PART A: DEWEY AND POPPER
(Get quote from Einstein re his nose for problems)
I. Introduction to Dewey's and Popper's Theories of Inquiry
If we paint with broad strokes and ignore for the moment philosophical niceties (such as their views on truth and induction!), there are striking parallels between Dewey's and Popper's theories of the growth of knowledge. Both are thorough-going fallibilists - none of our beliefs are immune to criticism and revision. The quest for certainty is ill-advised. Both emphasize the activity involved in even the most mundane cases of observation. Information is not simply impressed on blank wax tablets or accumulated in empty heads; it is always the result of a process of search, selection, interpretation.
Both note the continuities between common-sense inquiry and scientific reasoning while acknowledging the human tendency to pay more attention to events which corroborate our theories than to those which contradict it - critical reasoning must be learned.
Both stress the non-algorithmic aspects of reasoning - "thinking is not a sausage machine." Both philosophers view scientific inquiry in particular and knowledge acquisition in general as problem-solving. Since it is impossible either to analyze or to justify all our preconceptions, inquiry begins when we are faced with a gap or inconsistency within our knowledge system - perhaps something unexpected happens. Somehow a solution suggests itself to us. If we are reasoning critically, we will suspend judgment no matter how attractive the proposed solution may be. Instead, we will design experiments to test the implications of our hypothesis and also investigate alternative solutions to our problem.
Only if the proposed solution survives all the tests we can muster, can we consider the problem to be solved - and only for the time being since our knowledge situation is constantly changing.
Where Dewey and Popper differ - and I believe these differences to be deep and irreconcilable - is in their philosophical theories of these temporary end-points of inquiry. For Dewey, knowledge consists of psychologically compelling beliefs whose assertability is inductively warranted if the beliefs work satisfactorily. Popper, on the other hand, does not "believe in" beliefs, nor in inductive support. For him, knowledge is best understood when completely separated from the minds of the organisms which produced it. It consists of propositions which have withstood severe criticism. The only positive credential of knowledge statements is our failure to refute them - so far. Our aim is to find theories which are true in the correspondence sense although we can never hope to know they are true.
Much philosophical energy has already been spent on debates about the nature of truth and knowledge - and rightly so: these are important issues. But the focus of my analysis is a different one. I want to look more carefully at what Dewey and Popper say about the starting points of inquiry. What do they say about the nature of problems? And more importantly, what are their theories about how problems should be evaluated?
II. Dewey's Theory of Problems
Dewey describes and analyzes the starting points of inquiry in many places. The discussion below is my synthesis (and reconstruction) based primarily on How We Think (1910) and Logic, The Theory of Inquiry (1938). Juxtaposing passages written over several decades will obviously blur any subtle changes in Dewey's ideas on the subject. But, since the result is a rich and interesting theory of the origin and structure of problems, I believe the enterprise to be worthwhile.
As is typical of Dewey's discussion of any subject, he draws a variety of useful analytical distinctions while emphasizing the continuities and developmental processes which actually occur in nature. In a similar spirit, I will distinguish between the biological, psychological and intellectual aspects of human problems while recognizing the overlaps...
A prerequisite for any sort of deliberate inquiry is curiosity - Dewey calls it a "natural resource" for thinking (HWT, p. 29). In animals and very young children, curiosity takes the form of excess "organic energy" (p.31), a sort of "physiological uneasiness" which causes a profusion of more or less random exploratory behavior - poking, prying, sucking, fingering and thumping (p.31).
Dewey implies that the major function of this sort of behavior is the accumulation of information which may come in handy later on. He views the two-year-old's endless strings of "why" questions as being primarily an attempt to "eke out his store of experience" (p.32). It is only later that the "whys" are requests for explanations. Yet, the more directed activities of the exploring child are akin to the experimental processes which will predominate later. And there is a developmental continuity between the almost purely physiological curiosity of a baby in a highchair and the sense of intellectual wonder of an Einstein contemplating travels on a light ray.
In certain situations (exactly which ones we will describe later), there is superimposed onto the restless biological energy of curiosity the more-or-less irritating and frustrating psychological state of doubt. Dewey concurs with Pierce and James in finding the adoxastic state of active agnosticism painful, but necessary for effective inquiry.
