Deductive vs. Inductive reasoning

Deductive and inductive reasoning can in very loose, unspecific terms, be deemed opposite ways of coming to a conclusion; while deductive reasoning takes a general statement and makes specific observations, inductive reasoning uses specific instances to come to a generalization. However, there are many more pointed differences between these two systems which set them apart from each other.

Deductive reasoning can be based on knowledge that a person already has. For example, in order to solve a cryptogram, deductive reasoning is necessary. Since I know the English language as I try to solve a puzzle regarding the language, I know where all of the limitations and possibilities of the puzzle will be. Because I know how the alphabet works, I know that there are only so many places where double letters will be possible; if I need two identical letters to solve the puzzle, I know that there are only so many options and I could work around these limitations to deduce the other letters in a similar manner.


Deductive reasoning can also be expressed in if...then...but...therefore statements. 

For example, we might hypothesize that "The color of a mineral is determined by its crystal structure."

 And so we could test this hypothesis using deductive reasoning:
 If the color of a mineral is determined by its crystal structure; then all purple minerals should have the same crystal structure. But purple amethyst has a hexagonal structure and purple fluorite has an isometric structure (determined by observations). Therefore, the hypothesis is not supported or strengthened.
http://www.nakedscience.org/mrg/Deductive%20and%20Inductive%20Reasoning.htm 

 Deductive reasoning is the preferred type of reasoning when it comes to scientific study.


Inductive reasoning produces much less specific results. 

This is the kind of reasoning used if you have gradually built up an understanding of how something works. Rather than starting with laws and principles and making deductions, most people collect relevant experience and try to construct principles from it. http://www.nakedscience.org/mrg/Deductive%20and%20Inductive%20Reasoning.htm 

 If you were using inductive reasoning to make a connection between obesity and sugar intake, you might be able to make a chart which suggests that the more sugar a person consumes, the greater chance that they will be obese. You will be able to make a trend line demonstrating this relationship, but that is about it. It would be very unlikely that any particular instance plotted in the graph would actually fall on the trend line, so all you would have is a generalized explanation. Another problem with this type of reasoning is that by using this method, you cannot determine whether or not sugar would be the only cause of obesity. There could be several factors present in certain individual cases, but these would not be studied and would not be reflected in the trend line. Therefore, at best, you would only have a loose understanding of your topic.

The table below (Figure 7) summarises the most prevalent properties and differences between deductive and inductive reasoning which are important to keep in mind.

http://en.wikibooks.org/wiki/Cognitive_Psychology_and_Cognitive_Neuroscience/Reasoning_and_Decision_Making