healthiness of my diet is done with reference to the health of my organism, so it would make good sense and explain the tendency of so many commentators to engage in such ways of speaking23 to speak of true nonsense. As my diet does not display anything like the proper functioning of an organism, it would be nonsense to say that it is healthy considered in itself. Considered apart from its contributions to an organism, it is just a particular kind of predominantly organic stuff. Similar considerations apply with respect to nonsensical utterances. Considered apart from how the elements in a nonsensical sentence elsewhere contribute to truths, they have no sense, do nothing for me and say nothing. But as a healthy diet contributes to my health, if taken in the right way, nonsense can contribute to the propagation of propositions that are true or to the avoidance of utterances that are not in the business of truth.

Wittgenstein and Frege on Ascribing the Formal Concept Object We return now to our theme of meta-ontology. In this chapter, we have seen how Wittgenstein’s notion of the formal concept “object” and the related notion of showing addresses the worries regarding Fregean metaontology presented in chapter 4. In order to characterise the nonsense that has been formulated in previous chapters, I conclude by emphasising relevant differences between the topic that concerned Frege and the theological case study in ontology that we have been conducting. To further characterise Fregean meta-ontology, I suggest an important dif_____________ 22 As e.g. Hacker (2000, p. 357, 368) does. Both McGinn (1999) and Diamond (1991/2000, p. 153) roundly suggest that one thinks so if one thinks there is metaphysically substantial nonsense. 23 As well as explaining Wittgenstein’s own claim that the work contains true thoughts. See for example the preface to TLP.

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ference between the point of using the formal concept “object” in the TLP and in Frege’s writings. The point is different in so far as Frege and Wittgenstein applied the context principle locally and with full generality, respectively. What has been done in our case study was, like Frege’s, a local investigation, rather than an attempt to say something about any linguistic representation. The epistemology of faces only goes so far in shedding light on the Tractarian notion of being shown something about logical and syntactic features of language. The finer delights of wine-tasting are to me largely an ineffable experience, but I am well aware of the existence of a sophisticated vocabulary for expressing in detail the delights of this experience. Similarly with faces: There is no barrier in principle to expressing, by means of language, details of faces qua the features that make them immediately recognisable to us. This makes for a contrast with the topics of the TLP, where the distinction between showing and saying is exclusive, and where there is that which we must remain silent about. That which is shown is in principle inexpressible as the subject of a proposition. Before rushing to the task of attempting a remedy of this breakdown in comparison, we should enquire about the relevance of Tractarian nonsense for what has taken place in previous chapters. All that has been argued in the present chapter is that strings of words that do not depict a possible state of affairs can communicate and so be substantial. We have done this by making room for something between being a mere sign that is in all ways semantically insignificant and being a symbol, where the sign symbolises as part of a true or false proposition. In Philosophical Investigations (§133), Wittgenstein introduces a distinction between what he calls problems and the single problem. In the following section, Wittgenstein goes on to quote an informal version of the general form of proposition, and in speaking of the single problem, he may well have had in mind the question that had preoccupied him during the time of writing the TLP: The nature of the proposition and a general account of language. To understand what Wittgenstein could mean by problems in the pluralwe return to a consideration of the nature of the task that Frege undertook in FA and that we have undertaken with our theological case study. In the Fregean cases, what appeared like a distinct region of language was under consideration. Frege confronted different theories of number. Some of them would have number ascriptions understood as ascribing a property to an object, just like we ascribe physical properties to objects. Some linguistic analogies would suggest such an understanding of statements of number, and Frege had to point to convincing disanalogies to

