Page archived courtesy of the Geocities Archive Project
Please help us spread the word by liking or sharing the Facebook link below :-)


Ever since the beginning of modern science there has been a belief among scientists, philosophers, and even lay people, that there is a scientific method. What this method consists in and how it actually works--about this there is conflicting opinion but most believe there is such a method. It is this method, they believe, that enables scientists to produce knowledge of a kind unsurpassed by anything known to humankind, except pure mathematics. In the last fifty years, however, the situation has changed. While many scientists and lay people still believe that there is a scientific method, more and more philosophers have gone over to Popper's view that there is no such thing. According to Popper there is no method that would lead us to knowledge, or even closer to it. Popper says there is a method that would help us make scientific discoveries: the method of conjectures and refutations. But these discoveries are not discoveries of what the world is really like; they are only discoveries of theories that, hopefully, will be able to stand up to many attempted refutations before they are finally refuted. What the world is really like we do not know, Popper says. In carrying out scientific research we hope our theories will come closer and closer to giving us a true description of the world, but while it is legitimate or even essential for us to have this hope, we can have no indication that it is ever realised, according to Popper.

I shared Popper's view on scientific method for quite some time, but an idea occurred to me some time ago (around the late seventies) that Popper might not be right about scientific method after all. As I have said, Popper thinks that we can have no indication whatsoever whether our theories are coming closer to the truth (even though we hope they are). The idea that occurred to me tells me that there are indications of this kind (Lai [1988]). Because of this idea, I found I had to revamp my understanding of scientific method in major ways. This revamping took some time because, like renovating an old house, one change led to another. By this time what I have achieved, or so it seems to me, is nothing less than a 'revolution' (as in 'scientific revolution'). My understanding of scientific method now is not only different from Popper's but, as far as I can tell, different from all current and earlier understandings. To give readers a quick idea of what I have done I set out in this note some of the more radical changes, together with brief explanations. For more details readers can go to my web site:

Scientific Method is About Following Clues

Of the many changes I have made to my understanding of scientific method this, I think, is the most important.1 This change shows most clearly that my thinking on scientific method has undergone a revolution. Let me explain.

It is commonly known that we follow clues to find things hidden from us. When a crime has been committed, to find out what happened detectives follow clues. They do this instead of rounding up people at random and torturing them until they confess. At least, this (i.e. following clues) is what they should do. When a scientist has made a discovery it is legitimate to ask, 'What clues led you to it?' Scientists want knowledge and it is by following clues that they uncover knowledge that they--and humankind--originally did not possess. Now there is nothing exceptional about this; it is just the kind of thing we do nowadays. Things were different once upon a time, however. At an earlier period people were not used to following clues.

However, although it has become common practice to follow clues it is part of common understanding that if we want to know, clues are not sufficient. According to conventional wisdom clues can suggest theories but cannot prove them. Clues may suggest the butler did it but we cannot on that account put butler in jail. A dream suggested to Kekule the structure of the benzene molecule but his fame does not rest just on this dream. Clues are useful; they are nice to have; but whether a theory is true cannot be proved by clues--this is what most people nowadays would say, especially philosophers.

Can a theory ever be proved? Or disproved? Or neither? There has been much disagreement among philosophers. But when philosophers debate this question the word 'clue' does not usually appear. They will be talking about the requirements of logic and the nature of empirical evidence and things of that kind but not clues.

Now what I have discovered is something very different from this accepted view. Scientific method, I have discovered, is intimately connected with following clues. In scientific research, if we want our theories to be correct we have to follow scientific method and the statement of the method incorporates, or should incorporate, the word 'clue'. In evaluating a theory as to whether it is likely to be true, clues play a crucial role. Clues are not incidental to the discovery process, I have come to recognise: they are not things that are nice to have but which we can do without. Clues do not just provide us with a problem, for the solution of which we then need theories. It is true that clues suggest theories, but they also help us evaluate them. Clues can tell us whether our theories are likely to be true or close to being true.

What I have just said will shock a lot of people. But the strange thing is, we know in practice that it is true. In practice we evaluate theories by clues!

