CHAPTER 7
PHILOSOPHICAL MODELS OF SCIENTIFIC PROBLEMS
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In the last chapter we surveyed various formal accounts of problems and/or questions and made our own preliminary attempt to relate these characterizations to the sorts of problems found in scientific inquiry. Now we will look at the writings of four philosophers of science who have specifically addressed the issue of the structure of scientific problems. It turns out that none give a comprehensive account, but each does make a significant addition to one aspect of the theory of scientific problems.
7.1 Nickles: The Constraint-Inclusion Model of Problems
In 1978 Thomas Nickles convened a Leonard Memorial Conference on the topic of the rationality of scientific discovery and edited two volumes of Proceedings. Although there had been scattered writings on the logic of discovery before this (e.g., Herbert Simon's Models of Discovery and articles in Studies of History and Philosophy of Science by Heinz Post, Jon Dorling and others), this Conference is a useful marker for the recent resurgence of philosophical interest in heuristics and generative methods. As philosophers of science turned from analyses of the structure of mature scientific systems to theorizing about the growth of science, it was perhaps inevitable that questions about discovery should arise. The chief function of Kuhnian exemplars was to serve as models or analogues which would aid the normal scientist in discovering extensions of the paradigm. Lakatos introduced the notion of the positive heuristic of a research programme which guided the refinement of theoretical models. He also "trisected" the concept of the acceptance of a scientific statement by distinguishing acceptability1 (a prior appraisal of suitability for testing) (Pof I, p.170) from acceptability2 (positive corroboration after severe testing) (p.173) and acceptability3 (a non-Popperian assessment of overall reliability) (p.181ff). Laudan (pp.108-109), using other terminology, had distinguished between the context of pursuit (a proper part of the old context of discovery and related to Lakatos' acceptance1) and the context of acceptance (somewhat comparable to the old context of justification).
So the beachheads had been established and the time was ripe for D-day, an all out invasion of the no-philosopher's land of discovery. Nickles' own views about the importance of discovery have become more radical since that conference. He now argues that the old concept of the justification of a mature scientific claim in terms of its consequences must be complemented by an account of the justification which accrues from the "discoverability" of that claim, i.e. an analysis of the various generative paths which could have led (have the logical potential of leading) to the discovery of the claim. (See his "Beyond Divorce," Salzburg, and "Positive Science" papers). Nickles' claims about the two sorts of justification rest on a purportedly sharp distinction between reasoning to a theory and reasoning from it (Divorce ms., p.12) which I think is undercut by the symmetry of the statistical relevance condition namely,
p(h, e.b) > p(h, b) just if p(e, h.b) > p(e, b)
so it would appear that e "leads to" h just if e "follows" (weakly) from" h. But we need not pursue this issue here. We must instead see what Nickles says about the structure of problems and their role in scientific discovery.
In his "What Is A Problem That We May Solve It?" Nickles gives a succinct characterization of his constraint-inclusion model of scientific problems: "... a problem consists of all the conditions or constraints on the solution plus the demand that the solution (an object satisfying the constraints) be found." (p.109). In earlier papers which include an historical analysis of the Blackbody Problem, Nickles provided a rough typology of the constraints which arise out of empirical, logical, theoretical, methodological, and metaphysical considerations (Planck paper). Of particular importance is what Nickles calls the 'limit constraint' or what Post had earlier called the 'correspondence condition', which requires that "an adequate problem solution reduce, in the appropriate limit or approximation, to an available ... theory or law which holds in the limit but is otherwise defective." (p.238) In the Blackbody problem, both the Wien and the Rayleigh distributions functioned as limits for the prospective new theory. Since the set of constraints on a deep problem like Planck's is so diverse, Nickles suggested that "... [a] better way of analyzing problems is as ordered or structured sets, in which the constraints are classified according to function and weighted as to importance and degree of flexibility. This suggests a matrix form of representation." (FSA 1978, p.141) Nickles, like Popper, considers problems to have an objective existence, sometimes an agent can uncover new constraints already present within a system without thereby changing the problem itself. In his Leonard Conference paper Nickles also discusses cases where it was, he says, rational to give up certain constraints entirely (VRI, ) and Lugg describes historical examples of problems which are "overdetermined", i.e. problems where it is impossible to satisfy all the constraints simultaneously.
Despite this elaborate fine structure and his recognition that the matrix changes frequently, Nickles' inclusion model simply identifies a problem with the complete set of constraints. He objects to Lugg's distinction between problem and setting and Popper's talk of problems vs. problem-situations by saying "I know of no basis for discriminating those constraints which do belong to the problem proper from those which do not, so I include all constraints in the problem." (p.109) Nickles realizes this leads to a very rapid rate of problem-change in the history of science. When experimenters extended their measurements of blackbody radiation to the low frequency end of the spectrum, (thus introducing new data constraints) he would say the problem of blackbody radiation itself thereby changed, although it obviously bore a striking family resemblance to the previous problem.
In many cases, questions about individuation or definitions are not fundamental and are best settled by conventional fiat. However, I feel I must take issue with Nickles' constraint-inclusion model because it obliterates too many useful distinctions, especially that between a condition which determines what is a correct answer to a question and one which acts as a clue in the process of finding an answer.
Contrast the following simple example: Suppose in each case we are first given an open task and then the clauses are added one by one:
1) Find an x, such that:
a) x is a number
b) which is prime
c) less than 90
d) more than 10
e) whose digits (expressed in base 10) add up to 6.
In this example, each clause narrows the class of permissible solutions. As we add these constraints we do change the problem dramatically. Now compare this problem:
2) Find an x, such that:
a) it is my age in years
b) which is a prime
c) less than 90
d) more than 10
e) whose digits add up to 6.