Pierce is especially emphatic on both of these points:
"Doubt is an uneasy and dissatisfied state from which we struggle to free ourselves...(R., p. 8). (He compares doubt to both hunger and the irritation of a nerve.) "...the mere putting of a proposition into the interrogative form does not stimulate the mind to any struggle after belief. There must be a real and living doubt, and without this, all discussion is idle" (R., p. 9).
James describes the psychological condition which motivates inquiry as "an inward trouble to which his mind till then had been a stranger, and from which he seeks to escape..." (J., p.31).
Dewey describes the state as one of "perplexity, hesitation, doubt" (p. 9). It is "a condition of mental unrest and disturbance" (p. 13). It is tempting to adopt any solution to our problem immediately because the "suspense is likely to be somewhat painful" (p. 13). Dewey, like Pierce, stresses that the difficulty must be felt before effective inquiry can proceed. In applying his theory to education, he says:
"Instruction in subject matter that does not fit into any problem already stirring in the student's own experience, or that is not presented in such a way as to arouse a problem is worse than useless for intellectual purposes." (p. 199)
And in Logic we read: "...to set up a problem that does not grow out of an actual [indeterminate] situation is to start on a course of dead work..." (p. 108).
Although feeling doubt is a necessary antecedent condition for inquiry, Dewey points out that such feelings can be pathological in origin and have nothing to do with the agent's actual situation (Logic, p. 106). Curiosity supplies the general energy for exploration. The irritation of a specific doubt stimulates us to seek the relief of belief. But which situations provoke doubt? Where do problems come from? Dewey says that a problem arises whenever anything - "no matter how slight and commonplace in character - perplexes and challenges the mind so that it makes belief at all uncertain..." (HWT, p. 9).
One type of problem arises in what Dewey calls a "forked-road situation" (p. 11). In such cases, our destination (goal) is clear, but we are uncertain as to which road (means) leads to it. Here, the main purpose of inquiry is to fill in gaps in our knowledge in order that we may achieve some practical end. We are resolving dissonances between what we have and what we want.
A second sort of problem described by Dewey is the case in which something unexpected happens. (In his example, the weather suddenly turns cool.) Here the problem, as Dewey describes it, is to find the significance of the perplexing observation. Does the cooler air indicate rain? Although we may have immediate practical reasons for wanting to know, we need not. Humans seem to need to have their ideas fit together in a unified, orderly manner.
Animals also seek out suitable methods for achieving their goals and may be surprised by unusual events, but they do not have full-fledged problems in Dewey's sense. He stresses that an indeterminate situation does not lead to inquiry until it is judged to be problematic (Logic, p. 107). So we see there is an important intellectual or cognitive component in the most mundane of human problems.
Scientific problems differ from commonsense problems in that they are less immediately tied to the practical goals of "establish[ing] objects of use and enjoyment..." (Logic, p. 115). The subject matter of science is also of a higher level of abstraction.
To summarize, according to Dewey knowledge is the outcome of inquiry, and inquiry begins with problems. For a problem to occur to X, it would appear that for Dewey at least four conditions must be fulfilled (this is my list, not Dewey's):
(1) X must really be in a situation which is "open" or "indeterminate,"
(2) that situation must induce in X a feeling of specific doubt,
(3) X must judge the situation to be problematic by at least vaguely articulating what is doubtful about it (later analysis may sharpen the problem), and
(4) X must have the intention of resolving the indeterminacy.
III. Brief Discussion of Dewey's Theory
To the modern reader who has been raised on a regimen of antipsychologistic philosophy, the necessity of feeling doubt may be puzzling. If I cognitively appraise my situation as problematic and set off to investigate it, why must I also experience the irritation of doubt in order for successful inquiry to ensue?
In Pierce's case, I think he required real, living doubt in order to rule out certain sorts of abstruse scholastic (in the bad sense) philosophizing which he found to be completely sterile. Requiring the feeling is also a barrier to Pyrrhonian skepticism - most of us are unable to muster up sincere doubt about the number of fingers on our hands.
