Begging the Question (Circular Argument, Petitio Principii)

Begging the Question is a fallacy that occurs when the conclusion of an argument is contained in the premises used to support it. Hence, the argument is said to beg the question it purports to prove. Alternatively, it may be said to go in circles. As the result of this pattern is an argument in which support for the conclusion assumes its own truth, it effectively provides no substantive basis upon which to accept the truth of the conclusion.

In most cases, the premise will be sufficient from that of the conclusion to make recognition difficult for those engaged in the conversation to recognize it. In others, the argument may be sufficiently complex that a speaker fails to notice (or hopes their audience won’t notice) they have stuck their conclusion back into the premises of the argument. In still others, the truth of the conclusion is assumed tacitly by other premises within the argument. Either way, it often takes some reflection to see that the conclusion matches one of the premises of the argument in question.

Take for example the following arguments:

“I know god exists, because the Bible tells me so, and I know the Bible is correct, because it is the word of God.”

“God does not exist. That’s just a myth!”

In the first case, the notion that Bible is the word of god assumes that God exists, so the conclusion of the argument is assumed by the premise offered in support of his existence. Hence, the argument is circular in virtue of an implied premise that matches the conclusion.

In the second, the notion that God is just a myth assumes that he is not real in the first place, so an argument dismissing belief in God on this basis assumes that he is not real to begin with. So, if the second statement is understood to be a reason for believing the first, the result is a circular argument.

Circular argumentation (or begging the question) is an incredibly common fallacy. The problems with this fallacy are actually rather central to the nature of logic and reasoning itself, particularly insofar as they illustrate the practical significance of providing a reason to believe something in the first place.

Oddly Interactive Problem: As noted above, what makes a circular argument a fallacy is the failure to provide any reasons to believe the conclusion which are not dependent on the conclusion itself. As some have noted, (Perelman and Olbrechts-Tyteca, for example pp. 112-114), this not strictly speaking a failure of logic. It is a failure of rhetoric. By some tests (e.g. truth tables), a circular argument seems to pass with flying colors. So, why isn’t it valid? Some would actually say that it is valid, though still fallacious. Others might just say it is invalid. Either way, the problem is the argument produces no new reason to believe its conclusion, hence the argument fails to accomplish what people normally use arguments for; it fails as a means of persuasion. It is as much a failure of social interaction as it is a failure of reasoning.

Begs the question“: In discussing a belief or claim, one might hear someone say; “this begs the question of…” Of course this is roughly equivalent to suggest that the matter “raises the question of…” This bothers some people to no end, because a raising a question is not the same as committing the logical fallacy of begging the question. On the other hand, the usage often carries some implication that a specific answer to the question they wish to raise has already been assumed by those advocating the belief or claim which triggered their comment. This isn’t quite equivalent to the fallacy of begging the question, but it does bear a certain family resemblance, so to speak. The usage does not, strictly speaking, match common logical definitions of the fallacy, but isn’t entirely devoid of sense. In any event, language usage varies.

Circularity of Reasoning: There is an interesting problem in epistemology insofar as we can find a degree of reasoning in many theories, perhaps even most. …possible all of them? Likewise if you examine people’s world views in general, you will likely find a degree of circularity in the relationship between their basic premises about how the world works and what it means to know something and the particular conclusions they draw about the world around them. What separates the circularity of reasoning on such a grand scale and that of a circular argument is the scope of the subject matter. Whether or not that is sufficient to resolve any of the problems in question is another question, but one does sometimes hear people talk about whether or not a given instance of circular reasoning is vicious. Presumably, a ‘yes’ answer means trouble, A ‘no’ gets you a pass. Whether or not the distinction can be made on the basis of a non-circular argument is another question, as is any question about whether or not the circularity of the distinction would itself be vicious.

Reflexivity can be a real bitch!

Synonyms: I have seen some folks distinguish begging the question from circular argumentation. The wikipedia entries in question currently do so emphasizing the notion that a circular argument begins with the conclusion it purports to prove whereas the entry on begging the question merely suggests the conclusion is assumed in the premises. there is certainly room to draw a significant distinction there, but the usage is not standardized. In practice, most people seem to use these terms interchangeably.

