Conjectural Dogma and its Revision [Karl Popper]

Karl Popper

Although many great scientists such as Albert Einstein, Jacques Monod and Sir John Eccles have publicly acknowledged their debt to Popper, for presenting the ultimate scientific method, his work is still not fully accepted by science. It is especially ignored by the science of learning, where it should be making a considerable impact. Today scientists and school children still have to struggle with the concept of induction, even though, Karl Popper has shown that induction does not exist and is in fact a misunderstanding of how learning takes place.

Francis Bacon. Induction is the inferring of general law from particular instances and it was developed as a methodology of science by Francis Bacon. Francis Bacon, saw it as a way of understanding nature in an unbiased way, as in his view it derived laws from neutral observation. It found easy acceptance because ordinary people found it comforting. It seemed to be an integral part of how our brains work, and so it was, the primitive animal part. Why do I say that? Because any animal with a brain can form a conjecture from a series of instances. To be fair to Bacon his method did include a testing phase, but this was seen as a way of verifying results and not as a way of trying to see if the results were false. Indeed before Bacon nobody had tried to put down principles of how science should proceed and thus pseudoscience existed on equal terms with science. Even scientists as eminent as Newton worked with both pseudoscience and science. What Bacon came up with was a real improvement as far as scientific method was concerned because such a method essentially did not exist before him. 

Induction. Inductive argument, starts with the details of observation which anchors persuasion in reality. It starts from immediate sensory data of what can be seen and touched and then moves to the big picture of ideas, principles and general rules. Starting from the small and building up to the big can be less threatening than starting with the big stuff. Scientists came to believe they could create scientific laws by observing a number of phenomena, finding similarities and deriving a law which explained all the observations. However, the rules of induction seem "rubbery": they concern generalization of the "all" from the "some", and involve evidence, probabilities and best explanations - which can be wrong, even when the evidence is true. Inductive arguments are always open to question as, by definition, the conclusion is a bigger bag than the evidence on which it is based. Conclusions can be wrong if observations are faulty or are drawn from an unrepresentative sample. More importantly inductive conclusions can be wrong despite any number of observations, because there is no way every instance can be examined. How many ravens were seen to be black, before a white one was seen in Japan? How many white swans were seen, before a black one was seen in Australia?

Supporters of induction such as John Stuart Mill would tell us that all "general facts" are based on induction and that therefore deduction and logic cannot even begin until there have been observations and something has been induced from them. Supporters will tell us induction lies at the root of the scientific method that has done so much to advance humanity in the last 500 years. They will say properly applied scientific method is inductive reasoning in its purest form. They will say that the core of inductive reasoning is the ability to look at outcomes, events, ideas and observations, and draw these together to reach a unified conclusion.

Theory comes first. Popper points out, that the above, is not the commonsense, it at first, seems to be. Popper suggests rather, that we are indeed unable to even begin to make observations, if we do not have a theory. Without theory, he suggests that all observations are random, and therefore meaningless. Further it follows that if we already have a theory, we are better off trying to disprove the theory rather than verify or find additional evidence for it. Popper thus, provided us with a better way of proceeding in science. It is better because it leads us away from looking for positive examples and makes us look for negative examples. Instead of looking for what fits in with our pattern we are forced to try and find ways in which the pattern could be broken. By creating a hypothesis and testing it, we open our theory to the possibility of being wrong. Thus we abandon the straight forward, untested idea of induction.

Some sciences seem to profit from the idea of Induction. It is true that some sciences such as archeology and biology tend to involve the collection of many observations without much in the way of theory being formed. But they are still guided by theory, even if it is theory that has been held for many many years. It is in such sciences, that little in the way of disproving theory can be undertaken or expected. People working in such sciences may well be helped in an accumulative process, by what they understand to be induction. However, as rigorous scientists they would not be indulging in outlandish claims, but rather letting their observations speak for them. This method of proceeding in science has worked for 500 years and this site does not wish to tell scientists they cannot use it. However, it seems that induction, unconstrained by scientific rigor, can lead us far astray. The ordinary person does not understand the tentativeness with which apparent induction has to be approached, but usually thinks he understands it very well indeed.