Let me give a simple example. Suppose Detective F and Detective M are working separately to solve the same crime. They each have a theory as to who is responsible. Detective F tells you what clues her theory is based on. Detective M frankly tells you that his theory is not based on any clues at all. Now both theories could be false, this we have to admit. But of the two which is more likely to be right?

Now based on what most of us know about clues, most of us would say F's theory. A theory not based on any clues, in colloquial terms, is a wild guess. Wild guesses have little chance of being right. But a theory based on clues has a better chance. How much better depends on how specific the clues are. Not all clues are the same. Some are firmer in their suggestion than others. This shows us that clues do not just suggest, but participate also in evaluating how likely to be true their suggestions are.

But this is not all. Since crime detection is complicated let us move from crime detection to cryptanalysis (cracking ciphers) for an illustration of a second point. Suppose you are trying to decipher a secret message in which a three-letter word, SFH occurs. Earlier clues in the message have suggested to you that the first two letters could be TW, among other possibilities. But you want to try TW first, so you translate the first two letters to TW. After you have done this, what do you have?



Lo and behold, you have a new clue! a new clue telling you what the third letter is likely to be.

Now when we have a new clue our natural tendency is to go on immediately to try to find out what this new clue means. Clues are rare; but they are also the things that can tell us what we want to know. When we have found a new clue we of course will be eager to find out what it can tell us. If the first two letters are TW, what is the third? This is the question we will naturally ask. Rare is the person who can put it aside and go on and do something else.

But let us put it aside and do something else. Let us now ask the following. You have clues telling you that the first two letters could be TW. This of course is only a hypothesis; it could be wrong. But you have applied this hypothesis to SFH. As a result you have a new clue, TW?. The question we now want to ask is, what does this new clue tell you about your hypothesis that the first two letters are TW? Is it more likely now that this hypothesis is true?

Notice at this point that the only answer that you can give (if you listen to common sense) is that this hypothesis is likely to be correct. Now that a new clues has appeared the hypothesis is likely to be correct that the first two letters are TW. This hypothesis could still be false, but the chance that it is false is much lower than before. The appearance of the new clue increases the likelihood that the hypothesis is right that the first two letters are TW.

So, what are we doing here? We are using a clue to confirm a hypothesis! However outrageous this may sound, in practice we do use the appearance of new clues to confirm what old clues have suggested. Wrong hypotheses suggested by old clues sometimes lead to false clues by coincidence, but coincidences are rare. Moreover, false clues peter out. They do not lead on to more and more new clues. When more and more new clues appear the hypotheses that lead to them are likely to be right.

In investigations we should follow clues. Hypotheses answering to clues have a much better chance of being right than wild guesses. And when hypotheses answering to clues lead to new clues, the chances that these hypotheses are right increases. In practice we do evaluate the epistemic status of theories by appealing to clues. Clues do not just suggest; they can also tell us how good their suggestions are.

Now what has all this to do with scientific method?

It has to do with scientific method in the following way. Scientific method by definition is the method that leads to knowledge. When we follow clues we aim at knowledge. In this process when the hypotheses we propose in answer to clues lead to new clues, these hypotheses have a chance of being right.2 The more new clues they lead to the more likely to be right they are. Scientific method therefore can be stated very simply in the following way: Follow clues and develop new clues from old.

It is important that we point out right away that while scientific method can be stated simply, following it is hard. Any one who has had experience in following clues will know it is hard to follow clues, and harder still to develop new clues from old. Not all investigations are as simple as cracking a simple cipher. And even that is not easy if we are doing it for the first time. Indeed, when we are following clues things sometimes can get so complicated that we debate with ourselves as to whether we are still following clues or just making things up.

It is difficult to follow clues. When I say there is a scientific method it should not be taken to mean that it is easy to make discoveries.

