This article is from the Atheism FAQ, by mathew firstname.lastname@example.org with numerous contributions by others.
Note that I am not claiming that logic is the only way of conducting
discussion and debate. Whether logic is universally applicable is
itself an issue which is very much open to debate. This document only
explains how to use logic; you must decide whether logic is the right
tool for the job.
Note also that this document deals only with simple boolean logic.
Other sorts of mathematical logic, such as fuzzy logic, obey different
rules. When people talk about logical arguments, though, they usually
mean the type being described here.
One problem with boolean logic is that people don't have to be
consistent in their goals and desires. People use fuzzy logic and
non-logical reasoning to handle their conflicting goals; boolean logic
isn't good enough. For example:
"John wishes to speak to the person in charge. The person in charge
is Steve. Therefore John wishes to speak to Steve."
Logically, that's a totally valid argument. However, John may have a
conflicting goal of avoiding Steve, meaning that the answer obtained
by logical reasoning may be inapplicable to real life. Garlic tastes
good, strawberry ice cream tastes good, but strawberry garlic ice
cream is only logically a good idea.
Sometimes, principles of valid reasoning which were thought to be
universal have turned out to be false. For example, for a long time
the principles of Euclidean geometry were thought to be universal
However, keeping those caveats and limitations in mind, let's go on to
consider the basics of boolean logic.