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have the view lose its appeal.24 Other views of number statements were dealt with in a similar fashion. For example, some were renounced with reference to the problems they presented for an account of the numbers zero and one. In confronting other views of the nature of number-statements, Frege put to use knowledge of simple arithmetical language. The knowledge displayed included both simple statements of number as well as knowledge of inferential patterns in other areas of language. In short, Frege had to appeal to some kind of common ground. It must be remembered that the destructive work was carried out before his subsequent presentation of logicism in FA. It was a form of ground-clearing, and the common ground consisted in appeal to number statements as they are used by all of us. These would be statements about the number of apples and (decks of) cards including the inferences such statements warrant. Though at times appealing to particular features of his vernacular – the general feeling for the German language – the ways of speaking and the inferences they warranted should be recognisable in any vernacular. Sometimes Frege was so fortunate that linguistic distinctions accord with those of everyday language, while at other times unearthing the similarities and dissimilarities in logical form would take more work. Surely, one of Frege’s great achievements was the example he provided of a sophisticated sensitivity to language and its logical forms. Did his opponents, such as Mill and Schröder speak nonsense when they put forward their views of number? Not necessarily, but Frege’s writings can suitably be seen as a variety of the method in TLP 6.53. While not pointing out which signs had not received certain meanings in their symbolism, he produced reminders of the meaning that we have ascribed to numerals in certain concatenations. In short, in statements of number, there was a bedrock of meaning of sufficient strength to allow Frege to suggest that if the signs for numbers were suggested to be of the logical form and meaning as suggested by e.g. Mill, one would simply not be using numerals the way one ought. In such a setting, we may speak of the context principle being applied to one of the problems of philosophy. Frege was not trying to think generally about how or whether language hooks on to reality or the preconditions for meaningful language at a general level – the problem that the TLP sought to address. Rather, his use of the context principle presupposed knowledge of logical forms, and was in that way comparable to that _____________ 24 For example, we say “two boots” as well as “red boots”, but we may ascribe different numbers to the “same external phenomenon” (FA §46) which makes for the disanalogy. The ascription of number is relativised to a concept.

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of a linguist approaching an uninterpreted language, and using the language with which the linguist is familiar to throw light on the uninterpreted language. In chapter 2 we used the notion of conceptual debt to point out that Frege did not seek to say something general about representation, but relied on agreed-on cases of well formed propositions and inferences generally considered to be valid. Wittgenstein suggested: The rules of logical syntax must follow of themselves if we only know how every single sign signifies. (TLP 3.334)

In the case of arithmetic, Frege could safely assume that we know how every single sign signifies, because there is strong agreement on the meaning of basic statements of number. Though at times logically opaque, they are logically in order in so far as we know how to use number statements and what inferences they warrant. On this basis, Frege could – and others can – make a strong case that numerals are singular terms that refer to objects. However, this makes for a contrast with the situation that faced us when we tried to shed light on how the sign “God” functions. Here, it is not the case that we “all know” how the relevant parts of language signify. There is far more fluidity in this region of language, and consequently it will become harder to take issue with different understandings of its logical form in the way that Frege did with arithmetic. As long as linguists setting out to describe the distinctiveness of the Israelite religion have a legitimate complaint that “none of the terms ‘henotheistic’, ‘monolatrous’ or ‘monotheistic’ is suitable for describing the phenomena intended” (Moor, 1997, p. 8) there is a fluidity in the relevant region of language to an extent that engaging in discussion in the way that Frege did, becomes next to futile. Chapter 3 surveyed how Ayer and Durrant seemed to locate this futility in what would have been the equivalent of the bedrock of arithmetical statements: language about the Judeo-Christian god as found in scripture. Supposedly, when Ayer and Durrant in different ways suggested that theism is confused and use of “God” likewise, they took this to be a problem with the way people of Judeo-Christian persuasion are supposed to address their god. I have not undertaken a history of the distinctly philosophical notion of “theism”, but I nevertheless take it that previous chapters have shown that the problem – crystallised in Moor’s complaints – may well lie with a philosophical position called “theism” rather than with a theologically informed way of using the word “God”. In short, the problem is that often we do not know how the sign “god” signifies or, alternatively put, we know of many incompatible ways that the sign

