This article is from the Atheism FAQ, by mathew firstname.lastname@example.org with numerous contributions by others.
The fallacy of accident / Sweeping generalization / Dicto simpliciter
A sweeping generalization occurs when a general rule is applied to a
particular situation, but the features of that particular situation
mean the rule is inapplicable. It's the error made when you go from
the general to the specific. For example:
"Christians generally dislike atheists. You are a Christian, so you
must dislike atheists."
This fallacy is often committed by people who try to decide moral and
legal questions by mechanically applying general rules.
Converse accident / Hasty generalization
This fallacy is the reverse of the Fallacy of Accident. It occurs when
you form a general rule by examining only a few specific cases which
aren't representative of all possible cases. For example:
"Jim Bakker was an insincere Christian. Therefore all Christians
Non causa pro causa
The fallacy of Non Causa Pro Causa occurs when something is identified
as the cause of an event, but it has not actually been shown to be the
cause. For example:
"I took an aspirin and prayed to God, and my headache disappeared.
So God cured me of the headache."
This is known as a false cause fallacy.
Post hoc ergo propter hoc
The fallacy of Post Hoc Ergo Propter Hoc occurs when something is
assumed to be the cause of an event merely because it happened before
that event. For example:
"The Soviet Union collapsed after instituting state atheism.
Therefore we must avoid atheism for the same reasons."
This is another type of false cause fallacy.
Cum hoc ergo propter hoc
This fallacy is similar to post hoc ergo propter hoc. The fallacy is
to assert that because two events occur together, they must be
causally related. It's a fallacy because it ignores other factors that
may be the cause(s) of the events.
Petitio principii / Begging the question
This fallacy occurs when the premises are at least as questionable as
the conclusion reached. For example:
"Aliens are abducting innocent victims every week. The government
must know what is going on. Therefore the government is in league
with the aliens."
Circulus in demonstrando
This fallacy occurs if you assume as a premise the conclusion which
you wish to reach. Often, the proposition is rephrased so that the
fallacy appears to be a valid argument. For example:
"Homosexuals must not be allowed to hold government office. Hence
any government official who is revealed to be a homosexual will
lose his job. Therefore homosexuals will do anything to hide their
secret, and will be open to blackmail. Therefore homosexuals cannot
be allowed to hold government office."
Note that the argument is entirely circular; the premise is the same
as the conclusion. An argument like the above has actually been cited
as the reason for the British Secret Services' official ban on
homosexual employees. Another example is the classic:
"We know that God exists because the Bible tells us so. And we know
that the Bible is true because it is the word of God."
Circular arguments are surprisingly common, unfortunately. If you've
already reached a particular conclusion once, it's easy to
accidentally make it an assertion when explaining your reasoning to