Representation, Meaning and Truth

Philosophers of all ages have found the concepts of meaning and truth to pose serious problems. In this essay I try to show that, while these problems are far from trivial, a study of the function and purpose of language can throw some light on them.

REPRESENTATION

In everyday life we frequently meet one thing which represents another. The position of the hands of a clock represents the time, the figure "4" represents the number of players in a game of bridge, the word "cat" represents the animal in front of the fire, and a flag can represent a country. The word "cat" itself can be represented in different ways, for it may be spoken, written, recorded on audio equipment or stored in a computer. Further examples are provided by the picture on the wall which may represent a sunset, and the bar code on a can of food which represents its contents. In each case we have three elements; there is the thing that is represented, and which we shall call the "object"; there is the representation, which we call the "symbol"; and there is the set of rules determining what symbol relates to what subject, and we call this the "coding".

In most cases the form of representation has been devised by humans or by nature to serve some clear purpose. The only essential property of the symbol is that it enables the corresponding object to be identified, so that each symbol must correspond to no more than one object, or to a clearly defined class of objects. Thus there is only one number which we designate by the figure "4", and only one class of animal denoted by "cat". There is no need for the reverse relationship to be unique; we can describe the number of bridge players by writing either "4" or "four". The English language illustrates this latter point well, for alternative words can often be found having the same or similar meanings.

This is all so familiar that it comes as a surprise to realise that examples of one thing representing another occur only where living organisms are involved; in a wholly inanimate world there are no examples of representation or coding. If one searches deeply enough it may be possible to find an occasional doubtful exception to this rule; there may be rare cases on an uninhabited planet that a natural feature behaves like a crude pinhole camera and casts an image of the sun on a nearby surface, or a stone leaves an impression of its shape in the mud. But such occurrences will be purely accidental, and not of sufficient importance to contradict the broad assertion that representation is a process wholly restricted to living things. This is not to imply that intelligent creatures are required; indeed one of the most striking examples of coding here on earth has been operating since the very first life appeared, for the process of reproduction itself depends upon the way an organism's structure is encoded in its genetic material. No life forms as we know them could exist without this capacity to represent the form of the offspring in a small part of the parent, thereby permitting the creation of the next generation on which multiplication and evolution depend.

OBJECTS, CODING AND SYMBOLS

The next three paragraphs discuss briefly the sorts of entities that can serve as elements in the representation process. Consider firstly the object of a representation. The list is almost endless. A material object can be represented by a picture or a word, a word can be represented by a printed string of letters, a fact can be represented by a statement, a sound can be represented by a recording. Perhaps more controversially, I maintain that a belief, a mental picture or an intention are represented by patterns of activity in the brain, as are dreams, sensations and memories.

The different forms the symbol can take are equally diverse. A spoken word consists of sounds in the air, a written word comprises marks on paper, and recorded sounds may be spots on a disc. Other forms of representation may be currents in a wire or connections in the brain. There is no limit to the other forms that could have been adopted by man or nature to serve as symbols. The only requirement is an entity with a sufficiently detailed and adaptable structure to allow a large enough number of different configurations, to mirror the range of objects which are to be represented.

The method of coding also can take many different forms. In some cases there may be no systematic rule, but just a list of objects and their corresponding symbols. There is no logical reason why a cat and a dog are not called, respectively, "dog" and "cat". Likewise there is no reason why the figure "4" or the word "four" should mean what they do; but on the other hand when we deal with larger numbers, such as 1997, the "place value" of the individual digits is determined by rigid rules. The rules relating commercial products to their bar codes have been clearly specified by manufacturers, and the way in which sounds are encoded on a CD is determined by a complex set of formulae in the so-called "red book". It will be seen that some of these methods have arisen quite by accident. We do not know whether any alternative molecular structures other than DNA could carry the genetic code, but we believe the scheme which does apply has developed simply by the trial and error methods of natural selection. Our own use of spoken language, and later of writing, have both developed in a haphazard manner, and could have turned out very differently. In each case it is perhaps remarkable how successful the development has been, but the uncontrolled manner of their evolution has resulted in gross inefficiencies. Much of the information in the DNA of the higher organisms serves no purpose, and a deliberately designed language such as Esperanto can be much more compact and logical than any natural language.