Tautology: Circular argumentation shares a lot in common with tautology, enough so that the two are often confused with one another. A tautology may be described as an assertion that is true by every possible variation of the truth value of its components. If I say, “It is safe to go outside, unless it is not,” that statement is true for all possible truth values, because its individual components are contradictory. One will always be true and one will always be false. So, my statement to the effect that one or the other is true will always be true, regardless of the facts. By way of contrast, If I say, “Either Bob has my Pen or Bill has it,” then if neither of them has it, my statement is false. This is the way most assertions work. Falsehood is at least possible. A tautology is true regardless of the particulars. Another way of putting it would be to say that it is true by virtue of its logical form (e.g. A or not A). The problem with tautologies is that they don’t tell us much about the real world, so to speak. They might be used on occasion to help us organize information, but they do not commit a speaker to any specific account of the facts.

I have seen the difference between a tautology and a circular argument explained in a few different ways, but the most clear explanation that I am aware of is to think of a tautology as a feature of a single statement whereas a circular argument is a feature of an argument.

King’s Pushback

Introduction: This is part of an article entitled, “The Real Reasons All the Top Chess Players Are Men,” written by Wei Ji Ma. It was published in Slate Magazine on December 11th. In this piece, tries to counter a common claim that men are inherently better at chess than women by considering a number of social factors which Wei argues could better explain known disparities between the number of successful men and women participating in competitive chess.

Key Facts: The Cable Series, “The Queen’s Gambit,” features a story-line in which a woman fights her way up the ranks of professional chess to become the world champion. When the Queen’s Gambit was released, it triggered a wave of discussions about the gap between men and women in the top ranks of chess competition. Several voices argued that the women are under-represented in chess championships for reasons of inherent inability. The author of this argument makes a case for social construction as a more likely cause of the difference. The passage below focuses specifically on the impact of the belief in inherent ability on the social construction of gender differences relevant to competitive chess.

Text: “The idea that innate chess ability is critical for success—rather than a commitment to studying the game to get better and better at it—might itself keep the participation gap wide in the first place. Andrei Cimpian, Princeton University philosopher Sarah-Jane Leslie, and colleagues studied 30 academic disciplines in the U.S. and found a strong negative correlation between the pervasiveness of innate-ability beliefs and the proportion of female Ph.D.s. Moreover, very young children already internalize beliefs that men are more brilliant than women. A 2017 study showed that 6-year-old girls in the U.S. are already less likely to believe that members of their gender are “really, really smart,” and that they begin avoiding activities that are said to be for children who are “really, really smart.” There we have it: a shockingly early start for the participation gap in chess.”

ANALYSIS

Comments: To fully assess the value of the original argument, the passage above would have to be considered alongside Wei’s account of several other confounding variables which might explain the relative lack of successful women in competitive chess, as well as his critique of the case made for inherent ability. Doing so would of course put the analysis beyond the scope of a simple exercise. So, we are just dealing with this passage here, but that does touch upon questions as to how one might best think of the specific conclusion to be drawn from this specific passage. It should be kept in mind that Wei isn’t trying to settle the whole issue in this one passage; he is using it to establish one point in a larger argument.

Statements: This argument is pretty straight forward. I have omitted a hedge from the first statement.

[1] “The idea that innate chess ability is critical for success—rather than a commitment to studying the game to get better and better at it— …keeps the participation gap wide in the first place.

[2] Andrei Cimpian, Princeton University philosopher Sarah-Jane Leslie, and colleagues studied 30 academic disciplines in the U.S. and found a strong negative correlation between the pervasiveness of innate-ability beliefs and the proportion of female Ph.D.s.

Moreover

[3] Very young children already internalize beliefs that men are more brilliant than women.

[4] A 2017 study showed that 6-year-old girls in the U.S. are already less likely to believe that members of their gender are “really, really smart,”

[5] [The same study showed that] they begin avoiding activities that are said to be for children who are “really, really smart.”

