Begging the Question or petitio principii
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 difficult cases, the premise is a consequence of the conclusion. Begging the question is a form of circular reasoning.
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
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).
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).
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?“
Since I’m not lying, it follows that I’m telling the truth.
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.
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).
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’s Sophistici 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 premisses 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.