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Sherlock Holmes follows clues. So do scientists. So do most of us, probably all. By following clues we find out things we originally did not know. We find out on our own, without asking those who already know. Sherlock Holmes does not go amongst the criminals and announce, 'Black Peter was murdered last night. Which of you committed this dastardly deed? Come forward and confess!' Sherlock Holmes does not do this; neither do scientists ring God up in the middle of the night and ask, 'Is e really equal to mc2?'

If there are clues and we are clever enough we do not need to be told. If we say we find out by following clues when in fact we are told, we are cheating. Talent is required in following clues. No talent is required in accepting what we are told. Moreover, if we simply accept what we are told, how do we know we are not being lied to? How, if not by following clues?

Clues can lead to knowledge. It is true that we have to respond to them in the appropriate way; otherwise, even though they are there we still will not find out. This is the difference between Sherlock Holmes and Watson. They could be faced with the same clues, but Sherlock Holmes finds out and Watson has to have it explained to him. But although we have to respond to them in the proper way clues nevertheless play a crucial role. Without clues even Sherlock Holmes cannot do anything.

Why are clues like this? What are they? Why do they have this power of leading us on, so that if we respond appropriately, we will arrive at knowledge that we formerly did not possess? It is true that this knowledge will not be absolutely certain. It is true also that some of the details may be missing or not perfectly correct. Still, this knowledge is far from mere guess. If it were, it would have little chance of being right, but knowledge obtained by following clues is likely to be right even though not absolutely certain.

Philosophers have been asking for a long time how knowledge is possible. At first they thought knowledge that is absolutely certain was possible; their only question was how. After recognising that knowledge that is absolutely certain is not possible, they ask how the kind of knowledge scientists obtain is possible, fully understanding that this kind of knowledge is not absolutely certain and may not be perfect in other ways. However, despite the interest in this kind of knowledge, the kind of knowledge that clues lead to, we do not find the question asked all that often (if at all), the question what clues are. It is well known that scientific knowledge is obtained by following clues (why for example do the planets move in elliptical orbits?), but this has not made the question any more prominent. I think it is time that this neglect be made good. If we know what clues are we should not be surprised to find that we can then explain why scientists and Sherlock Holmes and others can reach the kind of knowledge that they can reach, the kind of knowledge that elsewhere I have called approximate knowledge.

Because the question what clue are is not frequently asked we—and by 'we' I include philosophers—often find it hard to 'think straight' about them (clues), so much so that we often involve ourselves in contradictions despite our unwillingness to do so. Let me give two examples:

Example One. People often say clues can only suggest theories, but can never prove them. For proof, they say, you need something else.1 Now, obviously, these people think what they say is true. It is true, they think, that clues can only suggest, but can never give any strong grounds for thinking that what they suggest is true or close to the truth or even likely to be such. However if you ask them, if you have ten clues and they all suggest that the butler did it, is it then likely that the butler did it?—if you ask them this question, they are likely to say, of course!2

So, can clues prove or not? Do clues just suggest? Or can they both suggest and prove? That is, give us strong grounds for thinking that the theories suggested are true.

Example Two. Everyone knows that by following clues we can find out things we originally did not know. But if you ask them, is it surprising that we can find out?, they are likely to say no; it is not surprising at all. Why? Because, they say, in a sense we knew all along. Now they are always very certain about this, for if we did not know, they ask, how would we know what the clues mean? If we know what the clues mean we must have known all along what we will eventually find out.

So do clues lead to things that we originally did not know or not? We cannot say they both do and don't.

If we know what clues are we should be able to explain why we can uncover knowledge by following clues. In the course of doing this we should also be able to explain, and to do so without involving ourselves in contradictions, whether clues can prove as well as suggest, and whether or not we know all along what we will eventually find out.

So what are clues? Why by following them can we find out things we originally did not know? To answer this question let us use as example the following simple case.