Human brains and the curse of induction. The problem with induction is that we want it to exist, we want it to work. Why is that? Well, our brains have evolved into mechanisms for scanning the environment for patterns that may be true. We want those patterns to turn out to be true, because this is part of the primal functioning of the brain. Our ability to prove things wrong developed later, and we use it mostly for trying to prove others wrong, not ourselves. But any good scientist knows, that any theory that is to be taken remotely seriously is one that has been rigorously tested, one that has run the gauntlet of those who would prove it false. So a theory is not validated, it is instead, that we are unable to invalidate it or disprove it.

Snake oil, Erich Von Daniken and Dan Brown. Induction can be used, and has been used, in ways that are in keeping with rigorous scientific methodology, but induction is not used that way in everyday life by the man in the street. Suppose ten people tell us that snake oil cured them of something. Suddenly we want to believe snake oil is a cure all. Snake oil has not been tested in any way but we want to believe anyway. Erich Von Daniken writes a book called "Chariots of the Gods" documenting ancient marvels and suggesting it could be the work of aliens and suddenly thousands of people want to believe and do believe that aliens have visited Earth in the distant past. Never mind all the other explanations for Von Daniken's drawings and structures, it is a good story and we don't want it to be proved wrong. Stranger still, Dan Brown writes a book called the "Da Vinci Code" and suddenly people want to believe in a conspiracy by the Catholic Church to suppress the love life of Jesus Christ. Brown professes no evidence at all, no instances other than the imaginary ones in his novel, yet still people believe.

Alien abduction. A person has a dream about aliens abducting them, they meet with other people who have had similar dreams, and suddenly the group starts believing they have been abducted by aliens. Never mind all the other explanations for their experiences, just dreams, hypnagogic (the intermediate state between wakefulness and sleep that precedes sleep) imagery and hypnopompic (the intermediate state between sleep and wakefulness that precedes full wakefulness) imagery. Dreamlike images can seem very real when experienced in these half wakeful states. Also do not forget people inevitably exaggerate their experiences to make them more interesting, and some people just plain lie to get attention. The point is, that even a thousand instances of people believing they were abducted mean nothing, if the experiences cannot be tested. Induction fools us again and again, because we are so busy trying to prove ourselves right, that we do not try to prove ourselves wrong.

Deferring to authority. Part of the problem is that most of our learning is done by listening to and reading the words of others and very little is done though designing and and executing tests of existing theories. Thus we always have to defer to the authority of those others. That's fine, but how do we know what is authoritative and what is not? Can we be sure the books we learned from at school were authoritative? No we can't. But apart from the fact they are well out of date when we leave school, they were probably mostly okay. But then what? We are out in the world and suddenly there are best selling books called "The Secret" or "Chariots of the Gods" and they look as authoritative as any other. What about TV shows, or movies about the destruction of the World Trade Center, or what we read in newspapers and magazines. These media are trying to entertain us not educate us. Expect the sensational not an examination of the truth of things.

How does unchecked induction function? Let us look at the world of quackery. The history of medicine is littered with charlatans, because we have an inbuilt healing system in our bodies. Because of our body's ability to heal itself, almost anything can be offered up as a cure for an ailment, and probably has been. Our body heals itself, but we give credit to some version of snake oil. Here's how it works. We get sick. Someone we trust tells us about the healing power of say crystals, or maybe we read about it somewhere. In any case, we decide to try the crystals and lo and behold we get better. Amazing yes? No! It is just a coincidence. Maybe our body healed itself, or something else like medicine from a doctor did the trick. Next time we get sick we try the crystals again. This time the crystals do not seem to work. We are sick for a long time, but we persist with the crystals until finally we do get better. Wow, now the crystals have worked twice. We are reading about crystals thousands of people give testimony that crystals have worked for them. The evidence linking crystals with healing was arrived at by an inductive process. We are only looking at the positive instances. We are only noticing when crystals seem to work. We are using a process of generalizing from the particular to the general, but we are not trying to disprove the health giving properties of crystals.

