On Language and Meaning

Posted: 23 August 2014 | Author: sageandonions | Filed under: Language, Philosophy | Tags: bertrand russell, David Bourland, E-Prime, JL Austin, language, Meaning, Ostension, philosophy, Quine, Wittgenstein | 3 Comments

So many philosophical discussions seem to end up in confusion over words, that I wonder whether that is all that such discussions are: fancy piles of words, with no meaning, that we continually rearrange to see whether they look better when lined up this way than that. Yet many philosophical discussions, particularly some of those those about ethics, politics, religions, logic and science, are very valuable, and can help people live more successful, fulfilling, happier lives. So it seems worth trying to find a way to decide which discussions are meaningful and which are not. This essay sets out the results of my attempts to do that.

Finding meaning via a tree of definitions

My first observation is that we cannot find the meaning of a statement by looking up all the words of the statement in a dictionary. A dictionary defines every word in terms of other words. If we look up each of those other words, and so on, it won’t be long at all before we find ourselves going round in circles, looking up words that we have already looked up.

Digression: here’s a fun parlour game. Everybody picks a word. You look it up in the dictionary, choose the seventh word in the definition (or the last word if there are less than seven words), look that up, and so on until you are sent back to a word you have already looked up. The person that has to look up the most words before closing a loop wins. Or you can reverse the game and make the winner the one that closes a loop in the fewest lookups.

Now think about what happens if we look up all the words in each definition, rather than just the seventh one. Then we will have created a branching tree of definitions. We start with one word, then have to look up maybe twelve different words used in its definition. For each of those words we need to look up each of the different words used in their definition, and so on. The trunk of the tree is the first word. Every definition we look up is a place where the tree splits into several branches.

What we need, to terminate this process and arrive at a final understanding, are leaves. Because the leaf is where the recursive branching process of a tree finally stops.

We are not going to find leaves in a dictionary (yeah I know, pages are also called leaves, ha ha), nor yet in Google or Wikipedia, which are just different forms of dictionary. So where could we find them? The most natural way to find them is to look at the methods employed by a group of people that learn language without the aid of dictionaries – toddlers. A toddler learns a new word by observing others use the word in connection with a certain phenomenon. They learn ‘jump’ by observing people say sentences containing the word ‘jump’ when there is jumping going on. They learn ‘dog’ by observing people say sentences containing the word ‘dog’ in the presence of dogs, maybe accompanied by the speaker helpfully pointing to the dog, or a picture of a dog. They learn blue by being shown blue things while being told ‘blue!’ They learn ‘above’ by hearing that word while attention is drawn to one thing that is above another.

Ludwig Wittgenstein called this method of learning language ‘ostension’, and regarded an ‘ostensive definition’ as a naming of a phenomenon while pointing to it. Ostensive learning is most obvious with toddlers, but it is not confined to them. Most people tend to pick up new words by ostension throughout their life. Things like local slang, or the latest buzzword or jargon used within a specific trade are mostly learned ostensively. That is how I learned, in the early 2000s, that we can say ‘my team is going to verse Little Boggling High School in rugby‘ rather than ‘we are going to play Little Boggling High School in rugby‘. When explorers encounter people speaking languages they do not know, they learn to communicate by ostension. That is less common now, but one imagines it was a frequent occurrence in the 18^th and 19^th centuries.

Even ostension is not enough to completely terminate the search for meaning though. As Wittgenstein observed, when somebody points at something and names it, we still need the mental equipment necessary to associate the sound of the name with the thing. It appears that that equipment is built-in (‘hard-wired’) rather than learned, as are a range of other mental processes we instinctively perform, such as learning from experience (the ‘principle of induction’) and our ability to interpret our sensations in terms of a continuum with three spatial dimensions and one time dimension (an innate ability that Immanuel Kant calls ‘the Transcendental Aesthetic’). We evolved to have those abilities hard-wired, because ancestors that did not have them quickly perished.

Although we have those learning capabilities built-in, I do not think we have any actual words built in to our brains at birth. So far as I know, there is no word that is universal across all Earthly languages – No, not even ‘No!’ or a shake of the head. Hence, I can only think of two ways that we learn words, or other parts of language: by definitions that we invent (eg for new words or new uses of words we invent) or that are provided to us, that use only words we already know; and by ostension. My theory is that every part of language we learn is acquired by one of those two methods. If somebody can identify another way humans can learn language, I will have to revise my theory, but for the remainder of this essay I will assume it to be accurate.

