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Petitio Principii or Begging the Question

Abstract: The varieties of petitio principii (begging the question or circular argument) are explained with illustrative examples and links to self-check quizzes.

  1. Petitio Principii (begging the question) is the fallacy of assuming in a premise a statement which is taken to have the same meaning as the conclusion of the argument. Thus, what is to be proved has already been assumed in the premises.

    1. The informal structure of the petitio principii is often similar to one of the following schemata:

      Some Informal Structures of Petitio Principii

      Immediate (hysteron proteron):
      Statement p′ is true.
      Statement p is true. (Where p is a paraphrase of p′.)

      Grammatical or Logical Immediate Inference
      Statement p is true.
      Statement not-p is not true.

      Circular (circulus in probano):
      Statement p is true.
      Statement q is true.
      Statement r is true.
      Statement p is true.



    2. Because the sense of the conclusion (or a suitable paraphrase of the conclusion) is stated in a premise of the argument, the premise would be proved as well by the evidence provided by the conclusion, if the order of statements were reversed. Petitio principii is most commonly known as the fallacy of begging the question even though the term “begging the question” has other vernacular uses.[1]

      1. The term “petitio principii” is used more often in the context of formal logic and the logic of proof than in the context of informal logic.

      2. The term “begging the question” is used most often in the context of informal logic: conversational reasoning, disputation, debate, argumentation, or dialectical reasoning.

    3. Petitio principii can occur as a formal fallacy even though it is usually classified as an informal fallacy.[2]

      1. Strictly speaking, petitio principii or begging the question is a valid but fallacious argument. The argument is defined as fallacious since the conclusion does not logically follow from a premise whose truth has been previously established. Thus, the argument does not prove anything that was already not already known.

        David Sanford points out if “the primary purpose of argument is to increase the degree of reasonable confidence which one has in the truth of the conclusion … every question-begging argument fails this purpose.”[3] Thus, even though petitio principii arguments do not founder logically, they do so epistemologically.

      2. Since some instances of petitio principii can be reformulated as as a syllogism where the conclusion follows from one premise and the other premise is superfluous,[4] the argument is logically valid but does not prove the truth of the conclusion since that statement has already been assumed as a premise.

        E.g., “All men are mortal so Socrates is mortal.”

        If we know the first statement is true, then we also know the second statement is true. There would seem to be no need to state the minor premise that Socrates is a man, since that is the person being referred to as the subject of the conclusion.

    4. Petitio principii is sometimes defined as a simple or immediate argument, whereas circular reasoning is said to involve two or more arguments and so is a mediate argument. (From a logical point of view, distinguishing immediate from mediate circular reasoning is not essential and is only done so for purposes of classification.)

      Nevertheless, most current textbooks conflate petitio principii, begging the question, and circular reasoning (circulus in probano) as interchangeable terms. However this is not the case in much of the academic literature. Douglas Walton, for example, makes the distinction by noting that circular arguments can fail to establish their conclusion in several ways, but immediate begging-the-question arguments fail only the probative function of argument (i.e., begging-the-question arguments do not prove the conclusion.)[5]

  2. The main forms of the petitio principii discussed below include:

    1. Immediate argument (hysteron proteron) occurs when the fallacy occurs as a simple premise-conclusion argument. Some examples include these varieties:

      1. Question-begging epithets (sometimes called question-begging appellatives) are terms or phrases employed in stating the same thing as that which is to be proved. Question-begging epithets are effectively used as emotively significant terms (i.e., slanted language) which presuppose expressions used elsewhere in the argument.

        E.g., “Fundamentally God is just and loving because he rewards the good and punishes the wicked.”[6]

      2. Assuming an abstract statement to be proved from a premise in the form of a more concrete statement is another use of question-begging epithets:

        “[T]he lodestone attracts iron because it possesses the magnetic quality.”[7]

    2. Circular reasoning often is described as a mediate argument occurring in an extensive, often convoluted, argument where what is to be demonstrated has already been assumed in the evidential part of reasoning.

      The same or other arguments closely related to circular reasoning (circulus probando) include reasoning in a vicious circle (circulus vitiosus) and reasoning in a virtuous circle (circulus virtuosus).[8]

      Reasoning in a virtuous circle is not usually considered fallacious since it is more or less based on a coherence theory of truth — not a correspondence (or referential) theory. More on this is described below in section IV.

    3. In argumentation, an effective way to expose an adversary's petitio principii is to request for evidence of the truth of the premises. The proponent is then hard-pressed not to repeat the conclusion. E.g., to the oft-cited example “God exists because the Bible says so, and the Bible is true because it comes from God,” an appropriate question to reveal the circularity is to ask how the proponent knows that God exists and the Bible is factual.[9]

    4. On the standard view of informal fallacy theory (i.e., what is taught in most textbooks), often the reason petitio principii is considered to be a fallacy is not that the inference is invalid (because any statement is indeed equivalent to itself), but that the argument can be deceptive.[10] Nevertheless, identification of fallacious reasoning ought to be based on logical rather than psychological principles. Consequently, from a logical point of view, the fallacy is said to occur because a statement does not prove itself as a conclusion of an argument. A conclusion must have a different source from itself for reasons, grounds or evidence of its truth.

