Deductive vs Inductive Reasoning

Deductive reasoning is exemplified by formulating conclusions based on logic rooted in firm, true, fundamental facts (axioms).  For instance, a person sees a winged animal. The person concludes the animal can fly based on that evidence.  This conclusion has a high probability of being correct and is an exercise in deductive reasoning.

What is inductive reasoning?  Inductive reasoning takes observational evidence and reverse engineers the situation to find a likely cause.  Let us look at the winged animal example from a different angle.  Suppose the person sees the same animal high above in the sky, too high to see the animal's wings.  The observer now concludes, based on the evidence, that the animal must have wings.  Again, this conclusion is highly probable, but the person would only know absolutely if the animal landed or flew at a lower altitude.

So, what is the purpose for comparing and contrasting these two types of logical reasoning?  I have heard it suggested by opposing groups that these two approaches are mutually exclusive to such a degree that only one or the other is valid in certain situations.  It is here where my opinion differs.

The approaches are mutually exclusive for the most part (there is an exception)*, but deductive and inductive reasoning are necessarily complementary in most practical problem solving scenarios.  This is the origin of my dissent.  Let me give an example.

Imagine a mechanic that starts a new job in a factory.  Let us track his approaches to problem solving as he gains more and more experience.

In the beginning, the mechanic has little knowledge about the factory's machinery.  He relies primarily on the knowledge of those men or women with more experience to provide him with the solutions to the most common problems they have encountered. 

If the mechanic is an independent person, he will, before asking anyone, try to diagnose the problems with the machinery through inductive reasoning.  If something is getting hot, he will inductively construct reasons to explain the problem such as friction or faulty electrical equipment.

Suppose the overheating is a rare problem and his peers have no advice.  The man has no choice but to approach the problem by taking the machine apart and exploring the parts.  Here the mechanic learns fundamental information about the workings of the machinery, all while investigating the validity of his hypotheses concerning the overheating.

He uses the fundamental information about the parts of the machine, which parts move, which are static, etc. and employs deductive reasoning to narrow his search.  He soon finds some worn bearings, a part many mechanics would likely suspect.  He concludes the heat was caused by friction.

Awe! His inductive reasoning was correct.  In addition, however, his deductive reasoning was just as handy.  Both types of logical reasoning were equally important in his fixing the machine.

I would argue that the mechanic's tandem use of deductive and inductive reasoning is the most efficient method to solve problems.  That is to say, it is important to weigh probable inductive scenarios against a foundation of fundamental knowledge, and allow deductive reasoning, based on that knowledge, to converge with the likely scenarios.

In other words, the likeliness of any one inductive scenario can be limited with good fundamental knowledge.  For example, suppose the mechanic took apart the machinery and noticed that no electrical equipment was near the area where the overheating occurred.  This fundamental knowledge immediately reduced the probability of electrical overheating to zero.

In the real world, the number of inductive speculations that should be considered can and must be practically limited by eliminating improbable scenarios based on a foundation of fundamental knowledge.

So, the lesson to be learned here is that gaining fundamental knowledge is very important to efficient problem solving by sharpening one's ability to formulate probable inductive scenarios.  Always start with the fundamentals!



*Exception:  Using the winged animal example from above, the person sees the animal up close and notices the wings.  The person goes on to conclude that the animal has wings.  Although this seems like a silly example, it is the only type of situation where deductive and inductive reasoning are equivalent. Follow @DerrelWalters