Foolish Logic

by Alexander Bastidas Fry

Logics When we face difficult questions vague answers can offer a feeling of clarity that binary answers cannot. The laws of nature and the foibles of humans do not always allow strict classification into true and false. Even when such a dichotomy exists how do we find the absolute truth? And what is more, how do we know the right question? Everything and everyone seems to have an answer and a question. During moments of introspection, the full moon may even ask you a question, or offer an answer with clarity. The moon is an object that is utterly real and tangible, but it is never quite present or reachable. It alludes to a bright idea that has no consequence. Take this old story,

A monk sat in the forest with three students. He took out his fan and placed it in front of him, saying, “Without calling it a fan, tell me what this is.”

The first said, “You could not call it a slop-bucket.” The master poked him with his stick.

The second and third students were actually rocks that the master had mistaken for students, because it was getting very dark. Suddenly, the master and his pupil felt afraid and alone.

In the distance a wolf howled.

The Zen tradition of paradoxical or even seemingly nonsensical stories like this, a koan, is to provoke doubt in understanding. Or to provoke true insight. Either way we would be fools to not take wisdom offered when there are wolves in the distance, sharks circling, or clouds gathering. Old Buddhist, Zen, and Sufi stories are searching for wisdom or answers to threats hidden in that shadows. But often the stories show all the search is for naught, there is nothing in the shadows. Indeed, many of the reoccurring themes and animals in those stories are not situations we encounter today. In the city there are troubled people on the corner and parking tickets. As I look out the window I see someone getting written a parking ticket. I think that a sort of modern koan is that parking signs that are always written in the negatory; statements which do not state what is permitted, only things which are un-permitted. The modern world casts new-old spells on people. What wisdom do we need in the modern world?

To begin we need a premise on which to weigh the universe. Logic is a rather universal phenomenon. Pity that it is so common that it has become so cheap. An examination of our basic premises is necessary. Western logic traditions, scientists, and politicians, do not tolerate contradictions well. They demand that everything must be either true or false. This true and false dichotomy is quite useful in stating whether two numbers are equal, whether the experiment is reproducible, or whether the verdict is guilty or innocent. However, there are other kinds of answers and questions. Other forms of logic allow that some statements are true, false, true and false, or neither true or false. There may even be the ineffable questions and answers.

If two individuals share the same premises and share the same sharp logic they should not find contradictions in their conclusions. Yet each of us has contradictions inside us already. The predicate of the human condition itself presents contradictions. And the consequences of this are real.

Take for example the political arena. The tragedy of politics is no farce. The fate of billions of humans relies upon the hubris of leaders. The worst leaders are the leaders that eschew compromise, tyrants. The fundamental premise that you should never compromise is a nearly winning game when played against someone whose fundamental premise is that they should always compromise. Compromise with the uncompromising is a losing game. Separate from the workings of our abstract system that allows thought (symbols, alphabets, grammars, axioms, inference rules) there are meta-rules that society and groups have imposed.

The examination of how modern political structures operates shows us that our binary logic assumptions about the world have real world consequences. If we operate under the assumption that two sides cannot compromise, but that one side must win this is like assuming reality is an exclusive disjunction logical operator (represented graphically in the upper left of the figure shown). That is case A or case B must occur, but not A and B together; even if A and B are equal a compromise is un-allowed. This is rather what voting in a two party system is like even when both parties are pretty much the same.

Another situation we could consider is operating under the assumption that two sides must compromise or nothing. This is like some dystopian law where if a compromise is not met then the whole thing is off. It is like either we both share equally, or not at all. This is the logical biconditional (represented graphically in the upper right of the figure shown). This means it is A if and only if B; you can take A and B together equal or not at all.

There is good reason to use such unambiguous systems when setting laws. Yet, adherence to particular logical ideologies can be devastating to discourse. In particular, the true or false dichotomy together with a never compromise worldview is dangerous. It doesn't reflect the natural universe and it doesn't reflect the internal vagueness of the human condition. For ages philosophers have advocated for open worldviews that allow compromise.

We should be careful here to differentiate between logic systems and ideological worldviews. Logic systems define symbols, alphabets, grammars, axioms, and inference rules whereas ideologies are the premises that we take as fundamental then apply our logic systems to. They are different concepts, but ultimately certain premises can actually restrict what logic systems are acceptable. Presumptive notions of how logic works affects our perception of the questions themselves; the Buddhist, Zen, and Sufi stories are illuminating the very presumptions we make about logic and the questions we can ask.

The effort to assign truths to all situations in human or even the most formal logic systems is eventually doomed. With enough facts in hand you can conclude anything, but some of those conclusions will be false. On the other hand with a smaller set of facts and premises you will make less conclusions, but you will probably not make any erroneous conclusions. A sound logic would only allow true statements (but not all true statements) to be found, and a complete logic would allow all true statements (but also some false statements) to be found. There are many deep arguments from modern logic, and old riddles, that demonstrate that we cannot have both simultaneously. Traditionally we sacrifice completeness in order to preserve consistency. Humans value consistency because it allows us to make predictions about the world. A contradiction in a formal system leads to ex falso quodilbet; an explosion of possibilities that renders the predictive powers of a system adrift.

A lack of consistency in the right context is the kind of foolish wisdom that allows the nuances of reality to be fully probed. We see examples of this in the interpretation of quantum mechanics, in the exploration of the human condition, or even in the words of a good politician. To be able to defy the premise on which you stand and to conclude contradictory statements is an adventure in knowledge, but it is an adventure for fools, wise fools.