A "fallacy" is a mode of thought that is asserted (by calling it a "fallacy") to lead us easily into error, or to not usefully contribute to the project of distinguishing truth from falsehood. For example, Argumentum Ad Hitlerum is a 'fallacy' because while Hitler did a number of bad things, he also ate vegetables, so "Hitler did X" is not a reliable means of arguing that nobody should do X.

Related: Disagreement, Heuristics & Biases

Informal vs Formal Fallacy

An informal fallacy refers to a flawed argument, where the premises do not support the conclusion. It can, however, have a valid logical format. This type of fallacy is commonly divided in two main groups: material fallacies and verbal fallacies.

Material fallacies, concerned with the content of the argument, can be divivided following Aristotle's taxonomy from his work Organon. One such example is the famous Straw Man fallacy:

Person A has position X: We should focus our efforts on Friendly AI research.
Person B distorts position X to something close, but different, Y: So you think we should just give up on webdesign?!
Person B attacks position Y: That's stupid, websites are such a great way of spreading information!

Verbal fallacies, on the other hand, deal with the way the words are used. These include examples such as Equivocation - using words ambiguously or with double meanings - and Proof by Verbosity, where one overwhelms his listener with lots of material in an complicated way.

A formal fallacy, contrasting with informal fallacies, refers to a pattern of reasoning which is wrong due to a flaw in the logical structure of the argument. As such, this deductive fallacy does not imply any information about the premises or the conclusion - its their connection that's wrongly stated. Both can be correct and the argument can be wrong because the conclusion doesn't follow from the premises as it is said to.

False Fallacies & Awareness

Matters can be further complicated by arguing parties incorrectly claiming that an assertion is false due to a fallacy. For example, if one party was to declare “Albert Einstein has claimed that time and space are relative qualities of the Universe.”, another party might responded by saying that this is an ‘’’argument from authority’’’. However, Albert Einstein’s claims are based on detailed mathematical models that identify him as an expert in this field of inquiry, rather than a casual observer. We are thus facing a kind of meta-fallacy which is wrong by itself.

Recognizing fallacies in everyday arguments can be difficult due to complicated patterns of communication that mask the logical connections between statements. At the same time, informal fallacies can also take advantage of the emotional or psychological weaknesses of the listener. It is thus important to develop the ability to recognize them in arguments, so as to reduce the likelihood of being tricked or cheated. This ability becomes even more important when dealing with today's mass media, where the intention is to influence behavior and change beliefs, from political campaigns to simple local newspapers.

Further Reading & References

Aristotle's On Sophistical Refutations
Damer, T. Edward (2008). Attacking Faulty Reasoning: A Practical Guide to Fallacy-free Arguments (6 ed.). Cengage Learning. pp. 130. ISBN 978-0-495-09506-4.
John Woods (2004). The death of argument: fallacies in agent based reasoning. Springer. ISBN 978-1-4020-2663-8.
Logical Fallacies A peer-reviewed academic resource.
Infinite regression Wikipedia entry

See Also

Aumann's agreement theorem
Disagreement
Information cascade