  3. The least convincing kind of petitio principii is the repetition of the same words in the same order in both premise and conclusion. Such an argument is not informative but might be given in unusual circumstances, e.g., the speaker is very tired, talking to a subordinate or a child, in anger, or perhaps even using phatic language.[11]

    1. E.g., consider this typical example from from a story by Guy de Maupassant:
      “Monsieur Daron, very perplexed, said excitedly: ‘Look, he must have died of something! What do you think it was?”

      The doctor threw up his hands.
      ‘I've no idea, no idea at all. He died because he died, that's all.’”[12]
    2. A similar version of this fallacy occurs when the conclusion or the premise is rephrased to appear as though it's a different statement The rephrasing can be by rewording a premise with a synonymous phrase or with phrase such that both propositions state what amount to the same thing.

      1. Typical synonymous or interchangeable rephrasing instances are similar to these examples:

        “They [egos] understand this kind of sense, because it is sensible to them.”[13]

        “[I]t [the soul] is immortal, because it does not really perish.”[14]

      2. Jeremy Bentham points out the use of question-begging epithets or question-begging appellatives which assume the point at issue through the use of emotively laden language. He points out “the mode of using the fallacy with the greatest effect, and least risk of detection,—namely, by the employment of a single appellative”[15]

        E.g.,“Effective learning occurs during short study periods because your study time is not wasted in longer stretches of drudgery.”

      3. Or consider the example provided by William Stanley Jevons: “It would be a Petitio Principii to argue that [a] doctrine is heresy, and therefore it ought to be condemned. To assert that it is heresy is to beg the question, because every one understands by heresy a doctrine which is to be condemned.”[16]

      4. An illustrative example of pointing out the use of a question-begging epithet is shown in the following exchange of letters in the London Review of Books:

        Christopher Eddy writes, “Markus Eichorn claims that Frans de Waal's ‘elegant experiments on primates have shown evidence of intentionality in communication’ There is other evidence, even more compelling, that dumb animals do not communicate.”[17]

        Adam Sandell replies, “Christopher Eddy thinks that communication isn't possible for what he likes to call ‘dumb animals’, a circularity by which he means “non-human animals”.[18]

    3. Jevons observes that petitio principii often occurs when Saxon, Latin, or Greek words are used arguments which express the much the same thing in different terms.[19]

      Whatley concurs that since English is composed of words taken from other languages which are synonymous, the same statement can be present in premise and conclusion. The following argument by Whatley is used in many textbooks and papers as a paradigm example of begging the question:

      “[T]o allow every man an unbounded freedom of speech, must always be, on the whole, advantageous to the State; for it is highly conducive to the interest of the community, that each individual should enjoy a liberty perfectly unlimited of expressing his sentiments.”[20]

      However, this example shows how contextually dependent such arguments can be subject to interpretation. Walton, the preeminent logician for begging the question, states at one point this argument is, “ the classic case of the equivalency type of circularity.” Yet, it seems clear that there remains a contentious point of equivalency not only between “every man” and “every individual” in 18th century England and today but also between the significant difference of denotation of “the State” and “the community.”[21]

    4. Another common kind of petitio principii ensues from the transformation of a conclusion into a premise using logical or grammatical principles.

      1. “You know that God is a just and loving God because God is God and cannot be unjust or unloving.”

      2. “There are many juvenile delinquents since many juveniles break the law, and the reason so many juveniles break the law is that they are juvenile delinquents.”

  4. In circular reasoning (circulus in probando) the conclusion is assumed as a premise either immediately in the argument or else assumed mediately as a premise in a series of arguments. (The distinction between immediate and mediate circular reasoning is not of particular logical or epistemological consequence.)

    1. In direct or immediate circular arguments, the conclusion is explicitly assumed in the premise of that argument and, generally speaking, is easily recognized unless it is part of an extended narrative. An immediate viciously circular argument is present whenever the premise used for accepting the conclusion is the same statement as the conclusion itself.

      1. The vicious circularity is obvious in the following example since it is of the form of A because of B and B because of A:

        “The Soul is simple because it is immortal, and it must be immortal because it is simple.”[22]

      2. Here is another example of the same form but the fallacy is accomplished by means of paraphrase:

        “Iraq can be subject to a suspension of law and forced to swallow the prescriptions of the neo-liberal order, precisely because it remains outside the protection of international law. and it remains outside the protection of international law because it has not become fully integrated into the neo-liberal order.”[23]

      3. An example from Émile Durkheim's writing is of the same form but occurs over the scope of over one hundred pages. Durkheim adduces evidence that (1) religion is the source of the forms of society, and, as well, (2) Durkheim presents evidence that the forms of society determine the character of religion. What follows are the essential premises and conclusions of his circular argument:

        First, the premises:

        (1) “[L]aw, morals and even scientific thought itself were born of religion”[24] and “[T]he most diverse methods and practices, both those that make possible the continuation of the moral life (law, morals, beaux-arts) and those serving the material life (the natural, technical and practical sciences), are either directly or indirectly derived from religion.”[25]

        And, second, the conclusions:

        (2) “We regard it [i.e., the religious nature of man] as the product of social causes, we consider it impossible to find it, if we leave aside his social environment.“ and “[R]eligious evolution … depends upon social conditions”[26]

    2. In philosophy and science, petitio principii can be accomplished through the use of definition to posit “facts.”

      1. For example, the biologist Agassiz argued for the immutability of species in this manner:

        ”It was a great step in the progress of science when it was ascertained that species have fixed characters, and that they do not change in the course of time. … Geology only shows that at different periods there have existed different species. The question we are now examining involves only the fixity or mutability of species during one epoch, one era, one period in the history of our globe. And nothing furnishes the slightest argument in favor of their mutability; on the contrary … species are fixed.”[27]