In case #2, the first clause itself fixes the answer. The prime number clause may be useful to a person who is trying to guess my age; the information in clauses c) and d) is probably already known to the problem-solver; clause e) makes it possible to find the answer without looking at my birth certificate. In this case I would want to say that the problem is certainly not changed as clauses (b), (c) and (d) are added, although (b) might in some cases be very useful. If, because of poor records, my birth can only be pinpointed within a three-year period, clause (b) tells you that it must be 51, not 50 or 52.
What about (e)? Since we now can use number-theoretic methods instead of empirical ones, we might be tempted to see this as a change. Note, however, that although problem #1 can only be criticized by showing that the clauses are logically inconsistent, in problem #2 we can challenge the later clauses on the grounds that they are false--if I am actually 57, the add-up-to-6 clause is a very bad clue indeed.
So I would conclude that in #2, adding the last clause is just adding a clue. But consider the reverse order. Suppose to problem #1, I add a clause saying that the number in question must represent my age. Have I now changed the problem? I would say yes. But this seems to indicate that the order in which the constraints are stated makes a difference!
To me, the upshot of all this discussion is the following: Nickles was wrong to give up the category/condition distinction which we found in both Polya and the erotetic logicians. At the very least we need to pay special attention to the constraint which tells us whether the problem is about propositions, numbers, or physical objects. I am not saying that we generally need very subtle ontological analysis in order to locate what type of problem we're dealing with--I'm generally willing to gloss over the details of your mathematical Platonism or your views on propositions, but I do want to know whether the problem's category is numbers or physical magnitudes.
So the constraint which tells us the general ontological domain or category in which the solution resides is a constitutive part of the problem. I would also distinguish between constraints which fix or determine the reference within that domain and clauses which merely furnish clues. Nickles would undoubtedly reply that my distinctions between categories, constraints, and clues are often hard to draw in practice and given the philosophical turmoil over reference, essential properties, incommensurability, the analytic-synthetic distinction, and the Goddess knows what else, neither are there any theoretical foundations for these demarcations.
But I think we must insist on not lumping everything together, no matter how crude and fallible our distinctions are. Otherwise we will subvert the whole idea of heuristics. The point of a heuristic is to help us find a solution to a problem which has already been set. Consider the simple "hill climbing" heuristic used by both mountaineers and AI programmers which says that if you want to arrive at the summit, it's a good idea to choose paths going up rather than down. If we make this a constraint in Nickles' sense, then we would have to say that any climber who violated this guideline on the way to the summit had thereby solved a different problem. This is too reminiscent of the conceptual proliferation caused by strict operational definitions to be acceptable.
There is a second reason to reject Nickles' "inclusiveness". It frequently happens in the history of ideas that there are two or more competing responses to what is ordinarily referred to as the "same" problem and that each proposed "solution" (again in a pre-analytic sense) has different desirable features. Think, for example, of the various responses to the paradoxes in set-theory or the competing interpretations of quantum mechanics or the debate between adherents of Tycho and Copernicus. Both Tycho and Copernicus "solved" the problem of describing planetary positions and apparent magnitudes using uniform circular motion. In addition, Tycho's system had the very desirable properties of keeping the earth stationary and predicting no stellar parallax, while Copernicus' system had the nice features of providing a non-ad hoc explanation of why the angle between the sun and the inner planets was always small and gave a much simpler explanation of retrograde motion. Now if we follow Nickles inclusive tendency and call such desiderata constraints (though perhaps "flexible" ones) and incorporate them into the definition of the astronomical problem, we will then have to say that the problem solved by Tycho's system was different from that solved by Copernicus. But then Tycho and Copernicus can no longer be viewed as alternative solutions to the same astronomical problem: (Note that Copernicans accepted as a constraint the general requirement that astronomy and physics be consistent although they denied that this implied geocentrism.) We will instead have to say that the debate was about the choice between theories which solved incommensurable problems. If Nickles wants to avoid this situation, he will have to give us at least a rough idea of how to distinguish between constraints and desiderata. But this is exactly the task which he is trying to avoid.
Nickles has done an admirable job of reminding us of the complex nature of real scientific problems and their conceptual environment, and his idea of a matrix of constraints which vary in importance and flexibility is a useful one. But I think we lose too much analytic power by identifying the problem with the entire matrix. My suggestion is to limit the problem to the set of constraints which determine the solution product, and not to include, as part of the problem itself, factors which may influence our path to that final product. Neither should we include within the definition of the problem properties of the solution which are desirable, but not essential.
I am not claiming that the distinctions between category, constraints, clues, and desiderata are always clear cut. But just as in the more familiar case of theory comparison, we increase the possibility for criticism and competition by making our definitions of basic concepts as minimal and non-controversial as possible. Of course, there is a sense in which Tycho and Copernicus were working on different astronomical problems, just as there is a sense in which Copernicus' concept of the earth (a planet) was different from Tycho's. But there is a narrower sense in which they were the same. Focusing on the shared meanings makes it easier both for historians to describe the debate and for scientists to resolve it.
7.2 Hattiangadi: Problems as Inconsistencies with a Historical Structure
Hattiangadi's two-part paper on the structure of problems was written just before the publication of Laudan's book and the Leonard Conference on Discovery. Like Laudan, Hattiangadi argues that viewing science as a problem-solving activity allows us to make better sense of scientific method: "... every reasonable methodological rule regarding the evaluations of scientific theories can be understood in terms of the adequacy of solutions to problems whose structure reflects intellectual traditions." (II, 53) He highlights the role of "discriminatory" problems, i.e. problems which are solved by only one of two rival traditions (II, 57). Thus "debates lend significance to facts" (II, 60) and a new theory which can solve discriminatory problems in both of the rival traditions will automatically be given a high appraisal. There is no need to add, as Popper does, the rather vague requirement that new theories should "proceed from some simple, new, and powerful, unifying idea." (Quoted in II, 66).
Like Nickles, Hattiangadi describes the rich variety of desiderata placed on acceptable solutions to the typical scientific problem (I, p.363) and emphasizes that problems must be given an historical and contextual identity: "In a different intellectual context the same question may well have been different problems if each was prompted by a different reason." (I, p.364) In particular, whenever historians are tempted to say that the 'same old' problem has come up again, they should look further because most likely the new variant has more structure and sets forth different explanatory desiderata. (II, p.5).