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symbolises. As a consequence of this, the syntax of that sign may indeed appear confused. While not having produced anything like the formal apparatus of Frege’s conceptual notation – and thus not having the same means of avoiding confusion in our symbolism – we have drawn attention to a sign, “YHWH” that was introduced as a proper name. We have furthermore suggested how some current reflection on theology appears to use the word “god” as a concept as well as a name in a way that does not accurately reflect biblical use. None of these usages reflects the logical transformation that took place when the name “YHWH” became part of a concept that was in some ways intended to be different from other concepts of a god. Neither was it clear that it took sufficient account of a faithful explication of the sortal that accompanies use of the name “God”. The ascription of formal concepts to expressions in regions of language are, as Frege said, needed as long as there is potential confusion regarding how signs symbolise. In short, as long as signs appear to be used to symbolise in different ways from those suggested by certain canonical ways of speaking, the ascription of formal concepts can rightly be called for. Clearly, the nature of the canon will vary with different subject areas such as theology or arithmetic and will carry different levels of conviction. Philosophers and others are after all a long way from agreeing on the meaning of the sign “God”. We can summarise the Fregean point of using “object” in the following adaptation of a passage from TLP 3.323 f.: In the proposition “God is a god” – where the first word is a proper name and the last a sortal – these words have not merely different meanings but they are different symbols. Thus there easily arises the most fundamental confusion of which the whole of philosophy of religion is full. In order to avoid these errors, we must employ a symbolism that does not apply the same sign in different symbols without making clear that this is what we are doing.

In the TLP, there is a different point of using “object” and other formal concepts. Such fairly local concerns as time-keeping, or less local statements of number, are not offered much interest in the TLP. Whereas the Fregean application of the context principle made use of our intimate knowledge of the logical forms of certain propositions, such as the ones we use to speak about the Earth, in TLP, Wittgenstein sought to speak about objects qua any representation: The problem. Frege felt he could safely say that “[t]hought is in essentials the same everywhere: it is not true that there are different kinds of laws of thought to suit the different kinds of objects thought about” (FA p. III), and the idea of an application of the context principle to an area of thought, such as theology or mathematics, would be useless if this was not assumed. This is an assumption that we have not

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sought to establish in our treatment of Fregean meta-ontology, but it is an assumption that the TLP tries to address. The context principle is not being applied to any particular area of thought. The context principle is thought of with full generality – regarding any expression with a sense. Consequently, we should say that the strands of the nonsense that we encounter in the TLP have a different topic and point than the Fregean, which may yet be different from other cases of nonsense. For instance, our “time-nonsense” did communicate something about time-keeping. Frege’s FA communicated something about numbers by means of sentences like “numbers are objects”, and we have communicated by means of sentences like “‘god’ is a sortal”. Meanwhile, the TLP should be seen as an attempt to communicate something about representation as such. For the nonsense to be about and communicate regarding time-keeping, god and numerals, some acquaintance with the relevant region of language must be assumed. In the Tractarian case, then, what is relied upon for the reasoning to be effective is simply the existence of linguistic representation and the logic it involves. By means of nonsense, we are brought to appreciate something about the nature of this representation. Fregean meta-ontology has shown its philosophical relevance on two accounts. Firstly, it has served to explicate a clear concept of an object by means of which one can conduct a local ontological investigation, in our case concerning the existence of God. A central part of the clarification has consisted in the ascription of the concepts “singular term”, “object” and “sortal”. By means of these concepts we have been helped to see how logical syntax takes care of itself, as alluded to in the concluding section of chapter 1. We cannot stamp a symbol the wrong way (e.g. a concept as an object), but with ascription of the formal concepts, we can throw light on how signs in fact function in a given context. Secondly, Fregean metaontology draws the boundaries between a philosophical question and a non-philosophical question in a way that goes against the grain of much philosophical debate over realism in theology. While the Fregean approach to ontology has led some philosophers to speak of cheapness, the approach has the strength that it underlines the importance of a careful understanding of the relevant sortals being employed in the region of language under investigation. On these two accounts, Fregean meta-ontology seeks to attain a clear understanding of a given subject – the avowed goal of much philosophy.

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Index Index Abbildung 72 Abgott 102, 106 Alston, W. P. 138 analogy 8, 19, 22 Anscombe, G. E. M. viii, 85, 169 Aquinas, T. 29, 99, 103 Aristotle 6, 8, 16, 42, 65 Armstrong, D. 20 Ayer, A. J. 83, 84, 172 Barth, K. 24, 87, 88, 111, 116 Barth, Karl 58 Bauckham, R. 104 Bedeutung 31, 66, 136, 137 Bell, D. 31 Benacerraf, P. 19, 20, 56, 140 Bentham, J. 30 Berkeley, G. 30 Burge, T. 4, 18 Burgess, J. P. 57 Burnett, J. S. 94, 97, 98 Butler, S. 7 Byrne, P. 1 Carnap, R. 35, 153 Carroll, L. 45 causality and belief generation 19 and reference 20, 54, 55, 59, 79, 84 external to mathematical practice 57 Cavell, S. 30 Chihara, C. 16, 24, 27 Christianity and Judaism 109 Collins, A. W. 34, 76 Colyvan, M. 16, 18 compositionality 13

