A phenomenon familiar both to science students and to historians of science provides a clue here. Science students routinely say that they have read through and fully understood a chapter of their textbook, yet nevertheless encounter difficulties at several points when solving the problems at the end of that chapter. Usually such difficulties are resolved in the same way. The student, with or without the help of his professor, discovers how to treat his problem as like a problem he has already encountered. Grasping the resemblance and the analogical relation between two distinct problems, the student can relate the symbols to one another and apply them to nature in ways that have previously proved effective.
A law-statement, for example f=ma, functions as a tool, directing the student toward what sort of resemblance he should seek and giving him confidence in the unified form of experience in which the situation comes to be felt. In my view, as in the case of f=ma or of any other symbolic generalization, the ability to see a variety of situations as resembling one another is the principal achievement the student gains by working examples, whether with pencil and paper or in a well-equipped laboratory. Though there will be great individual variation in the number of such problems, after completing a certain amount of problem-solving, the student comes, as a scientist, to handle the situations that confront him in the same experiential form as do the other members of his professional group. For that student, those situations are no longer the same as those he faced when his training began. During that period he has been assimilated into a time-honored and group-approved way of seeing things.
The role of similarity relations acquired in this way is also clearly apparent among scientists. When scientists solve problems, they solve them by modeling them on earlier problem-solutions, and their reliance on symbolic generalizations is usually extremely slight. Galileo discovered that a ball rolling down an inclined plane acquires enough velocity to return it to the same vertical height on a second incline of any slope, and he learned to treat that experimental situation as a pendulum with a point-mass. Huyghens then solved the problem of the center of oscillation in the motion of a physical pendulum, and this was possible by imagining that the extended form of the pendulum was composed of Galileo’s point-pendula, and that at any point in the swing the connections between the point-pendula were instantaneously severed. After the connections were cut, each point-pendulum would swing freely, but when each reached its highest point, their collective center of gravity would rise only to the height from which the center of gravity of the extended pendulum had begun to fall, just as in the case of Galileo’s pendulum. Finally, Daniel Bernoulli found a way to make the flow of water from an orifice analogous to Huyghens’s pendulum. Determine, during an infinitesimal interval of time, the descent of the center of gravity of the water in the tank and at the outlet. Then suppose that each particle of water subsequently rises separately to the greatest height possible with the velocity it has acquired during that interval. The rise of the center of each particle must then be equal to the descent of the center of the water in the tank and at the outlet. From this way of viewing the problem, the long-sought speed of efflux was at last immediately derived.11) As with the theme of applying the same scientific law or law-sketch, this example should begin to make clear what I mean by saying that one learns from problems to understand situations as belonging to the same kind. At the same time, such examples should also make clear why I speak of a coherent knowledge of nature that is acquired while learning similarity relations and is thereafter embodied not so much in rules or laws as in a way of viewing physical situations. The three problems given as examples, all standard examples for eighteenth-century mechanicians, develop a single law of nature. This law, known as the “principle of vis viva,” is usually stated as follows: “actual descent is equal to potential ascent.” Bernoulli’s application of this law suggests how logical a consequence it was. Nevertheless, the literal statement of the law, taken by itself, has virtually no power. Give that law to a present-day physics major who knows the words and can solve all such problems but now adopts a different method; then imagine what those words could tell someone who, though the words are all familiar, does not even know the problems. For that person, this generalization will begin to function only when he has learned to recognize “actual descents” and “potential ascents” as elements of nature, and that means learning something about situations that nature does or does not present prior to the law. That sort of learning is not obtained entirely by verbal means. Rather, it comes when the words are given to the science student together with concrete examples of how those words actually function. Nature and terms are learned together. To borrow once again Michael Polanyi’s apt expression, what emerges from such a process is “tacit knowledge,” knowledge learned by doing science rather than by acquiring the rules needed for doing science.
4. Tacit Knowledge and Intuition
This reference to the rejection of rules that coexist with tacit knowledge reveals another problem.
That problem seems not to have been well understood by my critics and appears to have provided grounds for charges of subjectivity and irrationality. Some readers seem to have felt that I was attempting to make science rest on unanalyzable individual intuitions rather than on logic and law. But that interpretation is misguided in two essential respects. First, if I am speaking of intuitions at all, those intuitions are not individual. They are, rather, the tested and shared possessions of the members of a successful group, and the beginner acquires them through training as part of his preparation for becoming a member of the group.