And like many writers on discovery Hattiangadi thinks that the phenomenon of simultaneous or multiple discoveries can best be understood in terms of shared problems which are often dramatized through intellectual debates. But let us now focus on some of the novel and more controversial features of Hattiangadi's theory of problems, especially his thesis that all problems arise from inconsistencies. (For a more detailed critique, see Giunti.)
It is a commonplace in writings on problems to begin by noting that problems involve difficulties. For example, Polya says:
"In general, a desire may or may not lead to a problem. If the desire brings to my mind immediately, without any difficulty, some obvious action that is likely to attain the desired object, there is no problem. ... A problem is a 'great' problem if it is very difficult, it is just a 'little' problem if it is just a little difficult. Yet some degree of difficulty belongs to the very notion of a problem: where there is no difficulty, there is no problem," (II, p.117).
For Newell and Simon the difficulty is one of lack of knowledge: "A person is confronted with a problem when he wants something and does not know immediately what series of actions he can perform to get it." (N & S, p.72) In erotetic logic, however, no assumption is made that the questioner does not already know the answer (she might be a lawyer eliciting testimony just for the record) nor that the answer is difficult to find. So any attempt to associate problems with questions should at least add something about the difficulty of the questions.
Hattiangadi takes the idea that problems involve difficulties very seriously. "A problem is a hurdle that we must surmount in order to achieve a goal." (I, p.347) In the case of practical problems, there is always a specific goal and particular barriers which stand in our way. But what is the goal in the case of intellectual problems? Hattiangadi, though not adverse to talking about the truth and falsity of scientific theories, finds it unhelpful to posit TRUTH or EXPLANATION as the telos of scientific inquiry because these aims are too general. Which truths should we seek? Which phenomena require explanation? Neither does he find it illuminating to explain scientific inquiry as being propelled by an innate curiosity drive. Why are scientists at a given time curious about some things and not others? To solve the problem of why scientists avidly tackle some questions and ignore others, Hattiangadi makes the bold claim that all intellectual problems involve inconsistencies. The driving force of all scientific problem solving is the goal of removing inconsistencies from our belief system while retaining as much explanatory power as possible.
Hattiangadi argues that inconsistencies always pose an intellectual problem. Even though for practical purposes it may be possible to keep our conflicting beliefs in separate compartments, this will not do for the intellectual because it is only by juxtaposing various beliefs in novel ways that we can use them "to draw new ingenious conclusions." (I, p.352). Compartmentalization thwarts our ability to exploit some of the most interesting consequences of our system.
But must all scientific problems involve inconsistencies? Hattiangadi's argument is on behalf of the converse not as explicit nor as complete as I would have liked. Let me try to sketch what might be said on behalf of his thesis. Obviously many of the kinds of scientific problems we have previously discussed involve inconsistencies in a straightforward way--Popperian refutations (or Kuhnian anomalies), clashes between theories in mutually relevant disciplines (such as Aristotelian physics and Copernican astronomy), and contradictions within the foundations of a science (recall Berkeley's concern over infinitesimals).
But what about the search for the three elements missing from Mendeleev's Periodic Table? Or the filling-in-the-gaps activities of Kuhnian normal scientists? It seems to me that Hattiangadi has two choices here. First he could say, I suppose, that the Table predicts their existence, but given our total empirical findings so far, they don't exist. (Of course, we don't really know they don't exist, but in the absence of the Table, we`d probably bet they didn't.) A similar analysis could be given for much of normal science. Or Hattiangadi might take the tack that gap-filling, though necessary for science, is not problem-solving. After all, test tube washing and calculating standard deviations are a vital part of science but are not themselves problem solving activities because they are routine--we know how to do them. I find neither move convincing.
Neither does Hattiangadi's account accomodate the problem of looking for explanations of known regularities, e.g., why does the sun rise every day, why do objects fall to the ground with uniform acceleration, why is the sky blue? These are surely legitimate and difficult scientific questions but what inconsistencies motivate us to answer them? Again I will partially construct an answer on his behalf by referring to what Hattiangadi says in other parts of his essay. First, Hattiangadi (following Agassi) points out, that scientists do not constantly and indiscriminately look for explanations for everything. Instead there is a remarkable coordination and focusing of scientific investigations. (I, p.1.) (Laudan also remarks on scientists' selectivity as does Abel in his article, "What Is An Explanandum?") What, then, makes a request for explanation not just an idle question but a real problem? Hattiangadi's answer is that a question becomes intriguing "only if there is a good answer to its radical converse. Thus 'why is the sky dark at night?' is a ... problem only for a physicist who knows why it should not be dark at night ..." (I, p.364)
So to return to my first example, on this view we try to explain the regularity of the sun only if we think it shouldn't be/couldn't be moving in such a fashion. (Perhaps we believe it needs a mover or we can't imagine where it goes at night.) Gravity becomes problematic if we think all forces should act through contact and a blue sky is mysterious if we don't know about refraction. Perhaps to mark those questions which are problems we should phrase them as "How possibly could this process work?" or "Why on earth does this regularity occur?" Here again we generally don't have a strict inconsistency, but we do have an improbability--we ask for an explanation of a regularity R only if the probability of R on the rest of our knowledge is low (but it need not be zero).
So problems arising out of Popper's violated expectations and Laudan's internal and external conceptual problems both involve inconsistencies. And it is even plausible to claim that we are only motivated to search for explanations of known regularities when they are surprising vis-a-vis the rest of our background knowledge. However, it is harder to find an inconsistency, even of the "soft" variety, behind most of the gap-filling activities of normal science--but on the other hand we already realized that the difficulties of normal science had more to do with instrumentation or calculation than with central theoretical issues.
