This article was last modified on May 9, 2005.


On Puzzles Without Solutions

Do puzzles require solutions? That is, by definition, must a puzzle have a solution in order to be properly identified as a puzzle? I will explore the technical as well as general definition of puzzles, go over some supplementary issues, and see what sense can be made of all this. My goal? Nothing more than an exercise in the English language, with little or no practical insight to speak of. So relax, open your mind, and come along for a linguistic journey.

A Technical Definition

Under the technical definition, a puzzle is defined as such partly because it has a solution. The cognitive science department at Princeton University (according to Google) identifies a puzzle as “a particularly baffling problem that is said to have a correct solution.”

Thomas Kuhn goes into much greater detail on this matter. He defines a puzzle as “that special category of problems that can serve to test ingenuity or skill in solution.” [Kuhn: 36] Here the emphasis seems more on the use of brain power to isolate what a puzzle is, though the solution aspect is mentioned and he elaborates on the next page. He states, “Though intrinsic value is no criterion for a puzzle, the assured existence of a solution is.” [Kuhn: 37] Adding to the Princeton definition, Kuhn notices a second criterion in the presence of rules. He says, “There must also be rules that limit both the nature of acceptable solutions and the steps by which they are to be obtained.” [Kuhn:38]

Using a crossword puzzle as an example, a rule does exist in what an acceptable solution is: there is only one correct answer per clue, you cannot simply fill in the squares with any word or letters or your choosing. A rule also exists as to how these answers must be obtained: you must either know the definition in your head or look up the answer in an outside source; referring to the back of the magazine for solutions violates the rules and you have failed to solve the puzzle correctly.

But is Kuhn the final word on what a puzzle is?

A Common Sense Definition

Common sense (that which we experience day to day without reflective thought) tells us that puzzles need not have solutions, or at least this is not what we identify them by. The Wikipedia (according to Google) identifies a puzzle as “a problem or enigma presented as entertainment”, without mention of a solution at all. This is not surprising, for when we think of a puzzle, we likely first think of “crossword puzzles” or “jigsaw puzzles” which we do not immediately think of as having solutions. While we know that such puzzles do have solutions, we identify them by visual stimuli (their shape, perhaps) rather than any other definable means.

It is worth noting that the common sense definition is in no way contradictory to the technical definition. While never mentioning the need for a solution, their is at no time a mention that puzzles may exist without solutions. If all puzzles require solutions, they would still be “problems or enigmas” for us. The common sense definition is merely less precise, as we would expect from it. A dog, for example, does not cease to be the technical “quadriped mammal of the canine variety” simply because common sense prefers to say “a four-legged hairy animal often used as a pet.”

One might take exception to the use of the word “entertainment” in the definition. And this is where common sense falls short. While our thoughts turn immediately to crossword and jigsaw puzzles (entertainment), common sense ignores the otherwise abstract uses of various terms. A police detective or a scientist would not mind calling their investigations puzzles or their work puzzling, but they might take some offence at the idea of their work being entertainment.

Aside: Medicine Analogous to Philosophy

Medicine is one field of puzzles that probably would not prefer to think of what they do as entertainment. Discerning new ways to perform a surgery is hardly light-hearted or humorous.

Wittgenstein noticed the similarity between philosophy and medicine. He said, “The philosopher treats a question; like an illness.” [Schulte: 22] If Ayer (see below) is correct in stated that philosophy is puzzle solving, than surely we can surmise that medicine is puzzle solving, too. (Some might recall the video game “Dr. Mario” which very literally combined medicine with puzzle solving.) So we ask: if medicine is puzzle solving, are these medical puzzles entertainment? And do they necessarily have solutions?

Theoretical Puzzles Without Solutions

In theory, could we not have a jigsaw puzzle where the pieces did not fit together? Or a crossword puzzle where the words simply didn’t fit where they were supposed to be written? If so, is this still a puzzle? One would think so, because what would you call an impossible crossword puzzle if not a crossword puzzle? So we are left to decide whether to come up with a new name for such entities or to conclude that puzzles, by definition, need not require solutions.

Another theoretical problem is how does one determine whether a puzzle is a puzzle until after the completion of it? If all puzzles require solutions, we could not rightfully know if something we called a puzzle was what we called it until after the work was done. We could only say something “was a puzzle”, never that it “is a puzzle”. We often assume we know the answer. Probability shows us that by looking at a jigsaw puzzle or a crossword puzzle we can assume their is a solution, since this is what we have come to expect. But what of the more abstract uses?