A consequence of this theory is that, if there is any word that I cannot trace through a tree of definitions, without circularity, to a full set of ostensive leaves, then I do not know what that word means! Even a single non-terminating branch in the tree is enough to make the word meaningless.

One can think of the ‘depth‘ of the tree as the maximum number of definitions one has to pass through to get to the farthest leaf, and the ‘breadth‘ of the tree as the number of leaves. For ostensively defined words, like the above examples of ‘dog’, ‘blue’ and ‘jump’, both breadth and depth are only 1. We know what they mean without having to think of other words. Some words, while not ostensively defined themselves, will be explicable solely in terms of ostensively defined words, and have a tree depth of 2. ‘Panther’ might be an example, defined as ‘black leopard’, if we have access to pictures of leopards but no pictures of panthers.

For abstract words such as ‘evaluate’ or ‘pretend’, the tree of definitions will be quite deep and it can be daunting to trace back to the ostensive leaves from which the meaning is ultimately derived. Yet it seems that it must be possible, because we have come to understand those words and, according to my theory, we could not have done that unless we had traversed such a tree in the course of our learning our language.

It’s worth noting here that for many words we will have more than one tree of definitions available to us. As long as they ultimately convey the same meaning, that is no problem. Indeed, it is to be expected, given the rambling, nonlinear way in which we learn language. Some observers feel that there are so many intersecting trees of definition that a person’s vocabulary is more like a web than a set of trees (I think Quine’s view, from his essay ‘Two Dogmas of Empiricism’ is something like that). But that doesn’t change the fact that ultimately that web must terminate in – be surrounded or supported by a frame of – leaves of words that we have learned by ostension.

Some occasionally meaningless words

That’s enough theory. Let’s get down to case studies of word uses that I think are meaningless. Here are some of the main culprits: ‘be’, ‘true’, ‘possible’, ‘random’ and ’cause’.

Now I don’t mean to say that any sentence containing any of those words is meaningless. Otherwise most of this essay would be meaningless, given that it contains some of those words. Indeed, the verb ‘to be’ is present in almost every piece of English ever written. I am referring only to cases where one of those words is used as if it were fundamentally understood and, like a word that is learned ostensively, needs no definition – an activity that takes place most often in philosophical discussions, especially in the field of Ontology (the study of ‘what there is‘) or Metaphysics more broadly.

There is an easy test for whether a use of a word is meaningless. Let us call a word whose meaning I am calling into question a ‘challenged word‘. A word whose meaning, as used in the sentence, can be indicated by ostension cannot be a challenged word (note that none of the four words listed above can be taught by ostension). For other words, if a sentence containing the challenged word can be translated to a sentence, or sequence of sentences, that does not contain that word, or any synonym thereof, without any loss of meaning, then the use of the word in that sentence may be able to be considered meaningful. Otherwise it cannot. I say ‘may’ rather than ‘can’ because it is possible that the translation will throw the burden of definition onto a related but not synonymous word, and that challenging that word leads, possibly after a small number of additional challenges, back to the word we started with. So this ‘translation test’ for meaninglessness can give false negatives (ie fail to identify meaningless uses of words), but it will not give false negatives (accusations of meaninglessness when there is meaning there).

The translation test, applied to ‘to be’

Here’s how this ‘translation test’ works, applied to several different uses of the verb ‘to be’. There are a number of different ways in which this verb can be used. For each case I label the type of use (bold text), show the archetypal grammatical form of its use (plain text. The word ‘copula’ denotes an instance of ‘to be’), then provide a sample sentence and a translation that avoids use of the challenged word.

identity, of the form “noun copula definite-noun”:
1. This is Freya;
2. Translation: People call this person Freya.
class membership, of the form “noun copula noun”:
1. The cat is an animal;
2. Translation: The class of animals includes this cat.
predication, of the form “noun copula adjective”:
1. The cat is furry;
2. Translation: Fur covers most of the cat’s body.
auxiliary active, of the form “noun copula verb”:
1. The cat is sleeping;
2. Translation: The cat sleeps.
auxiliary passive, of the form “noun copula verb”:
1. The cat is bitten by the dog;
2. Translation: The dog bites the cat.
existence, of the form “there copula noun”:
1. There is a cat
2. Translation: not always possible – see below.
location, of the form “noun copula place-phrase”:
1. The cat is on the mat;
2. Translation: The mat has a cat on it.