Language is perhaps the most important example of representation for humans. It clearly developed in its early stages as a means of communication, with obvious survival advantages. But subsequently language has acquired a number of additional uses besides that of transmitting information. Man had powers of reasoning far above those of any other animal even before the growth of language, but since then language has become an essential component in the thinking process itself quite apart from its value in communicating. Much of what we call "logical" thought is conducted more simply by manipulating symbols than by abstract reasoning, and man's brain must quickly have adapted itself to using words for such symbols in its thinking as well as for speaking. Today some people make more use of verbal reasoning than others, but for everyone it provides a valuable tool in certain kinds of thought.

Since the invention of writing, words have acquired many more uses. Without them, how could we send our thoughts to distant places, how keep them fresh to jog our own memories in the future, how record them for posterity or store them in a computer? Words, coded in one form or another, today play a vital role in almost all our activities.

Valuable extensions to language have become available in the form of mathematics and symbolic logic. Anything that can be said in the language of mathematics can be said without it, but often at much greater length. If a group of objects can be put into one-to-one relationship with the stars * *, and another group can be put into such a relationship with the stars * *, then the two groups together will stand in one-to-one relationship with * * * *. But it is much simpler to say "2 + 2 = 4".

MEANING AND TRUTH

At the same time language has presented several intractable problems to our philosophers. The value of verbal propositions lies in their possessing meaning; trying to understand the concept of "meaning", or to define it clearly, can tie the thoughtful scholar in knots. And worse, some statements are true and some false; any definition of truth raises many riddles. It is two thousand years since Pontius Pilate exclaimed, "What is truth?" And it is several more centuries since Parmenides argued that, because we can make true statements about a man even after his death, he must in some sense still exist.

I believe that many apparent problems surrounding meaning and truth evaporate when it is remembered that words and language are no more than representations of objects, processes or facts. A word is simply a symbol representing something in the real world, or an activity or a characteristic; its meaning is simply that which it represents. A statement is a group of symbols representing a fact; the fact is the meaning of the statement. Philosophers may disagree over what actually exists; they may argue over whether an object's characteristics, or its past existence, are real. Many such disagreements are purely semantic; two people can quarrel over the existence of the colour "green" only because they have not agreed a definition of the word "exist". But this does not impinge on our present discussion. It must be remembered that language exists to serve a purpose; the word "green" exists only because there is something for it to represent, real or unreal, and the meaning of "green" is that something. Similarly, propositions exist in order to relate symbolically to facts in the real world; a proposition is true if it correctly represents such a fact or state of affairs; it is false if it fails to correspond in this way with the world.

In the initial stages of the development of language, its chief purpose was to codify facts into sounds in order to communicate them to other people. If this codification had always been done accurately, then the idea of truth or falsehood would never have arisen. But it would soon be discovered that this is not always the case. Ancient man would occasionally say from the back of his cave, "It is raining", when in fact the rain had stopped. He may sometimes have said, "We have two pigeons in the larder", forgetting that one had been eaten yesterday. More reprehensibly, he would sometimes find it to his advantage to make statements which he knew to be false; he could say to his neighbour, "One of your cows has escaped", hoping to steal his neighbour's possessions, or take advantage of his wife, in his absence. Thus, although all statements purport to relate accurately to facts, the realisation would arise that some did not; some are true and some untrue. Meaning would have no significance in a world devoid of life, for in such a world there are no examples of representation. Meaning is the relationship between a symbol and the corresponding object. Truth has significance only in a world peopled by intelligent creatures like ourselves, capable of stating, or at least of thinking, facts about the world.