In science we have to ask questions that are likely to lead to disproof, such as the following: What about all the times when the crystals did not work? Were we taking other medicine? How many times were these other people cured with crystals? Could some of these other people be lying or confused? How does crystallography fit in with what you know about science? From these questions you can create a hypothesis and build trials for finding conditions within which your theory either appears to work or not work. The most effective way to use these trials is to try and prove the theory wrong, while at the same time hoping it does not prove to be invalid.

Ultimately induction is useless in trying to make something scientifically acceptable, if it is currently unacceptable to science. So much is this so, that induction might as to well not really be considered to exist at all. Yet the average person believes he uses it all the time, and is fooled by it over and over. 

Popper says in his book "Unended Quest":

"As for induction (or inductive logic, or inductive behavior, or learning by induction or by repetition or by "instruction") I assert that there is no such thing." "I suggested that all scientific discussion ["I suggest learning" edit.] start with a problem (P1) to which we offer some sort of tentative solution - a tentative theory (TT); this theory is then criticized, in an attempt at error elimination (EE); and as in the case of dialectic, this process renews itself: the theory and its critical revision give rise to new problems (P2) Later, I condensed this into the following schema:
P1 -> TT -> EE -> P2, a schema which I often used in lectures."

Learning without induction. Popper shows that rather than perform a number of repetitions when we are learning we, as thinking creatures, first conjecture a possible solution to a problem. Then we either actively test it, as a scientist would, or accept it till the events of life seem to corroborate it or refute it. (Not only does Popper show that we create and revise conjecture from analysis of sensory input, but that sensory input can only be perceived through existing theory.) For our purposes all learning should be understood to take this developmental form. The psychiatrist Anthony Storr arrived at the following conclusion about getting to know people:

"When we enter a new situation in life and are confronted by a new person, we bring with us the prejudices of past and our previous expectation of people. These prejudices we project on the new person. Indeed, getting to know a person is largely a matter of withdrawing projections; of dispelling the smoke-screen of what we imagine he is like and replacing it with the reality of what he actually is like."

Popper would agree with this, but would extend it to getting to know about anything. He would also restrict it to approaching a more realistic mental model of that thing, without ever being able to know it completely. In other words, we can never truly know reality, and we initially perceive it through the smoke-screen of our previous conjectures. Popper often calls this smoke-screen dogma because often, and particularly in the early learning of children, these conjectures are considered to be true until invalidated. Also this invalidation by critical error elimination comes with great difficulty, and is usually not given up easily. While we are infants, and to some extent all our lives, these conjectures (both the conjectures that are tested and the conjectures not actively tested) are understood as dogma, not as conjecture. That is to say, the conjecture is totally accepted as being true. Unlike real dogma, however, this kind of dogma can be and is, by force of inconsistency with external events, subject to critical error elimination and is eventually discarded.

"Every clarification breeds new questions." Arthur Bloch

Popper proposes, that all learning occurs by paring back our misconceptions and replacing them with more accurate conceptions. He suggests this is true whether the work of scientists, the actions of a new born child or any other thinking creature. Popper insists that the creation of new conjecture comes about mostly as a result of older conjecture being found inconsistent with incoming data and thus refuted as part of error elimination. Thus a hole is left in the learner's map of reality, which he tries to fill by creating new conjecture, which then invokes new error elimination. This seems to work, but a problem occurs if we go back far enough. Where does the first conjecture or dogma come from? Popper explains this by suggesting that all creatures are conceived with some inborn expectations. (For humans very rudimentary instinctual expectations.) The beauty of this is that the inborn expectations do not have to be valid, and are immediately subject to error elimination and the formation of new conjecture.

The discovery path. So what does all this mean in terms of learning? It means that we start off in life with a need for our world or environment to make sense and be consistent. We try to make it consistent by forming conjecture as to how it is consistent. We are then faced with two possibilities. We can experiment to find the limits in which our conjecture will work by finding where it does not work, or we can accept it till subsequent events refute it. Either way it will eventually be subjected to criticism and or error elimination.

