Problemology: the Study of Problems and their Nature Lecture Notes from the 111th Diogenesis Lecture on 2022/6/5 • Read time 9min There is no formal study of problems and as it turns out, that's a problem. The first person who tried to formalize a rigorous systematic architecture for studying problems seems to be Por Charles François who was a Belgian cyberneticist and systems scientist that recently died in 2019. In his work Problemology: a Methodology for the Discovery and Management of Complex Problems he defines a problem as: What we do perceive as a “problem” - personally, or as members of a group - is some situation which we view as damaging, harmful (to us !, even if useful for other people), or could become so in one or another way, in some sense, at some time. This generally implies an evaluation in accordance to our personal expectations and criteria about “good” or “bad”... which is of course mostly subjective and not necessarily shared by all other participants in the situation. He also gives some detail on the distinction between a simple and complex problem but for this lecture I want to focus on the way in which he has defined problems generally. This paper doesn't give a formal definition of what a problem is, merely that it's something we (and 'we' is also not well-defined) view as damaging or harmful in 'some' sense at 'some' time, which is so incredibly vague and broad that it wouldn't pass it's own standards for determining whether or not this definition was problematic. A definition this broad gives indeterminable results. Accordingly, we need a way to evaluate our own criteria about “good”, “useful”, “bad”, “dangerous”, etc... that should as far as possible be free from our own prejudices, illusions (optimism versus pessimism, for example), irrational wishes or desires, personal interests, clans or political parties, ideologies, etc... Obviously, all these conditions are quite demanding... and most frequently ignored. He seems aware here that the definition tells us little about any kind of objective problem yet he also fails to give a real alternative. He says that of the degree to which problems are problems: Ignoring that one has a problem is probably the worst of all problems. This seems strange since his definition of generally sensed damaged or harm is most generally recognized by others as death, yet here he would think that ignoring that you could die is the real problem, not death itself. A weird place to arrive at for a cyberneticist. This seems self-defeating so I think it's fair to re-order his list of 'worst problems' but we can concern ourselves with that later. In '95 Paris Arnopoulos publishes Prolegomena to Problemology: a Definition of Social Problems in which he says about problems that: The first question which must be answered before going any further is: what is a problem? Obviously, to begin with, this is a matter of definition, and as such it is both easy and difficult to do. It is easy because definitions are arbitrary and a priori conceptual devices, so anything can be defined in any way. Yet, to facilitate communication, one must respect popular and traditional meanings of common sense, so we fit-in our definition to generally acceptable standards. This is already pretty vague and implies an interpretation where problems are somehow objects relative only to the one defining them. He settles on the definition that a problem is simply: a disturbing situation. This definition obviously seems too broad, but he gives a little more flesh to this definition saying he uses it because: it emphasizes the situational nature of the problems with which we are particularly concerned. By situation we mean a specific condition or state of affairs which draws attention to itself. Situations, therefore, are salient points upon which interest is focused and as such describe the essence of problems. In this sense, real problems of this world are disturbances in the various configurations of matter-energy within space-time. Since we are not interested here in symbolic or semantic problems, the above meaning will do very well to concentrate our study to empirical problems of human concern. We are, therefore, excluding from our purview mathematical questions, intellectual puzzles, or psychological malaises, although they are problems of sorts, instead focusing our attention to actual external events which disturb us. The problem with this fleshed-out version of his definition is that it is now too narrow, as it excludes many abstract problems that cause concern, distress, emotional, and sometimes physical harm. This is ironic given that by excluding abstract problems the author also ends up excluding some of the concrete problems he wishes to focus on. For example, the purely abstract and internal psychological problems that create school shooters are now outside of his ability to account for or describe in his definition of problems. Both definitions given so far are either too broad or too narrow. To reiterate: The first definition from François is almost purely subjective and cannot itself determine whether something is actually a problem - only that you might some time in the future decide it is without any rigorous criteria for how that determination is made. François' paper does later describe ways in which a system would internally determine problems and try to self-correct, but the way this happens is not a component of the definition of problems, meaning the definition is not formal. The second definition from Arnopoulos is seemingly unconcerned with the source of