Here we have a cryptogram (an encrypted message). If readers would look over it carefully they will find in this cryptogram clues. For example, there are the two letters SB at the beginning of the first word. This combination occurs a second time, at the beginning of the second word. What does this suggest?

I think most readers will have some idea what SB might stand for. This is to say, they can see that SB in our cryptogram is, or at least could be, a clue. Now the question we are asking is, why? Why do we think or suspect that SB is a clue? What is it about SB that makes it into a clue?

Because we have a simple case here it is easy to find the answer. SB is a clue because it reminds us of a characteristic of the English language. In English many words begin with TH, or SH, or CH. SB could stand for one of these.

Why is the English language like this? Why do words in the English language begin more frequently in certain ways? There are twenty-six letters in the English alphabet. Why is it not equally probable that the first letter of any word should be any of these twenty-six letters? That is, equally probable that it should be A, or B, or C, or D, etc.?

We all know the answer. A language is not a random collection of symbols. We do not take a fistful of letters, throw it onto the table, and thereby create a language. A language has a structure. Its structure may not be simple; it may not be well defined; it may not be easy to find out; but it has a structure. In the English language there are rules governing how letters are put together to form words, and how words are put together to form sentences. Because a language has a structure it has certain characteristics. It is a characteristic of the English language that many of its words begin with TH, for example.

So, what are clue?

From what we have just said we can see that clues are nothing more than the characteristics of structures, disguised. It is a characteristic of the English language that many of its words begin with TH. In our cryptogram we do not see TH at the beginning of any word, but we see SB at the beginning of two. SB, we say, could be TH in disguise.

SB, we say, is a clue. We call SB a clue because it could be hiding one of the characteristics of the English language.

Could we be wrong about SB? Are we certain at this point that SB is a clue? Do we have to be certain?

It is important to notice that we do not. If we have had any experience in following clues we will know there is often a high degree of uncertainty where clues are concerned, the reason why in practice we often warn ourselves to be careful with them (as readers under their breath must have been warning me). It is common experience that something we think is a clue turns out later on not to be. It is easy to make mistakes about clues. Clues are clear only from hindsight …

How then can clues lead to knowledge?! If we are not even certain whether something is a clue, how can that something tell us anything we want to know? If we want knowledge do we not need to start with something that is certain? Something that is absolutely certain?

Our experience in following clues tells us we do not. If anything is uncertain, clues are uncertain. Yet over and over again they lead to knowledge.

It is a prejudice that we have acquired that to find knowledge we have to start with something about which we are absolutely certain. To disabuse ourselves of this prejudice I recommend close attention to what we do when following clues. Ask ourselves when engaged in this activity whether we are absolutely certain of anything. If we do this we will find we never are. Yet by following clues we can discover things we formerly did not know.

How is this possible? How can a process not anchored at any point to absolute certainty lead to knowledge?

Those who have experience in following clues know the answer to this question even though they may not be in the habit of articulating it. One clue may be uncertain, but many will not be. In our example, if SB is our only clue we cannot be certain what it stands for, and even whether it is a clue. But SB is not the only clue in our cryptogram; there are others, as readers can easily discover. When we find more and more clues we will be more and more certain whether they are indeed clues, and also what each one of them means. Clues are the characteristics of structures (disguised). The more characteristics of a structure we can detect the easier it is to pin down that structure, or to reconstruct it. This is no different from locating a person we have never met. Let me explain.

People often think, to find a person we have to have met the person at one time. If not, they ask, how can we recognise the person even if we should have found her? But we don't have to have met the person. We don't even need a photograph. We can find this person if we have sufficient, and sufficiently reliable, information about her—for example, if we know where she was born, when, who her parents are, if she is married, if she has children, what their names are, what she works at, and so on. The more such information we have, the easier it is to locate this person.

Now readers will ask, do we not have to make certain that this information is correct? This information on which we are going to base our search? If the information is false we will never find the person.

