CONTENTS

1   INTRODUCTION

2   COMMUNICATION AND REPRESENTATION

3   SAYING ABOUT

4   NAMES AND PICTURES

5   THE ROLE OF CONCEPTS AND RELATIONS IN PICTURES

6   SENTENCES AS PICTURES

7   CONCLUSION

1   INTRODUCTION

The theoretical background of this discussion is provided by three theses of Frege concerning the nature of language. The formulation is taken from Dummett’s "Frege Philosophy of Language", first edition (referred to hereafter as FPL1), in chapter 6, "Some Theses of Frege’s on Sense and Reference". The three theses are the following (numbers 7, 5 and 10 respectively in FPL1). 

The three theses are only parts of Frege’s theory of language. The fact that other parts, especially the notion of sense, are not discussed here, does not imply that they are considered to be of lesser importance. It is simply that this particular essay focuses on the notion of reference. In addition, for purposes of simplicity, the discussion is largely restricted to a fragment of language: that comprised by names, predicates and sentences. 

The striking thing which emerges from the three theses is that for Frege the reference has a multiple structure - there are different forms of reference for names, predicates and sentences. (In this I follow Dummett in holding that Frege’s later treatment of truth-values as types of object, and therefore of sentences as types of name, was misguided, and contrary to the main thrust of his theory of language.) If the realism embodied in the third thesis is taken seriously, then this three-fold division of reference is part of the ontology of the world, and yet it is a part of ontology which is determined by the nature of saying rather than by the nature of the world itself. To persist with realism we have to say that the Fregean structure of reference is a non-trivial feature of ontology which nevertheless is ontologically neutral, putting no constraints on what can be true of the world. (In another essay, on the passage of time and McTaggart’s paradox, I suggest that there may be possible, and indeed actual, features of the world which cannot be fully referred to within language, which escape the mechanism of saying. This compromises the status of language as a perfectly ontologically neutral mechanism for reference, but not to the extent that one is forced to accept logical relativism.) 
 

2   COMMUNICATION AND REPRESENTATION

As an example of a system of communication which is not language, consider the calls of the vervet monkeys. They have a highly developed system of calls, being able, for example, to distinguish in their alarm calls the distinction between, 
 

"Look out, here comes an eagle"

"Look out, here comes a snake"

The detachable bits found within items of linguistic communication are not confined to those representing objects. As well as just representing objects, language has to say something about them. The relation, "... says something about ..." is the primary subject matter of this essay. We have seen how this happens already in the linguistic renderings of the content of the vervet calls. Once the bit standing for the respective predators is taken out we are left with the incomplete fragment, "Look out, here comes a ...". 

3   SAYING ABOUT

Although the reference to the object can be done in non-linguistic ways, no amount of using names or pictures can say something about the object. This act is irreducibly linguistic, and is at the heart of what (literal, assertoric) language is about. One might try to make the above assertion by embedding a picture of Saturn in a picture of the solar system, showing all the planets in their positions relative to the sun. But this picture does not succeed in saying anything about Saturn. It shows its position, so that, using the picture, someone who recognised the sub-picture of Saturn could answer the question, "Which is the fifth planet from the sun?" But this question and the full answer to it require language in their formulation. 

This is why predicates are incomplete expressions. There is within the sentence an atomic mechanism of saying, something that cannot be built up out of non-saying components. When we take a name out of a sentence, the piece that is left is still a sentence, a means of saying, albeit an incomplete one. If that bit were lost, the resulting component could not be used to construct other sentences which could be used in assertion. (This is contrary to Dummett’s thesis that only when bound to second-order predicates, such as the quantifiers, need (first-order) predicates be considered incomplete.) 

To say that there is an irreducible element of saying in the sentence, which can not be built up out of simpler components, looks like an unnecessary mystification of a simple situation in which sentences are built up out of words. Suitable combinations of these words are understood by users of the language to stand for the possible contents of assertions. To insist on the "irreducible spirit of saying" looks rather like some sort of "logical vitalism"? 