Hattiangadi's conception of scientists as being driven by the need to eliminate inconsistencies accounts for a surprising amount of scientific activity, but it can't be the whole story. First of all, it does not explain severe testing. Why should scientists deliberately try to generate inconsistencies through failed predictions? It seems to me we need both a carrot and a stick--scientists not only try to avoid inconsistencies but also strive for truth/verisimilitude/good solutions or some such positive goal. Of course, one could deny, as Kuhn does, that scientists ever knowingly conduct severe tests, but I doubt if Hattiangadi would like this way out.
There is a second difficulty with positing the removal of inconsistencies as the only scientific motive. There is a very simple way of solving any problem of inconsistency, namely, by simply excising one (or both) of the clashing statements from the system. And this in fact is the way we often handle superficial clashes in our beliefs--what Hattiangadi calls problems with only a minimal structure. But in the second part of his paper he discusses 'deep' problems, i.e. inconsistencies which are "linked to a history of tacit debates". (II, p.l50). In these cases we look for a solution which satisfies a 'maximal' set of desiderata. (II, p.51).
I will not present the details of Hattiangadi's model of historical structure (however, see Giunti). The general idea seems to be that tomorrow's solution to today's inconsistencies should not reopen yesterday's problems. No modern theory of optics should fail to account for diffraction fringes (a problem for the corpuscular theory) or the fact that the color of a light ray is unchanged by passing through a second prism (a problem for early wave theory). Since Hattiangadi stresses the important role of 'discriminatory' problems which only occur when there are two or more alternative traditions, scientists must possess at least a potted version of history; in particular they must remember the great triumphs over rivals (less they arise again and vanquish us today).
Here again, Hattiangadi's account explains many scientific value judgments. Crucial experiments are remembered and their results retained by later theories. But other phenomena which have never been in dispute may also be seen as core explananda. In the case of light, it has always been known that light travels faster than sound and in more nearly straight lines than does sound. (We can't see around corners.) These phenomena need to be explained whether or not a rival theory has dealt with them.
To summarize: Hattiangadi overstates the connection between inconsistency and problematicity but he does place on our agenda the importance of including in our analysis of problems an account of what makes them problematic! I am less persuaded by his attempt to relate what he calls "explanatory desiderata" (which are very similar to some of Nickles' "constraints") to the historical structure of intellectual debates. First of all, although there are many long-standing debates in science--atomists vs. plenists, reductionists vs. emergentists, saltationists vs. gradualists--it seems to me possible that science could progress without them. So I am suspicious of any methodology which makes competition central, such as Laudan's refusal to award negative weight to an anomaly until a rival solves it or Hattiangadi's emphasis on discriminatory problems. Traditions also progress through an internal dialectic.
A second uneasiness has to do with Hattiangadi's use of history. Now he clearly says that, unlike Laudan and Lakatos, he does not evaluate research traditions in terms of their "impetus" (II, p.71). What a research programme has done recently is not peculiarly relevant to its appraisal. But yet Hattiangadi seems to feel that the history of solved and unsolved problems within a tradition is somehow relevant to the setting of conditions of adequacy on new theories. This seems wrong to me. It may be important to structure explanatory desiderata in some way, but I fail to see why the structure should be historical.
7.3 Van Fraassen: The Context of Why-Questions
Van Fraassen proposes a theory of scientific explanation in which explanations are viewed as answers to questions which are posed within a particular pragmatic context. There are at least two sorts of contextual factors which arise in the scientific case according to van Fraassen--the assumed contrast class and the type of relevance relation which is requested. I will illustrate each element using his common sense illustrations. Later on we'll look at some scientific examples.
First, an example of how different contexts provide different contrast classes which in turn changes the sort of answer which is called for:
"Why did Adam eat the apple?" might be construed, according to circumstances, in at least three different ways:
a) Why did Adam (as opposed to Eve, the snake, etc.) eat the apple?
b) Why did Adam eat the apple (instead of giving it back, throwing it away, etc.)?
c) Why did Adam eat the apple (but not the fig, or other fruits in the Garden)?
A perfectly acceptable answer to one variant might provide no answer at all to the other two variants. Thus van Fraassen argues that to construe explanation requests as being of the form, Why is it the case that P?, is too crude. We should instead view the basic structure as:
Why is it the case that P in contrast to other members of X, viz. P1, P2 ...? (X is the contrast-class). (Sci Image, p.127).
This analysis has the immediate consequence that a Hempelian D-N explanation with P as a conclusion will generally not answer the expanded question because it will not tell us why the other members of the contrast class did not occur. The premises which give a Hempelian explanation of why Adam ate the apple may not imply that Eve didn't. It also turns out that a Salmonian S-R explanation will not be satisfactory to van Fraassen unless the probability of the target property in the homogeneous sub-set of the reference class to which the explanandum item belongs happens to be higher than any of the other homogeneous subsets. As van Fraassen puts it, any satisfactory answer "must adduce information that favours P in contrast to other members of X." (Sci. Image, p.128).
I will sidestep the discussion about requirements for explanation and return to van Fraassesn's model of why-questions. He is obviously right about the different possible readings of the uninflected why-p. His analysis in terms of contrast-classes illuminates various puzzling pragmatic features of questions. For example, Aristotle objects to the question, why do the angles of this brass triangle (or isosceles triangle) equal two right angles, saying that the subject is not general enough. We might now add that by modifying triangle we might mislead the listener into thinking that the intended contrast-class is other kinds of triangle and that the answer should favor brass or isosceles triangles. By the same token we can now see more clearly what's going on in the minimal case of Hempelian explanation:
Q: Why is this raven black?
A: All ravens are black.
If the question is understood as having other ravens as a contrast-class then it harbors a mistaken supposition and the answer is a correction. If on the other hand, the intended contrast is other colors, then the answer does at least favor the indicated item, black, although it may not satisfy other requirements we may wish to impose on scientific explanations.
