Basics of Logical Problem Solving

Many fields use logic in their efforts to solve problems; the one everyone in familiar with is mathematics, but logical problem solving also appears in history, political science, chemistry, physics, and many other fields. Logical problem solving is the basis of both deductive reasoning and critical thinking.

There are many pieces to logical thinking, including both the structure or process of logical problem solving, the limitations of logical problem solving, and the interaction of logical problem solving and creative thinking. However, none of these areas can be fully explored until the basics of logical thinking are understood. There are four basic logical tactics, and one attitude which helps in logical thinking.

Tactic 1: Define your terms

Many times the problem is stated using complex terms or phrases. Trigonometric identities are a classic example of this condition. However, complex ideas are constructed from simpler ideas being combined; this makes for a fairly common first tactic of defining the concepts involved. By replacing the complex with a combination of simpler concepts, we can understand what pieces are involved in the problem.

For example, let's look at history. In an effort to understand the causes of the Crusades, we could start defining the medieval society by listing the forces involved. There were religious forces, economic forces, social forces, and philosophical forces, all of which combined to make up the European medieval culture. By defining those forces, by listing what forces were present and what forces were not, we can get a better understanding of the situation, and with that understanding, move on to another logical tactic.

Tactic 2: Divide and Conquer

Serious problems have many pieces; usually too many pieces to understand all at once. So one logical tactic of problem solving is to divide the original problem into pieces, and then work on each piece separately. By dividing the original large problem into pieces, we have smaller pieces to work with, which are (hopefully) easier to understand. Then, when the pieces are understood, we can put them back together and address the original problem.

For an example of this tactic, consider the economic understanding of the American robber barons. When trying to discover why they were so effective, we can divide our research into several areas, and discuss their impact in each of these specific areas. We could discuss their economic impact, their political impact, and their cultural impact. By understanding each of these areas, we can understand a part of the phenomenon of the American robber barons. Then we can integrate the pieces back into a complete discussion of these people.

Tactic 3: Look for patterns

Very seldom is a subject matter totally unique. Usually there are patterns of concepts and interactions. By understanding these patterns, we can take lessons from one field and apply them to another field. This allows us to use logical problem solving in areas where it can be more effective, transferring the results into other areas.

An example of this type of reasoning is Douglas Hofstadler's book, "Godel, Escher, Back". The author finds similar patterns of concepts in mathematics, music and art to reason about artificial intelligence. The book is constantly switching from one field to another, working in the second field, and then bringing the results back to the first field, all the while investigating the ideas and principles of artificial intelligence. Patterns form the basis of how the author moves through the concepts involved.

Tactic 4: Drawing pictures

Pictures are images which can be used to demonstrate relationships which are difficult to describe. How can one adequately describe a rainbow verbally, yet how immediate is a picture of one? By creating pictures, both physically and imaginatively, an idea can be expressed in ways that go beyond words. Pictures allow the force and energy of emotion to be interwoven between the clarity and clearness of logic. Think of the Sistine Chapel, of Beethoven's Fifth Symphony, and of the poetry of Shakespeare words in "The Tempest". All of these constructs are a logical exploration of an idea, given power by the use of images and pictures. Pictures are more than just a way of communicating; they are a way of logical investigation.

In business, we create pictures called "process maps", which show the steps of a process and the interactions of the involved parties. These process maps can then be used to find bottlenecks, to understand where performance issues are critical, and where decisions have to be made. This allows businesses to perform more efficiently and effectively.

Attitude: Focus on the target

When problem solving, you must constantly keep your focus on the target, the desired outcome. It is very easy to become sidetracked, to get involved in areas which, while interesting, do not move towards the solution. By constantly reviewing the desired result and by monitoring your progress toward that result, you can usually see when you have strayed too far from the path of solution.

A great help here is to have a mentor or accountability partner. This is someone who is not part of the problem solving effort but who has a good enough grasp of the situation to evaluate your progress. It is very easy to lose your way in the details; by having such an outsider monitor your progress, you can pull yourself out of the morass of details and back to the high road of solution.

Conclusion

Logical thought is one technique available in problem solving, and a very powerful one. If you work at logical problem solving, honing your skills and efforts, it can provide excellent results.