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Begging the question
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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 or circular reasoning. The first known definition in the West is by the Greek philosopher Aristotle around 350 BC, in his book Prior Analytics.
A common mistake is to use the phrase "begging the question" to refer to an argument where the premises are as questionable as the conclusion.
Latin term was incorporated into English in the sixteenth century.
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Encyclopedia
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 or circular reasoning. The first known definition in the West is by the Greek philosopher Aristotle around 350 BC, in his book Prior Analytics.
A common mistake is to use the phrase "begging the question" to refer to an argument where the premises are as questionable as the conclusion.
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 a syllogism. That is, when the given argument depends on what it is trying to support, and as a result, the proposition is being used to prove itself. For example:
- "Why am I the boss? It's because I call the shots around here."
- "Of course I had a reason, or I wouldn't have done it."
- "I didn't steal it. I'm no thief!"
These statements strongly suggest logical arguments (A is true because B is true) that don't actually provide any proof, because they are circular (in each case B can only be true if A is already assumed to be true).
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.
Instances of petitio principii are formally logical, and in fact logically valid – that is, the conclusion does follow from the premise – they are tautological.
Formally speaking, the fallacy of petitio principii has the following structure (P and Q are propositions):
- Q only if P.
- P.
- Therefore, Q.
- (unspoken) P only if Q.
The syntactic presentation is rarely this transparent: if it were, it wouldn't have any convincing power. Usually, this means that the argument isn't actually an instance of simple deductive reasoning in the first place, but only superficially takes that form. For instance, the remark concerning God's existence quoted here is really just a shorthand for the following reasoning (or variants of it):
- (1) The writings in question are true on all specific points we can verify. (With arguments in each case.)
- (2, from 1) Hence, we have good reason to assume that they are completely truthful throughout.
- (3) The writings describe many events that demonstrate the existence of God.
- (4, from 2 and 3) Hence, these descriptions must be truthful, so God must exist. (It actually suffices for just one of them to be truthful.)
- (5) If the writings had been authored by man, they would not have been true on all of these points. (With arguments in each of these cases.)
- (6, from 1 and 5) Hence, they must have been authored by someone other than man.
- (7, from 2 and 5) Hence, we have good reason to assume the existence of someone who, unlike man, is completely truthful, and who authored these writings.
- (8, from 7) This someone is God.
What we see here is not an instance of circular reasoning, but two different arguments, only partly deductive, for the existence of an all-knowing higher being who wrote the writings in question.
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 less firmly based than the conclusion (the premise can be false while the conclusion is true - that is, the premise is logically "stronger" than the conclusion).
More generally, "begging the question" can be considered the following:
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 , 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 in its discussion.
Valid circular reasoning
The fallacy in begging the question or circular reasoning in its usual sense lies not in the circularity of the argument, but in the initial assumption of the truth of one of the premisses, or, as Douglas Walton puts it: "Arguing in a circle becomes a fallacy of petitio principii or begging the question where an attempt is made to evade the burden of proving one of the premisses of an argument by basing it on the prior acceptance of the conclusion to be proved." While acknowledging the need for proof or observation of such a premiss, circular reasoning can be a useful tool in logic or mathematics. It can be used to prove the reverse of an argument, which could otherwise be very difficult. In other words, if the last statement in a line of proofs can be connected to the first, all arguments in this line work both ways.
To illustrate this, assume that 'A ? B' means that statement A is shown to prove statement B (but not the other way around). Now if we know that A ? B ? C ? D and we find that D ? A, we can complete the circle and by simple logic we can deduce that A ? B ? C ? D. In fact, we can put the statements in any order, e.g. C ? A ? D ? B is also true. It can be said that the premisses A, B, C and D are equivalent, i.e. they are found to contain exactly the same information. If we can observe or prove any of these statements, the others must also be true. This observation or proof is obviously crucial, it forms a line to the circle in order to make the entire argument valid. Of course, this works for any number of steps in a circular argument.
Colloquial usage
Sometimes to beg the question is used 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, 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."
See also
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