in metaphor 5 Conant, J. 155, 156, 158, 160 concept boundary-drawer 42, 64, 143 question of existence of 53 realised 136, 137 Concept Script 41, 129, 136, 168 context principle vi, 30, 125, 151, 158 and ontology 28, 31, 32 and theories of meaning 31 apparent violations of 65 concerns class of propositions 48 linguistic evidence against 65, 66, 67 local application 50, 170, 171, 172 non-restricted use 128, 170, 174 strong reading 144, 160, 161 Darstellung 72 Darwin, C. R. 78 Davidson, D. 5 Devitt, M. 7, 18, 23, 54, 167 Diamond, C. viii, 126, 155, 157, 159, 160, 161, 165, 168 Donne, J. 5 Dorr, C. 34 Dummett, M. A. E. vi, 16, 18, 22, 32, 33, 37, 44, 46, 49, 63, 65, 67, 69, 122, 131, 135, 138 Durrant, M. 53, 88, 89, 92, 93, 105 Dworkin, R. 16 elohim 96, 98, 101

188 and King 107 elucidation 14, 22, 83, 87, 94 epistemology 20, 21, 27, 31, 32, 38, 39, 47, 57, 60, 77 and logical form 166, 167 reliabilism 20, 56, 57 ethics 125 Evans, M. G. J. 42 existential generalisation 10, 17, 45, 50, 59 fiction 10, 40 Field, H. 19, 20, 21, 34, 57, 88 focal meaning 9, 18 Ford, D. 6 formal concept 150, 165, 170, 173 frames in TLP 158 Frege, G. vi appeal to feeling for German language 49, 50, 171 charity 14, 19 conception of logic 148 fight against language 85 function 131 and predicate 127 and sameness of content 136 as a pattern for deriving a value 134 attempt at naming 132, 133, 134 index of a 132, 133, 134 Geach, P. T. 42, 88, 89, 92, 134, 137 God and simplicity 29, 103 sign for a name 83, 94, 96, 97, 99 a sortal 29, 83, 106, 107 both name and sortal 91 confused 84, 88 disambiguated 120, 121 not a proper name 89, 105 not transliterated 89, 101 transliterated 104 Goldfarb, W. 155, 157

Index

Goldman, A. 20 Gödel, Kurt 4, 27, 57 Hacker, P. M. S. 112, 126, 157, 159, 169 Hale, B. 35, 56 Hawley, K. 60 Heck, R. G. Jr. 58, 61 Heidegger, M. 16, 154 Heil, J. 79 Hick, J. 15 Hirsch, E. 62 Hochberg, H. 66, 67, 74, 75 Hurtado, L. 109 Hyder, D. 71, 142 Haack, S. 1 idealism 39 indispensability 5, 21 Jesus and disciples 96 and name of God 104 Christ 100 his kingship 109, 110 tempted 109 thelord 104 Kant, I. 15, 16, 17, 34 Keil, F. C. 12 Kierkegaard, S. 85 king concept of appears altered 108, 109, 110, 111 concept of in OT and NT 109 deuteronomic law regarding the 108 Kraus, K. 84, 85 Landini, G. 8, 149 Lemaire, A. 94, 96, 97 Levinson, B. L. 107, 108 Linnebo, Ø. 22, 56, 57 logic cannot make mistakes in 25, 127 nature of 29 takes care of itself 25