In Dewey's case, the requirement on emotional state fits in well with his general psycho-epistemological approach and his extension of the biological concept of homeostasis to the growth of knowledge. When our belief system is unsettled, we struggle to bring it back into equilibrium. The hungry organism restlessly explores its environment until satisfied by food. The doubting mind engages in inquiry until it finds satisfactory beliefs. The theory also explains why poking unwanted information down kids does not result in effective learning.
But is the theory true? Is the feeling of specific doubt necessary for successful inquiry? And is instruction in material which satisfies no problem in the child's life "worse than useless?" Emotional states are notoriously difficult to disambiguate and identify, and I know of no relevant research on this question, so I'll just rely on informal examples drawn from my own experience.
Let's begin by looking at paradigm cases of intense doubt. Especially excruciating is the state of romantic uncertainty where one is reduced to pulling off daisy petals: "She loves me - she loves me not." A more serious example is in an operating room: "Will they find cancer? Will they be able to remove it all?"
The intensity of doubt in these cases seems to accrue from two sources: First of all a lot hinges on the outcome of our query. Secondly, there is really very little we can do in the way of appropriate inquiry - pulling petals or reading the patient's horoscope in the newspaper are clearly idle and ineffective substitutes for real inquiry. So far so good for Dewey's theory - deeply problematic situations induce intense doubt which builds up unless discharged by inquiry.
Let us now consider some examples of intense inquiry and ask what feelings seem to be motivating the activity. Recently I watched two children play Ripper, a computerized adventure game. The object of the game is to find and destroy Jack-the-Ripper, before too many maidens are killed. To do so, there are many sub-problems to be solved - codes to decipher, secret doors to be opened, rats and cobras barring the way - and there are a variety of resource people available to help - Sherlock Holmes, Florence Nightengale, Roentgen, Madame Curie. The children exhibited classic problem-solving techniques. Some sub-problems could only be solved by brute-force trial and error elimination, others required insight and creativity. At certain junctures, they needed to consult a dictionary or encyclopedia. (At one point they even telephoned the local reference librarian!) They soon found out how important it was to keep records of both their successful and unsuccessful conjectures.
All of these activities were conducted with the utmost seriousness over a period of nearly six hours. (Suppertime finally intervened.) By the end of the afternoon, although the game was not over, they had learned a good deal - how to open the secret door, which wing of the building that Ripper was in, how to drive off the rats, etc. An adult might add that they had also learned some historical facts (e.g., that Roentgen invented x-rays) and perhaps even some methodological maxims (e.g., the importance of keeping records).
But was the children's activity stimulated by the irritation or tension of specific doubt? Was it really the need to have specific knowledge of where the Ripper was or how to open the door that kept them going? I think not: the major satisfaction they seemed to get out of the game was the sheer joy of problem-solving. They didn't really care about the specific content of the beliefs which they formed (it didn't matter where the Ripper was as long as they caught him) and, hence, it is misleading to say that it was specific doubts which impelled them. Their primary motive was not to find out about the Ripper or the door or the rats; what impelled them was not the desire to know, but the desire to achieve as problem-solvers. Yet their efforts yielded knowledge.
Another example is that of the paid consultant or information-gatherer - I am thinking of jobs ranging from census-taker to laboratory technician to reference librarian to scientists working on federal contracts. Such people may feel no need whatsoever to know how many homeless people live in Bloomington or the percentage FSH in my blood serum or Karl Popper's horoscope sign or the diameter of the exit hole of a bullet fired into a goat. Yet they engage in more or less complicated forms of inquiry in order to find these things out. They are not motivated by the need to resolve doubt, but by the need to make a living. (They may also derive enjoyment from the act of problem-solving.)
My interim conclusions are as follows: Much successful inquiry is motivated by doubt, but not all is. If the doubt is too intense, bad methods of inquiry may be adopted (especially if there is no better method immediately available). In other cases inquiry is motivated by the pure joy of problem-solving, not out of overwhelming interest in the subject matter itself. This emotional mode probably predominates in games, but it also plays an important role in mathematics and "pure" science. For example, many mathematicians didn't care much either way how the 4-color map problem turned out - they just wanted to solve it. And in ordinary life, people may also derive pleasure from the elegance of a solution to a very pressing, practical problem.