It is interesting to consider how whole heirarchies of coding can arise. Think, for a moment, of a large animal contentedly grazing in a field, and obviously ready to give milk. I am, of course, describing a cow, but wished to do so without using the word. I hoped to conjure up in your brain a non-verbal picture of the animal which we represent by the word "cow". The word in its original form is just a pattern of sounds, but several further codifications of the word itself are possible; it can be written down, or spoken into a microphone, or translated into French. And the written word can be further coded in a word processor or an e-mail message. We can use the idea of "meaning" to describe the relationship any of these representations has to any other higher up the heirarchy, but not to any lower down. Thus the electronic signals of the e-mail can be said to mean the word "cow", the written word "cow" means the same word in spoken form, which itself represents the animal in the field. But the animal does not represent the word or the electrical signal.

Some early forms of writing dispensed altogether with one stage in the chain of representation. The written word "cow" represents phonetically the same spoken word, which itself represents the animal. But in heiroglyphic writing the symbol for a cow relates directly to the animal, and not to the word. It is perhaps not too fanciful to believe that scholars trained in heiroglyphic script use words less in their private thinking that those whose writing is in words.

The idea of truth is more restricted than the idea of meaning. The only components of language possessing the property of truth or falsehood are statements, in whatever form these may exist, whether spoken, written or stored in a computer. Individual words can have meaning, but cannot in themselves be either true or false, and the same applies to questions and commands. The concept of thruth, however, can apply also to some non-linguistic entities, and in particular to beliefs; it is important to notice that a belief may or may not be in linguistic form. Man certainly had beliefs before he could use language, and so indeed have some animals. A dog may run to the door, believing that its master is about to enter, when in fact the visitor is someone else; the false belief clearly is held in non-verbal form. On the other hand, when we think to ourselves, "I have a thousand pounds in the bank", the belief is simply verbal. We do not form a picture of a thousand individual pound coins. Whether or not a belief is held linguistically it can still be false if we have made a mistake or been deceived.

MEANING: SOME DIFFICULTIES

So at first sight all the perplexities associated with the idea of meaning seem to disappear when we think of it simply as the relationship between the elements of an object and those of its corresponding symbol. Let us take as a simple example the statement "The cat is drinking milk". We can picture this situation without using words, a situation containing a number of features, the cat, the milk, and the act of drinking, and these features are joined into a particular structure. The actual sentence, "The cat is drinking milk", also consists of elements and a structure, and the two structures are related by the rules of syntax and semantics of the English language. The features and relationships of the situation are themselves the meaning of the sentence. The meanings of the words have grown up by accident as the language has developed, and are purely conventional. The order of the words is also important; we did not say "Milk is drinking the cat", and the rules determining this order have also developed accidently. The rules of grammar also are conventional, although A. N. Chomsky (b.1928) teaches us that these rules must owe something to our genetic endowment. The ease with which a young child can be taught to use them by parents with no particular teaching skills strongly suggests that a basis exists in the brain soon after birth for acqiring the complex expertise required for meaningful and grammatical speech.

But we have taken a particularly simple example. The statement we used as illustration describes a true contingent fact. Difficulties emerge if we consider some other types of statement, such as those that are untrue, those relating to the past, or those describing value judgements. It was cases such as these which prompted the Logical Positivists to assert their "Verification Principle", that the meaning of a statement is the method by which it would be verified. We clearly cannot take this literally; the method by which we verify that the cat is drinking milk is to look and see, and surely the act of looking is not the meaning of the statement. But if we allow that their definition slightly over-states the case, the principle still fails to indicate how we should regard many statements which we know intuitively to be meaningful, statements regarding aesthetics or morals, or other people's thoughts. Perhaps the "Picture Theory" of the early Wittgenstein comes closer to the doctrine I am advocating; he maintained that a sentence represents a fact in the same way a picture represents a scene. But this also is not so much a definition as an analogy. A picture of a sunset looks something like a sunset, while the word "cat" looks nothing like a cat. A further level of abstraction is required in relating a word to its meaning, the level containing the rules by which the vocabulary of the language is determined. And this vocabulary can describe anything about which we can think, whether past or present, true or untrue, concrete or abstract. It is man-made, and can serve any purpose we wish.