The counter-argument is to say that the doctrine is one of atomism rather than vitalism. The question is, where does one start from? The Fregean analysis of language shows that the lexical category "word", on which natural language is founded, is systematically misleading when it comes to the understanding of the deeper structure and function of language. Instead the starting points are name and sentence. Before analysis, the sentence stands for one of the two truth values, but does not show in its form how it does this. That is to say, it does not express its thought explicitly. 

Taking English as an example of a natural, word-based language, we are left with the puzzle of what the function of verbs is. We are told that to be a sentence a compound expression must contain a verb, but we are not told why. Is this just a purely linguistic convention? We are told, when learning grammar, that verbs stand for actions. In the sentence "John runs", the name "John" stands for a person, and "runs" stands for what he is doing. But this explanation does not stand up to examination. The word which stands for the action involved is the verbal noun, "running". Fregean analysis dispels this difficulty. We see that verbs are the imperfect natural language representation of incomplete expressions. The full mechanism is scattered across verbs, adjectives and common nouns, the latter two being elevated to predicatehood by the use of the verb "to be". 

4   NAMES AND PICTURES

"x is a gas giant and x has prominent rings."

But suppose the written form of the language uses pictograms. Are these names or pictures. If they are defined linguistically, then they are names. But if the pictorial elements, for example the rings on a pictogram representing Saturn, are used to establish its sense, then they are pictures. Spoken language is made out of sound, and therefore has to be conventional (except when the sounds are used to depict other sounds). Writing which depicts the sounds rather than the referents inherits that pure conventionality and is thus able to be more purely linguistic. 

We often use pictures within language when linguistic description becomes to complicated: "Oh, this is too complicated for me to describe. Let me draw you a picture instead". The limitations of words can be illustrated by the challenge, "describe a spiral staircase without moving your hands". In fact it is not impossible to describe a spiral staircase accurately purely in words, but to do so requires one to devise an elaborate geometrical vocabulary first. This procedure of building up systematically a new vocabulary is the bread and butter of mathematics, but it is not common in natural language. The difficulty in describing a spiral staircase lies in the fact that our natural vocabulary is not rich enough for the task. The need for the enhanced vocabulary is not a symptom of the inadequacy of language, but rather of the intrinsic complexity of the concept "spiral staircase". Complex concepts require a complex vocabulary for their expression. The success of mathematics shows that it is possible to build up a vocabulary which expresses this sort of complexity, but the problem then is that many people would be unable to understand what was being said. Mathematical thought is on the margins of the capability of the human brain. 

So in many cases a picture is indeed worth a thousand words. But the thesis of this essay is that there is a residuum of language which no amount of depicting can replace. These are the words which say something about the object, whether it is referred to by a name, depicted by a picture or pointed to directly by ostension. 
 

5   THE ROLE OF CONCEPTS AND RELATIONS IN PICTURES

Note that although predicates are intrinsically linguistic, as realists we must assert that the concepts they refer to are objective features of the world, with a reality independent of language. But concepts bear the mark of the mode of reference, namely incompleteness. What concepts are, their nature, the concept of concept, can be explained only by reference to the mechanisms of saying, but which concept-senses succeed in referring is a matter entirely for the world. 

To look further into the role of concepts and relations in pictures, let us consider again the picture of the solar system, with each planet being shown in its relative position to the sun, and (on a different scale) with its own relative diameter. The sub-pictures of each planet have enough detail, in addition to diameter, to make them recognisable to anyone with a reasonable knowledge of astronomy. This picture then shows, but does not assert, the truth of statements like, "Saturn is the fifth planet out from the sun". The relation "fifth out from the sun" is not depicted in this diagram, but rather the relation itself is there. The diagram preserves the "out from the sun" order relations between the planets. But does the diagram contain the concept "... is a planet" or does it simply depict it? 

For simplicity, let us take "... is a planet" to mean "... orbits the sun". (In practice we have to put on other restrictions, to exclude moons, which orbit something else which in turn orbit the sun, asteroids, which are too small, and companion stars.) The notion of "orbit" contains the idea of motion, and so cannot be shown in its own right on a static picture drawn on a piece of paper. There is of course nothing to stop us extending our notion of pictures to moving pictures. An orrery is an old-fashioned moving picture of the solar system, and an animated image on a computer screen in a multi-media treatise on astronomy is a modern version. Both of these generalised pictures contain the concept of planethood, defined as one object moving around each other. 

