Begging the Question or petitio principii

_{Jan 01 . 2010}

The truth of the conclusion is assumed by the premises. Often, the conclusion is simply restated in the premises in a slightly different form. In more subtle cases, the premise is a consequence of the conclusion. Begging the question is a form of circular reasoning.

Elaboration

To beg the question is to assume its truth or falsity without proof. This does not mean a direct assumption of truth or falsity but an indirect assumption reached in a circuitous manner by an appearance of logical reasoning. In logic this error is called petitio principi. It may appear in many different forms but the following are the most frequently encountered: A. Arguing in a circle. This error involves more than one syllogism. It begins by assuming the truth of a premise, next upon this premise a conclusion is built and then finally this very conclusion is used in an attempt to prove the premise with which the syllogism was begun. … B. Directly assuming the point at issue. In directly assuming the truth of the point at issue much language is employed which tends to conceal the lack of real proof. Stripped of their wealth of expression such so-called arguments appear as bare unsupported assertions.
Ketcham, Theory and Practice of Argumentation and Debate, pp. 250-1

Song: “Begs the Question Mark” by Nathan Jacobson

[Intro]
Yeah
Class in session
Today: begging the question
Uh

[Narrative Intro]
At the curb, a regular beggar
Fingerless gloves, styrofoam cupper
A cardboard sign, needs a fix, upper
Mark stops by, meets the question
“Can you spare some change?”
"Well, um…, that begs the question:
"Pardon me, but what's it for?"
"I need money 'cause I'm poor!"

Wait, no disrespect! Allow me to interject
A point of clarification (to avoid equivocation)
Got no problem with further questions, but
This lesson is about begging the question (logically)
Assuming the point in question (petitio principii)
Not a follow-up question, not an interrogation

[Verse 1]
Let's get back to the logic lesson
Might seem elementary, Watson
But that dubious claim you posit
It's got a fatal fallacy, a pox on it
You assumed the point in question
Your premise just is your conclusion
Po’ boy, you begged the question
Circular reasoning, that's flat broke
Wheels spinning, bent the spoke
False start, back to the starting line
Else this logic is just doing laps

[Chorus]
You keep “begging the question”
It's the reason for this lesson
Question ain’t got the answer
That’s why we're questioning
The slack line of reasoning
This story lacks tension
Hangs untethered to a reason
Look, don't jump to therefore
Without a premise heretofore
An inference from evidence
Wherefore, this-and-such, hence

[Verse 2]
Let's get fit, Exercise One
Hypothesis: "It's survival of the fittest”
Question Mark: "Which are the fittest?"
"Those are the ones that survive."
Exclamation Mark: "That's no explanation!"
Neanderthal, you're begging the question
Same stretch, two reps, stop flexin'
Chuck, you ain’t proved the biology
Quotation Mark: Popper says tautology
Theory's endangered, unfit descendants
Roaches scurry for concrete evidence
Dinosaurs scavenging to stay alive
Hyenas laugh foolishly, "I will survive!"

[Chorus]
You keep “begging the question”
Questions ain’t got no answers
Dodo eyes, still no answer
That’s why we were asking
This story line lacks tension
A slack line, untethered to a reason
Anchor the point to evidence
Can't jump straight to therefore
Without evidence in the heretofore

[Verse 3]
Let's get the spirit, Exercise Two
It’s God’s word, trust this religious text
Divine testament, angel of light sent
Says right here in this prooftext
No need to put it to the test
Smith says it’s the most correct-est
Smiley face on, nameplate on jacket
Assumption slid into the inner pocket
Problem is, trust you have to earn
How about archaeology to discern
Historical reliability, fulfilled prophecy
Proven philosophy, maybe a resurrection
A demonstration, some substantiation

[Bridge]
Is it petty if I call it out? (call it out)
Or am I helpful if I spell it out? (spell it out)

[Chorus]
Instruction's up, for your reflection
Mark well, let's not beg the question
Copy and paste, premise to conclusion
Throw in a synonym, change a letter
Assert, it's the best because it's better
Sneak around, start at the end
Somehow still never arrivin'

[Outro]
Beggars can't be choosers, but there's
Reason enough for all us schmoozers

Direct Link

Examples

An elementary example

Since I’m not lying, it follows that I’m telling the truth.