        As Darwin points out, Agassiz's circularity in defining the immutability of species is accomplished by assuming no species exist between historical periods.[28]

      2. And Locke's definition of justice illustrates this kind of vicious circular reasoning:

        “Where there is no property, there is no injustice, is a proposition as certain as any demonstration in Euclid: for the idea of proper, being a right to anything, and the idea to which the name injustice is given, being the invasion or violation of that right; it is evident that these ideas being thus established, and these names annexed to them, I can as certainly know this proposition to be true, as that a triangle has three angles equal to two right ones.[29]

    3. The fallacy in mediate circular reasoning (circulus in probando) is sometimes difficult to detect in long, dense arguments. Moreover, the precise nature, definition and limits of application of this fallacy have been in dispute since the 17th century.

      One form of this variety of petitio prinicpii is the use of an intermediate step or steps in shifting from the premise to a statement of the same meaning in the conclusion. Essentially there is a linking of premises through subconclusions to a conclusion which returns to the beginning. This form of petitio principii is described as arguing in a mediate vicious circle. Consider the following argument in which the terms are labeled for convenience of analysis:

      1. “Intuitions[C] are true representations in consciousness[B] and since any formative image from the unconscious[A] is an intuition[C], these images[A] are true representations in consciousness[B].

        That being the case (i.e., [A] being [B]), and because all true representations in consciousness[B], not being representations from sense experience, are intuitions[C], it follows that all formative images from the unconscious[A] are intuitions[C].”

      2. Note the vicious circularity in the form of the foregoing argument as represented by the red text:

        All C is B.
        All A is C
        All A is B.

        All B is C.
        All A is B.
        All A is C.

    4. Mutually dependent instances of modus ponens also serve an an example of vicious circular reasoning or circulus vitiosus as when the conclusion of one argument becomes a premise of the next argument in order to prove a premise of the first argument.

      Consider this two-part purported argument for free will:

      If people have free will, people are morally responsible.
      People have free will.
      People are morally responsible.

      If people are morally responsible, then people have free will.
      People are morally responsible.
      People have free will.

    5. Arguments like these occasionally occur in religious, philosophical, and literary passages:

      1. “Chronicles are only a minuscule portion of God's recorded details about people throughout time. … he records everything. … At the end of time, all will know that God is just and loving, because we all will have access to those open books. God's books will proclaim that he's eternally right and accurate.”[30]

      2. “I once overheard three brothers dividing two candy bars. The oldest one gave each of the two younger ones half of a candy bar, and kept a whole bar for himself. When asked why he got more candy, he said he was the smartest. A few minutes later, one of the younger ones asked why he was the smartest, and in reply the oldest said ‘Because I have more candy.’”[31]

    6. The main difficulties in evaluating complex instances of petitio principii include attempting to diagram extensive arguments by sorting out evidential priority order of reasons and then constructing all tacit reasons and conclusions.

  5. The most difficult kind of petitio principii to identify is the kind where one of the premises and the eventual conclusion have exceedingly similar “propositional content.” I.e., the statements are suitable paraphrases of each other (without meaning exactly the same thing), and each depends upon the other for its truth. This variety of petitio principii often is the occasion of controversy about “how much of a difference makes a difference” for the occurrence of non-synonymity.

    1. A controversial example involves the case of an analytical tautology where one premise seems to include the conclusion in its meaning. E.g.,

      All Euclidean triangles are plane figures.
      This triangle is an Euclidean triangle.
      This triangle is a plane figure.

      The minor premise “This triangle is an Euclidean triangle” necessarily includes by definition the conclusion that it is a plane figure. Some logicians allow this syllogism to be logically valid but not informative. Thus, the syllogism would be identified as petitio principii.[32]

    2. In Moliére's play Le Malade Imaginaire, the Primus Doctor states …
      “‘Opium produces sleep’ to which I reply, ‘Because there is in it that dormative power whose nature makes the senses drowsy.’”[33]
    3. The following example of rephrased propositional content, provided by Ian Hacking, is a description of a petitio principii in economic theory committed by the statistician Ernst Engel:

      “A law has been named after Engel … Engel's law states that ‘the poorer the individual, the family or a people, the greater must be the percentage of the income needed for the maintenance of physical sustenance, and of this a greater proportion must be allowed for food.’ It is odd to find this as a law, since Engel had used the proportion of outgoings on food as the measure of material standard of living.”[34]

    4. A more controversial example is illustrated from the writings of Sigmund Freud where he relates an illustration of his argument that all dreams are wish-fulfillments because any dream which does not fulfill a wish does fulfill the wish to prove his theory wrong. So, on this interpretation of the following passage, his reasoning is essentially that all dreams are wish-fulfillments because any non-wish-fulfillment dream is actually a dream of wish-fulfillment:

