Solving all Problems. Impossible? Yes.

 

Can We Ever Solve Every Problem?

G Donald Allen

Introduction. The fundamental problem of this section is to consider reasons why we have not yet reached the point in human evolution where we can solve all of our problems. This seems to have a popular origin in the Sherlock Holmes film, “Dressed to Kill[1],” where Dr. Watson, expresses the notion, “There is not a problem the mind can set that the mind cannot solve.” In the next section, we show quite the opposite. Some of the greatest of unsolvable problems are related to brain capacity, evolution, conceptuality, prediction, scale, vagueness, complexity, and more. These present roadblocks to problem-solving, and form the background for many almost unsolvable problems. There are multiple reasons, by no means the smallest class of them being the so-called impossible problems to be considered in another chapter. As well, we need to discuss further methodologies for solutions to come in the next chapter. Here are a few examples, presented as yet another list.

The Problems with Problems. Among the many problems having limited are no solutions are death and taxes. Include also family problems, child problems, work problems, mental problems, financial problems, illness, and personal problems. These are mostly forever problems. No matter how much wealth or poverty, how social or personal the community, these strike everyone. Some escape with a light dose, but nobody is immune. In this chapter we look   Here we look at a few examples of insoluble problems not only of our time but of all time. For brevity, they are presented as yet another list, a short list, though, of only 15 types. Exclusions are the so-called trolley problems and variants, noted for posing moral conflicts, and the newest problem of all, AI. Later.  

1.      Many problems have multiple solutions, depending on the mental tools you use, such as belief, deduction, faith, abduction, intuition, emotions, and several more. Between people, tribes, cities, and nations, these tools have differentiated possible problem solutions more than any other. We frequently see alternative solutions offered by secular and nonsecular stakeholders. Other times business and labor interests suggest the opposite view, or sometimes, with zoning vs free-zoning constituents. Such problems do get solved, usually with a contrary resolution.  Between nations, we always see a bifurcation between those wanting war and those preferring peace.

2.  More generally, these problems and proposed solutions have conflicting, or at least competing values, for example, profit vs working conditions,  personal vs societal, small vs big business, child vs parent, plaintive vs defendant, and so on. Again, solutions can be imposed but not to the satisfaction of all. Most probably, this is why we humans often have leaders or otherwise designated authorities.  The best way to determine authority is certainly a long-unsolved problem, nor may it ever be. Thus, we have unsolvable problems with no fully acceptable solution on how to solve them. On the other hand, the law is the most perfect of imperfect human conflicting value systems ever devised. With a hierarchy of courts, a standard for evidence, a procedure for presentations, a jury of peers, and finally with an ultimate supreme authority[2], all cases are decided – though never to the satisfaction of all players.

3.  Many problems have no clear solutions, such as “Does God exist?” Or, “What is infinity?” One is existential and the other is conceptual. As well, these problems and consequent solutions depend on the mental tools used. These are impossible problems, of course, and further discussion of them will come later.

4.  Many problems have vague predicates, making them insoluble. For example, “All swans are beautiful.” Alternatively, consider the Heap Paradox[3], wherein we ask when adding grains of sand to a pile, it transitions to a heap. (Scale and vagueness.) At first blush, you may say, we could suggest purging vagueness from the language.  This has proved to be extremely difficult[4]^,[5], leading to a stilted language.

5.  Many problems seem to transcend our mental capacity. For example, “What is the nature of time?[6]” (Conceptual.) Or, when will humans be able to see in the ultraviolet (UV) spectrum? (Evolutionary.) The human brain’s capacity is usually underplayed in the literature for many reasons, among them being we can’t conceive of a vastly intelligent brain, nor can we conceive of what problems an advanced brain would find solvable. Nor can we predict in what way(s) the human may evolve.

6.  Almost all prediction problems, depending on the precision required, are impossible or unsolvable owing to systemic chaotic[7]^,[8] behavior, instability, or insufficient knowledge of initial conditions. For example, what is the temperature in New York City at noon one hundred years from now, much less three years from now? Similarly, we cannot know the past in such detail as in the question, “What did Julius Caesar have for breakfast on the Ides of March?” Many answers to questions of evolution are based on abduction, best guesses, with supporting evidence only.

7.  Many problems have billions or trillions of variables, making them impossible to model. We include here all problems of complexity. Computers and artificial intelligence (AI) may solve these problems far sooner. This leads to the number of factors anyone or a group can grapple with. Most of us can handle at best less than a dozen distinct major factors in our reckoning about a problem. More than that confuse problem understanding, and therefore results in confused solutions.

8.  Many problems are wicked[9], meaning they have no complete clarity as to what to solve for, hundreds of factors, where to begin, and how to proceed. In addition, such problems don’t have solutions per se, rather offering good or bad, or fast or slow, for example. All these problems are complex, so complex they could be termed hyper-complex.

9.  Many problems have undecidable solutions. That is, there are true propositions that can never be proved. See, Gödel's undecidability theorem established less than a century ago. Before that, it was hoped that all problems, math problems at least, had a solution. Wicked problems are in a human sense undecidable, given that no clean, unique solution is ever given. The Brooklyn Bridge[10] is a classic example. It was so overdesigned that factors such as shoddy materials, graft, foundational issues, and others still gave us a bridge with lasting durability.

