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.