      “A contradiction to my theory of dream produced by another of my women patients (the cleverest of all my dreamers) was resolved more simply, but upon the same pattern: namely that the nonfulfillment of one wish meant the fulfillment of another. One day I had been explaining to her that dreams are fulfillments of wishes. Next day she brought me a dream in which she was traveling down with her mother-in-law to the place in the country where they were to spend their holidays together. Now I knew that she had violently rebelled against the idea of spending the summer near her mother-in-law and that a few days earlier she had successfully avoided the propinquity she dreaded by engaging rooms in a far distant resort. And now her dream had undone the solution she had wished for; was not this the sharpest contradiction of my theory that in dreams wishes are fulfilled? No doubt; and it was only necessary to follow the dream's logical consequence in order to arrive at its interpretation. The dream showed that I was wrong. Thus it was her wish that I might be wrong, and her dream showed that wish fulfilled [italics original]”[35]

  6. Arguing in a virtuous circle (circulus virtuosus) occurs when justifying, explaining, or proving a statement on the basis of a general theory, philosophy, or world view. That system is constructed of a web of mutually logically dependent statements such that the truth of any particular statement is logically derivable from the truth of other statements in the system. Whenever such justification is informative, no fallacy is said to occur since the reasoning fulfills the epistemological or probative function of an argument.

    1. Consequently the soundness of a virtuously circular argument is based on the fact that the conclusion is already known to be true as it follows from other statement in the system of statements.

    2. The truth of premises which support such a theory are supposed to be able to be established by assumption, argument, empirical reference, or pragmatic practice, although these antecedents are not addressed in virtuous circle arguments.

    3. In virtuous circular reasoning, the soundness of the argument is said to be established internally — i.e., it follows logically from other statements. The particular inference is rendered informative by the presence of the other statements in the system.

      1. However, in debates between two different world views, each disputant justifies assertions in terms of other statements accepted as true in accordance with their respective views. And their disagreement stems from the particular inconsistencies between the corresponding different statements embedded in each respective viewpoint under discussion.

      2. So the resolution of the clash of theoretical differences can only be resolved through some externally justifiable standard — presumably based on some kind of empirical validation.

  7. A number of other techniques in disputation are sometimes confused with petitio principii or begging the question.

    1. Assuming the truth of a statement without argument, by itself, is not necessarily petitio principii or begging the question. Every disagreement must start from statements assumed as premises. Circularity occurs when a non-self-evident assumed statement is used in an argument to prove itself.

    2. The fallacy of begging the question is not a case of proving something beside the question or something irrelevant to the issue under consideration. That is, circular reasoning is not simply missing the point at issue.[36] Such passages as these, however, are interpreted as a diversionary tactic making use of the fallacies of irrelevance most often designated as either ignoratio elenchi or red herring.

      E.g., consider this non sequitur:
      “Understanding is immortal because the truths of the Universe will always be immortal.”[37]
      Supplying the missing premise,
      “Understandings are truths of the universe”
      reveals the lack of circularity.

    3. On occasion, the scope of the fallacy has been mistakenly extended to include the rephrasing in terms of a vacuous, meaningless expression, or a truism which, although not falsifiable, does not add anything or give any additional information. So in the context of the argument, it is claimed the “reasoning” provided has the import of saying much the same thing, i.e., arguing in a circle.

      Here are two typical examples of vacuous reasoning:

      1. ”[The] five-year tenure as [city] Police Chief came to an abrupt end Monday evening. … ‘The reason for the discharge as that we want to move ahead in a different direction,’ [the Mayor] said. ‘His services were no longer needed.’[38]

      2. “The attractive interaction between the lodestone and iron [is] caused by xiang gan (mutual influence), a sympathetic response between two interacting entities.… [S}ome items attract others, while some cannot, because their qui is different and consequently they cannot mutually influence one another.”[39]

    4. Name-calling or ad hominem attacks can be viewed as question-begging epithets, but such arguments should not be confused with the fallacy of begging the question, as some logic textbooks have done.[40] It is important to remember that not every emotively-laden adjective used in disputation begs the question at issue.

    5. Quite often, petitio principii can only be accurately identified within the context of a presentation or discussion, not in isolation of that context. As in all informal fallacy evaluations, the context of the passage is vital.

      1. Petitio principii arguments can suffer from a certain degree of ambiguity and vagueness due to lack of knowledge of their context and intention. Many informal logicians argue that, in general, circular reasoning cannot be judged in the absence of dialogue. In the following argument, a dialogical approach is clearly necessary in order to rule out circularity:
        ”Autonomous vehicles will be nice for everyone, because they will let people get on with something worthwhile as they travel.”[41]
        Does “get on with something worthwhile” mean “get on their way with a worthwhile vehicle ” (as opposed to run-down public transportation) or does the phrase mean “do a worthwhile activity when traveling”?

      2. Consider the following argument which appears to be circular:

        “I do it because that's what I do.”[42]

        The argument seems to conclude “I do it” from the assumption that I do it. The author might be arguing that the truth of the statement, “I do it,” is based on the empirical fact that I do it. However, the context of the passage is suggested from a couple of snippets in its continuation …
        “I design a magazine and do Internet work in my spare time because it is my magazine and Internet work … I've see[n] people li[v]e their lives wishing they were doing something else, wishing they had different opportunities …”[43]
        So since the intent of the excerpt of the argument is something like this …
        I do it because it is something I enjoy and do well.
        … the argument does not seem to be a petitio principii.

      3. Identification of the following example hinges on the meaning of ”grounded.” Circularity occurs if contextually “grounded” means ”grounded in the divine”:
        “St. James was divinely inspired when he wrote his epistle, and therefore the story must have been well grounded.”[44]
    6. Finally, it's important to point out that circularity in explanations and definitions are not fallacies per se. Nevertheless, vicious circularity in explanation and definition is uninformative. Arguments are intended to increase knowledge, whereas explanations function to increase understanding. Consequently, circularity in arguments does not increase belief or conviction, but some kinds of circularity in explanations, if not vicious, can do so.[45] In the following examples, no fallacy occurs because the passages are intended as explanations.