People can also be induced with money to learn or make new discoveries. Knowledge producers may be more efficient if they are also motivated by epistemological hunger, but it is not a pre-condition for inquiry.
If my conclusions above are correct, then the set of motivating factors available to the teacher becomes richer (although the moral decision as to how to use them becomes more complicated). If it is socially mandatory that certain information be mastered (not everyone would accept that there is any such material), and if it is not possible to get every student in a class to feel interested and intrigued by the problematic subject matter, there are still at least two motivational techniques available - one is to introduce the student to the pleasures of problem-solving in general. (I think Dewey would have no objection whatsoever to this strategy and perhaps even had something similar in mind when he said...) The second one is much cruder - bribe the recalcitrant learner! There are obvious ethical restrictions on the circumstances in which this technique should be used, but it at times may be more honest than trying to make the student pretend to be interested. By "bribing," I include any reward which is extrinsic both to the knowledge gained and to the process of obtaining it. Common bribes include bonuses added to the weekly allowance for good grades, gold stars, smiles from the teacher, early recess, etc.
An interesting problem now arises as to the optimum balance between internally-induced motivation to solve a problem and that which comes from outside. We will return to this issue later when we discuss the appraisal of problems.
IV. Popper's Theory of Problems
Already in the preface of his first published book, Logik der Forschung (1934), Popper was describing inquiry in terms of problem-situations. However, his most complete account is found in the essays which comprise Objective Knowledge: An Evolutionary Approach (1972). My account will draw mainly on these later writings. I cannot address here the question of the development of Popper's ideas nor the interaction between Popper's views of problems and those of his former student, Joseph Agassi, who also writes on the topic.
According to Popper, the process which leads to knowledge begins with problems (See OK, pp. 144-45.). The type of problem which Popper refers to most frequently is that arising from violated expectations, a case where "a theory has run into difficulties" (p. ). Examples of problems of violated expectations include the case of a newborn foal who sucks on the hair under the mare's front legs and is disappointed until it finds its way to the back, as well as the case of Newtonian astronomers who did not expect the results to the Eddington eclipse expedition which detected light bending in a gravitational field. The foal's expectations are unconscious and the "theory" which is in difficulty is inborn while the astronomers deliberately derive a prediction from a theory they learned in seminars. But Popper emphasizes the formal similarities in their problem-situations.
Popper also mentions practical problems, cases in which we search for methods to obtain a goal. Again, the procedure need not be conscious - he cites the example of a hungry amoeba who learns to swim towards a light in order to get food. A common intellectual goal is the desire for explanations. Such problems can range all the way from the specific and mundane ("A dead rat has been discovered, and we wish to know what happened to it.") (OK, p. 350) to the most profound and philosophical, e.g., how can we understand change (C&R,;p. 80)?
Although the examples of problems cited above would probably be quite acceptable to Dewey, Popper's analysis of problem is quite different. Popper prefers to "speak of problems in an objective, or non-psychological sense" (OK, p. 246). (The reader may wonder if Popper's concept of problem may be equivalent to Dewey's concept of indeterminate situation. We'll see that the disagreements are more than terminological.)
Thus for Popper, biologists are not speaking metaphorically when they say "the evolution of the eye solves the problem of giving a moving animal a timely warning to change direction before bumping into something hard." Species solve problems through genetic variation and natural selection; individual animals (such as the baby foal) solve problems by random exploration and the habituation of behavior patterns which are successful; scientists solve problems through the method of theoretical conjectures and empirical refutations.
Isn't the fact that the scientist's inquiry is a conscious, deliberate one, while the evolution of species is neither conscious nor goal-directed, make an overwhelming difference? Popper down-plays the role of consciousness at least as far as the structure of problems is concerned. The reason he gives is the following: People often carry out inquiry without having a clear idea of what their problem is, and sometimes the problem they objectively solve is radically different from the subjective problem which initiated the inquiry. He gives the example of Kepler who set out to discover the harmony of the spheres, but actually succeeded in finding the laws of planetary motion (OK, p. 246). He says it is only by hindsight that we can accurately identify problems. But although Popper is not impressed with the differences in consciousness and intentionality in defining the problems which face an amoeba and an Einstein, he does stress the differences in the methods of error elimination which they use.
