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### Inductive vs. Deductive Reasoning

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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.
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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/
```
Associated Topics:
High School Logic

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