beside the question

Begging the question

In logic, begging the question has traditionally described a type of logical fallacy (also called petitio principii) in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. Begging the question is related to the fallacy known as circular argument, circulus in probando, vicious circle or circular reasoning. The first known definition in the West is by the Greek philosopher Aristotle around 350 BC, in his book Prior Analytics.

In contemporary usage, "begging the question" often refers to an argument where the premises are as questionable as the conclusion.

In popular usage, "begging the question" is often used to mean that a statement invites another obvious question. This usage is disparaged. "Raises the question" may be appropriate.

History

The Latin term was incorporated into English in the sixteenth century. The Latin version, Petitio Principii (from peto, petere, petivi, petitus: attack, aim at, desire, beg, entreat, ask (for), reach towards, make for; principii: genitive of principium: beginning or principle), literally means "begging or taking for granted of the beginning or of a principle." That is, the premise (the principle, the beginning) depends on the truth of the very matter in question. The Latin phrase comes from the Greek en archei aiteisthai in Aristotle's Prior Analytics II xvi:

Begging or assuming the point at issue consists (to take the expression in its widest sense) in failing to demonstrate the required proposition. But there are several other ways in which this may happen; for example, if the argument has not taken syllogistic form at all […]. If, however, the relation of B to C is such that they are identical, or that they are clearly convertible, or that one applies to the other, then he is begging the point at issue.

Fowler's Deductive Logic (1887) argues that the Latin origin is more properly Petitio Quæsiti which translates as "begging the question."

Traditional usage

"That begs the question" is an appropriate reply when a circular argument is used within one syllogism. That is, when the deduction contains a proposition that assumes the very thing the argument 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 not lying:

Suppose Paul believes what he (Paul) says.
Therefore, Paul is not lying.

Although these statements have a logical form, they do nothing to convince one of the honesty of the speaker because the matter (that is, what the words actually symbolize) of the major premise (that Paul believes what he says) and the conclusion are actually the same thing. The speaker is stating a tautology "If Paul believes what he says, then Paul is not lying".

Another common instance is found when computations lead to identities: someone is trying to solve an equation and in the course of the attempt reduces a mathematical expression to itself. The general process of solution might be legitimate, but its application to the particular question is incorrect.

Such arguments are formally logical. That is, the conclusion does formally follow; however, since it is materially identical to the major premise, the argument is said to be materially invalid. All self-circular arguments have this characteristic: that the proposition to be proved is assumed at some point in the argument.

Formally speaking, the fallacy of petitio principii has the following structure: For some proposition p,

p implies q
suppose p
therefore, q.

The syntactic presentation of the fallacy is rarely this transparent, as is shown, for example, in the above argument purportedly proving Paul is telling the truth.

Contemporary usage and variations

The traditional Aristotelian usage is frequently supplanted by a contemporary usage that refers to presenting evidence (in support of a conclusion) that is less likely to be accepted than merely asserting the conclusion.

A specific form of this 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 morally wrong.

If the first premise is accepted as an axiom within some moral system or code, this reasoning is a sound 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.

John Woods categorizes "begging the question" more generally, as:

Let T be a thesis advanced by Smith. Let A be a proposition forwarded by Jones as counting against T. Then Jones begs the question against Smith’s thesis T if:

A is damaging to T,
A is not conceded by Smith, does not follow from propositions already conceded by Smith, and
is not otherwise ascribable to Smith as what we might call a “reasonable presumption” or a “default” (for example, the belief that water is wet or that Washington is the capital city of the United States).

Fowler's Modern English Usage classifies begging the question in a similar fashion (for example, in contrast to the meanings from Merriam-Webster, the Oxford English Dictionary, and the American Heritage Dictionary). Fowler states that it is "The fallacy of founding a conclusion on a basis that as much needs to be proved as the conclusion itself."

In a related sense, the phrase is occasionally used to mean "avoiding the question". Those who use this variation are explaining that the argument lacks a premise, and they have missed the self-circularity of the argument because of it.

Related fallacies

Begging the question is related to the fallacy of circular reasoning. The distinction between the two concepts is as follows: Circular reasoning is the basing of two conclusions each upon the other (or possibly with more intermediate steps). That is, if you follow a chain of arguments and conclusions (a proof or series of proofs), one of the conclusions is presumed by an earlier conclusion. Begging the question can occur within one argument and consequent conclusion. For example, A causes B because A comes before B, therefore B is caused by A. While arguments made using circular reasoning can be considered valid (God/Bible argument put forward by St. Anselm

during the 11th century) either side of the argument leans heavily upon the other under an assumed truth basis. In strict sense, begging the question occurs if and only if the conclusion is implicitly or explicitly a component of an immediate premise. It is usually accepted, though, to use the term begging the question in place of circular argument.

Begging the question is also related to the fallacy of many questions — a fallacy more commonly known as "loaded questions", that is committed when a question presupposes something that has not been proven or accepted by all the people involved.

Modern usage

More recently, to beg the question has been used by some to mean "to raise the question", or "the question really ought to be addressed". An example of such a use would be, "This year's budget deficit is half a trillion dollars. This begs the question: how are we ever going to balance the budget?" Although proponents of the traditional meaning will criticize this formally incorrect usage, it has nonetheless come into widespread use and in informal contexts may actually be the more common use of the term. The phrases circular reasoning, circular logic, and circular arguments have come to be used in places where logicians would tend to use "beg the question".

A possible origin for this confusion in usage is the likeness of the word "beg" to the word "beget", which can mean "to originate." The phrase "to beget the question" might have been confused in time with the similar-sounding (but very different) notion from logic "to beg the question". An example of this usage is found in An Enquiry Concerning Human Understanding by David Hume, published in 1748: "This begets a very natural question; What is meant by a sceptic?" (Section XII).

Another possible origin is that the situation is such that the most obvious question to be asked is the question given, as if the situation is anthropomorphically begging, or pleading, for the participants to ask the question. For example, "This year's budget deficit is half a trillion dollars. The most obvious question to ask is: how are we ever going to balance the budget?"

Arguments over such usage are an example of debate over linguistic prescription and description. As John McIntyre (copyeditor), Baltimore Sun assistant managing editor, puts it: "Writers who were not taught logic in school — evidently a great many — will think that 'to beg a question' means 'to give rise to a question.' In that they are like the multitude of writers who have appropriated technical but dimly understood language. A parameter, for example, is 'a constant, with variable values, used as a referent for determining other variables.' If you are a mathematician, that definition from Webster's New World College Dictionary probably means something to you. If you are not a mathematician, you are probably using parameter to mean a boundary or limit or guideline, or perhaps nothing in particular. People do write this way. Some even talk this way. Eventually, loose applications of technical terms to different contexts find their way into the dictionary, some embedding themselves in the language. That is fine. But in the interval, anyone who wishes to write precisely will be cautious.