All of these have satisfactory translations except possibly 6 – existence. Whether 6 can be translated depends on context. If I were pointing at the cat, a suitable translation would be ‘Look! do you see that cat?‘ Alternatively, I might be telling you about a house you are going to visit, whose occupant has a house cat. Then it could translate as ‘You may come across the occupant’s cat when you visit‘. Even if the statement were a bare assertion of existence, such as a claim that, contrary to rumours of extinction, there is still at least one live cat in the world, we could still translate it. In that case an acceptable translation would be: ‘If you could line up all the animals in the world today and inspect them one by one, you would find that at least one of them belonged to the cat species‘.

Notice that most of these translations remove the challenged word by introducing references to experienced observations. That is the easiest way of planning a tree of definitions that can be traced to ostensive leaves. Since all ostensive leaves come from observed experiences, using words that connect to experiences – whether past, future or hypothetical – makes the tree of definition easier to imagine.

It is only when the speaker tries to divorce their meaning from experience that the translation test is failed, and meaning consequently evaporates. Examples of this are:

I think, therefore I am
The consecrated host is the actual body and blood of Jesus Christ, even though it doesn’t look, feel, smell or taste like it
The Father, Son and Holy Ghost are three separate persons but they are one essence, substance and nature
Electrons are there all the time, even when we are not observing them
If Captain Kirk’s body were duplicated atom for atom by a malfunction of the Star Trek teleporter, one of those duplicates would be him, and one would not.
The future already exists [note that ‘exist’ is just a synonym for ‘be’]
Notions in physics like ‘spacetime’ and the ‘quantum wave function’ are not just mathematical abstractions. They really exist.

These sentences, each of them the subject of endless philosophical debates over the ages, are incapable of being translated into sentences that do not contain the challenged word (in bold), because they are shut off from any possible connection with actual or potential experience. According to my theory, they are thus meaningless, and the associated philosophical debates amount to no more than shovelling piles of words around and arranging them in pretty ways.

That may seem like a big claim, and on little evidence. But if the claim is wrong, it should be easy enough to demonstrate that. All that is needed is to explain what those statements mean in non-circular terms. Nobody has managed to do that in the history of philosophy, and it’s not for want of asking.

It’s worth noting that all of those untranslatable examples are cases of either the ‘identity’ or the ‘existence’ use of ‘to be’, that we identified in the above list of different uses. Items 8, 11, 13 and 14 are ‘existence’, and items 9, 10 and 12 are ‘identity’. In my experience all untranslatable, and hence meaningless, uses of ‘to be’ fall into those categories. Not all uses in those categories are meaningless though. Above I described some cases of the ‘Existence’ use that were translatable. Some cases if the ‘Identity’ use are also translatable. I will deal with one that is a famous example that is often used in philosophy, known as ‘Frege’s Puzzle‘ because it was created in the 1890s by the German logician Gottlob Frege. It is as follows:

The early Ancient Greeks thought that Hesperus, the Evening Star, and Phosphorus, the Morning Star were distinct celestial bodies. Later in Ancient Greek civilisation they came to the conclusion that they were the same celestial body – the planet we now call Venus. Frege says that no reasonable person would deny the truth of the sentence ‘Hesperus is Hesperus‘, but somebody that didn’t know that the Morning and Evening Stars were sights of the same physical object at different times could reasonably reject the suggestion that ‘Hesperus is Phosphorus‘. This spurred the creation of a whole genre of philosophical literature discussing the meanings of the phrases ‘Hesperus is Hesperus‘ and ‘Hesperus is Phosphorus‘.

Here is my translation of ‘Hesperus is Phosphorus‘.

‘The sight of a light in the sky just after sunset, which people call Hesperus, and the sight of a light in the sky just before dawn, which people call Phosphorus, both arise from light waves from the Sun reflected off a single large rocky object that orbits the Sun‘.

Nothing mystical and metaphysical happens in this sentence. Here the ‘identity’ use of ‘is’ just serves to tell us that two different things we see at different times come from a common physical object.

On the other hand the sentence ‘Hesperus is Hesperus‘ cannot be translated, because it is meaningless. It is a sentence that we are well rid of.