Interestingly enough we do not have to be certain that this information is correct (as those experienced in following clues will know). For we can begin our search based on the information as it is given. When we have found the person we know then that the information is reliable. If the information had been false; if it had been simply made up; it would have been a miracle indeed if we actually find a real person answering to it. Keep in mind here we are not talking about one or two particulars about this person, but a long list.

Now the same holds in relation to clues. The more clues we have the easier it is to determine whether they really are clues; we do not have to be certain of them in advance. Clues are clear from hindsight. They are clear from hindsight because by that time we will have 'found the person'. This is to say, when by following clues we can find those structures the clues point to, we know then that these clues are genuine. We do not have to be certain that they are genuine to start with.3

It is a characteristic of the clue-following process that from highly uncertain beginnings, we can find out a great deal, doing so with greater and greater certainty. This characteristic of the clue-following process is well known in practice (it has been made the premise of many a detective story), but not often enough remarked upon. People often say clues can be vague and can mean many things, but they seldom add that as we find more and more clues they, these clues, together can narrow down the possibilities.

That starting with vague and uncertain clues we can find out more and more is a useful point to keep in mind. For people often ask how we know anything to start with. For example, suppose we say we know Q because we know P. They will ask, but how do you know P to start with? By this they mean how do we know P absolutely for certain to start with. Since we do not know anything absolutely for certain to start with their implication is that we do not know Q either; in fact, that we do not know anything at all. But this reasoning is fallacious. I do not know absolutely for certain that SB is a clue to start with; yet I could eventually find out with a high degree of certainty (but not absolute certainty) whether SB stands for TH. In the clue-following process certainty increases as we find out more and more; we do not need, and do not have, absolute certainty at the beginning. God (presumably) can be absolutely certain about many things; we human beings cannot be absolutely certain even of one. But human beings can follow clues. By following clues they find out things they originally did not know.

It is important that we know what clues are. If we know, we can explain why human beings who can never be absolutely certain of anything can nevertheless uncover (approximate) knowledge.

Do clues only suggest theories, or can they prove as well, that is, render these theories more certain? From what we now know about clues we can see that clues never just suggest; they always contribute to the certainty of the theories they suggest. Clues are the characteristics of structures (disguised). Different structures have different characteristics. These structures may have some characteristics in common, but they cannot have all characteristics in common and still be different. When we find a clue, therefore, it will always suggest to us a limited range of theories only, and not just any theory. A clue makes some theories more probable while ruling out others. In that it does, a clue never just suggests; it also contributes to the proof. This is why when we have a large number of clues all pointing to the butler, it is then likely that the butler did it.

Do we ever discover anything new by following clues? Suppose we eventually discovered that the butler did it. Does this mean that we knew all along that it was the butler? To discover anything by following clues, we at least have to be able to suspect what the clues mean. If we do not even suspect that SB might stand for TH we will never discover that it does stand for TH. But to suspect we have to know. If we do not know English we will never suspect that SB might stand for TH. Now if this is true of SB, could it not be true of the whole process of following clues? In following clues we have to know a whole lot before we can start. But if we know this much already, is it surprising that we should discover what we eventually discover. As the saying goes, it is just a matter of putting two and two together. But nothing new is obtained by putting two and two together. Two and two is exactly four.

When we are successful in following clues we often have the feeling that although we are successful we are not discovering anything new. Is this feeling correct?

Now that we know what clues are we can see that it is not correct. When we are successful in following clues we do in fact discover things that we did not know before . To be clear about this there are a number of things to keep in mind. I will now go through some of these.

- Clues are the characteristics of structures in disguise. What is under disguise is not known until the disguise is removed. In following clues, at the beginning the things we will eventually discover are under disguise. Because they are under disguise we do not know what they are. We only know what they are at the end, after the disguise has been removed.

- Disguises can be heavy or light. Some disguises are so light that we have no difficulty in recognising what they are supposed to hide. But we should not think that just because some disguises are light, all are. If we did, we could easily have the feeling that we know all along what we eventually will find out.