First of all, species or individual animals generally physically suffer or die in the process of selection. But in the case of human beings we can generally arrange experiments so that "our [mistaken] hypotheses die in our stead" (OK, p. 248). Secondly, this enables us actively to seek criticism of our theories, to test them severely. Thus, when we deliberately set out to solve a problem, we can be much more efficient about it than animals can. (Humans who are unaware of their problem are also quite bumbling in eliminating errors.)
For Popper, although theories are generated by humans, theories can in turn autonomously generate problems of which no human being is aware. For example, when people first invented the integers (perhaps using a Brouwer-like construction), the problem of whether there is a largest prime also came into existence (although people only worried about it much later). Whether a problem is solved or not is also determined by looking at the objective state of the arguments which could be constructed for and against a proposed solution. Whether people actually accept those arguments or cease feeling puzzled is not relevant.
To dramatize the difference between the objective status of a problem and our feelings about it, Popper places them in different worlds. Roughly speaking, World-1 contains the objects traditionally studied by natural science (e.g., electrons and chairs). World-2 contains psychological states (e.g., feelings of doubt, beliefs). And World-3 contains "the objective contents of thought" (e.g., theories, arguments, problems).
Although minds in W-2 (contained in W-1 bodies) produce everything in W-3, no mind working either individually or collectively can be subjectively aware of everything in W-3. (We can't think about each integer nor actually derive every Euclidean Theorem.) Popper claims the growth of knowledge is best understood by concentrating on the logical relations between W-3 objects, not on the psychological states of the people who produce and manipulate them.
To summarize, for Popper propositional knowledge is the product of problem-solving. Problem-solving is more efficient when we are psychologically aware of the problem and deliberately apply critical methods in evaluating our tentative solutions. However, we are not always fully conscious of our own problem-situations and non-conscious organisms also solve problems. The products of biological problem-solving through natural selection, e.g., organs such as the eye, or birds' nests, are embodiments of theories (p. ), and thus also are presumably forms of knowledge.
V. Brief Discussion of Popper's Theory
Popper's conception of objective problems in a world of propositions and arguments provides a useful framework for attempts to give more formal accounts of the structure of problems. We could replace vague, quasi-psychologistic talk of "violated expectations" by analyses in terms of logical inconsistencies between theoretical systems and singular observation statements. Of course, logic doesn't tell us which statements count as observations nor which theories are "accepted" (No problem arises if a theory already considered to be false leads to a prediction failure.), but one might reasonably hope to give non-psychologistic accounts of these additional factors, as indeed Popper has.
By giving an objective account of problems, one can explain why there is often considerable inter-subjective agreement among scientists on what is problematic about a particular theory. (There is something really "out there" which makes them feel puzzled.) And one can clarify Dewey's point about neurotic feelings of doubt not being adequate for inquiry - the doubt must arise from a situation which is objectively open or indeterminate.
But although Popper's notion of objective problem is very useful, I think Popper may underestimate the importance of the psychological aspects of problems. I will develop this point by listing various points at which we must refer to the subjective problem-situation in order to understand the growth of knowledge.
Let us suppose that humans have generated propositions T and O - both now reside in W-3. Let us further suppose that T ~O, but the deduction is abstruse and so no one has noticed. Objectively, there is now a problem in W-3, but no inquiry will result until someone comes to believe that T ~O.
At this point, Popper might wish to add the explicit proposition, T ~O, to W-3 and draw some distinction between potential logical consequences of our theories and those which have actually been drawn. This seems fair enough. The derivation of ~O from T constitutes a powerful argument against T and creating new arguments surely is a contribution to knowledge. (Recall Galileo's wonderful criticism of the Aristotelian law of falling bodies - if two cannonballs, while falling, should somehow be tied together to form a mass twice as heavy, according to Aristotle's theory, they should speed up, but this is absurd.) However, this does mean that only those features of W-3 which people notice can contribute to the growth of knowledge.