[6] There we have it: a shockingly early start for the participation gap in chess.

Diagram: The argument appears to produce three separate inferences in serial form with the final conclusion being the first sentence.

Discussion: The main themes associated with this argument would include; Begging the Question, Causation, Hedges, Statistics.

Begging the Question: There is at least one way of reading the first inference which would render it a circular argument.

Causation: The essential point of the argument is to assign a causative factor to the gender disparities in chess. This passage of this article makes the case that belief in innate talent creates a self-fulfilling prophesy, depressing interest in chess by women reducing expectations for their performance. These two studies cited may not be sufficient to demonstrate the social expectations outlined in these studies, though they are probably sufficient to undermine the case for innate ability as a sufficient explanation in it itself.

In the end, a more exhaustive account of relevant studies would be needed to account for all the variables.

Hedges: Notice that the opening lines of this argument use the phrasing “might be” in setting up the case that belief in innate ability constitutes a self-fulfilling prophesy. Most likely, this reflects the nature of the publication. In effect, the author is turning out a quick response to the topic at hand rather than the results of exhaustive research. The hedge this reminds us that his conclusions are tentative at best, offered as food for thought rather than as a final verdict on the topic at hand.

In omitting the hedge from the wording of the first statement, I am treating them more as a kind of affect display than a feature of the statement in question. Some might disagree with this approach, suggesting that the actual question is merely whether or not belief in innate ability MIGHT deter women from participating in chess. This would water the topic down to the point of being pointless, so I think it better to treat the claim in question as a solid assertion of the link, and the presence of the hedge as indicating something about the relative confidence of the author rather than as a feature of the claim in question.

Statistics: The argument refers to 3 separate findings from 2 separate studies. Whether or not these are enough to establish the truth of the author’s conclusion is something of an open question. Barring specific questions about the data in the study and/or the conclusions drawn from it, a reader might still be justified in wishing to consider additional variables. Still, the studies cited above do seem to provide some reason to believe, as Wei does, that belief in innate ability is itself a factor in the gender disparities present in competitive chess.

Evaluation: I am just going to comment briefly on each of the 3 inferences in this argument.

4->3: Here the author is essentially taking a specific study, to the effect that young girls already equal intelligence with gender, to demonstrate a larger claim that young children generally show this belief.

One might raise some questions as to whether the study in question demonstrates that female children are coming under the influence of stereotypes at age 6 or simply becoming aware of innate differences. Few social scientists at this point would entertain the latter option, and the authors appear to take it as axiomatic that belief in gender disparity is a stereotype, but as this author of this argument uses the study to show that social construction is the cause of gender disparities in chess rather than innate ability, this builds a degree of circularity into the argument, at least as applied to this first inference.

At least as stated, the inference from 4 to 3 appears to be invalid. Additional information may change this, but the information is not present in the immediate argument presented above.

3+5->6: Statement 3 is a general claim about the early impact of belief in gender stereotypes dealing with intelligence and statement suggests that at least one study shoes that girls as young as 6 begin avoiding activities they associate with it. Statement 6 attributes gender disparities in relevant activities to these factors.

The premises certainly do make a plausible case for the conclusion. How convincing one finds that case is another question. It would be reasonable to ask for consideration of additional variables, some of which are dealt with in the rest of the article and/or even to look for more exhaustive studies on the topic at hand. Of course, it would also be reasonable to expect of someone holding out for such information that they would look at the research in question if it was offered. If that is too time consuming, then it might well be argued, the material at hand ought to be sufficient for at least a tentative conclusion.

Note that the circularity mentioned in the first inference based on the study of young girls is less relevant to this inference insofar as the observation that girls begin avoiding tasks associated with innate intelligence does establish a behavioral impact of the belief in question. Whether or not there might be some case for the accuracy of such beliefs, the case for a behavioral impact of such beliefs is supported by the study.

2+6->1: This inference combines the case for early avoidance of intellectual activities by girls as a result of stereotyping with a parallel observation about a relative lack of adult female participation in scholarly fields strongly associated with innate ability to make the case for belief in innate ability as a deterrent to female participation in chess.

