Dear Stefan,
Please let me be clear. I was NOT using predicate logic to formalise a definition of wicked problems. I stated my explicit view in the post to which you refer that there is no appropriate way to create a mathematical formalisation of wicked problems. Please read the post again [below]. I quote Rittel and Webber (1973) directly, stating that their definition is quite workable.
My use of predicate logic was ONLY a restatement of Terry's truncated restatement, the statement that "wicked problems are not solvable." This single, simple statement can be stated in predicate logic. Rittel and Webber's description of wicked problems cannot be stated in predicate logic, in calculus, or in any mathematical form.
As I stated earlier, I believe that Terry did not manage to mathematize Rittel and Webber. Neither did Stefanie.
I did not try to do so. The logical statement
--snip--
Let X be the set of wicked problems
Let Y be the set of solvable problems
No X is Y
--snip--
is only a restatement of Terry's proposition to show that that "wicked problems are not solvable." My purpose was to show that there was no need for a lengthy mathematical formalisation to restate those five words.
Again, let me be clear. I did not attempt to formalise Rittel and Webber. I believe that it is impossible to formalise Rittel and Webber.
Warm wishes,
Ken
Ken Friedman, PhD, DSc (hc), FDRS | University Distinguished Professor | Swinburne University of Technology | Melbourne, Australia | University email [log in to unmask]<mailto:[log in to unmask]> | Private email [log in to unmask]<mailto:[log in to unmask]> | Mobile +61 404 830 462 | Academia Page http://swinburne.academia.edu/KenFriedman
Guest Professor | College of Design and Innovation | Tongji University | Shanghai, China ||| Adjunct Professor | School of Creative Arts | James Cook University | Townsville, Australia
--
Reference
Rittel, Horst W J, and Melvin M. Webber. 1973. Policy Sciences, Vol. 4, (1973), 155-169.
--
Stefan Holmlid wrote:
--snip--
It is interesting to see what kinds of mathematics (apart from the logic of rhetoric) that are suggested to be used as formalizations of the "definition(s)" of wicked problems. All of them are approximations, from my point of view.
- Terry is suggesting using sets
- Stefanie is suggesting using calculus (or mathematical analysis)
- Ken uses predicate logic
Anyone who would like to contribute could dive into recurrence relations (or into differential equations maybe), dynamical systems analysis (esp probabilistics, chaos and bifurcations), lambda calculus, and probably others of a more numerical analysis nature.
Especially, care should be taken to understand whether deciding whether a problem is "wicked" or not is NP-complete or not. And whether the idea of "wicked problems" is a way of expressing that this specific class of problems are NP-hard
--snip--
Ken Friedman wrote:
--snip--
It's around 5 am in Melbourne. I have been lying awake, thinking through your post. I have come to the conclusion that whether or not the mathematics is correct, it is an overcomplicated series of functions even in terms of representing the proposition "wicked problems are not solvable."
To make sure that there is no confusion, I would like to restate the theory that I offered as a challenge to your claim that “all theories (any discipline) can be wholly and exactly represented as mathematical functions.”
While Rittel and Weber's concept of the wicked problem is a theory, it is a theory in a discipline where not all reasonable models or representations of issues in the discipline can be stated as mathematical functions. The precise problem is that these theories describe ambiguous or difficult situations in the world of human affairs in ways that make sense in human terms without being amenable to mathematical restatement or proof.
This theory is Rittel and Weber’s (1973: 161-166) theory of the wicked problem. Rittel and Weber describe a kind of problem known as a wicked problem with ten criteria:
“1) There is no definitive formulation of a wicked problem. 2) Wicked problems have no stopping rule. 3) Solutions to wicked problems are not true-or-false, but good-or-bad. 4) There is no immediate and no ultimate test of a solution to a wicked problem. 5) Every solution to a wicked problem is a 'one-shot operation'; because there is no opportunity to learn by trial-and-error, every attempt counts significantly. 6) Wicked problems do not have an enumerable (or an exhaustively describable) set of potential solutions, nor is there a well-described set of permissible operations that may be incorporated into the plan. 7) Every wicked problem is essentially unique. 8) Every wicked problem can be considered to be a symptom of another problem. 9) The existence of a discrepancy representing a wicked problem can be explained in numerous ways. The choice of explanation determines the nature of the problem’s resolution. 10) The planner has no right to be wrong.”
You restated part of this theory in a way that does not occur here anywhere. Rittel and Weber do not state that "wicked problems are not solvable." Instead, they assert that wicked problems have solutions of certain kinds, while acknowledging that every solution to any wicked problem is limited by specific factors.
I have been puzzling over the long series of mathematical propositions you offered as a translation of the statement "wicked problems are not solvable." It seems to be a kind of mathematical overkill.
The statement "wicked problems are not solvable" is another way of saying "no wicked problem is solvable." In the case of this specific and limited proposition, two terms suffice:
Let X be the set of wicked problems
Let Y be the set of solvable problems
No X is Y
Unless I am mistaken, this is a complete restatement of the proposition that "wicked problems are not solvable."
There is no need for the remaining series of mathematical propositions.
This is not a mathematical restatement of Rittel and Weber's description of wicked problems. It is a mathematical restatement of the proposition "wicked problems are not solvable."
The remaining mathematical propositions in your restatement seem to be unnecessary. It is not even clear that this treatment sheds light on the limited proposition "wicked problems are not solvable." Nothing in the statement "wicked problems are not solvable" defines the nature or attributes of "wicked problems" as the term is used here, nor does it state what makes this kind of problem unsolvable. Therefore, nothing in the mathematical treatment you propose sheds light on the undefined nature of entities in set Y. Once you define the nature of entities in set Y, you are adding qualities, attributes and terms that do not exist in the proposition, "wicked problems are not solvable." This statement simply says "no solvable problem is a wicked problem." The statement "wicked problems are not solvable" does not reveal any other aspect of the nature of wicked problems and it cannot be made to do so.
To define wicked problems more closely and to understand what makes them wicked requires a deeper and more precise description, as — for example — in Rittel and Weber's (1973) article.
This deeper description is not amenable to complete mathematical modelling. This, of course, is what makes engineering solutions to wicked problems difficult, and it explains why the tools of engineering so often fail to solve that class of problems defined by Rittel and Weber's ten terms.
I do not claim that people trained as engineers cannot solve wicked problems. I simply state that people who have been trained as engineers need tools other than mathematics and standard engineering solutions to do so.
--snip--
-----------------------------------------------------------------
PhD-Design mailing list <[log in to unmask]>
Discussion of PhD studies and related research in Design
Subscribe or Unsubscribe at https://www.jiscmail.ac.uk/phd-design
-----------------------------------------------------------------
|