This analysis also meshes well with our earlier discussion of what seemed to be varying strengths of presumptions. Let's consider the question of whether Adam ate the apple. Here again there are three simple variants. If we are asking the first one, whether Adam (as opposed to someone else) ate the apple, we are somewhat prepared to find out that Eve ate it, but will have our beliefs dramatically corrected if the answer which comes back is: No, because nobody ate anything! However, if our intended question was whether Adam ate the apple, that answer will not jolt us.
In the case of why-questions, we are not only presupposing the truth of the core proposition, but also the falsity (or lower probability) of all the propositions formed from the contrast class. This introduces the possibility of even more subtle variants of questions. When faced with the simple question, why do hot pokers emit red light, we must first determine whether the intended contrast is with hot pokers (as opposed to cold ones) or with red light (as opposed to blue light). And then we need to find more about what's in the contrast class. For ordinary people, the contrast class for red light would consist of other visible colors or perhaps no light at all, while an expert in blackbody radiation would take into consideration both the infrared and ultra-violet portions of the spectrum. One subtle way in which questions can change over time is through additions or deletions to the contrast-class. Since the class is rarely made explicit, these will be hard to detect, sometimes even for the person asking the question!
We can now see one reason why questions change in their degree of problematicity or ability to puzzle us as science progresses. According to van Fraassen, to ask, why P in contrast to other members of X, is to presuppose not only that P is true but that none of the contrasting claims are true. (Sci. Image, pp.144-45). Hattiangadi would say that a question is idle when our other background information (K) implies, or strongly suggests, both of these presuppositions. However, it becomes problematic either if K indicates not-P or if K favors some other member of X. As the context changes, a more favored member can enter the contrast class or drop out, thus changing the problematic nature of the core question.
Let us now turn to the second contextual aspect of why-questions, what van Fraassen calls the relation of explanatory relevance--the "respect-in-which a reason is requested, which determines what shall count as a possible explanatory factor." (Sci. Image, p.142) As an illustration, van Fraassen gives a modern version of part of Aristotle's discussion of the four causes:
Q: Why is the porch light on?
A1: Because company is coming.
A2: Because the switch is closed and electricity is flowing through it.
Depending on the context either answer could be the appropriate one. (A2 might be called for if electricians are trouble shooting the wiring, looking for a short circuit.)
One might think that this multiplicity of types of explanatory relevance would only be an issue in folk psychology or other informal treatments of human actions since final causes have been discredited in mature sciences. However, those who oppose unmitigated reduction have argued for the legitimacy and indispensability of explanations at various levels. Thus biologists investigate both proximate and ultimate causes of male aggression, with the physiologists focusing on factors such as testosterone levels and the sociobiologists looking at reproductive strategies. A geographer will explain the different rates of cooling of land and sea in terms of heat capacities while a physical chemist will talk about energies and modes of molecular vibration. Durkheim explained suicide in terms of societal factors such as anomie, but a biographer will give a detailed account of the idiosyncratic features leading up to a particular individual's suicide. A logic teacher will explain student success in applying modus tollens by saying they now understand the rule; an extreme behaviorist will point to the reinforcement schedule of smiles, nods, and check marks which led up to the desired performance. I am assuming in each of the above examples that the two proffered explanations are not inconsistent and that with work we could rephrase the question so that it explicitly calls for one sort of answer and not the other.
Van Fraassen's abstract model of why-questions consists of three factors, the core question (P), the contrast class (X), and a description of what sort of factor would be considered to be of explanatory relevance (R). He then says that any answer (A) to the question must not only favor P over X, but also stand in the called for relationship of explanatory relevance. (Sci. Image, p.143) Van Fraassen does not try to catalogue typical R's but judging from my examples above, it would seem R might appeal to psychological motives, prior physical events, properties of cells, or of molecules, or of atoms, macro or micro economic variables, social facts, proximate or ultimate causes, functional analyses, or what-have-you. Although van Fraassen does not explicitly say so, a consequence of his model is that a why-question presupposes that an explanatory factor of the designated R type does exist. But if we define R too narrowly we could end up having to say that when Becquerel discovered that it was his uranium sample which had fogged the photographic plates in his drawer he was not answering the question, why is this film exposed, because in the original context he was expecting the explanatory factor to be some kind of visible electro-magnetic radiation, not charged particles. Once again it is important not to build so much into the definition of a question that people end up never disagreeing about answers, but only about questions! Here again, I would rather use the weaker notions of desideratum or anticipation. Thus in the nature-nurture controversies over IQ, sex differences, personality attributes, mental disease, etc. the two parties divergence sharply on the kinds of explanations they expect to find (and often on what they hope to find), but our analysis should not allow that circumstance to make it logically impossible that they sometimes ask the same questions!
Van Fraassen's model of why-questions reminds us to look carefully at the context and not just at linguistic formulations when we try to figure out exactly what problems we (or other people) are trying to solve. His requirement that the contrast-class be specified is one way of disambiguating the phlogistonist's question, why do metals gain weight rapidly upon heating (instead of losing weight or remaining the same), from the early equilibrium theorist's question, why do metals gain weight rapidly upon heating (since caloric is a product of oxidation, it looks like it would inhibit the reaction). This device also lends itself nicely to Hattiangadi's account of problematicity--why-questions are particularly pressing when another member of the contrast class would have been expected. The requirement that the desired sort of explanatory relevance be made explicit is a useful way of clarifying the level of analysis on which people are working. But I find it too restrictive to require that the sought-for type of explanation always be built into the question. Possibly Descartes would have rigidly refused any explanation other than purely mechanical ones. If so, for him the question, why do iron filings move towards a magnet, should be rephrased as, what pushes iron filings towards the magnet. But a Newton, though he didn't particularly like forces acting at a distance, was prepared to countenance new kinds of explanatory factors if they were required. So for such scientists, a more open-ended why-question is the correct reading although modern scientists might absolutely refuse explanations in terms of final causes. We should only construe the question as restricting the form of the explanatory answer if the context unambiguously requires it. Being open to the possibility of new types of explanatory factors is generally a scientific virtue and we should give scientists (like everyone else) the benefit of the doubt.
