Inductive vs. Deductive Reasoning

Date: 07/24/2001 at 17:16:23
From: Angie
Subject: Inductive vs. Deductive Reasoning

I'm sure this is a simple question, but can you help me with the 
differences between inductive and deductive reasoning?  To me, the 
explanations I have seen sound virtually the same.

Date: 07/24/2001 at 21:53:44
From: Doctor Peterson
Subject: Re: Inductive vs. Deductive Reasoning

Hi, Angie.

Inductive reasoning starts with specific examples or observations, and 
"deduces" (a confusing term) the apparent rules or patterns that lie 
behind them. It's what a scientist or detective uses; it's never 
completely certain, because the next observation might contradict the 
theory, or at least require us to modify it. But it does connect our 
conclusions to the real world around us.

Deductive reasoning starts with the rules, and determines what the 
consequences will be. This is what we do in most of math, defining the 
rules for a mathematical entity (such as the commutative property of 
addition), and using those to prove that other, more complicated, 
facts are true. Here, we can be absolutely sure of our conclusions - 
as long as we assume the axioms are true. We would have to use 
inductive reasoning to decide whether our assumptions make sense in 
the world we live in, where it isn't safe just to assume anything!

I went to the Dr. Math search page and entered the words 

  inductive deductive

to see what we have said before. Here's a longer explanation with 
examples:

   Logic: Definitions
   http://mathforum.org/library/drmath/view/55620.html   

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/