There are no solutions to complex problems

This may sound like a rather bleak pronouncement and completely contrary to the way in which complex problems are presented and discussed by, amongst others, politicians, the media, and commentators – expert and otherwise. However, I believe we have a language problem that gets in the way of having informed discussions about complex problems and how we work to do something about them. I want to explain that whenever we hear a statement that articulates a claim to have a solution or fix to a complex problem the speaker is making a category mistake, in effect their claim is logically meaningless. To then discuss and debate such statements, especially by introducing quantitative measures of success such as targets, we compound the category mistake and waste effort – both time and resources – chasing after illusions. 

To support my argument, let’s start with considering the idea of problems that do have a solution. The simplest category is puzzles, and good examples range from crosswords and sudoku through to spatial puzzles like jigsaws and Rubik cubes. There is one solution that everyone can agree is correct, and while it is possible to not always find the solution (i.e., not complete the puzzle), or to only solve part of the puzzle, it is not possible to have an ambiguous solution. The answer is either right, wrong, or perhaps only partially right. Many maths problems fall into this ‘puzzle’ category too. Skills can be developed at solving such problems. We can set tests and examine the performance of the problem solver by not just checking for the right answer but also for them to ‘show working’. 

If we next look at the solution to a puzzle we can see that once we have produced it the problem ceases to exist. By ceases to exist I mean that the problem has a known solution and does not need to be found again. Of course, the solution can be kept secret or not communicated – that is, after all, the enduring property of puzzles as tests or enjoyment. The dictionary definition of solution just reaffirms this straightforward notion as a resolution or answer. In process terms, a process for solving or fixing a problem is a process that is designed to make the problem go away. The problem is solved or fixed and there is nothing else that needs to be done.

From this starting point of problems as puzzles with singular solutions it is not too difficult to extend the argument to problems that have multiple solutions but still nonetheless have the property that whichever solution is chosen to fix the problem, the problem remains fixed (or solved) and ceases to exist. Good examples here are algorithms or computer programs designed to address a specific problem. We could also re-cast the notion of a requirement or a constraint as a problem to be solved and accept that there will be multiple possible solutions that adequately satisfy the requirement/constraint. We might introduce some notion of efficiency – in use of resources and/or time – associated with each solution and therefore have some objective measure to choose between solutions. For example, there are many different algorithms for sorting a data set but for the same available computing resource, some algorithms would take less time to sort the data than others. We can think of this category of problems as well-defined.

By increasing the complexity of the problem, we start to run into difficulties in deciding whether we have a solution. We may be able to formulate the problem quite well in that we can write down a set of requirements and constraints, but solutions might be contested. For example, we may need to improve travel links between communities on either side of a river. There are many different ways of facilitating this ranging from a footbridge, road bridge, ferry, tunnel, rail bridge and so on. Problem formulation requires delving into what improve means and for whom, and deciding which solution to choose is a function of many considerations, not least budgets, timescales, impact on environment etc. After considering all these factors and embarking on a construction project following a well-defined problem formulation (as a specification or a project plan), we may still be in some doubt whether we have achieved a solution to the original problem.

The final class of problems defy both formulation and solution and have been variously labelled as wicked (following Rittel and Webber (1973, pp. 161-167)), or messy (following Ackoff, 1974, pp. 20-21)) or swampy (following Schön (1987, p. 3)). Using the definition of Rittel and Webber, so called wicked problems can be defined as follows (Yearworth, 2025, pp. 18-19):

1. There is no definitive formulation – formulating a wicked problem is the problem. It is not possible to approach a wicked problem with preconceived notions of how it might be addressed, the only way forward is to start a process of enquiry and develop ways forward from there. 
2. There are no stopping rules. The process of intervening is also the same as understanding the nature of the problem – the intervention is ‘good enough’ or the best that can be achieved within other limitations external to the process (e.g. time, budget, patience, etc.).
3. Interventions are not right or wrong, there are no formal decision rules for defining correctness, they can only be viewed as making things better or worse for certain interests. Judgments will depend on personal interests and values. 
4. There is no immediate or ultimate test for an intervention. Interventions will generate ‘waves of consequences over an extended – virtually an unbounded – period of time’. The consequences of an intervention are thus difficult to evaluate because the consequences will be continually changing. 
5. Interventions are ‘one-shot operations’, and experiments are difficult to conduct. Every intervention is consequential and effectively irreversible. Interventions are essentially unique in nature – we cannot intervene in the same problem context twice as our interventions change the problem context. 
6. There is no enumerable, exhaustively describable set of possible interventions. There are no criteria that enable us to judge whether we have found all of the interventions that are possible in a given problem context. It is a matter of realistic judgment about how expansive the process of enquiry should be.
7. Every wicked problem is essentially unique. ‘Essentially’ implies that aspects may be common, but to think in terms of categories or classes of wicked problems with common ‘solutions’ is misleading. 
8. Wicked problems can be considered symptoms of other problems, i.e., there is inherent systemicity in the world. ‘The level at which a problem is settled depends upon the self-confidence of the analyst and cannot be decided on logical grounds. There is nothing like a natural level of a wicked problem. Of course, the higher the level of a problem’s formulation, the broader and more general it becomes: and the more difficult it becomes to do something about it.’ 
9. Can be contested at the level of explanation; there is likely to be conflicting evidence or data. It is not possible to rigorously test hypotheses about interventions due to their unique circumstances.
10. Whereas scientific progress arises as a consequence of refuted hypotheses (in a sense, being wrong is good), in the area of policy and planning, decisions that have negative consequences are not tolerated (being wrong is not good).

In order to avoid the possibility of confusing the notion of solution with this type of complex problem I have introduced the use of intervention into this definition – the act of intervening in this type of problem context – and it is within this definition that the source of the category mistake can be found. We may intervene in these problem contexts but to say that we will solve or fix the problem is to logically contradict the definition. It would be perfectly reasonable to contest the definitions, but given the messiness of problem contexts that demand our attention I believe it is reasonable to assert that a category (or categories) of problem exist that are not puzzles or well defined/formulated (Also see Pidd (2009, p.44)). Our first action must be to structure the problem.

This category of problem is endemic and we must take heed of these properties. To blithely talk of solutions and fixes in the context of these types of complex problems is misleading. If this arises from a genuine misunderstanding about the nature of wicked/messy problems then perhaps it is understandable. However, journalists, politicians and expert commentators should be aware of these characteristics and to continue with using the language of solutions and fixes is to exhibit partiality or deliberate deceit. 

I write about this extensively in Section I of my book (Yearworth, 2025, pp. 1-43).

Ackoff, R. L. (1974). Redesigning the future: a systems approach to societal problems. Wiley-Interscience: New York; London

Pidd, M. (2009). Tools for thinking: modelling in management science (3rd ed.). John Wiley & Sons: Chichester.

Rittel, H., & Webber, M. (1973). Dilemmas in a general theory of planning. Policy Sciences, 4(2), 155–169. https://doi.org/10.1007/BF01405730

Schön, D. A. (1987). Educating the reflective practitioner. Jossey-Bass: San Francisco, CA

Yearworth, M. (2025). Problem Structuring: Methodology in Practice (1st ed.). John Wiley & Sons, Inc.: Hoboken. https://doi.org/10.1002/9781119744856