7.4 Bromberger and Predicaments
Beginning with a 1962 paper on the didactic promise of theories (T), Sylvain Bromberger has consistently viewed science as a question-answering enterprise. His best known papers analyze the relationship between explanation-giving and the answering of questions within certain knowledge situations called predicaments (1965, 1966, and 1971). His more recent work (1984, unpublished) deals directly with the central problem of this book, namely how can we rationally evaluate questions (or problems) before we know their answers? As usual, I will not always systematically summarize Bromberger's work. Instead I will select out those elements which promise to be useful to the present inquiry.
Bromberger discusses a variety of questions which scientists may have to deal with. The simplest type is a datum question: what is the boiling point of formaldehyde? (T, p.89) Data questions, which often ask for the value of determinables (unpublished 12), can sometimes be answered by direct observation or consulting a handbook. But in the more interesting case, their answers can be derived, using a formula. Thus the value of the period of a pendulum can be calculated from its length, or vice versa. Bromberger stresses the value of formulae and the theories which incorporate them (in unpublished 1984 he calls them "value adders"). However, he sharply distinguishes this sort of computation or derivation from the process of explanation.
Explanatory theories contain answers to a different sort of question (T, p.101) or to be more precise, they can be used to answer questions which are posed by a person who is in a very peculiar knowledge situation. "Imagine ... a situation in which every answer that we can think of to our question fails to meet the conditions on the question." (T, 100) Since we simultaneously believe that the question has a correct answer, but every imaginable solution is ruled out by our background knowledge, we are in what Bromberger calls a "p-predicament" where p stands for 'puzzled' or 'perplexed'. (T, p.101)
As an example of a predicament Bromberger describes a person who believes that a teakettle begins to whistle before it actually boils and also believes there must be some straight- forward explanation for this. Yet every account they can come up with seems to be ruled out. Perhaps they believe that it cannot be due to the air above the water; neither do they think it is due to the liberation of air dissolved in the water; they also reject heat vibrations as a cause and also (mistakenly) believe that the evolution of water vapor is insignificant until the water actually starts to boil. The form of a predicament is: Q has an answer; A1 ... An are the only candidates for answers (which I can think of); A1 ... An are all unacceptable. In ordinary life we often are in a predicament when we've lost our keys and have looked "everywhere" for them. A well-written detective story also puts readers in a predicament.
Let us now ask which types of questions can figure as the core of a predicament. The most straightforward way of formulating core questions in English is with the interrogatives 'how' or 'why': "How (on earth) did Houdini manage to escape?" "Why does the teakettle whistle just before it starts to boil?" But Bromberger does not want to tie his analysis to ordinary language, because we can rephrase how-or why-questions as "By what mechanism...?" or "What is the cause of ...?" (1966, 70) However, he does think that whether-questions cam never give rise to a predicament. If both 'yes' and 'no' are ruled out, Bromberger says we can no longer continue to think that the question is sound (admits of a correct answer) (1965, p.88). Likewise for questions about determinables, such as "what is the mass of ...?" In this case there are either an infinite number of possible answers (so we could not reject all of them) or, if the possible values are constrained to a finite set, we would again be forced to conclude that there is something wrong with the question should we wish to reject the entire set.
(I'm not sure what Bromberger would want to say about the cases in which our system generates logical paradoxes. To me, the question of whether `heterological' is itself heterological continues to seem sound until the paradox in unravelled even though both answers are unsatisfactory. Likewise for the question about the mass of the neutrino at the historical moment when the data first indicated that its mass was zero but its momentum was positive.)
P-predicaments, as defined, have a psychological component-- they depend on which solutions we have actually imagined so far. However, Bromberger also defines an objective notion namely, b-predicament: "Let us ... describe someone as in a b-predicament with regard to a question Q if and only if the question admits of a right answer ... but that answer is beyond what that person can ... generate from his mental repertoire ... Q is unanswerable relative to [his] set of propositions and concepts ..." (1966, p.70)
Bromberger claims that historically the discovery of deep scientific explanations has often been the result of a search for answers to questions that are objectively unanswerable relative to the prevailing belief system (i.e., questions which give rise to b-predicaments. (1966, p.70) We can now see why the recalcitrance of a problem can be a good reason for viewing it as important. If it puts lots of scientists into a p-predicament we then have reason to believe our scientific system is in a bona fide b-predicament - if so, we are facing a conceptual revolution, not just the failure to think of the obvious.
As we have seen, Bromberger thinks there is a close link between the sort of information required to resolve predicaments and the information conveyed by scientific explanations. He hopes to exploit this connection in order to get rid of certain puzzling features of Hempel's account (such as the problem of the flagpole (1966, p. 82) and the problem of trivial subsumption [1966, p.82]). Bromberger also believes that an analysis of predicaments will show why explanation is often, but not always, called for when the event is unexpected or when there is a plausible argument to a contrary of the explanandum (1966, pp.80-81). I would add that the need to resolve a predicament seems like a stronger motive for doing science than the less urgent sounding "quest for explanation", which is often cited as a major aim of scientific inquiry.
However, Bromberger's attempt to establish a connection between predicaments and explanations is only partially successful. First of all, very trivial questions can put one into a predicament. Bromberger gives as an example 'who was the author of De Fabrica?' which results in a b-predicament for the person who has never heard of Vesalius (1965, p. 96). Or to move to a more interesting case, on Bromberger's definition, we would have to say that before Galileo's telescope, astronomers were in both a p- and a b-predicament with respect to the question, "How can we find out whether Venus has phases?" (Note that they were not in a predicament about whether Venus had phases. Here they knew the possible answers were yes or no and it was not the case that both answers were ruled out.) The discovery of the telescope and its application to astronomy was a wonderful scientific achievement (new instruments, like new formulae, are "value adders"), but it was not the linchpin of a new scientific explanation.