As with the previous inference, the argument makes a plausible case. Whether or not it is convincing is another question.

Final Thoughts: Overall, I do find this to be a persuasive argument, but I believe at least part of this is due to the fact that I am inclined to accept the assumptions of a social constructivist position at the outset. As a case in favor of such a position, and against the view that there are innate differences between boys and girls on skills relevant to chess, I think it is still sufficient to establish the relevance of at least one competing variable, the reaction to belief in innate differences has an impact on human behavior. To rule out any underlying innate difference probably just takes more than you can accomplish with the paragraph above and many even with the article from which it is drawn.

Helpful Principles of Reasoning

Some of the ideas commonly cited as logical principles are probably better thought of as matters of argumentative ethics rather than the calculation of logical relations between different statements or propositions. They involve assumptions about how best to go about reasoning with others (which of course includes ideas about how to read and interpret the efforts of others to reason with us). The list of such ideas would certainly include: Burdens of Proof, Ockham’s Razor, and the Principle of Charity as well as some logical fallacies. Many assume that these principles are as much a part of any logical system as anything one might encounter in formal logic (say, the principle of double-negation). Others dismiss these ideas outright. I think it best, really, to regard them as practical decisions which help to facilitate a more productive approach to reasoning. One cannot give the same account of such principles that she might for concepts like double-negation, yet they can help us shape our arguments and our analysis of arguments into something more productive than it would be otherwise.

Burden of Proof: This is the notion that in any given debate, one side may bear more responsibility than the other for producing evidence in favor of its position. This principle is enshrined, for example, in the American legal system wherein we typically regard people as innocent until proven guilty (at least with respect to criminal charges). The notion has also generated a great deal of interest in the philosophy of religion wherein debates between atheists and believers often focus on questions about the responsibilities of each regarding the production of evidence for and against belief.

Much of the issue turns on questions about the (a)symmetry of affirmative and negative propositions. If we take any given proposition (p), the question arises as to whether or not its affirmation (p) is equivalent to its negation (not p). Given that P and Not P are contradictory propositions, this would seem to suggest that the two have equivalent value. If one is true, the other must be false. If it is false, then the other must be true. This would seem to suggest that any given proposition and its negation are equivalent for purposes of logical testing. That argument seems plausible, but it rests on a very formal approach to the subject. It doesn’t take into account some of the vagaries of semantics (questions of meaning) or the practical constraints that may skew the production of evidence and/or the significance that evidence would have in practical reasoning. This is where the case for asymmetry arises (i.e. the view that there are significant differences between the truth value of affirmative propositions and their negations).

One argument for asymmetry rests on the notion that negation (or at least some versions of negation) itself is inherently ambiguous. In some cases, such as predicate term negation, the conditions under which the truth of a negative claim could be established are fairly clear. If, for example someone were to say’ “Dan is in Barrow, Alaska,” I could say no, and I could do so on very definite grounds (i.e. that I am presently on vacation in Azusa, California). In this case, my rejection of the initial claim is based on a very clear condition in which the facts asserted in the claim are not consistent with the evidence at hand. If all negations were so simple, one could as easily accept the burden of proof for negative claims as one could for affirmations. But some negations are more complex than that. If I reject the claim that “colorless green ideas sleep furiously,” I could no longer point to a specific fact that disproves the proposition. Rather, my argument would pertain to the nonsensical nature of the statement itself (which was of course precisely the point of Noam Chomsky’s original presentation of it). Instead of proving the point wrong in any fact-based argument, I would be challenging the meaning the statement, and (if that statement had a legitimate proponent) challenging her to produce something more meaningful before moving on to questions about the factual evidence that would confirm or deny it. For this, and several other reasons, it is sometimes suggested that negation is more problematic than affirmation. To affirm that a statement is true, one must accept as meaningful all of its terms and affirm the state of affairs they describe. In contrast, one may reject a proposition on the basis of other concerns.

