I have suggested a method of dealing with problems in an earlier post. In a short reprise there are three steps: define the problem, develop possible solutions to the defined problem, and then select your favorite possible operational solution.

The crux of the approach is really based upon the problem definition. In doing so there are several types of information and data that will have to be considered.

The concept of axioms was probably first encountered in Plane Geometry. An axiom is a

claim which could be seen to be true without any need for proof. A postulate is an axiom, and so is an assumption. A theorem is something that can be proven by using previous theorems (which have been proven) and axioms. Much of this is mathematical jargon but it still is highly useful in considering problems of all types.

In defining a problem you must first consider what you know about the issue. What is fact? What do you know, absolutely know without any possible error about the problem? If you encounter a probable fact, but open to possible question, then that is equivalent to a theorem. It must be proven (in the mathematical sense) and rigidly defined in the world of humans. Is a fact true all the time? Then it is an axiom, or a postulate, or even an assumption. If a fact is true some of the time then what are the constraints which must be specified? Under what conditions is it true? You must know when something is true in order to build a problem definition. For a given set of circumstances a problem will have one set of facts; for a slightly different set of circumstances a problem will have another set of facts which may, or may not, be closely related to the first set of facts.

A simple example will illustrate. You build a system that allows you to see your enemy coming over a hill. Your system can see for 10 miles with clarity and precision. The hill is only 4 miles away. Will your system always work? The answer is no. If you are using your eyes, that will be true if it is a bright sunny day. But what if you are in a deep, opaque fog? The system will not let you see your enemy. So, the system works perfectly except for fog.

The problem is figuring out a system that will allow you to see your enemy when they come over the hill. It is not well defined. You have to also say under what weather conditions, day or night, etc. Once you have defined the problem (which I glossed over deliberately for the sake of the example) then your postulates (axioms and assumptions) will be understood.

This is not easy. It is not done in a blink of an eye. Yet grappling with the problem definition is critical for success in all fields of human endeavor. And failure to define the problem you are addressing with clarity and precision will almost certainly have unforeseen and potentially very unpleasant consequences.