Scientific method tells us not only to follow clues but develop new clues from old. To develop new clues we apply the hypotheses we have already advanced. We see this happening in science. In scientific research the hypotheses we advance do not retire to the sideline once we have determined they are likely to be right. Instead, whenever relevant they are employed in developing new clues. This is to say, there are feedback loops (positive) in the clue-following process. The more often a hypothesis participates in this loop, the more likely to be right it is. If it were wrong it could not have produced new clues over and over again. That there are these feedback loops in the clue-following process is the reason why we can have so much confidence in the so-called established theories in science. These are the theories scientists have used over and over again in analysing those situations which have produced new clues. If these theories were wrong, the later theories would simply not have been there because they would not have been proposed.

Scientific method is about following clues. We are not practising the scientific method when we are not following clues. Everyone knows that psychics are not scientists (and they themselves do not claim to be). Psychics do not follow clues.

What Are Clues?

What are clues? Why are they able to lead to knowledge? Why is it that they have the ability both to suggest and evaluate? This is a question we now have to ask. To us this is an important question even though it is not a question philosophers commonly ask. Our interest in this question is not so much on the word 'clue'. Call them what you like, it is still important for us to understand why there are things which can both suggest and evaluate and in this way lead us towards knowledge.

When I first raised this question, what are clues? I thought somebody must have answered it, since it is such a common thing nowadays to be following clues. To my surprise I could not find the answer written up anywhere. Fortunately for me the answer was not difficult to find since in trying to understand the clue-following process I have fallen into the habit of using as illustration simple examples in cryptanalysis. A well-known trick in deciphering a secret message written in English is to look for common characteristics of the English language in the secret message. When we have found one of these we will have found a clue. In English TH occurs often at the beginning of a word. Can we see a TH anywhere in the message? Of course in a secret message the THs will not be in plain view; they will have been disguised by the cipher. But we will look for them all the same, disguise or no; for they are the clues.

So what are clues? From our simple example we see that clues are but the characteristics of the hidden structures we want to know, understanding that these characteristics could be hidden each behind its own disguise. A secret message is not a random string of symbols. A secret message has a structure. If the secret message is in English it is a structure containing English words and phrases. Because we know the characteristics of the English language we can look for those clues which correspond to these characteristics. The task will be difficult because these characteristics will have been disguised.

Why will clues lead to knowledge? Now that we know what clues are we have a simple answer. Because clues are the characteristics of structures, when we have found enough clues we can reconstruct the structures of which they are the clues. The more clues we have the closer to the real thing is our reconstruction. And the more clues we have the easier it is to separate it from its neighbouring structures, that is, separate it from structures that come close to it. This is why we have to develop new clues from old since in most investigations we will not have many clues to start with. And this is why, too, clues not only suggest but confirm. If the reconstruction and the real thing have ten characteristics (clues) in common, it is likely that the two correspond. But if we find that they have twenty more characteristics (clues) in common, we can be a great deal surer of the correspondence.

A new study named after Theseus

Anyone who has followed clues will know it is not a simple business. Many things go on in this process and there are things we should do and things we should not. But no one so far has taken the trouble to collect together these Do's and Don'ts and find out the reasons behind them. If we want to understand the scientific method, this task of collecting together the Do's and Don'ts has to be taken up. I have made a beginning in my paper, 'Following clues: Do's and Don'ts' ( It is a long paper because there are many of these Do's and Don'ts. To give readers some flavour of what they are I give two examples of each below.

Do retrace your steps if in your attempt to advance the investigation you find all the ways forward blocked.

Explanation: In the clue-following process, clues correctly interpreted will lead to new clues. With new clues the investigation can advance. But when a major mistake is made no new clues will appear. Without new clues the investigation will come to a halt after the old clues have been used up. When this happens we will have to locate these mistakes and correct them. To do this we retrace our steps. That is, we re-examine our latest step first to see if we can find the mistake there. If we cannot, we go back one more step, and one more step, and so on. We do this because the mistake is more likely to be in the later steps than the earlier. If the mistake had been in the earlier steps the impasse should have occurred a long time ago, statistically speaking.

Do make use of approximations if they make an investigation easier.