      1. Circularity in the following explanation, however, is flawed because it produces inappreciable understanding:
        [T]he very conception of the aesthetic object [i]s that which gives pleasure simply because it is that it is, not because it is good for anything.[46]
      2. Whereas the following passage could be taken for a viciously circular argument, it is in context an informative explanation:
        [H]e was a contented and wealthy man — contented because he was wealthy, and wealthy because he was contented.[47]
        In senses of the words “wealthy” and “contented” are different in the last statement of this passage. The wealth is not monetary but spiritual and the contentment is not monetary but peace of mind.

        Consequently, the passage is not a circular argument but is a non-circular explanation.

    7. A presumed tautologous or analytic statement is said to beg the question when that statement is being used as a premise in an argument. E.g., John Locke argues that the Scholastic doctrine “Thinking is the essence of soul” begs the question of what is to be proved as to the nature of soul since the truth of the doctrine is not immediately evident.

      Locke uses “beg the question” in this sense when he states that inasmuch as the Scholastic belief that thinking is the essence of the soul is not self-evident, the belief begs the question. That is, the belief elicits the need to prove such an hypothesis prior to its use as a premise.[47] This particular use of begging the question is no longer classified as a petitio principii fallacy in the literature and in recent logic textbooks.

  8. The contemporary resurgence of interest into begging the question stem from Richard Robinson's 1971 paper distinguishing Aristotle's treatment in the Topics not as a fallacy but as rule breaking in the dialogue-game of elenchus from Aristotle's treatment in the Prior Analytics as an instance of argumentative self-evidence.[48]

    1. Walton argues that begging the question cannot be analyzed solely in terms of the statements used in critical discussions; the fallacy is best described as a pragmatic failure of dialogue since those statements' meanings are contextually determined.[49]

    2. Whether an argument is circular or not, then, depends on the context of the beliefs expressed in the critical discussion by the disputants about the statements presented — and does not depend upon the purely formal identity or equivalence of the statements being discussed.

    3. Occurrences of circular argument are somewhat subjective in these contexts since they are relative to the belief systems of the disputants. The context is determined by the dialogue leading up to the presentation of the argument. Therefore, identification of petitio principii is not just a formal evaluation of an argument, but is dependent upon how the premises are established within the context of a persuasive dialogue.

      As Alfred Sidgwick puts it: “What we can always do is to suspect the presence of a given fallacy, and to seek for clearer indication of it. But to fasten on the words of the argument and say confidently that our opponent is begging the question … is to put ourselves in a needlessly weak position. Indeed, the charge of begging the question is a peculiarly difficult one to substantiate.”[50]

  9. Circular reasoning occurs especially in the following philosophical issues:

    1. Free Will/Determinism Debate: To what extent and in what sense are motives a determining factor in choice and action. Circular reasoning together with verbal disagreements and ambiguous phraseology occurs often in free-will controversies. For example, to explain all actions in terms of causality is itself presupposing a deterministic theory.[51]

    2. Logical Proofs of Existence: Deductively, the existence of something cannot be proved from statements which do not already presuppose existence. As Søren Kierkegard argued, for example, Napoleon's existence cannot be proved by arguing …

      An [unknown] invaded Russia, lost the Waterloo campaign, was exiled to Elba, and so on.
      Napoleon is the [unknown].
      Therefore, Napoleon exists.

      The truth of the conclusion “Napoleon exists,” only logically follows if the [unknown] in the premises is already presumed to exist in a premise.[52]

    3. Deductive Reasoning: Some philosophers have worried that if logic and mathematics were merely verbal based on non-empirical statements, it would follow that these forms of reasoning are instances of petitio principii. For example, in reasoning from a general statement to a particular statement subsumed under that general statement, nothing would be proved since the conclusion would be already assumed as known. From the statement “All men are mortal,” if we know Socrates is a man, then it follows he's mortal. But this conclusion is just a particular instance of the general statement which subsumes “Socrates as well as other persons to be mortal.”[53]

      If an argument is a valid deductive argument, it's impossible for the conclusion to be false with true premises; consequently, it would seem that there can be no more information in the conclusion than that given from the outset in the premises. So logicians need an account for how deductive argumentation can prove something not already known in the premises themselves.[54]

      The nature and definition of begging the question raises questions about the essential features of the constitution of an argument. If an argument is defined as having at least two statements, then begging the question, containing one statement used twice, would not qualify as an argument at all.[55]

      If an argument is defined as having a minimum of two premises, then the immediate inferences of formal logic would not count as arguments.[56] And if a fallacy is defined as a form of deceptive reasoning then some instances of begging the question would be fallacies to some persons but not to others, depending upon who is deceived.[57] Finally, if a fallacy is defined merely as a violation of a rule of reasoning and argumentation, then validity alone would not be a sufficient condition for a good argument because instances of begging the question are valid arguments.[58]

    4. The Cartesian Cogito Proof: Descartes reasons that since he is thinking, he exists as a thinking being. Yet,the reason that Descartes uses to prove his existence cannot include the fact of his existence. But since Descartes' thinking seems to presuppose that Descartes exists, the argument already presupposes his existence in the premise. Circularity here also has to do with thinking is only reliable if there is a God. These are a few of the points being disputed about his arguments in Discourse on Method and in Meditations.[59]