Not all sentences of the form ‘X is X‘ are meaningless though. Some of them are capable of being translated. Recently an Australian politician known to be a loose cannon, let’s call him Bruce, made an outrageous public statement about something or other. The leader of Bruce’s party was asked by journalists what he thought of Bruce’s statement. That put the leader in a tricky position, caught between being seen to condone an outrageous opinion on the one hand or being seen as disloyal to a colleague on the other. The leader’s reply was ‘Oh well, you know, Bruce is Bruce.‘ The meaning of this statement was clear to all those that heard it. It was as follows:

‘As you all know, the politician Bruce that made that statement has displayed a habit of saying silly, offensive things from time to time in the past, although he acts acceptably most of the time. When he says obviously silly things like that, we don’t take them seriously and neither should you.‘

That’s a whole lot of meaning to pack into three little words. But language can be very expressive, if used with skill.

Conclusion

The lesson I have learned from all this deliberation is pretty simple: When confusion or misunderstanding arises over meaning, we can restore clarity by insisting on using only words whose meaning can be traced to ostension. The easiest way to test whether that is possible is to try to translate the passage into one that does not contain the challenged words – the ‘translation test’. Many passages written by ontologists, metaphysicians, theologians and others that try hard to be deep, fail this test. If we apply the test to a particularly confusing bit of writing and it fails, we would do best to consign the writing to the bin rather than waste further time on it. To apply the test fairly, we should ask the person who wrote the passage to translate it or, if they are dead, far away or otherwise unavailable, ask somebody that thinks they know what it means. But if they cannot do so, into the bin it goes!

I do not however want to create the impression that we should never talk about things we do not understand, or find impossible to clearly express. That is what the arts are for. When TS Eliot says

‘while the evening is stretched out against the sky, like a patient etherized upon a table‘,

we would be silly indeed to try to enumerate the ways in which an evening is really like an anaesthetised patient. The wonder of the phrase is in the emotions and images it conjures up, not the propositional information it conveys.

So by all means let us celebrate and revel in poetry, music, literature and the other arts. They form a central and essential part of my world, without which life itself would seem unbearable. But we should avoid confusing poetic speech with analytic speech. Poetry evokes imagery and emotion, but does not make logical propositions. If we start to mistake poetry for logic, we will end up in a terrible muddle.

Andrew Kirk

Bondi Junction, August 2014

PostScript

The ideas in this essay are my own, and do not seem to match exactly with those of anybody I know of. However, there have been very strong influences.

I get the impression that the writer to whose ideas this essay approximates most closely is JL Austin, of Oxford University, who is seen as the intellectual father of ‘Ordinary Language Philosophy’. I may be wrong about that however, as my exposure to Austin is only through secondary literature.

Ludwig Wittgenstein’s writings in ‘Philosophical Investigations’ and Bertrand Russell’s essays ‘On Denoting’ and ‘Knowledge by Acquaintance and Knowledge by Description’ are also very influential on these thoughts. I should note that Russell had a lifelong belief in Truth and Material Reality that I do not share. Wittgenstein seemed to share those beliefs when writing the Tractatus, but perhaps discarded them in later life.

Willard van Orman Quine’s essay ‘Two Dogmas of Empiricism’ seems very relevant, but I still don’t know what to make of it. It is a paradoxical essay, in that Quine was a brilliant logician, capable of scintillating clarity, yet that particular essay is written in loose language that makes it hard to understand what he is really saying in some parts.

There is a similarity between some of these ideas and those of the American Pragmatist philosophers Charles Peirce, William James and John Dewey.

Especially interesting to me are Alfred Korzybski and David Bourland, who promoted the use of the language ‘E-Prime’, which is English with all instances of the verb ‘to be’ removed. They saw that verb as a never-ending source of confusion, and maybe even socially harmful as well. Bourland wrote a number of books in E-Prime to show how well we could do without that verb. I understand that the author and thinker ‘Robert Anton Wilson’ wrote a number of novels in E-Prime. Most illustrious of all, Albert Ellis, the founder of Cognitive Behaviour Therapy, by far the most effective form of psychological treatment of depression and anxiety (and which I see as modernised Stoicism), favoured E-Prime and saw the use of ‘to be’ as a frequent source of blame and judgement that was psychologically harmful (‘He is wicked’ vs ‘He harmed many people when he did that’). The wikipedia article on E-Prime is a rewarding read.