So not all predicaments require an explanation for their resolution, but do all explanations resolve predicaments? Bromberger's characterization of predicaments involves complex belief states as well as questions, while explanations (at least when put in the form of Hempelian deductions) make no explicit mention of either questions or background knowledge, so how are these two very different sorts of items to be linked? Bromberger wrestles with this problem in various papers. In his original "Theories" paper, he offers the following general approach: "... what we call 'explanations' are or contain correct answers to questions with regard to which it is in principle possible to be in a p-predicament. This should be qualified but need not detain us now." (T, p.101) In that paper, his main task is to demarcate two different sorts of theories (his examples correspond roughly to what are informally called descriptive and explanatory theories) and he characterizes the second type in terms of predicaments: "Let Q be any question with regard to which it is in principle possible to be in a p-predicament; if A is a ... proposition not known to be true, and not known to be false, but that contains an answer to q, then A is a theory2 ... Thus a theory2 is a hypothetical explanation ..." (T, p. 102).
However, the application of this criterion is not a straight forward matter. For example, what is the status of Archimedes' Principle? Is it an explanatory theory? What sorts of questions does it answer? I think it depends crucially on which context we supply. Suppose just after Archimedes shouts, "Eureka", his beloved valet rushes into the bath and asks what's happened. Archimedes recites his new Principle: A solid heavier [sic] than a fluid ... will, when weighed in the fluid, be lighter than its true weight by the weight of the fluid displaced. (Heath, p. 258)
Wonderful, says the valet, but what questions does it answer? At this point, Archimedes describes how to use A to calculate the proportion of gold to silver in the King's crown, given data about the relative loss of weights of samples of pure gold, pure silver and the crown. (See Heath, pp. 259-60 for details)
Were you in a predicament about the % of gold in the crown, asks the valet? No, not really, says Archimedes. I knew the answer lay between 0% and 100%. What I was really puzzled about was how to measure it without harming the crown. But of course, strictly speaking, you can't derive "the way to measure..." from my Principle although that provided the key.
Too bad, says the valet. I was hoping you had discovered an explanatory theory, one which directly answers a question about which there is a predicament.
Wait, says Archimedes. In principle I could have discovered it as a resolution to a predicament. Suppose I had been lolling in my bath remembering our glorious vacation at the beach. I could have asked, why does my body feel so much lighter in the sea than in the bath? I could have tried various answers - the sea is a bigger body of water, sea water is colder, it's an illusion brought on my buoyant spirit when on vacation versus my depressed state when I'm home at work solving dumb problems about cattle and crowns for the King. But every answer I could think of was easily eliminated. I was in a real predicament. Then a possible solution came to me - the loss in weight corresponds to the weight of the fluid displaced. So if sea water is denser than fresh water, that would explain the effect and then my Principle would be an explanatory theory, not just a useful formula! I'm going down immediately to measure the density of sea water!
The above anecdote not only explains why Archimedes rushed out naked in the streets, but it also shows how easy it is to turn what appears to be non-explanatory formulae into the resolution of predicaments. The formula for a simple pendulum not only answers what-is questions, such as 'what is the length, given the period' or 'what is the period, given the length' but it also answers why-questions, such as 'why does the Grandfather clock tick more slowly than the cuckoo clock" Or "why do we raise the bob on the Grandfather clock when we want it to stop losing time?" These are questions which could in principle lead to a predicament. In fact any function of the form y=f(x) answers a question 'under what circumstances is y'>y?' which could easily generate a predicament.
As a context-independent criterion for distinguishing explanatory theories, Bromberger's condition that it answer questions which in principle could lead to predicaments does not work. However, this might simply mean that what counts as an explanation does depend on context (which is van Fraassen's position). And as my Archimedes fable illustrates, it may well turn out that how much value we place on a discovery depends on the difficulty or other properties of the historical question which it was actually intended to solve, not on its overall empirical content or any other context-independent property. It is a common-place that the degree of evidential support of a theory at a given time depends on the evidence actually available at that time. Bromberger's notion of predicament dramatizes the fact that the difficulty of a problem depends on the knowledge context. If we view theories as problem-solvers, it would then seem quite natural to evaluate one more highly if it appears to solve an unusually difficult problem. This cannot be the whole story, however, because as Popper emphasizes, theories (like other human productions) often have "unintended consequences", i.e., they turn out to solve problems which were never contemplated at the time of their first creation. We'll talk about this more later when we attack the evaluation problem head on.
I have criticized Bromberger's attempt to forge a link between predicaments and scientific explanations. But from the beginning Bromberger knew that things were not so simple. In his first major article on explanation he pointed out that we ought not be misled into thinking that the removal of a predicament always requires "theoretical instruction" (1965, p.96) and in his detailed theory of scientific explanation he requires that the answer to the why-questions which arise in science contain an "abnormic law" (1966, p.78). For our purposes, we need worry neither about Bromberger's precise definition of "abnormic" (1966, p.76) nor about the other requirements he puts on explanations (1966, p.78), but we will look at his general claim.
The simplest example of an abnormic law would be of this form: "No A is B, unless it is C". So to explain why this x which is an A has the property B, we point out that x happens to be an instance of C. It is interesting to note the striking parallels found in Salmon's theory of statistical explanation (l970). Salmon would call A the reference class, B the target property and C a statistically relevant partition, i.e. prob
(B, A . C) /= prob (B, A . ~ C). In Bromberger's deterministic examples these probabilities are either zero or one. (The motivation for Bromberger's fourth requirement that the antecedent not contain superfluous conjuncts which we haven't discussed here also seems to parallel Salmon's arguments for a broadness requirement.)