Furthermore, if people believe T and O are inconsistent (even though they aren't), they will try to solve a problem although it would seem that objectively no problem exists! For example, an early criticism of Darwinian theory (D) was that it could not explain the evolution of altruistic behavior (A). We now know that the argument was incorrect - sociobiologists describe a number of mechanisms, such as kin selection, which resolve the puzzle.
Here is a case where Darwin and Altruism were in W-3 and people also believed D ~A so that was also in W-3. However, ~(D ~A) follows from D so presumably that was also at least potentially in W-3. Yet people's inquiry was influenced by what was in some sense a "psuedo-problem" - or at least a problem based on a mistake. Nevertheless, the inquiry resulted in new knowledge, the discovery of kin selection!
I conclude that logical inconsistencies in W-3 are of no importance in the growth of knowledge until people notice them. And even "neurotic" problems (puzzlement based on inconsistencies which aren't really there!) can be important for the growth of knowledge. So it seems that the subjective awareness of problems is crucial.
Furthermore, there is the important matter of problem selection. At any given time, we are probably aware of an enormous number of problems. Not only are there the problems arising from known inconsistencies (Lakatos claimed that every theory lives in a "sea" of anomalies), there are also the explanatory problems which arise from gaps in our knowledge. Which problem will actually provoke inquiry?
Here, Popper admits that subjective experience may play a part in which problem we emphasize, or select as important (OK, pp. 166-67). Later in this essay we will explore the possibility of finding objective ways of evaluating problems. But it seems likely that there will always be an irreducible psychological element. I once heard a biology teacher at a fundamentalist college say that he experienced no difficulty in teaching evolutionary theory because his students kept their religion in one pocket and their biology in another even when he explicitly discussed conflicts between Genesis and evolutionary theory. By any objective criterion, the problems posed by this inconsistency are enormously important - as long as one remains a strict fundamentalist, either one's immortal soul or the integrity of science hangs in the balance. Yet his students refused to deal with it in any way, possibly because it's very importance made it too threatening. Here, Dewey's stress on actively felt doubt seems necessary. You can lead students to see the inconsistency and you can even argue that it's an important inconsistency, but that doesn't mean they will feel it's worth resolving. (When I was a philosophy student, we used to distinguish between genuine paradoxes and counterexamples we found boring which we dubbed "logician's nightmares.")
To sum up, I will propose a crude analogy. When people survey a W-1 landscape and set out to explore it, there will be lots of inter-subjective agreement, e.g., the mountain is to the right of the lake and those waterfalls look interesting. But there will also be lots of variations - some will not even see the edible mushrooms; other will judge them poisonous; still others will concentrate on birdwatching. Likewise, for W-3 landscapes. For example, everyone agrees that both nature and nurture influence human development, but there are enormous differences in the emphasis people place on each and hence on the problems they pursue. To some extent we can argue about these emphases (perhaps using a Lakatosian research program model), but my bet is that there is no way to completely objectify problem choice. (And even if there were, we wouldn't want everyone to pursue the "best" problems - just as when a child is lost, not everyone should look in the most likely places.)
I believe that any adequate theory of inquiry, even if we focus on the purest of scientific research, will have to include the scientist's subjective state as an independent variable.
VI. Introduction to the Evaluation Problem
We have seen that both Dewey and Popper oppose the traditional empiricist view that inquiry begins with fact collecting. Instead, they argue that the process of learning always begins with problems. Although their concrete examples of typical problems are rather similar, their philosophical analyses of problems are quite different. Dewey stresses the psychological aspects of problems and problem-solving; the drive of felt doubt only becomes quiescent when the mind finds a satisfactory belief. Popper, on the other hand, emphasizes the logical aspects: problems arise out of objective flaws in our knowledge, the most important type being an inconsistency. The problem is (tentatively) solved when we eliminate the inconsistency by proposing a new theory which stands up to objectively severe testing. In my discussions of each theory, I have hinted that some kind of synthesis of the two approaches would be desirable.
If we view learning as a problem-solving activity, a new question now arises: Are all problems on a par? Or are some more important than others?