Second, such intuitions are not in principle unanalyzable in character. On the contrary, I am currently experimenting with computer programs designed to investigate the properties of intuition at an elementary level.
There is nothing worth discussing here and now about those programs,12) but merely mentioning them will make my central point clear. When I speak of the knowledge that underlies shared exemplars, I am not speaking of a mode of learning that is less systematic or less analytic than knowledge embedded in rules, laws, or criteria of identification. Rather, I have in mind a mode of learning whose meaning is bound to be misinterpreted if it is first abstracted from exemplars and then reconstructed by means of rules that function in their place. Or, to express the same point differently, when I say that one learns from exemplars the ability to recognize a given situation as similar to something one has seen before and different from something else, I am not proposing a process that could not potentially be fully explained in terms of neural-cerebral mechanisms.
Rather, I am arguing that such an explanation, by its very nature, will not answer the question, “Similar with respect to what?” This question is a requirement for a rule, and in this case it concerns the qualifications for the criteria that bind particular situations into families of resemblance. And I am arguing that the temptation to seek limiting conditions, or at least a complete set of conditions, should be resisted in this case. What I oppose, however, is not system, but a particular kind of system.
To make this point concrete, I shall digress briefly here. Although where it leads now seems clear to me, my steady reliance in the first edition on phrases such as “the world changes” suggests that it did not always change. If two people stand in the same place and look in the same direction, then, on pain of solipsism, we must conclude that they receive nearly the same stimuli; if they are assumed to be staring fixedly, the stimuli are identical. But people do not see stimuli. Our knowledge of stimuli is extremely theoretical and abstract. Rather, stimuli give rise to sensations, and there is no compelling reason to suppose that the sensations of the two people mentioned above are identical. Sceptics will perhaps recall that color blindness was nowhere noticed until Dalton described it in 1794. On the contrary, most neural processes take place between the reception of a stimulus and the recognition of a sensation. Among the few things known with certainty about this are the following: the same stimuli can produce entirely different sensations. And finally, the pathway from stimulus to sensation is partly conditioned by a certain amount of training. Individuals raised in different scientific communities in some cases behave as though they saw different things. If we do not try to identify stimuli and sensations one-to-one, we will recognize that in reality they do so.
What should be noted here is that two groups whose members receive the same stimuli but systematically have different sensations are, in some sense, living in different worlds. We assume the existence of stimuli in order to explain our perceptions of the world, and we assume the invariability of perceptions in order to avoid both individual and social solipsism. I have not the slightest hesitation about either of these assumptions. But our world is, first of all, not filled with stimuli, but with the objects of our sensations, and these need not be the same for every individual or every group. Of course, insofar as individuals belong to the same group and therefore share education, language, experience, and culture, there is ample reason to suppose that their sensations are the same. How else could we understand the completeness of their communication and the commonality of their behavioral responses to their environment? They must see things and process stimuli in nearly the same way. But where group differentiation and specialization begin, we have no similar evidence to prove the invariability of sensation. It seems to me that it is mere parochialism that leads us to suppose that the pathway from stimulus to sensation is the same for the members of all groups.
Now, returning to exemplars and rules, what I have been trying to propose, however preliminary its form, is precisely this. One of the basic techniques by which members of a group—whether an entire cultural community or a subdivided group within some specialized field—learn to see the same things when confronted with the same stimuli is by exposure to examples of situations, examples that those who came before them in the group have already learned to see as similar to one another and as different from other situations. These similar situations may be the successive sensory presentations of that very individual—for instance, if it is one’s mother, she will eventually be accepted by sight as one’s mother and as someone different from one’s father or elder sister. Such similar situations may also be perceptions of the members of natural families, as when one distinguishes, for example, swans on the one hand from geese on the other. Or, for the members of a more specialized group, such situations may be examples of Newtonian cases, similar in that they can be treated as transformations of the symbolic expression f=ma, and different from situations to which a law-sketch of science is applied.
For the moment, let us first grant that something of this sort occurs. Must we say that what is acquired from exemplars is rules, and the ability to apply them?