Let us consider how our understanding of meaning can be applied to several different kinds of fact or situation, and the statements we make to describe them. A new difficulty arises if our statement relates to a general rather than a specific fact, such as "All cats drink milk". Where do we look for the state of affairs which this represents? There are several possible answers. It might be argued that such a generalisation can be performed only by a rational being, and the situation we seek is within the human brain. Or we might argue that the word "all" is merely an abbreviation: the statement replaces the conjunction of many terms, namely "Felix drinks milk, and Tiddles drinks milk, and ...". Yet a third solution is possible if we accept the absolute existence of sets; the thing we are looking for is a relationship between sets. Cats form a subset from the set of all creatures which drink milk.

This last interpretation allows us to treat analytic facts in the same way. If we accept the teaching of Russell, then the whole of logic and mathematics can be reduced to a theory of sets. "All bachelors are male" is a simple example of an analytic statement, and the elements of the sentence mirror the logical structure of the idea that "The set of all bachelors is a subset of the set of all males".

How are we to treat statements which are untrue? What situation corresponds to the statement "Paris is the capital of England"? There is clearly no such state of affairs in the real world, but it is possible to imagine a world in which it is true. So here we must look for our meaning only within the human imagination. It is the structure within the brain corresponding to Paris being the capital of England that corresponds with the untrue statement itself. An alternative interpretation has often been proposed involving the idea of "possible worlds"; it is maintained that a possible world exists in which Paris is indeed the capital of England, and this is where we find the fact to which the statement corresponds. But I maintain that this idea leads to many contradictions, as I try to explain in another essay on this website: Conditionals and Counterfactuals. You may consider these possible worlds to exist if you choose, but only as a pattern of thoughts in the brain, bringing us back to our previous definition.

A similar treatment is possible for untrue analytic facts. If no one can imagine a world in which "two and two make five", then the statement must be regarded as meaningless. But if anyone can imagine such a world, then his picture of the fact will itself involve a particular pattern of interconnections in his brain, and it is this structure to which the statement relates.

Negative facts can also be dealt with this way. How do we interpret "The cat is not drinking milk"? Presumably the real world cat-drinking-milk situation does not exist, and so the statement is not a codification of a real fact; but it would be uttered only by someone who had a picture in his mind of such a situation, or who certainly had had such a picture in the past. So the statement is a codification of the brain pattern corresponding to such a picture, of a cat which actually is drinking milk, but with the word "not" inserted to indicate that is does not correspond to a real world situation.

Value statements present another problem. Both the Positivists and the Wittgenstein of the Tractatus insisted that such statements can have no meaning, but we do not need to be so destructive. We are surely capable of thinking such thoughts as "That picture is beautiful" or "It is wrong to steal". If the thoughts can exist, there is no reason to forbid us from expressing them in words; the words represent the thoughts, and the meaning of the words consists of the thoughts themselves. It might indeed be the case that such judgements do no more than compare the picture or the action to some conventional canons of art or morals, but these conventions must possess some structure, as do the laws of a country, and our acceptance of these canons, whether conscious or unconscious, must be reflected as some arrangement within the brain. The corresponding statement represents our attempt to express the result of fitting our impression of the picture, or of the act of stealing, into this structure.

Some philosophers have found particular difficulty with statements relating to the past. Where do we look for the meaning of "The cat drank some milk yesterday"? Surely there is no reason why a statement we make today should not relate to a state of affairs that existed yesterday. There is no more difficulty with the event and the statement occurring at different times than there is when they occur in different places, as is usually the case. If we can say meaningfully, "The sun is a hundred million miles away", then so can we say, "Plato lived twenty-four centuries ago". And exactly the same applies to statements referring to the future. "The cat will drink milk tomorrow" relates the assertion to a state of affairs that may exist tomorrow. Because of our human limitations anyone making such a statement does not know whether it is true or false, but this does not reduce its significance.