In an important paper published in 1964 ("The Nature of Scientific Problems and Their Roots in Metaphysics"), Agassi posed this question in a historical mode. As a matter of fact, scientists tend to concentrate on only a handful of the problems which could be posed. "By what criteria," Agassi asks, "did the bulk of investigators of a given period decide which problem was fundamental or important (p. 189)?
Using a variety of historical examples, Agassi then argues that the major criterion is the relation of the scientific problem to topical metaphysical issues. I will discuss this thesis in more detail later.
In addition to posing the question about problem evaluation, Agassi's essay also shows why the coordination of problem choice amongst scientists is important. On a naive inductivist account, the most efficient use of scientific personnel would be to have each collect different sorts of facts. And it might at first appear that the problem-solving approach would also be best served by a perfect division of labor. Wouldn't the growth of knowledge be maximized if each scientist chose a different problem to solve?
However, Agassi points out that the conjectures-refutations approach works best when more than one person is involved. We need to consider a wide variety of solutions to a given problem and we need to search for a wide variety of possible criticisms to each proposed solution. And as Dewey emphasized, it is easy for a person to be prematurely satisfied with the first hypothesis which pops into mind. A community of friendly critics all interested in the same problem is invaluable. The implications of this point for education will be stressed later.
Another reason for needing a theory of the evaluation of problems emerges from Laudan's work. In Progress and Its Problems: Towards a Theory of Scientific Growth (1977), Larry Laudan presents a problem-centered account of the growth of science. In summarizing his theory, I will pass rather rapidly over the paths which are rather similar to things Popper or Dewey have said. Laudan's debt to each will, I trust, be obvious (though not to Laudan!). (See Guttin's review.)
Put very briefly, Laudan's theory goes as follows: the aim of science is to solve cognitive problems. There are two basic types of cognitive problems - he calls them empirical and conceptual. Conceptual problems arise out of inconsistencies; empirical problems arise when facts (or putative facts) are felt to be in need of explanation.
Laudan points out that the gaps or inconsistencies which we place a premium on solving can change dramatically over time. "Why is the sky blue?" was not a problem for the Greeks (although they had no solution for it). Yet it became a problem for 19th century astronomers. Inconsistencies between science and religion are sometimes taken to be problematic, but not always. Why are there changing reactions to potentially problematic situations? Why are there fashions in problems?
Laudan's own answer to this question is rather vague and appears to be circular. He refers to "research traditions" (which for our purposes, differ only subtly from Lakatosian research programmes or Kuhnian paradigms). He says research traditions set problems, rank them according to importance, and suggest methods of solution. Fair enough. But how then are research traditions evaluated? According to Laudan, it is in terms of their ability to generate theories which solve important problems!
Laudan's answer to the problem of problem evaluation is inadequate (See my for other difficulties in his theory.), but his account does highlight a new aspect of our problem. Suppose he is correct in saying that theories are evaluated (at least in part) in terms of how many important problems they solve. Suppose also that the fashions in problems sometimes depends in part on personal or political considerations. (For example, was the fact that Hilbert's famous list of twenty problems became the agenda for an entire generation of mathematicians based on their objective importance or was it partly a function of Hilbert's charisma? Why the current burst of interest in research on sex differences? It would be naive to suggest that it's entirely the result of the internal dynamics of science and has no connection to feminist political issues.)
It seems impossible (and unwise) to try to prevent the intrusion of idiosyncratic or political values into the choice of research problems - surely we should each be able to investigate what we like. However if the appraisal of a theory depends on how many important problems it solves (which seems plausible), but whether a problem is judged important or not depends on ideological considerations (which also seem plausible), then the cognitive status of science appears to be seriously jeopardized!
We have now raised the following questions about science:
a) How do scientists evaluate problems? How should they?
b) Do scientists appraise a scientific theory in terms of the number and importance of the problems it solves? Is this a good method of appraisal?
There are parallel issues concerning education:
a) Which problems do children find interesting? Should we try to change their tastes?
b) Do children appraise the value of what they learn in terms of the importance of the problems it immediately solves for them? Should they be encouraged to do so?
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