This expression is attractive, because our seeing a situation as like cases we have previously encountered is the result of neural processes wholly governed by physical and chemical laws. In this sense, once we have become accustomed to doing so, the recognition of similarity must be just as fully systematic as the beating of our hearts. Yet that very comparison also suggests that the process of recognition may be involuntary, a process over which we have no power of control. If that is so, then it becomes difficult to accept it as something that can be resolved by the application of rules and criteria. To discuss it in such terms implies that we are approaching alternatives—that, for example, we may have departed from some rule, misapplied some criterion, or tried out some other way of understanding things.13 In my view, these are precisely the sorts of things we cannot do at all.
Or, to put it more exactly, they are things we cannot do until we have come to have some sensation and to perceive something. After that, we often seek out criteria and make use of them. After that, we enter into interpretation, a deliberate process in which we choose among various alternatives that were not involved in perception itself. For instance, what we saw may have been something anomalous (recall the strange card game described earlier).
Suppose that, turning a corner, at a time when we thought she would be at home, we see our mother entering a shop downtown. Reflecting on what we have seen, we suddenly cry out, “That wasn’t Mother. Mother has red hair!” As we enter the shop, we see the woman once more and can no longer understand how we could have taken her for our mother. Again, suppose we see the tail feathers of a water bird feeding on the bottom of a shallow stream. Is that a swan or a goose? Reflecting on what our eyes have gathered, we compare in our minds that tail and its feathers with those of swans and geese we have seen before. Or perhaps, having become a first-rate scientist, we try to discover some general feature of the members of a natural family that we can already easily identify—say, the white color of swans. Once again, reflecting on what we have already perceived before, we search for a property common to the members of the given family.
All these are processes of reflective treatment, and within them we discover and develop criteria and rules. In other words, we interpret the sensations we already possess and try to analyze what what has been given means to us. In whatever way we do so, the processes involved are, in the end, neural, and therefore are regulated according to the very same physical and chemical laws that govern perception on the one hand and the beating of our hearts on the other. But the fact that the system satisfies the same laws in all three cases provides no reason to believe that our neural apparatus is designed to operate in the same way in interpretation as it does in perception or in the beating of our hearts. What I have been arguing against in this book is the attempt, traditional since Descartes but not before, to analyze perception as an interpretive process, as the unconscious interpretation of behavior after perception.
What makes it worth emphasizing the integrity of perception is, of course, the fact that most past experience is embodied in the neural system that transforms stimuli into sensations. A suitably organized mechanism of perception has survival value. To say that members of different groups may have different perceptions when confronted with the same stimuli does not mean that they can have just any perceptions at all. A group that, in this or that environment, could not distinguish wolves from dogs could not have survived. Likewise, a group of contemporary nuclear physicists would not survive as scientists if they lacked the ability to distinguish the tracks of alpha particles from those of electrons. Only those few ways of seeing and apprehending within a group that have withstood the tests the group employs are worth transmitting to the next generation. Likewise, we must speak of the experience and knowledge of nature contained in the route from stimulus to sensation because they have been selected, throughout history, for their success.
Perhaps “knowledge” is the wrong word, but there is a reason for using it. What is built into the neural processes that transform stimuli into sensations has the following characteristics. It has been transmitted through education. By trial, it has proved far more effective, in a group’s environment at the time, than its historical competitors.
And finally, through future education, and through the discovery of what does not fit the environment well, it will undergo change. These are the characteristics of knowledge, and they explain why I have come to use that word. But this is a peculiar usage, because one further characteristic is missing. We have no direct access to what it is we know, and we possess no rules or generalizations by which to express such knowledge. Rules that could provide such access would be related not to sensations but to stimuli, and stimuli can be known only through elaborate theory. Without that, the knowledge contained in the route from stimulus to sensation remains tacit.
Although this is clearly no more than an introduction and need not be correct in every detail, what has just been discussed about sensations has a literal meaning. At most, it is no more than a hypothesis about vision that must undergo experimental investigation, though perhaps not direct verification. But the discussion here of observation and perception, as has also been the case through most of the book, performs a metaphorical function. We do not see electrons; we see their traces, or we see bubbles of vapor in a cloud chamber.