Replacing Truth with Reason

Posted: 10 February 2013 | Author: sageandonions | Filed under: Language, Mathematics, Philosophy | Tags: bertrand russell, daniel dennett, Epistemology, holy grail, Logic, mathematics, Meaning, philosophy, science, Truth, Words | Leave a comment

“What is Truth” asked Pilate?

I’ve always been rather fond of that riposte in the New Testament. Good old Pontius sure put those scribes, priests and Pharisees – whatever they were – in their place. Is there more to it than just a great put-down though?

It sounds deep as well, although there’s always the risk that it may be faux deepness, or ‘deepity’ as Daniel Dennett would call it.

Now I’m not going to go all post-modern here, and suggest that everybody has their own version of truth. Nor am I going to suggest that Truth isn’t a useful concept. To ask Freda whether she thinks Bill is telling the truth is a meaningful and useful question. It is actually a speculation about the state of Bill’s mind. Is he telling us what his memory tells him happened, or not? No, what I’m wondering about is what is sometimes called Absolute Truth, the sort of thing exemplified by Bertrand Russell when he says ‘Edinburgh is North of London, whether anybody knows it or not.”

Sometimes Truth is held up as a sort of Holy Grail, the quest for which can fill one’s life with meaning. The Search For Truth is the sort of noble thing to which holy men and scientists alike are said to be dedicated. Indeed, it’s not that long ago that it was a key component of a little motto I made up for myself in an idle moment – “Truth, Beauty and Compassion” – a more inclusive version of St Paul’s triumvirate “Faith, Hope and Love”. I vacillated for a while over whether I should add “Reason” to my motto. I mostly omitted it, because things just seem so much neater in threes, as well as because there seemed to be too much overlap with Truth. Sometimes I included it though, because there seem to be things covered by Reason that are not covered by Truth. For example, one can use Reason to devise a strategy to win the heart of one’s true love, but this has little if anything to do with Truth. Recently though, I have sometimes felt inclined to drop Truth from the motto in favour of Reason, and I blame Kurt Godel for this, as I will explain in the next couple of paragraphs.

Godel and Truth

The logician Kurt Godel is most famous for his First Incompleteness Theorem, which destroyed the most ambitious mathematical project of the early 20^th century – the Hilbert Program, which was an attempt to find a way to formally prove everything that was believed to be true about arithmetic and basic mathematics. What Godel’s theorem showed was that, in any logical system that we use to write proofs, there will exist some logical statements that can neither be proved nor disproved, yet are perfectly meaningful. He did this by creating an ingenious variation of the famous ‘Liar Paradox’, which says ‘this statement is false’.

Now, in their attempt to make Godel’s discovery more interesting to a lay audience, some texts and sources claim that the theorem says that there are statements that are ‘true but not provable’. The trouble is that the ‘true’ part of this statement doesn’t have any clear meaning. The closest we can get is to observe that Godel’s theorem shows that there are statements that are unprovable in the chosen logical system, but for which we can prove, using a different logical system, something that is very similar to the original statement. So in that case the word ‘true’ doesn’t relate to some fundamental cosmic reality, but just to what can be proved in an alternative logical system. The word ‘true’ is superfluous as well as ambiguous here, as we can express everything Godel discovered using variants of the word ‘proved’ instead of true.

The realisation that ‘True’ is a useless word in this critical context made me wonder if there is any context in which it expresses something important, that cannot be more accurately described by other words. It is that question that I wish to explore here.

Science and Truth

Let’s start with science. Is that a search for truth? The task of science is to construct theories that relate past experiences (‘observations’) to one another in an ordered way and enable us to make predictions about future experiences, such as the appearance of comets or the effect of mixing hydrochloric acid with sodium hydroxide.