The young child. How then does this work for the young child? The young child is very motivated to find consistency in his environment (his reality). He forms conjectures, (dogmas) which lead him to have expectations of his environment. He probably does not consciously try to prove himself wrong but as his expectations are not fulfilled, his dogma is refuted nevertheless. Therefore he must produce new dogma to provide him with new expectations. Popper seems to believe, at this early stage it is not necessary to explain how the leap from nothing to a conjecture or dogma takes place. However, he implies that it is created out of a need. We need something, we reach out for it; the needing provides the explanation or conjecture. This is like saying, anything can be a tentative solution, and that the first conjectures are little better than random. Of course, later we can talk about guesses, intuition and correlation, but these elements are probably not available to the young child, who has not as yet developed a fully functioning map of his reality.

If Popper is right in all this, and it is commonly believed he is, it demonstrates a lot about how we learn and how we do not learn. For a start, it indicates that we probably learn nothing at all through repetition as such, and only learn by conjecture creation and error elimination. When learning a foreign language for instance, we will never really learn a word by repeatedly exposing ourselves to it in conjunction with its equivalent in our own language. We will only learn it by placing it in a number of contexts, and then proceeding through error elimination to discover if it is acceptable in those contexts. Let us look at what Popper says about learning in "Unended Quest".

He says: "I distinguished three main types of learning process, of which the first was the fundamental one:

1. Learning in the sense of discovery: (dogmatic) formation of theories or expectations, or regular behavior, checked by (critical) error elimination.

2. Learning by imitation. This can be shown to be a special case of 1.

3. Learning by 'repetition' or 'practicing', as in learning to play an instrument or to drive a car. Here my thesis is that (a) there is no genuine 'repetition' but rather (b) change through error elimination (following theory formation) and (c) a process which helps to make certain actions or reactions automatic, thereby allowing them to sink to a merely physiological level, and to be performed without attention."

Philosophy Popper informs us that there are three worlds:

1. World 1 is the objective world of reality. Popper believes in the existence of this objective reality. He does not believe that objective reality can ever be known. He suggests that we try to know objective reality by erecting theories about it.

2. World 2 is the subjective world within each individual. This is clearly that which is formed in the mind, and is a map or model of reality developed from the intermeshing of the theories we have about reality. This is not the entire content of World 2 as it must also include both invention and revision.

3. World 3 is the body of knowledge held in common in books computers and other forms of media. This is also a map or model of reality. Without world 3 we would be little better than cave men, for world 3 is a vast intricate map that no human could ever contain. It is our cultural heritage and more. It is the greatest minds of the past opened up, criticized and allowed to spill on to our own inadequate maps of reality, so allowing them to grow in a way that would otherwise be impossible. Again this is not the entire content of World 3 as it includes competing theories, problems, criticism, and revision.

We should try to be clear about these 3 worlds and how they relate to learning. If Popper is correct this explains a lot about learning. Obviously learning takes place in World 2 inside each individual. But only a small but important portion comes from direct interaction between World 1 and World 2. The major interaction in learning is between World 3 and World 2. Early learning involves much more interaction between reality and the learner. Babies are continually forming conjecture as to how the world works and testing the limits within which it works. But as our personal maps of reality become more complete, we begin to interact more and more with World 3.

World 3 enables us to begin to take in whole theories formed by others, and try to fit them into our personal cognitive structure. If the new theory does not contradict anything in our model, we accept it and it is assimilated into that model. If it does not fit, we may have to go back and revise our theories to enable it to fit. This usually requires we return to interaction with World 1 and test the theories. Alternatives are possible but not usually productive. We can refuse to accept the new theory from World 3, or we can hold two mutually exclusive theories as being correct. If the latter is used for predicting reality, inconsistency and even madness can result.