- Once we have gotten used to a disguise and what is behind it, the disguise becomes transparent. A spy whose cover is blown no longer has a cover, however much she insists upon it. Indeed, once we are used to a blown disguise we can take the disguise to be the real thing. Melvin always dresses up as Dracula on Halloween. When people see this particular Dracula on Halloween they all say, 'Hello, Melvin!' The Morse Code uses dots and dashes to disguise the alphabet, but radio operators trained in the Morse Code do not hear the dots and dashes, they hear the letters of the alphabet directly. For the same reason clues are clear from hindsight because by that time we will have been used to what they mean.

- There are structures within structures. To decipher a message in English we have to know English. But knowing English does not mean that we know the encrypted English message before we have deciphered it. This message has its own structure, which we have to work out by following clues. This means when we follow clues, although we have to know some structures to start with we can discover new structures that we originally did not know.

- The clue-following process is not a simple process. We often think, erroneously, that knowledge simply flows. It flows from the world into us. It flows from one person to another. An author lets the knowledge she has flow onto the pages of the book she is writing. Now if we accept this erroneous view it is easy to come to the conclusion that the knowledge we gain by following clues is in us right from the start. For we have to know certain things before we can detect clues. Since this is the case the knowledge we obtain by following clues must have come from this knowledge. Knowledge simply flows. It simply flows from one point to another. This is all that it does, according to this erroneous view. Now we need knowledge before we can detect clues. Where has this knowledge gone after we have found out what the clues mean? It must have gone into the knowledge we obtain. It must have gone into the knowledge we obtain at the end. Could there be more knowledge at the end than at the beginning? There cannot be, according to this erroneous view. Knowledge simply flows. If there were more knowledge at the end than at the beginning, there would have been knowledge that has not flowed from anywhere, and this is not possible according to this erroneous view.

Does knowledge simply flow from one point to another in the clue-following process? Is the clue-following process this simple? We can see that it is not. The clue-following process is complex. In relation to this process the flow analogy is totally inappropriate. As illustration suppose the following.

Suppose you are both a cryptanalyst and a cryptographer; that is, you both crack ciphers and make up ciphers. In the last few months you as a cryptographer have been working on a new cipher that you have invented. This cipher has many desirable qualities: it is easy to use (it takes only a few minutes to learn), easy to transport (it can be hidden inside a tube of toothpaste, for example), and, above all, unlike any cipher already known. Now this last is especially important. A cipher that resembles a cipher already known can be easily broken. Cryptanalysts study known ciphers to find out what their characteristics are. If your cipher resembles one of these known ciphers your opponents will have no difficulty detecting clues your cipher leaves behind. For this reason when we are inventing ciphers it is best that our inventions do not resemble any cipher already known. In the present instance you have succeeded in producing such a cipher. How do you know? You know because you have done what all good cryptographers do: you have examined and studied your new invention carefully, and have found that its characteristics are very different from the characteristics of any of the ciphers already known.

Tomorrow you are putting your new cipher into the field, that is, you are actually going to use it. In the meantime you have something else to do, something that has been occupying your attention. Early this morning you have intercepted a message, encrypted, sent out by your opponents to their own people, a message that you would like to read. But tried as you might you have not been able to find a single clue. You have tried all the ciphers known, but none of them helps you in the present instance. At this very moment you are still staring at this cryptogram

And all of a sudden you notice something in the cryptogram that literally makes you sit up! Something alarming. You notice in the intercepted cryptogram for the first time a clue. A clue that resembles the kind that your new cipher will leave behind!

You examine the cryptogram more carefully. To your horror (which quickly turns to glee) you discover other clues of the same sort! Clues only your kind of cipher can leave behind.

Are you going to use your new cipher tomorrow?

Not on your life! Instead, you will spend your time cracking theirs.

What has happened? Why will you not use your new cipher tomorrow, the cipher you have expended so much energy in creating?

The reason is simple. The coincidence of all coincidences, you and your opponents have invented the same kind of cipher!