10.  People everywhere asked long ago about when will there be a cure for rabies. Now we know. The solution to this problem was found only by developing new knowledge, in this case, based on a new germ theory of disease. But it does highlight the importance of an undiscovered country of new knowledge. In fact, science has developed in this way for all of time, with new knowledge saving the day and solving an unsolvable problem. We expect new knowledge will always be an important facet in extracting solutions from the bag of problems facing humanity. So to suggest we could solve all problems would imply we have all knowledge. This leads to more problems, as revealed in #12 just below.

11.  If you say some of these are uninteresting, then you can ask for the most uninteresting problem. Once named, it becomes interesting because of this. Thus, the problem “What problem is most uninteresting?” has no solution. This problem was adapted from mathematics to help make it appear less technical. Yet it applies in real life. For example, you could ask for the least important economic factor in the economy. Once given, it would be studied intensely to the point where it becomes interesting and why. Economists wrestle with the importance of economic factors daily. In general, asking about absolutes among vague or ambiguous variables is bound to result in conflicts. Currently, about fifty distinct theories of economics are viable.

12.  Similarly, you could ask the problem of listing all problems. But once achieved, you can generate a new problem by asking what any subcollection of problems have in common. Thus, you create a new problem, unless you assume this is in the full list. This means the set of all problems contains itself, and this creates (devilish) logical impossibilities. Check out the “Barber’s Paradox[11].” They are so devilish that even the mathematicians have literally outlawed them – except in a special “twilight zone” of philosopher-logicians. Few visit there.

13.  Similarly, you could ask to order all problems by difficulty. This implies you have a method to determine difficulty, a vague concept at best. Thus, the criteria for the word are variable and unusable. Technically, this is related to the notion of order, notoriously tricky even in mathematics.

14.  Many problems are created by language. But removing this difficulty invokes the difficulty of determining a new language, and this is fraught with unsolved logical difficulties. See the work of Alfred Tarski[12].

15.   Finally, we must face the truth[13]. Specifically, we need to define just what the truth is. After all, in most parlance, a solution is supposed to be the truth. Alas, we don’t know, at least to a consensus, what truth is though philosophers, clerics, scientists, psychologists, logicians, and just about everyone else have worked on this problem for millennia. For instance, anyone could walk into the backrooms of the monastery or physics lab, and hear completely different discussions on the origin of the universe.

Conclusions. The problems of problems, while not new, consumes many of us, now in an age with seemingly an infinity of problems, and big ones at that. Political wars, Climate wars, Trade wars, and even Kinetic wars rage around the globe. As well, living almost everywhere is more and more complex, while education is more and more failing. Institutions, so long the bastions of stability, are falling into ruin. Infrastructure is decaying before our eyes. The future of inexpensive energy is in doubt.  It is no wonder we discuss the solutions to problems in generality as we find them around every corner of our lives. The positive answer that yes we can solve all problems eventually cannot be confirmed. Indeed, many of the problems we face today are ever more complex, wicked, and just plain unsolvable.

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[1] Dressed to Kill, 1946, starring Basil Rathbone.

[2] Many institutions have tried to mimic the legal process with massive Policy and Procedure Manuals, wherein as many cases as are known contain appropriate remedies and resolutions. These, something like  print versions of chatGPT, are a poor substitutes for judgement and wisdom, i.e. poor solutions.

[3] Barker, C. (2009). "Vagueness". In Allan, Keith (ed.). Concise Encyclopedia of Semantics. Elsevier. p. 1037.

[4] Mahtani, Anna. Vagueness, 2018, doi:10.4324/9780415249126-X040-2. Routledge Encyclopedia of Philosophy, Taylor and Francis, https://www.rep.routledge.com/articles/thematic/vagueness/v-2.

[5] Williamson, Timothy (1994). Vagueness. London and New York: Routledge.

[6] Rovelli, Carlo, (2018). The Order of Time, Nature 556, 304-305. Rovelli puts forward the idea of ‘physics without time,’ that time is subjective, that forward in time is a consequence of increasting entropy.

[7] Gulick, Denny, Encounters with Chaos, McGraw-Hill, 1992.

[8] Gleick, James, Chaos : Making a New Science, Viking, 1987.

[9] Churchman, C. West (1967). "Wicked Problems". Management Science. 14 (4): B-141–B-146.

[10] McCullough, David (1983). "THE GREAT BRIDGE AND THE AMERICAN IMAGINATION". The New York Times. Retrieved 29 August 2018.

[11] The Philosophy of Logical Atomism, reprinted in The Collected Papers of Bertrand Russell, 1914-19, Vol 8., p. 228

[12] Alfred Tarski, 1935. "The Concept of Truth in Formalized Languages". Logic, Semantics, Metamathematics, Indianapolis: Hackett 1983, 2nd edition, 152–278.

[13] Alexis G. Burgess and John P. Burgess (2014), Truth, Princeton.