The form of the abnormic law immediately allows us to construct a predicament which could have preceded the explanation. If I believe the general rule, No A is B, I would certainly be in a predicament about the counter-instance x which is both A and B. Bromberger thinks episodes of this structure are frequent in the history of science, but are not necessary for the introduction of new abnormic laws. He makes the following intriguing remark: "A clear mark of scientific genius is the ability to see certain well-known facts as departures from general rules that may have no actual instances, but that could have had some, and the germane ability to ask why-questions that occur to no one else." (1966, p.81) I'm not sure what would be an example of the sort of situation he has in mind, perhaps an example where the uninstantiated general rule is an idealization, but in any case he clearly is allowing us to rationally reconstruct a hypothetical predicament for the actual explanation to resolve and abnormic laws make this easy to do.
Bromberger had hoped that his abnormic law model would get rid of the unpleasant symmetries which haunt Hempel's account. Unfortunately he didn't succeed. For a detailed critique see Teller (1974), but this simple example (taken from Teller) shows how the problem reappears in Bromberger's theory: "No piece of rubber is brittle unless it is very cold" can be used to explain why the O-rings on a rocket fractured. But unfortunately "No piece of rubber is very cold unless it is brittle" is also an abnormic law which "explains" why the rocket's brittle O-rings were very cold! Once again we feel the need for something like van Fraassen's requirement of explanatory relevance.
Another problem with the abnormic law model is that it rules out the possibility of explanations based on genuine exception-free universal laws! I agree with Bromberger that our actual attempts to find simple, unqualified laws are fallible and often unsatisfactory. But do we want to define explanation in terms of patched up versions (often adhoc) of old false generalizations? Perhaps we should rest content with the observation that predicaments play a very important role in the growth of science because they often lead to major conceptual and theoretical innovations.
To describe science as a problem-solving activity may conjure up an image of scientists always struggling to get out of an intellectual emergency. Certainly Hattiangadi's view that all problems are inconsistencies has an unpleasant connotation and you will recall that most of the types of problems discussed by Laudan carry negative weights (empirical anomalies and all varieties of conceptual problems). Popper says that science begins with problems and ends with problems, but cryptically remarks that we know we're making progress if the later problems are "deeper". Bromberger, as we have seen, talks a lot about predicaments, which also involve "soft" inconsistencies (though at the meta-level): we simultaneously believe that there is a correct answer though none of the available candidates will do and we believe our search to be exhaustive but can't prove that it is. But he also places a high value on scientific innovations which generate questions. (1984, sec. 2.2) Dalton did not know the atomic weight of chlorine but at least he knew it had one. Questions about the half-lives of isotopes did not even arise before the discovery of radioactivity.
Bromberger points out how much one has to know in order to be an "ignoramus" with respect to a question - one has to have good reason to believe that its presuppositions are true, know that it arises, and be in a position to establish that one does not already know the answer'.(1984, sec. 2.2) Thus, to use his example, upon being informed that my cat is pregnant, the question of who the father is does not arise unless I know the generalization that cats are not parthenogenic. General principles can generate questions as well as answer them! In Bromberger's evaluation scheme, which we will return to later, the answer to a question accrues what he calls "gosh" value for relieving us of ignorance, but also "golly" value (which is also positive) when it generates new accessible questions! More than ever we see the need to have a rational guide for the selection of those few questions which we might have the time and skill to answer.
Chapter VII: Bibliography
Dorling, Jon. (1973). "Demonstrative Induction: Its Significant Role in the History of Physics." Philosophy of Science, 19, 360-372.
Hattiangadi, J.N. (1978). "The Structure of Problems, Part I," Philosophy of Social Science, 8, 345-365.
Hattiangadi, J.N. (1979). "The Structure of Problems, Part II," Philosophy of Social Science, 9, 49-76.
Nickles, Thomas. (1980a). "Scientific Discovery and the Future of Philosophy of Science," in Scientific Discovery, Logic, and Rationality, T. Nickles, ed., Dordrecht: Reidel, 1-59.
Nickles, Thomas. (1980b). "Can Scientific Constraints Be Violated Rationally?" ibid., 285-315.
Nickles, Thomas. (1980c). "Scientific Problems: Three Empiricist Models," PSA, 1980, Vol. 1, 3-19.
Nickles, Thomas. (1981). "What Is a Problem that We May Solve It?" Synthese, 47, 85-118.
Nickles, Thomas. (1985). "Beyond Divorce: Current Status of the Discovery Debate," Philosophy of Science 52, 177-206.
Post, H.R. (1971). "Correspondence, Invariance and Heuristics: In Praise of Conservative Induction." Journal of Studies in History and Philosophy of Science, 2, no. 3, 213-255.
van Fraassen, Bas C. (April, 1977). "The Pragmatics of Explanation." American Philosophical Quarterly, Volume 14, Number 2, 143-150.
van Fraassen, Bas C. (1980). The Scientific Image. Oxford: Clarendon Press.
Chapter VIII: Bibliography
Archimedes, The Works of. Edited by T.L. Heath. New York: Dover Publications, Inc.
Bromberger, Sylvain. (1962-63). "A Theory about the Theory of Theory and about the Theory of Theories" in Philosophy of Science-Delaware Sem, Vol. 2, Bernard Baumrin, ed., 79-105.
Bromberger, Sylvain. (1965). "An Approach to Explanation" in Analytical Philosophy, R.J. Butler, Ed., 2nd Ser., Oxford, 73-105.
Bromberger, Sylvain. (1970). "Why-Questions" in Readings in the Philosophy of Science, Baruch Brody, ed., Prentice-Hall, 66-87.
Bromberger, Sylvain. (1971). "Science and the Forms of Ignorance" in Observation and Theory in Science, Ernest Nagel, Sylvain Bromberger, and Adolf Grunbaum, eds., Baltimore: Johns Hopkins Press, 45-67.
Bromberger, Sylvain. (1984). "On Pragmatic and Scientific Explanation: Comments on Achinstein's and Salmon's Papers" in PSA 1984, Volume 2, .
Bromberger, Sylvain. "Rational Ignorance." (unpublished).
Teller, Paul. (1974). "On Why-Questions." Nous 8, 371-380.