Are scientific theories ever true? Not many scientists or philosophers of science would claim that in any absolute sense. Any scientific theory, however useful, is eligible to be replaced by a more sophisticated one that better explains our observations. The first simple atomic theories were replaced by the Rutherford model in which a nucleus of protons and neutrons was surrounded by electrons whizzing around the outside. That was in turn replaced by Quantum Mechanics, and then we had quarks and other subatomic particles coming into the theory in the 1960s. Now physicists speculate on whether the subatomic particles in turn are just symptoms of some deeper underlying phenomenon such as vibrating strings in eleven dimensional space. It seems natural to suppose that there is some underlying final theory that tells everything, and that the theory is ‘True’ regardless of whether we eventually discover it. But that is by no means the only logical possibility. Here are two others:

There is an unending descending chain of theories, each more complicated than the one above it and including all its ancestors as special cases that are good approximations under restricted circumstances.
There are multiple theories that can explain the full range of possible experiences, all as valid as one another. The competing corpuscular and wave theories of light are crude examples of this. In the end, they both proved inadequate to explain all the experimental results obtained, but for a while they were both successful in explaining different aspects of the behaviour of light. There is no apparent reason why there could not be two or more different theories, each of which can by itself explain everything we experience.

Sometimes the Common Sense view of the world is that of course there is an underlying Truth – that quarks and electrons really exist and we just need to find out more about them. While I am passionately in favour of finding out more about quarks, I regard that as a desirable refinement of our theories, not a discovery of Truth. If we are to think in terms of common sense, I cannot help but observe that common sense tells me the table in front of me is a hard, solid, opaque object, not the strange collection of pinpricks and force-fields in empty space that quantum mechanics suggests. That is not to say I don’t ‘believe’ quantum mechanics. Quite the contrary. Rather it is to say that I don’t want to give common sense any privileged role in such a deliberation. And also, that the notion of Truth is compromised. Which is more true, my perception of the table as hard and solid, or the idea of it as an empty space with the odd tiny quark and electromagnetic force field? The practical response is that the question is meaningless. Both representations of the table have their uses, and are complementary. Table as solid object is useful if I want somewhere to put my kettle. Table as quarks is useful if I want to understand why it doesn’t collapse under the weight of the kettle (or how heavy a kettle I can put on it).

Perhaps a belief in Truth equates, in this context at least, to a Realist view of the world – that the world really is made of a specific sort of thing or things, and we just need to find out what it is. It is a belief in Reality, with a capital R.

But hold on, any moderately sane person believes in Reality don’t they? Well, it depends what one means by reality. I am sure I have been guilty of saying ‘so and so lives in a dream world – they have only a passing acquaintance with reality’. My defence is that I do not mean by this that so-and-so doesn’t believe in quarks. Rather, I mean that they do not reason about their experiences in such a way as to give a strong likelihood of their expectations of future experiences being fulfilled. Perhaps so-and-so has gone sun-bathing on the beach in the middle of a summer’s day, under the illusion that a coating of sunscreen will be enough to protect her for two hours in full sun. The ‘reality’ from which she is disconnected is that that evening she will have the experience of red, horribly painful skin, and two days after that she will have the experience of the skin peeling off in sheets. So-and-so’s delusion has nothing to do with her metaphysical opinion of quarks. It is about her inability to use reason to control the nature of her future experiences.

So it seems that when I use the word ‘reality’ in everyday intercourse, I am referring to what experiences we can expect in the future, and what we might be able to do to control those experiences.

Note that Reason, or Rationality, has stepped in here to fill the vacuum left by our jettisoning the notion of Truth.

Truth in other contexts

A belief in Truth is not limited to just quarks. At various times, people have proposed the existence of other forms of truth in the form of objects that exist independently of what people know. Moral rules, aesthetic truths and mathematics are key examples of this. A Moral Realist will claim that moral rules exist, and the purpose of moral education and ethical inquiry is to discover them. A mathematical realist will say the same thing about Pythagoras’s Theorem, or the number six. An aesthetic realist may be a rarer beast, but if I could find one, I would expect them to assert that Mozart’s Requiem is beautiful and Milli Vanilli is not.

Yet there is no more need to believe in such Truths than there is with quarks. I can develop a system of moral rules for my own use, or discover them in my own mind by reflection on my feelings. If I prefer something less subjective, I can define a moral truth to be any feeling about how to treat others that is shared by a large proportion of the human race.

With mathematics I can, if I wish, regard any mathematical concept as an invented idea that helps me arrange things in my mind and reason about what might happen next. I can take the view that everybody invents the mathematics that they use for themselves. So every toddler invents the number six, rather than discovering a pre-existing abstract object. Or perhaps they find a pre-existing pattern for the number six somewhere in their brain, placed there by evolution because of its usefulness to survival.

The more I reflect on this, the less value I see in maintaining a concept of Absolute Truth in the way one thinks about the world.