Explanation: Following clues is difficult. To make them less difficult we sometimes resort to approximations. Afterwards, when more is known we can then draw these approximations closer to the truth. But sometimes the chance for improving on the approximations later on is absent. In these cases it is till better to reach an approximate solution to the problem under investigation than no solution at all.

Investigators sometimes hesitate in using approximations. They think in the following way. An approximation is not the truth. What is not the truth is false. In an investigation we should keep strictly to the truth. Once falsity enters we will be misled and thus reach wrong results. But this argument is fallacious. In deductive reasoning, if we want to arrive at true conclusions we have to adhere strictly to the truth; we cannot allow falsity to enter at any point. But following clues is not deductive reasoning; nor is it like deductive reasoning (it is no more like deductive reasoning than photography is). Following clues is a kind of reconstruction. Approximations behave differently when we are following clues compared to when we are reasoning deductively. Approximations can be beneficial to an investigation by making it easier.

How is it that approximations can do this? To answer this question it is useful to look upon a clue as a small gap. In a three-letter word in which two letters are known there is a small gap: the missing letter. This small gap can be easily filled because the two known letters act as a clue. In a ten-letter word in which only one letter is known we do not yet have a clue. The gap is too large.

In following clues we do not mind small gaps: they can be filled easily, comparatively speaking. But we do not like large ones: they are hard or even impossible to fill. However, after filling in the smaller gaps sometimes the large ones become smaller. This is how new clues develop. In deciphering a secret message a ten-letter word in which only one letter is known could at a later stage become a ten-letter word in which nine is known.

So this is why approximations are permissible. To repeat, in following clues when small gaps are filled big gaps could become smaller. But even in filling in a small gap we do not have to do it all at once. We could partially fill it with an approximation, thus still leaving a gap, but a smaller one. Now, and this is important to notice, approximations introduced this way could still lead to new clues: big gaps could still become smaller when small gaps are only partially filled. With new clues we can find out more. When we know more we can turn back and fill in the remaining gaps if opportunity for doing so presents itself. If such an opportunity does not occur it is still better to have filled in most of the gaps than not to have filled in any at all.

That approximations are permissible in following clues explains why human beings with all their limitations can nevertheless come to know things they have never known before. Our senses are not perfect; they make mistakes; but on those occasions where the mistakes are not too large, rough but serviceable clues could be detected. When we form assumptions and hypotheses we are not likely to hit upon the truth every time; but when by chance they come close enough they could nevertheless lead to new clues and thus advance the investigation. The important thing in following clues is that we should be able to advance. Once we know more, even though our knowledge is rough and incomplete and uncertain, we can turn back and bring our earlier results closer to the truth.

Don't jump to conclusions.

Explanation: In following clues we are trying to reconstruct hidden structures. To construct each structure and to distinguish it from neighbouring structures we need many clues. If instead of looking for the large number of clues required we latch on to a much smaller number--say, one or a few--and use these to support the first idea that comes to mind, from which idea we would not budge, we are jumping to conclusions. Jumping to conclusions is clearly a mistake since the small number of clues employed cannot justify the conclusions drawn.

Don't take huge leaps.

Explanation: Clues are the characteristics of structures. To reconstruct a structure and to distinguish it from neighbouring structures we need many clues. This is to say, in trying to find out what a hidden structure is, each clue can tell us only a little. If we do not content ourselves with this; if, instead, we take huge leaps; if, for example, we tell a long, long story after finding just one clue, or after each clue; it is a good sign that we are no longer following clues, whatever we claim we are doing.

People who take huge leaps usually think and even claim they are following clues. They acknowledge that since clues do not always pinpoint the long stories they tell may not be true. But their mistake is not in taking their stories to be true; rather, it is in hanging too long a story on each of their clues. This mistake could be the result of inattention, or ignorance of what it is to follow clues.3

Taking huge leaps is different from jumping to conclusions in that those who take huge leaps tell long stories (for the clues they claim they have found) whereas those who jump to conclusions usually jump to relatively brief conclusions. Conspiracy theorists often take huge leaps. They find what they claim is a clue. Around this one clue they weave an intricate conspiracy which takes them pages and pages to explain. We jump to conclusion when we say the butler undoubtedly must be the murderer simply on the ground that he was holding a smoking gun.