But what is the status of planethood in the static drawing? Typically the diagram of the solar system will place the pictures of the planets on sun-centred circles or ellipses in an attempt to depict the orbits and thereby planethood. If that is not enough, then arrows tangential to the orbit pictures might be attached to the planet-pictures to re-inforce the intention to depict motion. But these devices are conventional, they are not the motion-itself. Here we are going beyond pure depicting, because of the limitations on what can be depicted in the chosen medium. The ellipses and arrows are the best we can do on a static picture - they contain all the spatial content of the motion, but can not contain the necessary temporal component. For someone who does not understand the diagrammatic conventions one has to break the Trappist vow of not using language and say: "these ellipses and arrows represent the motion of these objects around the sun, and thereby, the status of the objects as planet". 

This suggests that there is another distinct category between picture and sentence, namely the category of diagram. The diagram is like a picture in that it contains concepts rather than referring to them, but they are not the concepts being depicted, but rather ones which stand conventionally for them. Typically, given that we draw diagrams on two-dimensional paper, the concepts and relations contained in diagrams and used to represent the subject matter are two-dimensional spatial ones. For the diagram to work as such, the depicting and depicted concepts and relations have to share certain second-order features (order relations, topological and metrical structure). These second-order features are present in themselves in a diagram (as opposed to being referred to or conventionally depicted). A diagram can therefore be thought of as being a second-order picture. 

6   SENTENCES AS PICTURES 

The central theme of this essay has been how pictures and sentences do quite different things, even though in some generalised sense they are there to represent reality. And yet sentences do have a pictorial element to them. How can this be accommodated in an account based on the contrast between sentence and picture? 

The first pictorial feature of sentences is that they depict their sense. As Wittgenstein says in the Tractatus (4.022), "a sentence shows its sense". (Here I am translating "Satz" as "sentence" rather than "proposition".) A sentence cannot say what its sense is; the sense is presented directly to our understanding by the form of the sentence, and only when this is grasped can we begin to use the sentence to say something about reality. Frege’s essential critique of natural languages is that they depict senses badly. His conception of a Begriffsschrift is of a language purged of this defect, within which the sense of a sentence shines clearly through its lexical form. 

However while a sentence depicts its sense, it does not depict the reality of which it speaks. (This is, at least superficially, contrary to what is said in the Tractatus (4.01), "A sentence is a picture of reality". It is however quite beyond the scope of this short essay to confront systematically the account given here of saying and depicting with the picture theory of meaning developed in the Tractatus.) To reiterate: a sentence says that certain objects fall under certain concepts and relations, whereas a picture shows that they do, by having the representatives of the objects fall under the same concepts and relations (or in diagrams, concepts and relations which represent the features being depicted). 

The second pictorial feature of sentences is how they represent their own referents, namely the truth-values. We can not say that the thought expressed by the sentence is true; instead all we can do is bring forward in a certain conventional way a token of the sentence and rely on the convention that this act counts as asserting truth. In a purely linguistic sentence, that is, one purged of all pictorial elements, everything is expressed within the sentence except this final two-fold choice between truth or falsity. (It has to be a two-fold choice, because otherwise truth could not be asserted simply by bringing forward the token.) This is the irreducible element of depiction right at the end of the process of saying. 

Of course we do have within language the resources to talk about truth. We can attribute "... is true" to senses, using indirect speech: for example, 
 

"It is true that Saturn is the fifth planet out from the sun".

" ‘Saturn is the fifth planet out from the sun’ is true".

But these attributions of truth do not go any further to explain the notion of truth to us. They can not be used without invoking the assertion convention. However many times we iterate the process in the attempt to say, "... is true", the process has to terminate with an act of unadorned assertion. And in as much as these elaborated sentences say anything about Saturn, they collapse into the plain sentence, "Saturn is the fifth planet out from the sun". 

7   CONCLUSION

The purpose of labouring these points about the saying-depicting distinction is to begin the process of saying what saying is. This is done here largely by saying what it is not. The positive parts of the process will be attempted in a future essay. 
 
 

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