    5. Current applications of the importance of circular arguments involve the linking of ad verecunidam, ad hominem, and petitio principii in multi-agent systems of reasoning for trustworthy sources in artificial intelligence.[60]


Online Quizzes

Test your understanding of petitio principii, begging the question, and circular reasoning with the following quizzes:

Petitio Principii Examples Exercise
Fallacies of Presumption Examples Quiz I
Fallacies of Presumption Examples Quiz II
Fallacies of Presumption Examples Quiz III



Very few actual arguments show their circular character clearly on their face; as a rule the critic has to dig it out from the surrounding verbiage, with opportunities of discovering meanings that were never intended.

Alfred Sidgwick, Elementary Logic, (Cambridge: Cambridge University Press, 1914), 147.

Notes

1. What does it mean to beg the question? A.W. Sparkes concludes his discussion of the historical origin of the term in this way: “If an argument is to be successful, the truth of the premises must be admitted by both sides. When a disputant asserts a premise, he is, therefore, asking his opponent to grant it to him. When he asserts the conclusion as one of his premisses, he is asking his opponent to grant him the truth of the statement whose truth has been questioned: he is ‘begging the question.’“ [A.W. Sparkes “Begging the Question,” Journal of the History of Ideas, 27 no. 3 (Jul.-Sept. 1966), 464.]

Note that “question begging” is not in this use related to being prompted to raise a question. For example, if the premises are irrelevant to the conclusion of an argument, a question might raised or be elicited as to how the premises prove anything. This would not be an instance of the fallacy of question-begging. Thus the everyday (now accepted) use of the term question begging as “something that moves someone to react by asking a specific question” is not what is meant here in the logical sense of the argument of begging the question. An example of the non-argumentative use of “beg the question” would be: “‘Humorous’ is a word as question-begging as ‘artistic,’ and he would be a rash man who should try to define either.” [Stephen Lucius Gwynn, Irish Books and Irish People (Lytton: Australia: Talbot Press, 1919), np.] See “Usage Notes; Beg the Question,” Merriam-Webster https://www.merriam-webster.com/words-at-play/beg-the-question (accessed 27 Mar. 2017).

In ordinary language use, circularity and question-begging are names for the same fallacy; nevertheless, many logicians define them differently. In general, petitio principii or circularity is a formal argument where the conclusion is either equivalent to the premise or to one of the premises, or whose presence is necessary to the premise or necessary to prove one of the premises. In question begging, the premise and conclusion are logically equivalent or the premise implies the conclusion as a immediate inference. Superfluous premises might be present in either case. Thus, although instances of petitio principii (circularity) are distinguishable from instances of begging the question, on these definitions, some instances can be appropriately described as either mode of argument. But, then again, this distinction is not generally agreed upon in the current literature.

2. Aristotle, Prior Analytics trans. E.M. Edhill in The Basic Works of Aristotle, ed. Richard McKeon (New York: Random House, 1941), 65a 10-15. Also, Aristotle writes, “[W]henever a man tries to prove what is not self-evident by means of itself, then he begs the original question. This may be done by assuming what is in question at once; it is also possible to make a transition to other things which would naturally be proved through the thesis proposed, and demonstrate it through them.” Prior Analytics, 64b 36-40.

3. David H. Sanford, “Begging the Question,” Analysis 32 no. 6 (Jun. 1972), 197-199. DOI:10.2307/3327724

4. David Ross, Aristotle 5th ed. (London: Routledge, 1995), 37.

5. “… not all circular argument commit the fallacy of begging the question.” [Douglas N. Walton, “Begging the Question as a Pragmatic Fallacy,” Synthese 100 no. 1 (Feb. 1994), 96.] Smith recognizes the distinction between immediate and mediate circular arguments but gives little importance to the distinction. Michael P. Smith, “Virtuous Circles,” The Southern Journal of Philosophy 25 no.2 (Jun. 1987), 207.

6. Michael Wilcockson et al., A Student's Guide to A2 Religious Studies, (London: Rhinegold Publishing, 2005), 52.

7. Steven Nadler, The Philosopher, the Priest and the Painter: A Portrait of Descartes (Princeton, New Jersey: Princeton University Press, 2013), 30.

8. The question of circular reasoning is an active area of inquiry. Various theories are proposed from various contexts so that notions of epistemic, logical, pragmatic, dialectical, and functional are studied. Proposed accounts of circularity invariably depend on the contexts of formal or dialogue types. Two major current approaches are the epistemic (that of proving belief) and pragma-dialectical (that of devising procedural or rule-governed discussion).

9. J.R.T. Lamont writes that this argument is not circular since if Mr. Jones of the Water Conservation Board sends a letter, then Mr. Jones exists on the basis of the letter having been written so likewise God exists on the basis of the Bible having been written. In fact, all that can be known without further evidence is that the letter and the Bible have been written — by whom, does not follow from the existence of the writings. [J.R.T. Lamont “Believing That God Exists Because the Bible Says So,” Faith and Philosophy 13 no. 1 (Jan. 1994)) 121-124.] Gary Colwell also explores some contexts in which the non-circularity of such arguments depend upon the dialectical circumstances in which they are given. [Gary Colwell, God, The Bible and Circularity 11 no. 2 ( Spring 1989), 61-73]. Walton also examines this argument extensively from a pragmatic perspective. [Douglas Walton, “Begging the Question in Arguments Based on Testimony,” Argumentation 19 no. 1 (Mar. 2005), 97-99 and 101-106.] What these accounts seem to overlook is that the circularity of such arguments, from a logical point of view, is due to the inherent circularity of existence proofs.