most problems (percieved or otherwise) being the internal misjudgments of humans and therefore cannot itself determine whether something is actually a problem - only that a physical harm might occur despite the vast majority of physical harm coming from pleasurable activities we consider to be the opposite of problems like sports or really any strenuous physical activity. Conviently, RogueGod mentioned here that this kind of physical harm is generally seen as a solution, namely the solution to the problem of weakness. If we were to combine the critiques of the two papers linked above with some Deleuze we could probably synthesize a formal study of problems such that it was never subjective as to whether or not something was actually a problem. In particular, Deleuze says a 'real' problem is a problem precisely because it has no solution. It's interesting to note here that Deleuze is the first person mentioned so far that has suggested any kind of relation between problems and solutions in his definition - the other definitions were devoid of any description of solutions. It seems then that if we want to formalize a study of problems we have to define problems in a way that doesn't leave all existent things open to being problems arbitrarily, doesn't exclude an obvious source of problems being from either the abstract or concrete domains, and also includes a well-understood relation to solutions. Some open questions for us: 1. Are problems real objects 'out there' in the world or are they purely abstractions in our minds? - Logical contradictions cannot physically exist, does this create an issue for describing problems in the physical world? 2. Is defining a problem itself a problem? - Do meta-problems like Turing's halting problem or Gödel's incompleteness theorem suggest the question of determining if something is a problem is itself an indeterminable question? 3. What then is the rigorous, systematic, formal definition of a problem? Sneedmor raised a question about what distinguishes 'hard' problems in philosophy and we talked about how it's weird that hard problems are defined but general problems are not. A hard problem is one in which a problem operates over some domain and can interact down into the domain but the domain cannot interact back up to the problem. For example, the hard problem of consciousness is a hard problem because a complete physical description of reality doesn't do anything to describe consciousness - you could give the exact same physical description in which there was no consciousness. Therefore consciousness is something that accompanies the physical world, or interacts down into the physical domain, but in which the physical domain does not directly interact back up. If we know how to define a hard problem, then we can define a 'soft' problem as one where the domain in which a problem operates can be directly interacted with by the domain. However, when asking if these are the only two kinds of problems it becomes apparent that not only do we not know, but it seems difficult to determine what the final number of enumerated kinds of problems would be. This is exactly analogous to mathematics where asking a mathematician how many kinds of numbers there are will probably illicit a response of, "The natural numbers, the real numbers, the irrational numbers, the imaginary numbers," and so on. But if you ask if that's all the kinds for sure and no more kinds will ever be added, they have no idea. If numbers were well-defined entities, then we would know what their scope or domain was that they operate over and it wouldn't be unclear as to how many kinds there were. As a personal try at a definition of a problem I arrived at: a barrier stopping a piece of information or material from being obtained. This is a superficially good definition since it doesn't include all existent objects like François's definition, it doesn't exclude obvious causal sources like Arnopoulos's definition, and unlike Deleuze's definition it's internally resolvable as to whether or not a problem will have a solution (removing the barrier or obtaining the information/material is the solution). This definition does not have the meta-problem of being indeterminable. If you ask this definiton of a problem whether or not it's own definition is a problem it returns a definite 'no' since you can obtain the information of the definition. An additional advancement of this definition is that it also describes problems as things that non-persons can have. For example, when a pneumatic door tries to close but a chair is in the way, this is a problem for the door, resolved by removing the obstruction. Another example of a problem under this definition would be when you want to know the answer to a math problem but are obstructed by unknown variables or something similar. It seems like we have obviated the issues with the prior definitions. However, this definition fails in some pretty obvious ways as well, namely that it would not be a problem to shoot someone in a way that doesn't hinder their ability to perform their tasks. For example, shooting someone in the bicep and immediately stopping the bleeding so that they won't die and will be able to think and talk normally doesn't block them from obtaining information or material they would normally interact with or work to attain. But you shot them. If ethical problems are excluded by our definition of problems, then 'problems' simply don't describe the thing we are trying to describe. So it's still not a good definition. The discussion effectively concluded here.