What does this story, a story about coincidental co-invention, show us about the clue-following process? It shows us that the process is complex. It shows us that if we want to understand how knowledge is uncovered in this process, we cannot use the flow analogy. It is not a simple thing to decipher the message I have intercepted. It is true that eventually I will know what this message says, but this knowledge does not just flow into me. In following clues knowledge does not just flow from one point to another. To know, we have to find clues. Sometimes the knowledge we need in order to detect clues, we already possess. Sometimes we do not possess this knowledge. When we do not, we will have to invent structure after structure, and study all of them, and hope that one of these will leave behind the same clues as those we are interested in detecting. In our story we did not have to invent structure after structure only because by coincidence both we and our opponents have invented the same kind of structure (cipher).

When we follow clues and are successful we uncover knowledge. Obviously this knowledge does not come to us from the outside (since we have to figure out what the clues mean), but this does not mean it must have come from what we already know. The clue-following process is complex. It is complex enough that it cannot be represented by one or two arrows designating some kind of flow. It is true that in this process we will have to make use of knowledge we already possess, but we do not know in advance whether the knowledge we already possess is adequate. When it is not, acquiring knowledge of structures—which structures we ourselves have to construct—will have to become part of the process, as we have explained above. Even when it is, in addition to not knowing in advance that it is, we would not have known in advance which part of it is relevant. In our story about coincidental co-invention the knowledge we needed to detect clues was already in your possession, but we did not know it was relevant. In fact we did not expect it to be relevant: we thought we were the only ones to have invented this particular kind of cipher. We spent a whole morning trying out other kinds of ciphers first, ciphers that turned out to be irrelevant. If we knew in advance what we eventually found out we would not have wasted so much effort. Instead of beating around the bush we would have zoomed in to the kind of cipher our opponents were using and which we had also invented. Unfortunately for us, this was not something we could have done. We could not have zoomed in because we did not know.

Clues are the characteristics of structures in disguise. Unlike actors, clues do not remove their own disguises; we have to do it for them. And when the disguises have been removed we sometimes discover not just the individual items under the disguises but new structures that these items come together to form. Clues can lead us to knowledge we formerly did not have. They can do so in more ways than one (for additional examples see T. Lai, The Art of Detection). That there can be so many ways in which they can add to our knowledge is surprising if we keep thinking that knowledge can only flow from one point to another. But if we keep thinking that the only way to talk over long distances is by shouting, it is surprising too that telephones should work.

In this paper I have given two reasons why it is important that we should know what clues are. To repeat, if we know, we can 1)explain why fallible human beings who can never be absolutely certain of anything can yet uncover knowledge (and what kind of knowledge this is), and 2)be in a better position to avoid some of the common confusions that we fall into when thinking about clues.

There is a third reason why it is important that we should know what clues are. Unfortunately, because of space limitations I cannot expound upon this third reason in this paper. Nevertheless, I should mention briefly what it is.

I think we all know that it is not a simple thing to be following clues. The process is complex and it is easy to make mistakes (the reason why results obtained by following clues are often open to debate). In this process there are things we should do, and there are things we should not. If we do not do the things we should do we will never find the things we are looking for. If we do the things we should not do we will produce wrong results. Now if we know what clues are we can explain what these things are. In other words, if we know what clues are it will help us in a practical way when we are following clues because then we will know how we should properly go about this complex activity (for more on this topic see T. Lai, 'Following clues: do's and don'ts').

1 In explaining this something else some people will give you a long story in which the word 'induction' will feature prominently.

2 … particularly if they have read Sherlock Holmes: 'By a man's finger-nails, by his coat-sleeve, by his boots, by his trouser-knees, by the callosities of his forefinger and thumb, by his expression, by his shirt-cuff—by each of these things a man's calling is plainly revealed. That all united should fail to enlighten the competent inquirer in any case is almost inconceivable.' —Sherlock Holmes in A Study in Scarlet

3 This does not mean we have to take them on faith. If we do not find the structure that they point to, we will have reason to suspect that they may not be genuine.