10. For example, Copi writes, “It is customary to reserve the term ‘fallacy’ for arguments that, although incorrect, are psychologically persuasive.” I.M. Copi and Carl Cohen, Introduction to Logic 9th ed. (New York: Macmillan Publishing, 1994), 115.

11. Bronislaw Malinowski, “The Problem of Meaning in Primitive Languages,” in C.K. Ogden and I.A. Richards, The Meaning of Meaning (London: Kegan Paul, 1936), Supplement I: 296-366.

12. Guy de Maupassant, “An Old Man,” in Selected Stories, trans. Roger Colet (Franklin Center, Pennsylvania: Franklin Library, 1983), 298-299.

13. H. Schucman and W. Thetford, eds., Course in Miracles (Ancient Wisdom Publications, 2008), 86.

14. Origen, Origen Contra Celsum in The Writings of Origen, trans. Frederick Crombie, Vol. 2 (Edinburgh: T. & T. Clark 1872), 227.

15. Jeremy Bentham, The Book of Fallacies in The Works of Jeremy Bentham, Part VIII (Edinburgh: W. Tait, 1839), 436.

16. Wiliam Stanley Jevons, The Elements of Logic (New York: Butler, Sheldon & Company, 1883), 174. Douglas Walton notes after analyzing a similar argument, probably based on this one by Jevons, that circularity occurs only if “heresy” is persuasively defined whereby “heresy” means ”any view or statement that is opposed to official church doctrines of the time.” [Douglas Walton, Ethical Agumentation (New York: Rowman & Littlefield, 2003) 72] In such a case, the argument would be contextually circular for adherents of those church doctrines.

17. Christopher Eddy, “Letters: One Tree to Another,” London Review of Books 39 no. 6 (16 Mar. 2017), 4.

18. Adam Sadell, “Letters: One Tree to Another,” London Review of Books 39 no. 7 (30 Mar. 2017), 4.

19. W. Stanley Jevons,Elementary Lessons in Logic, (London: Macmillan and Co., 1895), 181.

20. Richard Whatley, Logic, 2nd ed. (London: John Joseph Griffin & Co., 1849), 76.

21. [Walton, Argumentation, 87.] This example exhibits the problem outlined by Alfred Sidgwick of interpreting discourse within a context based on unwarranted interpretation. His principle of access anticipated the dialogical structural approach taken a century later. [See also Douglas N. Walton and Erik C.W. Krabbe, Commitment in Dialogue: Basic Concepts of Interpersonal Reasoning (Albany, New York: SUNY Press, 1995).]

22. Alex C. Michalos, Improving Your Reasoning (Englewood Cliffs, NJ: Prentice-Hall, Inc., 1970), 28.

23. Fredy Cante and Hartmut Quehl, Handbook of Research on Transitional Justice and Peace Building in Turbulent Regions (Hershey, Pennsylvania: Information Science Reference, 2016), l310.

24 Émile Durkheim, The Elementary Forms of the Religious Life, trans. Joseph Ward Swain (1915; repr., Mineola, N.Y.: Dover Publications, Inc, 2008), 70.

25. Durkheim, 223.

26. Durkheim, 94.

27. Louis Agassiz, An Essay on Classification (London: Longman, Brown, Green, Longmans, and Roberts, 1859), 75-78.

28. Sir Francis Darwin, The Life and Letters of Charles Darwin, vol. 2 (London: John Murray, 1888), 333.

29. John Locke, An Essay Concerning Human Understanding, Vol. 2 (New York: Dover Publications, 1959), 208. This source of this argument according to Hobbes is the medieval schools of Law. Thomas Hobbes, Leviathan ed., G.A.J. Rogers and Karl Schuhmann, Vol 2 (New York: Continuum International, 2005), 115.

30. Jan Cookson, God Is … (Bloomington, Indiana: WestBow Press, 2013), 256.

31. Ernest J. Chave, Personality Development in Children (Chicago: Univ. of Chicago Press, 1937), 151.

32. E.g., J. N. Keynes, Formal Logic, 4th ed. (Oxford: Oxford University Press), 426. As reported in J. D. Mabbott, “Two Notes on Syllogism,“ Mind, New Series, 48 no. 191 (July, 1939), 328.

33. Translation from the source:

Opium facit dormire.
A quoi respondeo,
Quia est in eo
Virtus dormitiva,
Cujus est natura
Sensus assoupire.

Jean-Baptiste Poquelin dit Moliére, Le Malade Imaginaire (Act III, Interlude III) in Oeuvres, Vol. 6 (Paris: P. Didot, 1794), 505.

Although this example is sometimes cited as a tautological explanation, [William Stanley Jevons, Elementary Lesson in Logic (London: Macmillan and Co., 1870), 270] the argumentative petitio principii was interpreted by Charles Peirce to display a pragmatic difference between terms as a difference of “subjectal abstraction” (constructing a subject out of a predicate). [Charles Sanders Peirce, The New Elements of Mathematics, v. III/2 Mathematical Miscellanea, ed. Carolyn Eisele (The Hague: Mouton Publishers, 1976), 917].