A crime can be a puzzle, because we know from the beginning there is a criminal to be caught and whether we find him or not, a solution exists somewhere. But in medical science, this might not always be the case. Is cancer a puzzle? Perhaps no cure for cancer shall ever exist in this or on any possible world. Can we call cancer a puzzle if a solution exists at some infinite (unreachable) point in the future?

Puzzle Etymology

In my piece “Who or What is a Philosopher” I made the argument that a philosopher is someone who has become a master of words. I implied that inventing new definitions for old words could be considered philosophy, since as we are told it is better for us to be the master of words than for the words to be the master of us. However, in order for words and their definitions to have any meaning or power, they must be accepted by other people – else the entire purpose (communication) falls to pieces.

With the importance of a set definition in mind, we turn to etymology to find what the tradition meaning of puzzle is. Coincidentally, the etymology is completely puzzling.

Both Google and my collegiate dictionary offer the simple explanation of “origin unknown”, while adding the first use of the word “puzzle” occurred in 1602. But this simply is not good enough. Looking up “muzzle” (which has notably the same sounds) I find the word to be related to Middle French and ultimately Latin. On the hunch that puzzle followed a similar route, I checked for a cognate in the French language and was rewarded.

We find in Medieval French a word, “aposer” which means “to perplex.” From this we have the modern word “pusle” which means “to bewilder” or “to confound” (essentially the same thing). At the time of this first draft I have misplaced my Latin dictionary, though one supposes that the Medieval French could be traced directly to a Latin equivalent.

Why the dictionary or Google were not able to make such an obvious connection is unknown. Regardless, the word clearly stems from the verb rather than the noun form of “puzzle” which refers more to the feeling and less to the object causing this feeling. Which does us little good (assuming we can be puzzled by both solutionless and solvable puzzles).

Puzzles and Problems: Classes

As a side note, we should mention classes as used in definitions. A class is a set of objects. For example, the definition includes the phrase “a puzzle is a problem” which sorts puzzles into the class of problems. Why is this important?

Knowing that puzzles are problems sorts puzzles into a category. The definition tells us puzzles are entertaining or have a solution (depending on which one we use). But they also direct us to them being “problems” which means puzzles must also have all the qualities of a problem.

Conversely, since a puzzle is in the class of problems, we know that a problem is not in a class of puzzles. All puzzles must be problems, but not all problems are inherently puzzles. Some problems may (and probably do) exist that are not puzzles at all. So the key to defining a puzzle is to see what makes it different from all the problems which are not puzzles. Is the deciding factor a solution or entertainment?

You may also ask why there is a need to differentiate between puzzles and problems, as they are quite obviously different when we think about them. But perhaps not. Even such great minds as A. J. Ayer have confused the issue. At first, Ayer correctly identifies philosophy as the business of solving puzzles (because, after all, why attempt to find answers to something which has no answer). [Ayer: 26] But later, he seems to think puzzles and problems are interchangeable, when he asserts that “all genuine problems are at least theoretically capable of being solved.” [Ayer: 50] Can we say that? By what theory can all problems (not puzzles) be solved? Would this not make the gravity of a problem less significant to maintain the belief it would be solved inevitably? Though perhaps this is straying too far off the track.

Can Puzzles be Solutionless?

Do we accept the definition of puzzles as things which are entertaining or things with solutions (or some third option)? If one definition must be settled on, the definition offered by Kuhn must be the one we agree to.

Entertainment is no way to decide whether or not something is a puzzle. While many puzzles offer entertainment value, there is no reason to believe this is any guarantee. Many puzzles, such as those offered in school, may have no entertainment value whatsoever in the eyes of the students. This definition is entirely subjective.

However, we can agree that all puzzles require solutions. The idea of puzzles without solutions as presented above is not good enough. Simply because something appears to be one thing does not mean it cannot be another after closer examination. Keep in mind the ugly duckling who was in reality a swan. A crossword puzzle which ultimately has no solution was not a real crossword puzzle at all – it was false and becomes either a trick or a piece of art, not a puzzle. While there is every reason to intend for something to be what we think it is, as humans we may not always be correct in our first impressions.

Conclusion? A puzzle with no solution is no puzzle at all.

Sources

Ayer, Alfred Jules. Language, Truth and Logic. Dover Publications, 1952.

Kuhn, Thomas S. The Structure of Scientific Revolutions. University of Chicago Press, 1996.

Schulte, Joachim. Wittgenstein. State University of New York Press, 1992.

“Web Definitions for Puzzle”, Google.com (definitions are obtained from Google by typing “define x”, where “x” in this case is “puzzle”)

Also try another article under Philosophical
or another one of the writings of Gavin.

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