Begging the question of what constitutes a fair election

Should the Constitution of Virginia be amended to allow the General Assembly to temporarily adopt new congressional districts to restore fairness in the upcoming elections, while ensuring Virginia’s standard redistricting process resumes for all future redistricting after the 2030 census?

Begging the entailments of biblical justice

French, for example, decries the fact that white evangelicals are less likely than other groups to think that poverty, inequality, and racism are extremely serious threats to the country. “This is not the result,” French writes, “you’d expect from a community whose politics is centered around biblical justice.” French’s conclusion begs the question. Maybe evangelicals don’t care about biblical justice. Or maybe they have a different assessment of how bad each problem is and what biblical justice entails.
Kevin DeYoung, “The Temptation of the Jeremiad“, World Opinions (December 16, 2021).

Begging the cause of disparate outcomes

Many of the opponents of critical race theory claim its conclusions often rely on storytelling, rather than a compilation of evidence. … The theory often begs the question by making assumptions on the roots of societal problems through the lens of personal stories from ethnic minority groups and then pointing to disproportionate outcomes as evidence that institutional racism and white privilege are the culprits.
Tyler Arnold, “Virginia school board members targeted” at Just the News (June 18, 2021).

Methodological naturalism in the sciences

Robert Larmer argues that those who adopt methodological naturalism typically beg important questions concerning its justification. But rejecting methodological naturalism in no way prohibits scientists from searching for natural causes of physical phenomena. The issue is not whether it is legitimate to look for natural causes of physical phenomena, but rather the question-begging insistence that under no circumstances is it permissible ever to posit the direct intervention of a nonnatural agent into the physical order.
“Is Methodological Naturalism Question-Begging?“

Critique

Show that in order to believe that the premises are true we must already agree that the conclusion is true.

We have explained what begging the question means, and it is allowed that when assumptions are closely connected with the issue we may deny them and refuse to concede them as premises on the plea that they beg the question.

Commentary

On the new and old senses of the term

Beware. Over time, the historic use of the term “begging the question” in logic and rhetoric has been overtaken by another sense. That is, in modern usage, more often than not, saying something “begs the question” is usually meant to say that it strongly implies a follow-up question. For example:

Their judgement that invading Iraq was a mistake turned out to be correct, but only in hindsight, not foresight. Which begs the question — was the chaos in Iraq inevitable? We will never know the answer, but not knowing the answer does not mean the pre-war naysayers “saw more clearly than we did.”
A reader, “Hindsight” at The Atlantic (July 28, 2007).

Above the reader poses a follow-up suggested by the premise, but he does not “beg the question” in the traditional sense. To beg the question, the reader would need to assume without argument that “invading Iraq was a mistake”.

Research suggests that the differences in children’s ability to concentrate emerges early in development and that kids who show superior “attentional control” do better in school down the line. This begs the question: How early can you teach your child to concentrate?
Hans Villarica, “The Infant Brain Can Be Trained to Concentrate” at The Atlantic (September 6, 2011).

Another example.

If a person claims to merely “lack belief in God” that position begs for the follow-up question: “Are you the agnostic kind or the (positive) atheist kind?” If one halts at the point of merely “lacking belief in God,” then the intellectual train has stalled out before arriving at a good stop.
John D. Ferrer, “Some Definitional Drawbacks in Atheism” (May 24, 2015).

On the nuances of begging

Neither is it always easy to decide what constitutes “begging the question.” A standard treatment is to define petitio principii as “assuming what is to be proved.” This is helpful so far as it goes, but it is not always easy to reach agreement on the circumstances under which the objection that someone has “assumed what is to be proved,” and hence begged the question, is warranted. On pain of trivializing the charge of begging the question, it seems that the extreme view of Sextus Empiricus and John Stuart Mill that all deductive arguments commit this fallacy should be rejected, as should DeMorgan’s equally extreme view that no multipremised argument can be accused of this fallacy. Rejecting either extreme seems justified, but it leaves one with the often difficult task of deciding under what circumstances it is appropriate to accuse someone of committing the fallacy of petitio principii.
Robert A. Larmer, “Is Methodological Naturalism Question-Begging?“, Philosophia Christi, Vol 5. No. 1.

On complex examples of begging

Men ought not to steal:

A. Because it is wrong.
B. It is wrong because it is contrary to the Moral Law.
C. It is contrary to the Moral Law because it is forbidden in the Holy Scriptures.
D. It is forbidden in the Holy Scriptures because it is contrary to God’s will.
A. It is contrary to God’s will because it is wrong.