The previous paragraphs consider several different types of statement, and attempt to show that in each case its meaning can be defined as the state of affairs which is mirrored by the statement. But language serves several other purposes, two of the most important being giving commands and asking questions. When a speaker gives a command to a hearer, the former is conveying a wish that the latter will bring about some particular state of affairs; the command represents this state of affairs, and also contains elements indicating that it is a command and not a proposition. And the meaning of a question raises no new problems, for a question can also be thought of as a command. If I say, "Is the cat drinking milk?", I am merely giving the command "Tell me whether the statement 'the cat is drinking milk' is true". Once again the situation of the cat drinking milk is encoded into part of the sentence asking the question, and there is no difficulty defining the meaning of such a sentence.

PROBLEMS WITH TRUTH AND FALSEHOOD

Turning now from the consideration of meaning to that of truth, it would appear at first that the approach developed above solves all our problems. Statements have, as their original purpose, the communication of facts from person to person. As we have seen, the statement is a codification of the fact or structure, with language providing the rules of coding. So long as this process is carried out correctly we say the statement is true. A statement is untrue if the result of decoding it gives a structure which fails to match the real-world situation which it purports to describe. Thus the statement "The cat is drinking milk" is untrue if the real-world cat is actually drinking water, or if the dog is drinking the milk.

But philosophers have often found difficulty with this apparently simple definition. Some have argued that we cannot know which of our beliefs do indeed correspond with the world outside ourselves, for we have no access to that world other than through our own senses, on which all our judgement of what is true and false must depend. They maintain that the only test we can apply is to consider the totality of all our beliefs, and ask whether they are coherent; if not, we should adjust those which can most readily be changed to lead to consistency. Now it may indeed be the case that we can never know for certain which of our beliefs are true, but surely this should not influence what is meant by being true. The purpose of language is to represent an outside world, and language would never have developed but for the fact that people assume, most of the time, that this outside world exists in the form we perceive. A statement is true if it represents a fact that does pertain in this world.

Others, and particularly William James (1842-1910), have maintained that the truth of a proposition is related to the usefulness of accepting it. The superficial deficiencies of this doctrine tend to dissipate when it is considered at a deeper level. But I reject it because it remains too anthropocentric. Most of us feel that some statements are objectively true, without any reference to human needs or preferences.

Others have believed that the truth in any particular field of interest was the ideal limit to which we approach as we enquire into it, and our notions become increasingly simple and comprehensive. Once again this definition seems too self-centred to be plausible, and attributes a certain infallibility to man's thinking.

F. H. Bradley (1846-1924) believed a true proposition to be identical with the fact that makes it true. No rational realist can accept this today. A statement is a group of marks on paper, or sounds in the air; how can it be identical with a fact in the real world of cats, cities, men and women?

Alfred Tarski (1901-1983) realised that truth is purely a characteristic of language or belief, but maintained that truth in any language required a higher language, a metalanguage, in which to express it. Saying "S is true if and only if P" requires P to be in a higher language than S, and so on indefinitely. But this overlooks the fact that P may be a non-linguistic fact in the real world. P can be a real cow eating real grass, which involves no language, and S its representation in human speech. If we have a non-verbal recognition of fact P in the mind, then we can assert S, believing it to be true.

Some have maintained that the notion of truth is redundant; to assert that a proposition is true is exactly the same as to assert the proposition, and they have found ways of re-stating every kind of sentence containing the word "true" with one of identical meaning without it. This may be possible, but what does it achieve? There may often be ways of making statements more compact, but language is a tool for us to use as we wish. It is often more convenient to describe statements as "true" or "false" than to express the same idea in another way. We can easily be deceived here by the common mistake of confusing words with the concepts they represent. It is claimed that (i) "It is true that the cat is drinking milk" means simply (ii) "The cat is drinking milk"; the phrase "It is true" is redundant. Now this does show two different ways of making the same assertion, but they are indeed different; statement (i) is about a verbal formula, and declares it to be true, while (ii) is about a cat. It is unfortunate that modern linguistic practice discourages the use of quotation marks in all except the most essential passages. The first of the above statements would be better written as "It is true that 'the cat is drinking milk'", to emphasise that what is true is a sentence, and not a fact.