And some philosophers of science see in examples like Moliére's an inference to the nature of something from its effects (which might, or might not, be vacuous) and so oppose the thesis of the “causal inefficacy of dispositions.” But, on the account taken here, a dispositional property is considered necessarily connected to its causal relation, and so the Doctor's expressed logical or grammatical relation does not prove or explain anything. The concept of a power is necessarily contained in the concept of an effect.

See also Stephen P. Turner and Paul A. Roth, The Blackwell Guide to the Philosophy of the Social Sciences (London: John Wiley & Sons, 2008), 23.

Also, relevant in examples such as these is the contrast between an argument and an explanation.[33]

34. Ian Hacking, The Taming of Chance (Cambridge: Cambridge Univ. Press, 1990), 140. Hacking concludes, “To the innocent Engel's law looks like a tautology. Perhaps that is as it should be, given Engel's own scepticism about the very concept of statistical laws. Anything that did get called a law would be the consequence of a definition, not an inductive regularity.”

35. Sigmund Freud, The Interpretations of Dreams (New York: Avon, 1966), 185.

36. Quite a few debating textbooks extend the application of petitio principii to mean as well ignoratio elenchi or irrelevant conclusion. Alfred Sidgwick states some forms of petitio principii “would come almost equally well under the designation ignoratio elenchi (or misrepresenting the point at issue).” Alfred Sidwick, The Application of Logic (London: Macmillan and Co., 1910), 217.

37. Gonzalo Rodriguez-Fraile, A New Paradigm of Reality (Madrid: Foundation for Consciousness Development, 2015), np..

38. Adapted from Frank Bumb, “[Police Chief] Top Cop No More," Index-Journal 95 no. 108 (November 15, 2013), 1A.

39. Chen Cheng-Yih, “Magnetism in Chinese Culture,” in Encyclopaedia of the History of Science, Technology and Medicine in Non-Wester Cultures, ed. Helaine Selin, 2nd. ed., Vol I (New York: Springer Science and Business Media, 2008), 1263.

40. E.g., Roy Wood Sellars conflates the two fallacies in his discussion of question-begging epithets. Roy Wood Sellars, The Essentials of Logic (Boston: Houghton Mifflin Company, 1917), 150.

“Aparkalypse Now,” The Economist 423 no. 9035 (8 Apr. 2017), 12.

41. Janet Kuypers, The Boss Lady's Editorials (Gurnee, Illinois: Scars Publications, 2005), 68.

42. Kuypers, 68.

43. Thomas Chubb, A Collection of Tracts on Various Subjects, Vol. 2 (London: T. Cox, 1743 ), 32.

44. See Ulrike Hann, “The Problem of Circularity in Evidence, Argument, and Explanation,” Perspectives on Psychological Science 6 no. 2 (2011).

45. Karsten Harries, “The Need for Architecture,” in Architecture: Celebrating the Past, Designing the Future (New York: Visual Reference Publications, 2008), 19.

46. John Locke, An Essay Concerning Human Understanding, 13th. ed. (London: William Tegg & Co. 1849), 56.

Russel H. Conwell, “Acres of Diamonds,” in “Famous Speeches in History,” Emerson Kent.com (accessed 19 Apr. 2017).

48. Richard Robinson, “Begging the Question,” Analysis 31 no. 4 (Mar. 1971), 113-117. References for Aristotle: Topics 16b 31-33 and Prior Analytics B 16.

49. Douglas N. Watson, “Begging the Question As a Pragmatic Fallacy,” Synthese 100 no. 1 (Feb. 1994), 95-131.

50. Alfred Sidgwick, The Application of Logic (Macmillan and Co., 1910), 207.

51. Some of the elements of circular reasoning invoked on both sides of the debate are examined in dialogue form by Gary Colwell, “Freedom, Determinism, and Circular Reasoning,” Argumentation 8 no. 3 (Aug. 1994), 251-263.

See the discussion “Søren Kierkegaard, ‘God's Existence Cannot Be Proved,’‘ Introduction to Philosophical Inquiry Online

See the discussion Morris F. Cohen and Ernest Nagel, A Introduction to Logic and Scientific Method, (New York: Harcourt, Brace, 1934), 177-179

54. A summary of some of the difficulties is provided by Ian Rumfiftt, The Boundary Stones of Thought: An Essay in the Philosophy of Logic (Oxford University Press, 2015), 56-65.

55. See Dale Jacquette, “Logical Dimensions of Question-Begging Argument,” American Philosophical Quarterly 30 no. 4 (Oct. 1998). 317-327.

56. Robert Hoffman, “On Begging the Question at Any Time,” Analysis 32 no. 2 (Dec. 1971), 51.

57. Hans Vilhelm Hansen, “The Straw Thing of Fallacy Theory: The Standard Definition of ‘Fallacy,’“ Argumentation 16 no. 2(June 2002), 140-142.

58. C.L. Hamblin, Fallacies (London: Methuen & Co., Ltd., 1970), 14.

59. See for example Arnold Berleant, “Discussion on the Circularity of the Cogito,” Philosophy & Phenomenological Research 26 no. 3 (Mar. 1966), 431-433.

60. Walton, Douglas. Witness Testimony Evidence: Argumentation, Artificial Intelligence and Law (Cambridge, Cambridge University Press, 2008).


Readings: Petitio Principii

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