Index

logical discussion 127, 135, 145, 147, 148, 149, 160 logical form 48, 50, 79, 80, 125, 143, 152 and epistemology 167, 172, 174 logical truth criterion of 149 logicism 29, 127, 171 Long, P. 31, 132 Lowe, E. J. 58, 59, 130 Luther, M. 106 Mackie, J. 16 Mackie, P. 58 Maddy, P. 13, 14, 19 Maimonides, M. 29 Mark, D. M. 78 mass terms 53 Mayberry, J. P. 8, 67 McGinn, C. 54 McGinn, M. 112, 169 McManus, D. 45 Melia, J. 58, 77 metaphor 4, 5, 91 Mettinger, T. N. D. 94, 97, 107 Midgley, M. 153 Miller, R. B. 54, 55 Moberly, R. W. L. 94, 97, 103 Moor, J. C. D. 94, 107, 172 Moore, A. 1, 6, 7, 13 Moore, A. W. 163, 165 Moses 96, 100 theophany 96, 97, 99, 100 Müller-Lyer illusion 38 natural theology 118, 122 Neusner, J. 109 nominalism 20, 39 nonsense viii, 138, 150, 153, 154 and intention 162 appears as a sentence 160 as reminder of use of signs 163 austere 151, 155, 156, 158, 164 compared with breaking of chess rules 158, 163, 164

189 construed as representing states of affairs 165 Frege calls imprecision 165 kinds of 151, 155 no inference from 160 substantial 155, 156, 159, 160, 165 true 169 Nordmann, A. 71, 83, 155 object abstract vi, 20, 56, 57, 59, 60, 61, 141 and unrestricted quantification 143 artifactual 79 bare 54, 146 bogus 60, 63 duds and daps 61 incar 62 typical father 59 concept of a dummy sortal 145 and "thing" 15 and nonsense 126, 127 and ordinary objects 18, 19 assumed univocal 14 construed as a sortal 140, 142, 143 desiderata 20, 24, 28, 42, 58, 80 expressed by variable 159 Kant, I. 15 not a sortal 128, 167 not univocal 1, 2, 3, 5, 6, 7, 9, 10, 34, 61 spatial conception 19, 20, 21 thick and thin 3, 4, 61 vague 64 contrasted with other ontological categories 16, 76, 141, 142, 143, 148 dependent on existence of other objects 62, 64 fictional 40

190 going proxy for concept 136 independence a form of dependence 72 ordinary 21, 25, 31, 78, 79 Tractarian 71, 72 object- and meta-language 36 Ogden, C. K. 167 paradox liar vii of the concept horse vii, 127, 128, 129, 131, 135, 152 a fake problem 130 of vagueness 64 Russell's 135 Parsons, C. 3, 4, 18, 23 Paul alludes to divine name 104 and wisdom 110 on idols 119, 120 Peri, C. 108, 115 Phillips, D. Z. 2, 11 philosophy vi as an activity 126 as critique 83, 84 conjuring tricks in 19, 23 full of fundamental confusions 74 ordinary language 152 the problem and problems 172 philosophy of religion 11, 13, 15, 94, 122 Pilate 109, 110, 114 Plato 35 Platonism 2, 14, 16, 18, 20, 61, 63, 140, 143 contextual contrasted with traditional 63 relaxed 18 Poincaré, H. 2, 22 Potter, M. 31 problem of the criterion 49 Proops, I. 71, 130, 157, 160, 161 proper name and legal acts 95

Index

and transliteration 89 biblical tradition 95 calling on 104 capitalised 74, 83 part of a sortal 91, 92, 100 reluctance to use 103, 104 theophoric 95, 104 elohistic 104 sons of David and Saul 101 Yahwist 100 proposition account of central to TLP 149 as a fact about signs 133 as a picture 69, 72, 149 bipolarity 164 general form of 11, 13, 170 theory of the 66, 142 unity of 71, 129, 133, 144 psychologism 30, 31 Putnam, H. 2, 34, 36, 37, 55, 84 Quine, W. v. O. 1, 18, 22, 60, 78, 84 Ramal, R. 2 realism 9, 13, 14, 18, 24, 84 and mathematics vi, 2, 5, 13, 21, 23, 53 and theology vi, 6 christocentric 1, 7 external 35, 36 innocent 1 internal 34, 35, 36, 41 mathematics 143 moral 1 structural 2, 3 Reck, E. 30, 63 Resnik, M. D. 2, 39 Reynolds, S. L. 34, 38 Rosen, G. 57 Rumfitt, I. 49, 50 Rundle, B. 84 Russell, B. 58, 132, 140, 142, 144, 146, 154, 159, 167 Schneider, H. J. 130 Schrage, W. 119

