begging the question

The traditional use of the phrase begging the question'''' describes a type of logical fallacy (also called petitio principii'') in which the evidence given for a proposition is as much in need of proof as the proposition itself. A common form of begging the question is a circular argument, circulus in probando, vicious circle or circular reasoning in which the proposition to be proved is contained in one of the premises. As a concept in logic the first known definition in the West is by the Greek philosopher Aristotle around 350 B.C., in his book Prior Analytics''. In a somewhat controversial recent usage, the phrase is not associated with a logical fallacy, but is taken to mean that the statement draws attention to some particular issue. These different usages are discussed below.

Begging the question and circular argument

A circular argument is one which assumes the very thing it aims to prove; in essence, the proposition is used to prove itself, a tactic which in its simplest form is not very persuasive. For example here is an attempt to prove that Paul is telling the truth:

Suppose Paul is not lying when he speaks.
Whoever speaks and is not lying is telling the truth.
Therefore, Paul is telling the truth.

These statements are logical, but they do nothing to convince one of the truthfulness of the speaker. The problem is that in seeking to prove Paul's truthfulness, the speaker asks his audience to assume that Paul is telling the truth, so this actually proves "If Paul is not lying, then Paul is telling the truth." It is important to note that such arguments are logically valid. That is, the conclusion does in fact follow from the premises, since it is in some way identical to the premises. All circular arguments have this characteristic: that the proposition to be proved is assumed at some point in the argument. Formally speaking, a circular argument has the following structure. For some proposition p

p implies p
suppose p
therefore, p.

The syntactic presentation of circular reasoning is rarely this transparent, as is shown, for example, in the above argument purportedly proving Paul is telling the truth. The broader category of begging the question (of which a circular argument is a species) includes arguments that do not include the conclusion as one of the premises but do include a premise that is at least as dubious as the proposed conclusion. For example, the statement that one should not walk in the woods alone at night because Fairies are likely to bewitch you is an example of begging the question that is not a circular argument. Another example of begging the question is reducing an assertion to an instance of a more general assertion which is no more known to be true than the more specific assertion:

All intentional acts of killing human beings are morally wrong.
The death penalty is an intentional act of killing a human being.
Therefore the death penalty is wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a cogent argument against the death penalty. If not, it is in fact a weaker argument than a mere assertion that the death penalty is wrong, since the first premise is stronger than the conclusion. Reduction to a more general premise is often useful, particularly in mathematics: For instance, to prove that the sum of the first 244 integers is 29890, it is often easier to first prove a more general assertion, such as

The sum of the first n integers equals

{n \times (n+1) \over 2}.

Variations

In an obviously related sense the phrase is occasionally used to mean "avoiding the question". Those who use this variation have apparently missed the circularity of the argument, and understood the phrase to be pointing to a missed premise. More recently, Begging the question has been used as a synonym for "raising the question". For example, "This year's budget deficit is half a trillion dollars. This begs the question: how are we ever going to balance the budget?" Some familiar with the original usage regarded this usage as incorrect. A writer or speaker can use an alternate phrase such as "this raises the question" to avoid the conflict, or the appearance of ignorance of the original meaning.

History

The term itself was translated into English from Latin in the 16th century. The Latin version, Petitio Principii, could be translated more accurately as "petitioning the principle," meaning claiming the truth of the very matter in question, but the more pithy "begging the question" has become the well-known translation. A literal (as opposed to idiomatic) interpretation of the phrase would appear to yield an interpretation synonymous with "raising the question", which may explain the popularity of this usage.