Consider the binary expansion of Pi. Let F(n) be the statement that, for any m greater than or equal to n, there are more 1s than 0s in the first m bits of that binary expansion. Let S be the statement that there is some number n for which F(n) is true. There is no way of proving or disproving S by trial and error, because we cannot try out what happens with all the infinite number of combinations of values of m and n. Perhaps there’s a clever way of proving it or disproving it that doesn’t require trying an infinite number of combinations, just as we can prove that the sum of two odd numbers is always even, without trying it on all possible pairs of odd numbers. But nobody knows of one, and it seems entirely plausible that there is no such proof.

Yet most people would say that S is either true or false, but we just can’t know which. This seems to be a problem, because there are no words to explain what we mean by true or false here. Let us explore some more.

The Liar Paradox

The Liar Paradox is a statement that generates a contradiction, however you interpret it. One of its more sophisticated versions is ‘This sentence is not true’. If we suppose it’s true then what it says must be true, so it is not true, which contradicts our supposition that it’s true. If we suppose it’s false then what it says cannot be true, so it can’t be true that the sentence is not true, so the sentence must be true, which contradicts our supposition that it’s false. The third possibility is that the sentence is meaningless. But if it’s meaningless then it’s not true, which is exactly what the statement says is the case, so the statement is true, so it’s not meaningless, which contradicts our supposition that it is meaningless.

There are a number of ways to resolve this paradox. Most of them involve questioning what we mean by truth in this context. One possible meaning is provable – we say that something is true if and only if it can be proved. This has shades of Godel’s Theorem. If we take this approach then the paradox disappears because ‘This statement is not provable’ is not paradoxical if we require our proofs to be strictly logical (although one has to have at least a partial understanding of Godel’s theorem to see why that is so).

Another possible meaning is that a sentence is true if it accurately reflects our perception of reality (or just our perception, if we want to avoid the equally troublesome word ‘reality’), false if the opposite of the statement reflects that perception, and meaningless otherwise. This is a popular interpretation of ‘Truth’, which is called the ‘Correspondence Theory of Truth’. With that meaning, it is ‘true’ to say a soccer ball is round because, when we look at it, it looks round. With this meaning, we can resolve the paradox by observing that the sentence is meaningless because it doesn’t say anything about our perception of reality. All it does is talk about itself.

In both these resolutions, we have only been able to make sense out of the sentence by getting rid of the vague, undefined word ‘true’ and replacing it with a clear, pragmatic definition.

This realisation strengthens my feeling that the word True is a troublemaker, that sows confusion wherever it is used. Perhaps we really should dispense with it, except in causal, imprecise, everyday slang. But if so, what should we replace it with?

What can we replace Truth with?

The words ‘true’ and ‘truth’ are so much a part of everyday language that, if we were to discard them, replacement would be required on a large scale. For someone that subscribes to the Correspondence Theory, mentioned above, that theory provides a satisfactory way of defining the terms, and hence justifying their retention. The price that must be paid for that though, is believing that there is such a thing as Ultimate Reality – a unique description of the way things are, to which any other descriptions are only approximations. Furthermore, that description must exist regardless of whether anybody knows it.

Most people seem to hold that belief, and for them the dilemma ends there. But, for the reasons given above, I am skeptical, and certainly see no justification for such a belief in terms of other, more fundamental and intuitive concepts. All we can say with confidence is that we have experiences, and that there are models available – called scientific theories – to connect these experiences together in a patterned way and make predictions about what we may experience in future.

For someone that suffers this same ‘skeptical disability’ as me, the Correspondence Theory is not an option. So what, if anything, can we use instead?

My proposal is to replace it by ‘consistency with experience’. We will call a statement ‘true’ if it is consistent with both actual and potential future experience. By ‘consistent’ we mean there is no possible rational deduction from actual or potential experience that contradicts any part of the statement. So if June tells us that she has not eaten the last biscuit, that is not true if, upon inspecting the biscuit barrel, we would see that there are no biscuits left in there and, if we used an endoscope to inspect her stomach contents, we would find traces of that type of biscuit therein. It would also fail to be true if June’s statement was inconsistent with her own experience – that is, if she has had the experience of taking and eating the last biscuit. It would even fail to be true if June were a sleepwalker who has been known in the past to sleepwalk to the kitchen, take a snack and return to her bed without waking, and she woke this morning with a rash of a kind that she has only ever had before after eating that type of biscuit. In this latter case, June has not experienced eating the biscuit, but she can rationally deduce from her experience of the rash that she has probably eaten it in her sleep.