Index

Schröder, E. 42 Searle, J. 78 semantic externalism 117 sense and reference 31, 42 Shakespeare, W. 7 Shapiro, S. 2, 3, 13, 27, 147 shema 29, 103, 121 showing 155, 165 showing and saying 170 sign appears as word / symbol 74, 132, 135 cannot give wrong sense to 25 combinatorial possibilities 68, 69, 71, 73, 74, 134, 158, 163, 164 differs essentially between proposition and word 75 displayed 41 contrasted with symbol 8, 75, 131 introduction of new 24 mention 36 onomatopoeic 35 shared by several symbols 41, 92, 119 Simons, P. 131, 132, 134, 159 singular term and Aristotle's notion of substance 16 criteria of 41 and reflective equilibrium 49 distinguished from expression of generality 44, 45 does not admit plural 42 incomplete 48, 49, 50 not used as predicate 42 reflexive pronoun 29, 42, 43, 59 specification test 46, 47, 48 Skorupski, J. 31 Smiley, T. 31 Smith, B. 78

191 sortal 52, 53, 55, 63, 81, 88, 106, 173 and identification of objects 53 and taxonomy 55 growing capital letters 86 logical features 52 mistaken 54 pure 53 Stainton, R. J. 65 Steiner, M. 20 Sterelny, K. 54 Stern, D. 11 Strawson, P. F. 86 Stump, E. 103 Sullivan, P. M. 10, 50, 130, 132, 134, 152, 157, 158, 165, 168 Swinburne, R. 122 symbol attempt to make subject of a proposition 25, 127, 128, 148, 149 syntax primacy over ontology 30, 40, 50, 51, 60, 84, 129, 144 and idealism 39 Tennant, N. 39, 41 term (Principles of Mathematics) 144 theism 173 heno- 102, 172 mono- vii, 101, 102, 106, 108, 119, 121, 172 poly- 102, 120 theology and history 57, 94 theory of types 25, 154, 169 Thiselton, A. C. 108, 119, 120, 121 Thomasson, A. 60, 145, 146 true F 110, 111, 112, 113, 115 God 106 intelligibility of challenged 112, 113, 114 king 110 white 112

192 truth 29, 80 of language about God not investigated 87, 152 Tugendhat, E. 31 unrestricted quantification 10, 125, 131, 141, 142 vagueness 10, 64, 65, 146 van Inwagen, P. 58, 146, 167 verificationism 84 Visser, H. 71 Wagner, S. 14, 18 Wellhausen’s documentary hypothesis 97 Wetzel, L. 47, 48, 49, 50 White, R. M. 8, 12, 31, 110, 113, 114, 158 Wiggins, D. 60, 145 Williamson, T. 17, 18, 141 Wittgenstein’s later works and "game" 11, 12

Index

and logical status of "God" 86 and true F vii, 112 attention to differences 7 builders 65, 67, 68 context principle in 31 craving for generality 11 criticism of Fregean metaontology 61 family resemblance 11, 13 on naming 51 the problem and problems 170 time keeping on the Sun 160, 161, 164, 174 Wright, C. 48, 53, 56, 131, 141, 143, 144, 146, 152 Yablo, S. 4, 5, 19, 58 YHWH 98, 100 contrasted with other gods 97, 101 is king 107

Concordance of passages from the Tractatus 2.011 66 2.0122 66, 72, 135, 167 2.0123 167 2.17 70 2.182 73 3.14 70, 135 3.262 72 3.302 8 3.311 48, 72, 73 3.313 73, 134 3.314 48, 74 3.323 73 3.324 74 3.326 125 3.327 75 3.328 66 3.33 25 3.334 172 3.3341 133

3.4 72 4.0031 83 4.06 72 4.112 126 4.1211 166 4.122 166 4.1272 149, 159 4.1431 135 5.02 132 5.451 23 5.473 25 5.4732 25 5.4733 154 5.5261 68 5.5563 25 6.1271 148 6.2331 157 6.53 33, 37, 151, 152, 171 p. 18 140