On a more practical level, one can point to the difficulties that arise from specific contexts of contested claims. If I assert that one of my students (let’s call him ‘Bill’) cheated on a test, most people would regard it as unfair for me to suggest that it was Bill’s responsibility to prove me wrong. I would normally be expected to put mown reasons for saying this on the table. If I can produce evidence that he did cheat, then it might be fair to expect Bill to answer that evidence. So, for example, if I showed that his essay looked a lot like a Wikipedia entry, I would expect him to show that I was wrong or accept the consequences for cheating. What I could not do is expect Bill to prove that he had not cheated on the test himself without providing any reason to believe he had done so in the first place. (More important, I suspect that in such an example the Dean of Instruction at my college would expect me to produce an account of my reasons for thinking the student had cheated. Only then would she turn to the student for a response to the accusation.)

There is no Bill by the way, at least I’m not talking about one. If any past or future Bill’s read this, no I’m not talking about you. Really, I’m not.

This last example helps to illustrate something else that’s interesting about burdens of proof; it is only one component in a complex dialogue, one responsibility which may (or may not) fall to a particular party in a debate. Once an initial case for the affirmative side in a debate has been made, it is common to expect that a burden of moving the debate forward will pass to the other side. He or she cannot simply sit there and say ‘no, no, no’. At some point, she must address the claims made by others, either by producing a direct case of her own (i.e. proving the affirmative claim wrong, much as one might do in the case of predicate term negation) or by refuting some aspect of the case against her. Another consideration here lies in the way that possession of the burden of proof can also be tied to the privilege of shaping and defining the terms of debate. If I am attempting to prove that Bill cheated, then I am the one putting forward a specific case, applying a specific definition of what it means to cheat to the situation. Bill may take issue with any of these elements (including the definitions I apply to relevant terms), but in all likelihood, the terms of the debate will be set by my efforts to provide an initial case against him. So, the burden of proof is not a uniformly disadvantageous thing to carry into a discussion. It comes with benefits too.

The fact that burdens of proof are themselves subject to debate does provide one significant argument against invoking them. Their role in legal reasoning is set by established conventions, of course, but in less structured contexts such as the aforementioned debates between atheists and theists, questions about who does and who does not have the burden of proof are every bit as troublesome as those about whether or not God exists, who She is, or what sort of church She wants you to go to. So, instead of helping to shape a productive conversation, invoking this principle often serves to provide the sticking point which stops that debate from happening. This doesn’t make the concerns that lead people to argue for asymmetric burdens less valid, but it does serve to suggest that advancing them may not help you communicate effectively with any particular person.

Ockham’s Razor (alt. Occam’s Razor): This principle is attributed to the Franciscan Friar William of Ockham who formulation is usually translated as follows: “Plurality must never be posited without necessity.” Ockham wasn’t actually the first to articulate the principle, and he certainly wasn’t the last, but he was known to use this principle rather often. One of the more common reformulations of the rule reads; “Do not multiply entities beyond necessity.” Perhaps the expression most in keeping with the rule itself is; “The simplest explanation is the best.” Perhaps , we could simply say; “keep it simple stupid.”

…okay, that’s probably too simple.

Anyway, the concept here is that given different alternative explanations for the same thing, we ought to choose the one that makes the fewest assumptions possible. This is sometimes described as the principle of Ontological Parsimony. Now, this certainly doesn’t mean that we should opt for explanations faulty explanations on the grounds that they are often simpler than accurate ones. The idea here is to shed unnecessary assumptions when they do not actually add accuracy to the explanation. It is a rule of thumb that applies when all other things are equal.

Oddly enough, this principle of simplicity raises all sorts of interesting questions about the nature of reasoning in general, and about the practice of scientific explanation in particular, but for our purposes here it is enough to think of it as a good rule of thumb when considering alternative explanations with roughly equal explanatory value. This rule of thumb is not strictly a function of truth-functional relations between propositions, or even about how to weigh evidence. It comes into play only after the evidence is judged to fall equally on two or more theories (assuming that ever really happens), so it is more a question about the practical choices one makes when reasoning than the logical relations between inferences. Hence, its inclusion in this list.