So that’s my suggested replacement for Truth – consistency with experience. And since the key ingredient for assessing this consistency is Reason, I will adopt that as the third leg of my little motto: Compassion, Beauty and Reason!

Note that we haven’t really got rid of the word Truth. All we’ve done is redefine it. Or rather, defined it because, unless one subscribes to the Correspondence Theory, it was never properly defined in the first place.

This definition has some interesting implications.

Interesting Implications

Remember the above example of the statement S about the number pi? With this definition we have to conclude that, unless a proof one way or the other exists, S is neither true nor false, because there is no potential experience we could have that would confirm or deny it. In the mathematical context, true means the same thing as ‘provable’.

Further, even if there is a proof or disproof of S that we just haven’t found yet, Godel’s Theorem tells us there will be other statements that can be neither proven nor disproven. So we are now committed to saying that those things are neither true nor false.

On the other hand, we are empowered to say very clearly that provable statements like 2+2=4 are true, because we can easily go through the experience of proving them. Strictly, what we need to say is that ‘In Peano Arithmetic, 2+2=4’, because one could easily invent another system of arithmetic in which 2+2 equalled something else. So the statement is actually about the consistency of what we are saying with the rules of the system – in this case the axioms of Peano Arithmetic.

Here’s another one: ‘The universe will expand forever’. The current state of cosmological knowledge is that we do not know whether that will happen or whether the expansion will eventually slow and then reverse, ending in a Big Crunch. The Big Crunch will happen if the Cosmological Constant is positive, but not if it’s zero or negative. If the constant is positive or negative, we may one day be able to demonstrate that. But if it’s zero, we’ll never be able to demonstrate that, because there’s always the chance thet it’s a positive or negative value too small for us to detect. So if the cosmological constant is zero then the universe will expand forever but we can never know that that’s what it’s going to do. Under our new interpretation of ‘true’, we would have to say that this cosmological statement may be neither true nor false, as there can be no experience that can confirm or deny it. In fact so is the statement ‘The Cosmological Constant is zero’.

If this seems disconcerting, we can comfort ourselves with the idea that, for all the common , everyday uses of the word True, the definition gives us exactly the interpretation that we want:

“are you telling the Truth” means ‘is what you are telling me now consistent with your own experience of what you are talking about?’
“I feel cold” is true if the person saying it is currently having the experience of feeling cold.

So we can preserve a role for the word ‘True’ in our everyday language. What I think we can’t do without having to make unfounded assumptions about the existence and nature of Ultimate Reality, is elevate the concept to some universal principle that guides our understanding of the universe. “Reason” does a much better, and more practical, job.

Andrew Kirk, Bondi Junction, February 2012

Postscript

It occurred to me a few days after finishing the above essay that, if somebody nevertheless wishes to retain a notion of Absolute Truth in their worldview, perhaps for aesthetic reasons, or just because it fits with long-accustomed habit, one way to do so is to incorporate an omniscient conscious entity in the worldview. That way, Absolute Truth can simply be defined as what it is that this entity knows. This is entirely consistent with the above suggestion of defining truth in terms of experience because, as the entity is omniscient, it experiences every object or event.

This entity may sound a bit like what some people call God. But I should note that other attributes ascribed to God by the most popular Middle-Eastern religions of Christianity and Islam, such as omnipotence and being a creator, law maker and law enforcer, are not necessary in order to take this route to believing in Absolute Truth. Nor does this approach necessitate that there be only one omniscient entity.

If the entity is infinite then it could even know the truth status of the mathematical proposition S above. Knowing the truth status of S requires knowing an infinite amount of information but perhaps that would not be a problem for an infinite entity.

This approach has echoes of the way that George Berkeley completed his Idealist theory of existence. Berkeley’s theory says that only ideas exist, not matter, and he addressed the problem of whether objects exist when nobody is looking at or thinking of them by saying that they still exist as ideas in God’s mind.

Personally, I like the idea of a universe without Absolute Truth and have no need or wish to hypothesise such an entity. But it may be of comfort to those who do like the notion of Absolute Truth to know that there is a rational basis on which they can do so.

Andrew's Essays

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