The clue-following process deserves close study. Apart from providing us with a better understanding of the scientific method and the clue-following process, it should also make us better at following clues and better at judging the results arrived at by others who follow, or claim to follow, clues. To focus attention on this study and to draw people towards it we should give it a name. I have chosen Theseology, after Theseus who went into the Labyrinth to kill the Minotaur. To ensure that he could come out again from the Labyrinth Theseus unwound a ball of thread on his way in. When it came time for him to leave he retraced his steps by following the thread. Following clues is often compared to following a thread. Clearly, Theseology should not to be confused with Theology.

The thesis that scientific method is about following clues draws attention to a kind of study so far neglected: Theseology. That it does so is a good sign that this thesis--that scientific method is about following clues--marks a major departure from traditional attempts at understanding scientific method.

Neither Directly nor By Inference

Conventional wisdom--among philosophers as well as lay people--has it that knowledge comes to us either directly or by inference. Since knowledge obtained by following clues is indirect most people including philosophers think this kind of knowledge is obtained by inference. Now deductive reasoning is content-preserving. Deductive reasoning therefore cannot produce knowledge that we originally did not possess. What kind of inference can lead to the kind of knowledge obtained by following clues?

Some call this kind of reasoning inductive. But in doing this they have done nothing more than chosen a name since neither they nor anyone else can explain how any kind of content-enlarging reasoning can ever be valid.

Is it true that knowledge is obtained either directly or by inference? Are there only two possibilities? Can knowledge be obtained some other way?

The thesis that scientific method is about following clues tells us that knowledge does not have to be obtained either directly or by inference. There is a third way: follow clues and develop new clues from old. When we follow clues and succeed we will have reconstructed a structure that leaves behind the same clues as the one we want to know. Knowledge obtained in this complex way clearly cannot be said to be direct. Neither can it be said to have resulted from inference even though reasoning necessarily will have played a role. Reasoning plays a role too in photography but no one will think photographs result from reasoning, nor that they are inferred. When a vintage airplane is reconstructed, reasoning again will be involved, but no one will say the reconstructed airplane is some kind of conclusion which follows from some premises.

Either directly or by inference--this saying has been bandied about for ages. The thesis that scientific method is about following clues shows it up as a false dichotomy. This, I suggest, is another sign of the revolutionary character of this thesis, that is, the thesis that scientific method is about following clues.

The recognition that knowledge arrived at by following clues is not inferred allows us to resolve a number of confusions regarding scientific method. Before I close this section I would like to give just one example.

In following clues we often make use of the process of elimination: If there are a number of explanations for the same clue and we have eliminated all of them except one, that remaining explanation is likely to be the correct explanation. Now in practice most of us will have had occasion to resort to this process at one time or another. But there is a well-known objection to this process, voiced especially by those who like to look at scientific method from a logical point of view. Critics of the process of elimination say, the process will work only if in drawing up the list of possible explanations we have exhausted all possibilities. Only when this is the case can we say that the remaining possibility must be the true explanation. But, these critics say, logically speaking we can never be sure that we have exhausted all possibilities; logically speaking the number of possibilities is infinite.

Who is right? those who use the process of elimination or their critics? Is the process of elimination legitimate?

The proper answer to this question, I suggest, belongs to those who use the process of elimination. The process of elimination is legitimate. There are two important points to be made here. I take up the more interesting one first.

In using the process of elimination it does not matter all that much if we do not exhaust all possibilities. We will try our best of course but being human it is always possible that we might miss one or a few.

How then can the process work? critics will ask. How is it possible that in using the process of elimination we do not have to make absolutely sure that we have exhausted all possibilities?

To answer this question we have to keep in mind that in following clues shortcuts are important. The clue-following process is complex. In some cases if we do not resort to shortcuts we may never find the things we want to find at all. Shortcuts save time and time can be of the essence when following clues. There is no point in solving a problem if the solution requires running a computer for two thousand years. A criminal could have flown the coop if not caught in time. The process of elimination is a shortcut. As a shortcut it is perfectly legitimate.4 Let me explain.

