Logical Fallacies

Here we endeavor to organize a list of logical fallacies.

Overview of Logical Fallacies

A 'logical fallacy' is a structural, or purely formal defect in an argument. Logical fallacies fall into two varieties: invalid arguments, and circular arguments.

Invalid Arguments

An argument is said to be valid if and only if the truth of the premises guarantee the truth of the conclusion. It is invalid if and only if the conclusion does not necessarily follow from the premises. It is important to realize that calling an argument 'valid' is not the same as saying its conclusion is true. Logic does not concern itself with the content of an argument - only its form. From the standpoint of logic, the following is a perfectly valid argument:

(p1) Dinosaurs are still living;

(p2) If Dinosaurs are still living, then Elvis is still living;

(c1) Therefore, Elvis is still living.

If the two premises are true, then the conclusion must be true. You and I, of course, know that these premises are not in fact true - but their falsity is not a matter of pure logic. Simply because somebody says something false, it does not follow that that person has committed a logical fallacy.

Valid arguments fall into two categories: sound and unsound. A sound argument is a valid argument with true premises. An unsound argument is a valid argument with false premises. The above argument about dinosaurs is unsound.

Invalid arguments will always be logically fallacious. By way of example, the following are invalid arguments:

(p1) If x is a human male, then x is a human;

(p2) x is not a human male;

(c1) Therefore, x is not human.

(p1) If July is before June, then George Bush is the thirty-second president of the United States;

(p2) July is not before June;

(c1) Therefore, George Bush is not the thirty-second president of the United States.

Each of these arguments are invalid because they are of the form:

(p1) If A, then B

(p2) not-A

(c1) Therefore, not-B,

which is an invalid logical structure. Simply because the 'if'-clause of an 'if, then' statement is false does not mean that the 'then'-clause is false.

Circular Arguments

Circular Arguments are valid, but they are still considered logical fallacies. More accurately, they are simply useless - they establish nothing that they do not presuppose. The following are simple examples of circular arguments:

(p1) San Fransisco is in California;

(c2) Therefore, San Fransisco in is California.

(p1) Nobody likes Cherries;

(p2) If anyone liked cherries, then it wouldn't be the case that nobody likes cherries;

(c1) Therefore, nobody likes cherries.

(p1) God exists;

(p2) God knows everything;

(p3) God is not a liar;

(p4) God wrote the Bible;

(p5) The Bible says that God exists;

(c1) Therefore, God exists.

Because these argument must assume what they are attempting to prove, they are logically superfluous. In each case, the argument provides absolutely no support for the conclusion. We might just as well have stated the conclusion without argument. Most often, circular arguments hide their circularity by keeping one of their premises implicit, as in the following:

(p1) God is not a liar;

(p2) God wrote the Bible;

(p3) The Bible says that God exists;

(c1) Therefore, God exists.

Though it does not explicitly say so, this argument obviously depends upon a suppressed premise - namely, that God exists. More accurately, no one would accept the premises unless they had already accepted the conclusion.

Certain types of argumentation may be wrong or misleading without thereby constituting a 'logical fallacy.' It may be terrible to tell someone: 'agree with me or you will die,' but it is not terrible because of its logical structure. Similarly, we may feel that certain groups are too easily convinced to believe something or too quick to adopt a political position on the basis of emotion. However, their doing so does not constitute a logical fallacy.


Last updated by Nelson Dec 3, 2010.

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