Inductive and deductive reasoning are both approaches which can be used to evaluate information. They are used on a daily basis by people all over the world for tasks which range from perfecting a cookie recipe to developing new theories in the sciences. Each approach is very different, and it is important to be aware that both inductive and deductive reasoning can end up with false results, especially if the initial premise of the reasoning is false, in which case the results are said to be “unsound.”
Put simply, deductive reasoning involves moving from generalities to specifics by working through a series of reasoned statements. Inductive reasoning, on the other hand, takes a series of specific observations and tries to expand them into a more general theory.
A simplistic example of inductive reasoning might start with an observation such as “all of the cows I have ever seen are spotted.” One might, in turn, say that therefore all cows must be spotted. This is not actually the case, but given the available information, one might be forgiven for thinking it. The next step in this logic might involve attempting to find things which disprove the assertion that all cows are spotted, as might be done by asking other people if they have seen cows which are not spotted.
Inductive reasoning is commonly seen in the sciences when people want to make sense of a series of observation. Isaac Newton, for example, famously used inductive reasoning to develop a theory of gravity. Using observations, people can develop a theory to explain those observations, and seek out disproof of that theory. As can be seen in the cow example above, one of the major flaws with inductive reasoning is that it is dependent on observations, and when observations are incomplete, unsound results may be formulated.
In a famous example of inductive reasoning, some people in the ancient world believed that meat spontaneously gave rise to maggots. Their conclusion was based on the observation that if meat was left out, maggots would appear on it. Someone else decided to test this theory by seeking for disproof: Would it be possible to leave meat out and not have maggots appear? By sequestering meat in various containers next to fully exposed meat, the scientist realized that the maggots were, in fact, the result of eggs laid by flies.
With deductive reasoning, one takes a general theory or idea, tests it, and moves through a sequence of ideas to arrive at a specific conclusion. It is possible to arrive at an unsound result by using an initial premise which is false, as in this case: Every animal that eats mice is a cat. Rover eats mice. Therefore, Rover is a cat. The goal of deductive reasoning is to arrive at a valid chain of reasoning, in which each statement holds up to testing, but it is possible for deductive reasoning to be both valid and unsound.
The brain is so adept at both deductive and inductive reasoning that it often does it on a level which people are not fully aware of. Especially in the case of children, this type of reasoning is used to make sense of the world and the things observed in it. As can be seen, it is possible to use both approaches to explore a logical problem.
http://en.wikipedia.org/wiki/Logic
http://www.iep.utm.edu/ded-ind/