The more extended the circle, and the more involved the statement, the more difficult it is to detect this kind of fallacy.
Esenwein, How to Attract and Hold an Audience, p. 27

Aristotle’sSophistici Elenchi

Begging the question, or, assuming the point to be proved, is a specific case of failing to demonstrate a theorem. This occurs in various ways, either when the reasoning is inconclusive, or when the premisses are less evident than the conclusion, or equally devoid of evidence with the conclusion, or when they are its consequents rather than its antecedents. For demonstrative premises must be antecedent to the conclusion and more evident. None of these cases is begging the question. But some propositions being self-evident, others having a derivative evidence (for principles have their evidence in themselves, conclusions derive their evidence from other propositions), to attempt to make a proposition that is not self-evident evidence of itself is to beg the question

This may either be done by directly assuming the conclusion or by assuming what is properly a conclusion from a proposition as a premiss to prove that proposition, proving, for instance, A by B and B by C when C can only be proved by A. For this amounts to proving A by A. An example of this is the pre tended method of constructing parallels. Here the prover unconsciously assumes an operation which cannot be performed unless parallels have been constructed2. The proof therefore asserts a thing to be true if it is true, and if it were valid, all
propositions would be self- evident, which cannot be.

When the conclusion, C is A, and the major, B is A, are equally deficient in evidence, there is not of necessity a begging of the question, but there is clearly no demonstration; for that cannot be a premiss of demonstration which is no more evident than the conclusion . But if the middle and minor, C and B , are so related as to be identical, either because they are convertible or because the middle involves the minor, the argument is a begging of the question. For the major premiss, B is A, might be proved by the minor premiss and conclusion if the middle and minor are convertible. If it cannot be, it is only from the comparative extension of the terms, not from any other
relation. If they are convertible, we might, as was stated, prove the major premiss from the minor and conclusion, and we should have a circular proof of three propositions in which each would be alternately premiss and conclusion.

Similarly if the minor premiss, C is B, is no more evident than the conclusion, C is A, we have not necessarily a begging of the ion, but we have a failure of demonstration . If, however, the major and middle terms are identical, because they are convertible or because the major is involved in the middle, then we have a begging of the question as before “. For begging the question arises, as was explained, when a proposition not self- evident is made to prove itself.

If then begging the question is making a proposition not self-evident prove itself, and this is a failure of proof, from the premiss being no more evident than the conclusion, because the premiss and conclusion either affirm two identical predicates of an identical subject or an identical predicate of two identical subjects, the question cannot be begged in the second figure in either of these ways, but only in the figures that give an affirmative conclusion, namely, the first and third’.

In negative syllogisms there is a begging of the question in the first and third figures when an identical predicate is denied of two identical subjects, and it is not either premiss indifferently that begs the question but only the major 10. In the second figure there is a begging of the question when two identical predicates are denied of an identical subject, and it is not either premiss indifferently that begs the question but only the minor, because the position of terms in the other premiss of negative syllogisms is not homologous to the position of terms in the conclusion.
Begging the question in scientific discussion is what really satisfies these conditions, in dialectic what has the appearance
of doing so .

We have some further remarks in the Topica :—

What begging of the question is to the philosopher we have examined in the Analytics : what it is to the dialectician we will now explain. It appears to occur in five ways. The first and most manifest way is when the very thing that should be proved is assumed. This cannot easily pass undetected when the terms are the same, but when synonyms are used, or a name and a circumlocution, it may escape detection . A second way is when a particular ought to be proved and the universal is assumed : as , for instance, if we have to prove that contraries
are objects of a single science, and assume that opposites, their genus, are objects of a single science. It appears that what should be proved alone is assumed in company with other pro positions. A third way is when a universal ought to be proved and the particular is assumed ; as when what ought to be proved of all contraries is assumed of some. Here too it appears that what ought to be proved in company with other propositions is assumed alone. A fourth way is when we divide the problem to be proved and assume it in detail ; as if we have to prove that medicine is the science of health and disease and successively assume it to be the science of each. A fifth way is when two facts are reciprocally involved and we assume the one to prove the other; as if we assume that the side of a square is incommensurate to the diagonal when we have to prove that the diagonal is incommensurate to the side.