Popper's major contributions have all been concerned with this World 3 knowledge, especially how it comes into being, and how we can know if it is accurate. Because World 3 is very important to learning, due to World 2's interaction with it, Popper's understanding of it is critical to understanding learning. When Popper talks about knowledge, he means not the knowledge in individual minds, and certainly not the knowledge in objective reality, but the knowledge that has been placed in World 3. Let me try to distill Popper's understanding of World 3 knowledge and how it works:

1. Theories cannot be verified they can only be falsified or refuted. Popper shows that no amount of corroboration can ever validate a theory, but that a single instance of deviation can invalidate it. Not only that, but the amount of corroboration does not even improve the statistical probability that we are correct. As Bryan Magee points out in his book "Popper", if we have a theory that water boils at 100 degrees, we can obtain an enormous amount of corroborating evidence and still be wrong. We could be wrong, if we put a lid on the container or if we try it up a mountain. Worst of all, all the corroborating evidence would never have led us to doubt, let alone replace our original theory.

2. At a methodological level theories can not be falsified or refuted unless we formulate them in such a way as to show just how they could be refuted. This is because everything is subject to question; observation, definition etc. By constructing hypotheses that are testable, we allow that they may be wrong, and lay out how they may be refuted. However Popper goes on to show that theories can be immunized against criticism, by the use of a testable auxiliary hypothesis. When it was found that Newton's gravitational laws concerning the motion of the planets were not exactly obeyed in the movement of some planets, it could be said that the theory of gravitation in planetary movement was disproven. However an auxiliary hypothesis of the existence of an, as yet undetected planet immunized the theory. The theory was completely returned to it's previous status when a planet was discovered in the exact position required by the hypothesis. So even if a theory was formulated so as to clearly indicate how it could be refuted, the possibility exists that even if it was refuted, this need not necessarily be permanent as it could still be rescued.

3. We should therefore as an article of method not evade falsification or refutation. Instead we should formulate and present our theories as unambiguously and clearly as possible, to invite falsification or refutation. All knowledge is provisional and each theory must not only carry the seeds of its own destruction, but also organize or prepare the way for that destruction. On the other hand we should not abandon our theories lightly, for this would involve too uncritical an attitude toward testing, and would mean that the theories themselves were not tested as rigorously as they should be.

4. A scientific theory is one that openly exposes itself to testing. Theories that explain things without providing any way of being tested are unscientific and metaphysical or mythical in nature. A scientific theory must be testable, but a good theory formulated as an hypothesis will pin point where it can be disproved and how this may be tested.

5. Metaphysical theories are not useless and should not be discarded on the grounds that they are metaphysical. A theory that was at one time not testable, and therefore metaphysical, may with changed circumstances become testable and therefore scientific. A metaphysical theory may not only be meaningful, but it may actually be correct. Our inability to test it simply renders it unscientific. So if no scientific theory can be created to explain some phenomenon we would be foolish indeed to discard a metaphysical one. Indeed all science has its roots in metaphysics.

6. Criticism is the tool for determining if one theory is better than another. How well a theory can withstand criticism will determine which theory we hold to be the most correct or useful. Criticism may well be instrumental in proposing useful or superior empirical tests. However a theory's corroboration or refutation through empirical testing does not end critical error elimination, for the testing itself is subject to critical discussion. The out come of such discussion may be important in making comparisons that result in one theory being held as being preferable to another. Both scientific and metaphysical theories are subject to this kind of evaluation. Theories which can not be empirically tested may still be critically discussed, and have arguments for and against them compared, as a result of which one of them may appear preferable to another.

7. The importance of a theory has a lot to do with the amount of informative content in that theory. If we create a theory from which we derive a hypothesis stating that 1000 people will die, the information content of our theory is close to nil. People die all the time so this statement tells us very little. If we restrict our theory to say 1000 people will die in Singapore in the next month we are beginning to have information content. If we theorize 1000 will die of AIDS in Singapore in the next month we have a theory with high informative content but the probability that we are correct has diminished. We can widen the theory to say that a 1000 people in Singapore and 500 in China will die of AIDS over the next month. Our theory now has even more informative content but has become even less likely to be accurate. If two theories are put forward and empirical testing is indecisive in supporting a preference for one or the other, our preference should always be for theory with the greater informative content. As the informative content of a theory increases, the universality of its application, the amount of and usefulness of its predictions or its accuracy will also increase if it is corroborated. However the probability that it will be corroborated is in inverse proportion to the amount of its informative content.