We do not see electric current at all; instead we see the needle of an ammeter or a galvanometer. Yet earlier, especially in Section X, I proceeded consistently as though we perceived theoretical entities such as currents, electrons, and fields. I spoke as though we had learned to do so from the examination of exemplars, and even in such cases I spoke as though it were mistaken to replace the story of observation with a story of criteria and interpretation. The metaphor that transfers “seeing” into contexts such as these cannot be a sufficient basis for such claims. In the long run, it will have to be eliminated in favor of a more exact mode of discourse. The computer program mentioned above begins to suggest a way in which this might be done. But because both the space available and the degree of my present understanding are inadequate, the metaphor cannot be eliminated here.14) Instead, I will briefly attempt to support it. Seeing droplets, or seeing a needle pointing to a scale, is an elementary perceptual experience for someone unfamiliar with cloud-chamber experiments and ammeters.
Therefore, before conclusions can be reached about electrons or currents, careful observation, analysis, and interpretation are required (or some other intervention by external authority may be needed). But for someone who has learned about these instruments and has accumulated exemplary experience in using them, the position is entirely different, and a corresponding difference appears in the way he treats the stimuli he receives from them. His sensations of the vapor of his own breath on a cold winter day may be the same as those of an ordinary person, but when observing a cloud-chamber experiment he does not see droplets (here, literally), but the tracks of electrons, alpha particles, and so on. If you like, those tracks become criteria in interpretation, as indicators of the existence of the corresponding particles, but that path is different from, and shorter than, the one chosen by someone who explains the droplets.
Or suppose a scientist looks into an ammeter in order to read the scale indicated by the needle.
His sensations are probably the same as those of an ordinary person, especially if he has previously read other kinds of meter scales. But the scientist has seen the meter (again, often literally) in the context of the entire circuit, and he also knows something about the internal structure of the instrument. For him, the position of the needle is a criterion, but the scientist need only determine what value the meter indicates. For the ordinary person, by contrast, the position of the needle cannot serve as a criterion for anything other than itself. To explain it, he must examine the entire design of the internal and external wiring, experiment with batteries and magnets, and do various other things. In metaphorical expression no less than in the literal use of “SEEING,” interpretation begins where perception ends. These two processes are not the same, and what perception leaves for interpretation to complete varies dramatically according to the nature and amount of prior experience and training.
5. Exemplars, Incommensurability, and Revolutions
The discussion just given provides a basis for clarifying one further point of this book. This concerns my view of incommensurability—the inability to compare by the same standard—and of the importance of its effects on scientists who debate the choice between successive theories.15) In Sections X and XII, I argued that it is inevitable that the factions taking part in such debates see differently certain aspects of the experimental or observational situations on which both sides rely. But the vocabularies they use when discussing such situations must relate to nature in different ways, and their communication can only remain partial.
As a result, the superiority of one theory over another is something that cannot be proved in that debate.
What I argued instead was that each faction should strive to convert the other side through persuasion. Philosophers in particular seriously misinterpreted the intent of these parts of my discussion. Many of them, however, took me to hold the following belief.16) Advocates of theories incommensurable by a common standard cannot communicate with one another at all. Therefore, in debates over theory-choice, a theory must be selected on the basis of reasons that are fully satisfactory. Some mysterious act of apperception becomes the decisive factor leading to the conclusion actually reached. More than any other part of this book, it was because of the sentences that gave rise to this distorted interpretation that I was accused of irrationality.
First, reconsider my view. What I clearly
wish to make is a simple point, one that has long been familiar in the philosophy of science. Debates surrounding theory-adoption cannot be framed in a form completely analogous to logical or mathematical proof.
In logical or mathematical proof, the premises and rules of inference are specified from the starting point. When there is disagreement about the conclusion, the parties in the ensuing debate retrace their steps one by one, checking each step in light of the prior stipulations. At the end of such a process, one of them must admit that he has made a mistake and violated rules previously accepted. Once he admits this, he has nothing left to rely on, and thereafter his opponent’s proof gains the upper hand. If, instead, the two sides discover that they differ over the meaning or application of the stipulated rules, or realize that their earlier agreement does not provide sufficient grounds for proof, then the debate continues in the form it inevitably takes in a scientific revolution. Such a debate concerns premises, and, as a prelude to the possibility of proof, it relies on persuasion.