Suppose in drawing up the list we can think of ten possibilities. Suppose we do not want to take the shortcut; suppose we do not want to use the process of elimination; what then do we have to do?

We then will have to try all ten possibilities to see which, if any, leads to new clues!

So this is the reason why we will use the process of elimination when we can. For, if we can eliminate nine we will have only one to try; and if that one leads to new clues we will be one step closer to our quarry.

What if we manage to eliminate this remaining one as well? which in practice frequently happens. In that eventuality, as every one knows, we will have to go back to the drawing board--to see what possibilities we have left out. But even then the shortcut will have save us time: we have now eliminated ten instead of nine!

In deductive reasoning the Disjunctive Syllogism can stand by itself. p or q; not-p; therefore q. In following clues the process of elimination does not stand by itself; it is just a shortcut. In those instances in which we do not treat it as such we have only ourselves to blame (as remedy we should make a closer study of Theseology).

Now that I have made the more interesting of the two points let me go on to the second. Is it true that there is always an infinite number of possible explanations for a clue? Critics of the process of elimination say yes. I want to take the opposite position. It cannot be true, I now want to suggest, that there is always an infinite number of explanations. For if it were, no one would follow clues. We follow clues because clues reduce the field of possibilities. The more clues we have the narrower the field. As the saying goes, in following clues we are setting a noose around our quarry; we gradually tighten this noose; we hope one day there will be no room left for the quarry to wriggle free.

The process of elimination can be understood from the theseological point of view. If we try to understand this process without bringing in the concept of a clue at all; if we insist on looking at it purely from a logical point of view; we are bound to confuse ourselves. Knowledge obtained by following clues is not inferred; it is arrived at theseologically, that is, by following a thread.

Correspondence Without Direct Comparison

After we have added numbers together by following the addition algorithm there is no need to take out a counting board and do the addition all over again. The method / algorithm suffices. It is true that using the counting board to arrive at the sum is more direct, but when there is a method there is no need to check the result by the more direct method. So long as we have followed the algorithm correctly we know without any counting board that the result will be correct. Of course, if we want to, we can take out the counting board too, but if we do so we will find that the answers from the two methods will indeed correspond.

Now in looking for knowledge there is a method: follow clues and develop new clues from old. When we follow this method in solving crimes we know what happened during the crime before the criminals confess. When we follow this method in science we know that the results arrived at will correspond to reality without seeing things from God's point of view. In both cases the more new clues we develop, the surer we can be of the correspondence. Criminals are not all-knowing; they sometimes confess to the wrong crimes. We are not God; we cannot see things from His point of view. But there is no need for all-knowing criminals, nor for us to see things from God's point of view. There is a scientific method. When there is a method, the method suffices.

In adding numbers we can follow the addition algorithm and take out the counting board afterwards if we want to. In following clues can we do something similar?

We can. The simpler instances are afforded by cryptanalysis (cracking ciphers). In simulations of this kind of clue-following we can first crack a cipher by following the scientific method (that is, follow clues and develop new clues from old); after this is done we can ask to see the original. Another way is to create ciphers of our own and challenge others to crack them. We do not advise committing a crime and then waiting to be caught.

Many questions arise from the thesis that scientific method is about following clues. In this paper I have answered a few of them. For the rest I have to refer readers to my other writings as well as to future discussions. In this short note I can do no more than to suggest that perhaps a radically new look on scientific method is possible.


Tyrone Lai

Department of Philosophy

Memorial University of Newfoundland

St John's, Newfoundland

Canada A2C 5S7

1I came to this realisation about three years ago. I have known for a long time that clues play a role in science but for the longest time I did not recognise how very important this role was.

2By 'right', I mean either true or close to the truth.

3Even experienced investigators will sometimes take huge leaps. Our imagination has a tendency to run ahead of ourselves.

4For other shortcuts see Lai [1988].

5So long as we confine ourselves to reasoning.