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What is a Problem Space?

Would anything change if sensible things were conceived of as 'across' space, rather than 'in' space?

Mel Bochner (2008: 74)

Five approaches relevant to the elaboration of concept of a problem space are introduced here. A first pairing juxtaposes the methodology proposed by John Dewey, an early twentieth-century advocate of pragmatism with the approach to the 'artificial sciences' developed by Herbert Simon, one of the mid-twentieth-century founders of cognitive science. The second pairing is feminist theorist Donna Haraway and French sinologist François Jullien. The fifth approach is that of the anthropologist Arjun Appadurai. These final three authors all write at the end of the twentieth and the beginning of the twenty-first century.

The five are not introduced here because they are the 'best' exponents of problem spaces (as far as I am aware only Simon uses the term). Why I bring them together, despite their very different vocabularies and concerns, is that, in their discussions of methodology, all of them focus on the process of making or composing problems; that is, for none of them are problems pre-given. They are all also concerned with the surrounds, environments or contexts - the spaces - in or with which problems emerge; indeed, that they do not assume space to be a container for problems is the primary reason for their selection. Instead they consider sensible things - situations transforming into problems - as emerging in movements 'across' space, as the artist Mel Bochner puts it. At various points in the presentation of their approaches their contribution to an understanding of a compositional methodology is highlighted.

Approach 1: Dewey

First, the pragmatist John Dewey, for whom the process of inquiry emerges in the transformation of an indeterminate situation into a problem understood as a unified whole:

Inquiry is the controlled or directed transformation of an indeterminate situation into one that is so determinate in its constituent distinctions and relations as to convert the elements of the original situation into a unified whole. (1938: 108)

As Matthew Brown (2012) observes, this is a radical conception of inquiry. Inquiry is not a process of thought that takes place in the mind of an inquirer for Dewey, but a process of transforming a situation. As the Introduction outlined, this emphasis on the transformation of a situation becoming a problem is at the heart of compositional methodology.

But what does Dewey mean by situation? As Brown notes, there is certainly scope for a range of interpretations (see also Savransky 2016) as is clear from this long extract from Dewey's Logic: Theory of Inquiry:

I begin the discussion by introducing and explaining the denotative force of the word situation. Its import may perhaps be most readily indicated by means of a preliminary negative statement. What is designated by the word "situation" is not a single object or event or set of objects and events. For we never experience nor form judgements about objects and events in isolation, but only in connection with a contextual whole. This latter is what is called a "situation." I have mentioned the extent in which modern philosophy had been concerned with the problem of existence as perceptually and conceptually determined. The confusions and fallacies that attend the discussion of this problem have a direct and close connection with the difference between an object and a situation. Psychology has paid much attention to the question of the process of perception, and has for its purpose described the perceived object in terms of the results of analysis of the process. I pass over the fact that, no matter how legitimate the virtual identification of process and product may be for the special purpose of psychological theory, the identification is thoroughly dubious as a generalized ground of philosophical discussion and theory. I do so in order to call attention to the fact that by the very nature of the case the psychological treatment takes a singular object or event for the subject-matter of its analysis. In actual experience, there is never any such isolated singular object or event; an object or event is always a special part, phase, or aspect, of an environing experienced world - a situation. The singular object stands out conspicuously because of its especially focal and crucial position at a given time in determination of some problem of use or enjoyment which the total complex environment presents. There is always a field in which observation of this or that object or event occurs. Observation of the latter is made for the sake of finding out what that field is with reference to some active adaptive response to be made in carrying forward a course of behavior. One has only to recur to animal perception, occurring by means of sense organs, to note that isolation of what is perceived from the course of life-behavior would be not only futile, but obstructive, in many cases fatally so. (1991: 72-3)

So, for Dewey, the very distinction between object or problem and situation is not to be assumed; instead an object or problem is always part of a situation, a background or surrounding. That situation is not a single object or event; it is a contextual whole. This explication helps, to some degree, but what might Dewey mean by 'contextual whole': the immediate surroundings of a phenomenon, or the whole world? The interpretation that is of most relevance for a compositional methodology is that proposed by Brown; that is, for the purposes of inquiry, a situation can be taken to mean those aspects of the surrounding or whole world that preserve the 'connection and continuity' present in the experienced world while providing limiting conditions for generalization' (Dewey 1991: 7-8 in Brown 2012: 269).

What I take from this is that the establishment of connection and continuity in the process of inquiry should be the aim of compositional methodology, and the basis for the making of claims of epistemological value. Or to put this another way: a process of inquiry informed by compositional methodology aims to transform an indeterminate situation into a determinate situation, preserving connection and continuity while also operating limits for generalization. In the terms introduced in the last chapter, this involves acting on or operating limits, with-in and out-with a problem, to enable generative circulation across a problem space.

An original situation, Dewey argues, is 'open' in the sense that its constituents do not 'hang together'; it has a 'unique doubtfulness1 which makes that situation to be just and only the situation it is' (1938: 105). Such ontological 'trouble' or perplexity is not a deficit for Dewey but a provocation. To begin with, 'The way in which a problem is conceived decides what specific suggestions are entertained and which are dismissed; what data are selected and which rejected; it is the criterion for relevancy and irrelevancy of hypotheses and conceptual structures' (1938: 110). Inquiry, then, proceeds in terms of relations of correspondence between the observation of facts and the suggested meanings or ideas that arise. One does not automatically precede the other; rather, they operate in conjunction with each other, their inter-relationship displaying a kind of syncopated rhythm as the path of inquiry emerges.

Ideas, Dewey says, are 'anticipated consequences (forecasts) of what will happen when certain operations are executed under and with respect to observed conditions' (1991: 109). Neither facts nor ideas are self-sufficient or complete in themselves:

Facts are evidential and are tests of an idea in so far as they are capable of being organized with one another. The organization can be achieved only as they interact with one another. When the problematic situation is such as to require extensive inquiries to effect its resolution, a series of interactions intervenes. Some observed facts point to an idea that stands for a possible solution. This idea evokes more observations. Some of the newly observed facts link up with those previously observed and are such as to rule out other observed things with respect to their evidential function. The new order of facts suggests a modified idea (or hypothesis) which occasions new observations whose result again determines a new order of facts, and so on until the existing order is both unified and complete. In the course of this serial process, the ideas that represent possible solutions are tested or "proved." (1938: 117)

Inquiry thus involves developing the meaning of ideas in correspondence with observed facts: this is what is involved in the transformation of a situation into a problem in relations of connection and continuity. For Dewey, this distributed and dynamic process or path of inquiry should continue until a determinate situation, 'an objectively unified existential situation' (1938: 104) is reached.

Approach 2: Simon

Like Dewey, Herbert Simon is of the view that a problem is not given but must be created. In doing so, he introduces the concept of problem space:

Every problem-solving effort must begin with creating a representation for the problem - a problem space in which the search for the solution can take place. (1996: 108)

He...