One cannot have a genuine problem without a certain amount of desorientation. This gives rise to an epistemological question: How can the gulf between puzzlement and its dissolution be bridged? What accounts for the success in finding one's way through the problem-space, arriving at some satisfactory answer? There are of course commonsensical, empirically-minded answers to these questions but they miss their inherent philosophical exitement. This in turn consists in their inquiring about the conditions of a vital trade-in, namely between the pre-articulate needs of certain beings and the actual results of certain chosen procedures to alleviate them. I do not intend to go into epistemology here. My intention is to explore an analogy taken from literary criticism, regarding a problem as a narrative.
Narratives have been described as processes of transformation of the balance of elements that constitute their pretexts. The interruption of an initial equilibrium leads to the dispersal and refiguration of its components and finally to the establishment of a renewed equlilibrium. It is only in view of this whole operation that a given text can be classified as a narrative. It does not qualify as long as it does not fit into a step-by-step procedure designed to connect a disturbance to its resolution according to a set of principles conventionally agreed upon. The similarities of these features of a narrative to the previous remarks on problems are striking. Like a problem a narrative opens up the space of an expectation and has to deal with it in such a way as to conduct the listener towards its fulfillment. It is this process that accounts for the eventual success of a story. Analogously, I want to argue, problems can be solved because certain transformations are seen as steps in an ongoing procedure designed to accomplish the satisfaction of given needs. Neither the transformatory moves by themselves nor the mere givenness of a problem-space are sufficient to explain this possibility. To flesh this out I shall specify some of the conventions a narrative imposes on its subject matter. Three main features deserve mention here: formality, teleology and reflexivity.
A narrative as well as a problem is clearly marked off from the surrounding context. In both cases there is a beginning and an end, functioning as correlative points of demarcation. Starting a narrative or posing a question is an exit from ordinary life and an entrance into the more artificial realm of a story or a method to deal with a disturbance. Finishing a story or answering a question on the other hand has to be seen as an exit from the story-world or problem-space back into a real-life setting. In between those turning-points all procedures are relatively formal compared to the context out of which a story or a problem grows. It is essential to distinguish between the internal story- or problem-space and the location of this space within a larger environment that allows for such a space to be generated. Only from the point of view of this embedding of stories and problems can their internal developments make sense. In fact one has to be more precise: only if the formal procedures known from literary and methodological analysis are located within those turning-points can they be seen as developments at all, otherwise they are just aimless moves devoid of any forthright use. In a certain sense every problem has to have a formal solution, namely the result of the conventionally prescribed transformations that are executed within the problem-space that sets a problem apart from the context in which it becomes manifest. Algorithmic procedures are only a subspecies of strategies the mastery of which enables one to systematically connect the points of departure and of arrival of a story or a problem. In short: a problem is constituted by the fact that there exists a relativly formal way of bridging the gap between disequilibrium and reintegration evident in the expectation the telling of a story stimulates and the treatment of a problem adresses itself to.
Obviously there are different ways to conceptualize situations of apparent need and corresponding strategic remedies - but if one chooses to use narrative categories the employment of some teleological and reflexive patterns can not be avoided. Basically this derives from the fact that a narrative not only has to have a beginning and an end, but also something that might be called a gradient between its initial state and its consequent states. A story as well as a problem is neither guaranteed by a good start, nor by a good start together with some termination of the process. Narratives have to reach a conclusion, which is to say they have to exhibit a sense of destination, as if they were guided by a pre-established outcome. It has often been observed that one has to know where to look in order to ask the right questions. This is easily explained by regarding problems in the light of narratives. It is because of the overarching character of narration that it provides a vessel for teleological development.
We get an additional bonus by comparing categories from literature and methodology of science here. Nowadays stories are embattled exactly because of this feature of teleology and its suggestion of the omnipotent storyteller and the natural quality of what as a matter of fact are artificial constructs. Different genres of literary texts offer better opportunities to avantgarde writers. Philosophers wanting to be up to date likewise are weary of teleological and reflexive constructions explaining the march of progress, the advance of liberty or whatever. And with good reason because current problems should not be patched over by those popular meaning-creating devices. But here an illuminating difficulty arises. What do I mean by talking about ,,current problems''
According to what has been said there is no way to describe them except by using the narrative mode. (And it does seem to me that scientific procedures are more closely tied to it than the humanities because of their characteristic insistence on definite answers to their systematically organized inquiries.) So while the avantgarde in literature and philosophy legitimatly fights the narrative world-view I doubt that they can adress the questions I want to deal with. The avantgarde is itself a historical phenomenon and requires some story to appear as a plausible project. Now back to my topic, namely the function of formal procedures within a situation that is only accessible through some higher-level description. Teleology is one of its key-concepts, reflexivity is another one.
This additional concept is needed to grasp the nature of problem-solving. Finding something does not mean getting hold of anything you happen to like. Hitting on something unexpected is not finding an answer - even if it may stop a question. If a text, after a narrative start, at some point takes off into an altogether different direction, never returning to its initial plot, it is misdescribed as a narrative. Putting it positively: to find something is to accept it as the conclusion of a previous development, as an end to a given beginning it reflexivly relates to. Finding a solution also means responding to an expectation which cannot be read off from the bare minutiae of the construction. This condition therefore imposes a check on solutions. They have to respond to the need that was initially transformed into a problem. Arriving at the end of a story amounts to undergoing a reverse transformation, namely confronting a product the narrative has yielded with the expectations that gave rise to it and with those it gave rise to. This is the inescapable feed-back built into the concept of solution. Having assembled all these pieces we are in a position to employ them for clarification of (algorithmic) problem-solving.