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# Logical fallacy

A logical fallacy is an error of argument; it is a mistake in the way that the propositions (in the argument) are inter-related. When there is a fallacy (i.e. mistake) in the argument, then the argument is said to be invalid. That is, the conclusion does not follow (logically) from the propositions (sentences) advanced to support it. This structural mistake is not the same as the truth or falsity of the statements being made; the conclusion may be true, but it is said to be invalid because it doesn't follow from the arguments (premises) presented.

Arguments intended to persuade may be convincing to many listeners despite containing such fallacies. The truth of the premises may even significantly increase the probability of the truth of the conclusion. But they are nonetheless flawed. Recognizing these fallacies is sometimes difficult.

Here is an example of a fallacious argument. James wants to argue that all killing is wrong, so James argues as follows:

1. If one should not do X, all X is wrong. (X can be any action.)
2. One should not kill.
3. Therefore, all killing is wrong.

James has committed the logical fallacy of begging the question. In the argument, James says that one should not kill and presents the statement with no qualifiers. But to prove that, he would have to prove that all killing is wrong — which is what he is trying to argue for. A supporter of the death penalty might think that some killing is fine, for example, as punishment for the worst murderers. (In fact, some might maintain that in some cases one actually should kill: it is our grim duty, an unfortunate yet necessary part of justice.) The argument presupposes its conclusion: one of the premises assumes that the conclusion is true. An argument that begs the question should not convince anyone.

Here is another example of a logical fallacy. Suppose Barbara argues like this:

1. Andre is a good tennis player.
2. Therefore, Andre is good — a morally good person.

Here the problem is that the word "good" has different meanings, which is to say that it is an ambiguous word. In the premise, Barbara says that Andre is good at some particular activity, in this case tennis. In the conclusion, she says that Andre is a morally good person. Those are clearly two different senses of the word "good." The premise might be true and the conclusion can still be false: Andre might be the best tennis player in the world but a rotten person morally speaking. Appropriately, since it plays on an ambiguity, this sort of fallacy is called the fallacy of equivocation.

Some fallacies are used freely in the media and politics. For example, when one politician says to another, "You don't have moral authority to say X", he is making the argumentum ad hominem or personal attack fallacy — not addressing the argument but attacking the person who made it.

Arguably, the politician is not even attempting to make an argument, but is instead offering a moral rebuke. Identifying logical fallacies as such can be difficult.

In the opposite direction is the fallacy of argument from authority. A classic example of this is the Ipse dixit — "He himself said it" — used through the Middle Ages in reference to Aristotle. A modern use is "celebrity spokepersons" in advertisements: that product is good because your favorite celebrity endorses it.

While an appeal to authority is always a logical fallacy, it can be an appropriate rational argument if, for example, it is an appeal to expert testimony—a type of inductive argument.

By definition, logical fallacies are invalid, but they can often be written or rewritten so that they follow a valid argument form; and in that case, the challenge is to discover the false premise, which makes the argument unsound.