   

8. When a theory is refuted we are challenged to form a new theory that incorporates much of the old theory. Much of the old theory is usually still confirmed and needs to be accounted for in the new theory. In addition the evidence that has led to the refutation also needs to be accounted for. This requires a leap of imagination on the part of the creator, who takes it upon himself to invent something that has not existed before yet explains more than was explained before.

9. If we are able to devise a new theory which incorporates that which is still confirmed by the old theory yet accounts for the anomalous instance, we will have created a richer theory that produces more accurate and useful predictions. If we return to Magee's example of the boiling point of water, we will discover our new theory will tell us about the relationship between the old situation at sea level or in open containers and enable us to calculate differing boiling points for differing conditions. Our theory has not reduced its informative content but rather increased it considerably.

10. The growth of knowledge (World 3) if approached in this way will be focused so it continually approaches a more accurate approximation of what is the absolute truth of reality. In other words we are being asked to successively reinvent or reformulate a theory so it is each time more inclusive than before. This approach propels us closer to the universal truth. Though we know that we are continually drawing a more accurate map or reality we must also understand that we can never know if we have found it.

Prescience For Popper, it may be said that the only difference, between the prescientific and the scientific growth of knowledge, is that on a scientific level we consciously search for our errors.

Science and permanence.  All theories, according to Popper, were simply to be held as having a temporary possibility of being correct, until such time as they are disproved. In Poppers mind there was no way of knowing which theory would be flawed. So he deemed it best to hold they might all possibly be flawed. Popper proposed an open society where no permanent truth is held to exist. He held that in this way counter Ideas would be able to emerge more easily.

Metaphysics and pseudoscience. Popper spent a lot of time showing that much of so called science could not be science at all. A lot of psychology, and political science could not be rendered into hypotheses that could be tested. These so called sciences simply could not be proven wrong and were therefore not really scientific theories, but rather metaphysical theories. Popper admitted that there may be some value in these theories but that there was no way to have real confidence in them. Although Popper rejected psychology and political science on the grounds they they were not science, it is likely he would have approved of the rigorous scientific experimentation being currently performed in social psychology. Popper did not bother to attack other pseudo-sciences such as astrology much as he undoubtedly thought these so self evidently flawed as to be not worth the bother. In this he was probably wrong. It has now been fairly well established through scientific test that humans generally are far less logical than he thought, and prone to cling to induction, even when no causal link can be produced.

Popper trusted in reason. He believed in not just his own reason, but the reason of others. He believed very little of worth could come without criticism. He says:

"Faith in reason is not only a faith in our own reason but also - and even more - in that of others. Thus a rationalist, even if he believes himself to be intellectually superior to others will reject all claims to authority since he is aware that, if his intelligence is superior to others (which is hard for him to judge), it is also only in so far as he is capable of learning from criticism as well as from his own and other people's mistakes and that one can learn in this sense only if one takes others and their arguments seriously. Rationalism is therefore bound up with the idea that the other fellow has a right to be heard, and to defend his arguments."

Piaget and Popper. Like Popper, Piaget also found that the young child is motivated to find consistency in his environment (his reality). Piaget talks about schema or schemes by which he means a well defined sequence of physical or mental actions (which in turn can be considered conscious or unconscious conjecture in a dogmatic form). These schema or schemes lead the child to have expectations of his environment. Piaget shows that as his expectations are not fulfilled his schema or schemes are found insufficiently adaptive and he must therefore revise or alter these schema/schemes or create new ones to provide him with new expectations. Popper and Piaget's ideas are clearly moving along similar lines and we would be well advised to examine how these ideas support each other and not emphasize the differences or the use of different language.

The Open Society (Schools) Popper, in his book "The Open Society", tried to give some idea as to what a society might be like if it was to optimize in favor of a structure where his central thesis, critical error elimination, was paramount in all aspects of that society. In the open society, and for this site's purposes the open school, a forum of ideas is to be both encouraged and individually criticized. Only in this way, Popper believed, can we foster the ideas that promote the growth of knowledge, thus allowing man to function more fully. In such a society the formation of theories and the criticism of them would be encouraged to the fullest.