Principle of Charity: The principle of charity comes into play when to interpret another person’s reasoning. As it happens, we can often interpret what another person says in more than one way. If we are talking to them, or otherwise engaging in continuous dialogue (say by email or chat-room) we can sometimes clear this up by simply asking them what they mean, but if we are stuck with a written text and no clear way of soliciting clarification, then sometimes we have to choose between multiple plausible interpretations.

In such cases, the principle of charity would tell us to choose the interpretation that provides the most sound construction of the argument in question. As an extension of this, one ought to refrain from treating an ambiguous text as an argument if the only argument this then produces would then be obviously unsound.

This may seem like another way of telling people to play nice, but the principle of charity is also about ensuring that your own efforts to evaluate an argument are actually productive and useful. Given the opportunity to stick someone with an argument containing an accidental (unnecessary) flaw, will enable one to reject their reasoning, but if that flaw isn’t essential to their point, then the resulting evaluation will apply to a less intellectually useful version of their argument. By contrast, if you construe an ambiguous argument in the most charitable way possible, then should that argument prove unsound, your evaluation will be more decisive. By following the principle of charity, we choose not only to give those whose arguments we consider a better chance of approval, we also ensure that our own time and effort will be spent considering serious thoughts and substantive considerations.

I think the practical nature of this principle is self-evident. It is not strictly a function of logical relationships. One might add that there are clearly circumstances in which people may not wish to follow this rule of thumb. Certainly a Public Relations representative or a lawyer, perhaps even a politician, may gain some ground by exploiting ambiguities in the positions of their opponents. Whether or not that always helps them in the long run is an interesting question, but it seems fair to say that in at least some cases some people may accomplish their own goals better by violating this principle than by following it. In the realm of academic study, this is perhaps less likely than some of these other contexts. (Note that I do not say it never happens in academia, or even that it would never be sound practice to adopt an uncharitable interpretation of someone with an opposing view.) Suffice it to say that there are genuine benefits to following the principle of charity, and that such benefits have led many to recommend some version of it to those new to the subject.

Two additional considerations: Note that the principle of charity does not mean that one ought to improve upon the arguments of others before evaluating them. It sometimes happens that one will hear an argument and realize that you could improve upon it by changing some of its details. You can choose to do this or not as you see fit (perhaps after responding to the argument as it stands), but this isn’t really about the principle of charity. The principle of charity apples only insofar as one is considering plausible variations on the argument one has actually been presented.

Secondly, if a controversy generates sufficient interest in the public, it will produce a variety of different arguments in favor of different positions. When evaluating those positions, one may be confronted with a choice of different arguments with varying degrees of worth. One may even find that the less worthwhile arguments in favor of a position are significantly more popular than the more thoughtful variations. In such cases, I don’t believe there is anything wrong with commenting on the cheaper variations on a theme (it may even be helpful), providing that doing so does not become a substitute for responding to the better and more sound variants. One should also take care to avoid responding to the more thoughtful variations on a stance as though they were producing the cheaper (and more easily dismissed variants). Given sufficient time and space, it is often worthwhile to produce separate responses to the different variations of a position, dealing with each according to its own merits.

Fallacies: Some fallacies can be understood in terms of practical assumptions about the purpose and social context of reasoning.

Ad ignorantiam (appeal to ignorance): These arguments explicitly turn on questions about the burdens of proof required of participants in reasoning. While it is possible to think of the ad ignorantiam fallacy as occurring whenever someone fails to provide a reason for a conclusion, the possibility that burdens of proof may be skewed by the nature of the propositions in question puts this fallacy on the table whenever people raise such questions.

Circular Argument (begging the question): It’s one of the more interesting features of circular arguments that they actually pass some of the tests of deductive validity (if the premises of a circular argument are true, the conclusion must be true). That should make them valid arguments, right? Still, we don’t think of it that way, and the difference lies in the rhetorical purpose of making an argument in the first place. Simply put, a circular argument fails because it fails to provide a reason worthy of consideration. This is only a problem if we regard the purpose of the argument as one of providing a new reason to begin with. So, this fallacy brings us back to the practical significance of argumentation. It is less a problem of inference relations than a failure of persuasion.