Many people think that deductive and inductive reasoning are the same thing. It is assumed these words are synonymous. They are not. This lesson reveals the reality of these two types of reasoning.
Deductive and Inductive Reasoning
You have probably heard the words inductive and deductive reasoning many times before. Chances are you have even mixed the two up, or think that they mean the same thing. But, they are not the same at all. In fact, they are actually opposites!
You can think of inductive and deductive reasoning as a path from something you know to something you don't know. Each makes use of general knowledge and knowledge of a specific scenario - think of it like the difference between a large lake and an individual fish living in the lake. The beginning point and ending points are switched on each.
This lesson will introduce each type of reasoning through definitions, general examples and mathematical examples. Join me as we learn to reason.
Inductive Reasoning - Definition
Inductive reasoning starts with a specific scenario and makes conclusions about a general population. For our lake example, if you found a trout fish in a lake, you would assume that it is not the only fish in that lake. You may further conclude that all the fish in the lake are trout. You have induced from specific scenario information about the general population of the lake.
An interesting point with induction is that it allows for the conclusion to be false. It is simply a process of logical reasoning from a specific observation to a general theory of a population. The conclusion that all the fish in the lake are trout is very likely to be wrong; however, the process of induction was pure and logical. You could call it a valid guess.
Examples of Inductive Reasoning
A great example of inductive reasoning is the process a child goes through when introduced to something new. If a child has a dog at home, she knows that dogs have fur, four legs and a tail. If a child were to be introduced to a cat, that child may very well assume the cat is a dog. Why? Because the cat has fur, four legs and a tail. In the child's experience, this means dog. The child induces from her specific scenario something about a much larger population.
Another example: You know two men from England who love soccer. You meet another man who states he is from England. You are shocked to find out he does not like soccer! Why were you surprised? You had induced from the two specific scenarios something about the entire population of English males.
Not all inductions are wrong though; but because they are broader, many can lead to inaccurate conclusions. Often, in the real world, this is seen as 'jumping to conclusions.'
Mathematically speaking, inductive reasoning might take this form:
Step 1 - show that something is true for a specific item.
Step 2 - show that if it is true for one, then it must be true for the rest.
Often these involve complicated mathematical proofs (something that is beyond the scope of this lesson), but a simple example is the induction that the sum of two odd numbers is even.
- Start with a specific true statement: 1 is odd and 3 is odd, the sum of which is 4; an even number.
- Now show it is true for the rest: an odd number is an even number plus 1. Thus two odd numbers are really two even numbers plus 2.
- The sum of even numbers is always even.
Starting with a specific observation, we were able to make an induction about the entire population of odd numbers. Here's an easy way to remember the direction of induction. 'In-' is the prefix for 'increase,' which means to get bigger. Thus, induction means start small and get bigger.
Deductive Reasoning - Definition
As was mentioned before, deductive reasoning is the opposite of inductive reasoning. Here, we are starting with a statement about a population and drawing conclusions about a specific scenario. All sound deductions start with a true and valid statement about a population, thus conclude with a valid assumption about the specific scenario.
For our lake and fish example, If we are told that the lake is stocked with trout (a statement about the population of the lake), and then got a fish on the end of our line, we would deduce that the fish on our hook was a trout.
Deductive reasoning can be logical and result in a false statement only if the original generalization about the population was incorrect. If our fish ended up being a brim, we would know that it was not true that all fish in the pond were trout.
Deductive Reasoning Examples
An example of deductive reasoning: if you are aware that all sumo wrestlers are large men, and you were told that Todd is a sumo wrestler, you would expect Todd to be a large man. Another example: all mammals breathe air. Dolphins are mammals. Thus, dolphins must breathe air.
Mathematical deductions are the same: we take something we know to be true about all math and apply it to a specific scenario. Take 4 + x = 12. We know that as long as we do the same thing on both sides of the equal sign, the equation is still valid. Applying this theory about a population, we can deduce that x = 8. It is interesting to note that we use deductive reasoning in most aspects of typical mathematical solutions - using a formula acknowledged as valid for a population to deduce the solution to a specific set of numbers.
As an easy memory tool, remember that 'de-' is the prefix for 'decrease,' thus deductive reasoning is the one that starts with a larger population and is applied to a specific scenario.
In this lesson we learned that inductive reasoning takes information known about a specific scenario and applies it to a large population, while deductive reasoning takes information known about a population and applies it to a specific scenario. They are intriguingly similar processes that are exactly opposite in their procedural direction.
Most mathematical computations are achieved through deductive reasoning. The exception is that advanced proofs in math are solved through a series of inductive logic steps. I hope you've enjoyed this lesson. See you next time.
Once you are done with this lesson, you might be able to describe and compare inductive and deductive reasoning.