When the quotes are inserted, the above sentence illustrates the much more plausible doctrine known as "Disquotational Theory". This claims, and the above confirms, that the words "is true" serve the same purpose as the removal of quotation marks around a statement. Stating ' "S" is true' is exactly equivalent to stating S. We can agree with this, while insisting that it remains useful to keep the idea of truth in our language, even though every assertion which makes use of it can be made without it. We should not be denied the freedom to say either that cats drink milk, or that the statement "cats drink milk" is true.

Others have thought that problems of the "liar paradox" type show that something is wrong with our notion of truth. If we write down "This statement is false", then it is true if it is false, and false if it is true. Now the object to which this statement applies is the statement itself rather than anything in the outside world. In these circumstances we should not be surprised if an inconsistency arises. Try connecting the input of your hi-fi amplifier to the output. If the connection is made in one way, corresponding to "This statement is true", then all will be quiet. But if the connections are then reversed, corresponding to "This statement is false", you will create a "positive feedback loop", and all hell will break lose. If the amplifier is damaged you have only yourself to blame, for it was not meant to be treated in this way. Likewise, if we use language for an inappropriate purpose we are ourselves to blame if it behaves badly. This has nothing to do with the world outside, whose existence and behaviour owe nothing to language.

In classical logic, every proposition is supposed to be either true or false, with no possibility of middle ground, and this raises several questions. It seems clear that, however widely we extend the definitions of truth and falsehood, this dictum will restrict the range of what we may call a "proposition". On balance, it is preferable to admit that some propositions are true "to some extent", and that some others are "meaningless". Into the former category we place statements characterised by vagueness such as "John is tall", or "Dogs are dangerous". And few would deny that a statement such as "The king of France is married" should be described as meaningless, along with gibberish such as "Red eats tomorrow". But for well behaved propositions falling into neither of these classes, even if we are sometimes unsure what is meant by their truth or falsehood, this should cause us no concern if we remember that propositions are man-made, and that any paradoxes we may discover indicate at worst a fault in our language, and not something wrong with the outside world, or our conception of it. In a universe without living organisms there would be no such things as language, propositions, meaning, truth or falsehood.

TRUTH OF BELIEFS

In the paragraphs on "meaning" above, I maintained that the meaning of several different types of statement, for example untrue statements or those expressing value judgements, can only be defined as states of affairs within the human brain, as something imagined. Indeed the capacity people have for imagination is almost boundless. But considering now the truth or falsehood of human beliefs, these are much more tightly circumscribed than the truth or falsehood of propositions. We can knowingly make an untrue statement, but we cannot knowingly have an untrue belief. We have no control over our beliefs, a fact which makes very perplexing the Christian doctrine of "Blessed are those that have not seen, and yet have believed". It is as difficult to force oneself into a state of belief as into a state of love. It may, perhaps, be possible to express a verbal belief in a fact to which one does not inwardly subscribe, and this must be all that Christianity demands. And it is possible, of course, to weigh the evidence in one's mind for and against a certain doctrine, and so affect one's beliefs in this way, but if one is honest, the outcome of such deliberation cannot be influenced by an act of will. We cannot believe a proposition which we know to be untrue.

But with this limitation, the truth of a belief can be defined in the same way as we defined the truth of a statement. The structure of the connections within the brain corresponding to a true belief is a representation of a situation in the real world. In the case of an untrue belief then no such relationship exists. A difficulty arises with metaphysical beliefs, such as those concerning beauty or morals, for it will be recalled that we defined the meaning of statements in this category as themselves consisting of connections within the brain. But here another principle of redundancy comes into effect; if I think "I believe that picture is beautiful", then this is no different from thinking "That picture is beautiful". And I insist that the same applies to our impressions of right and wrong; if I think "I believe stealing is wrong", this amounts to no more than thinking "Stealing is wrong". In each case I am describing a state existing within my brain, a state which may have a profound effect on the way I behave, but which does not impinge in any other way on the world outside. The question of whether such moral beliefs are true or false is beyond the scope of this paper. But the thoughts themselves are just another example of one thing representing another according to some rules of coding, rules which are at present deeply hidden within the brain.