INFORMAL LOGIC XVI.l. Winter 1994

Denying the Antecedent: A Common ?

MICHAEL B. BURKE Indiana University

Key Words: ; ; informal logic; (2) How often can the fallacies justifiably logic. be charged? And note the advisability of Abstract: An argumentative passage that might considering the fallacies individually. It appear to be an instance of denying the antecedent may be that some fallacies, such as straw will generally admit of an alternative interpreta­ man and , are often tion, one on which the conditional contained by committed and can often be charged, that the passage is a preface to the rather others, such as ad ignorantium, are rarely than a premise of it. On this interpretation. which committed. and that still others, such as af­ generally is a more charitable one, the conditional firming the consequent, can seldom be plays a certain dialectical role and, in some cases, a rhetorical role as welL Assuming only a very charged even if they are frequently com­ weak principle of exigetical charity, I consider mitted. (Perhaps charity will almost al­ what it would take in a given case to justify ac­ ways require that an apparent example of cepting the less charitable interpretation. I then be taken as an in­ present evidence that those conditions are seldom ductive argument instead.) For pedagogi­ met. Indeed, I was unable to find a single pub­ cal as well as theoretical purposes it would lished argument that can justifiably be charged be desirable to have a sense, with respect with denying the antecedent. to each fallacy, both of the frequency with which it occurs and of the frequency with How often do real arguments, argu­ which it can justifiably be charged.4 ments actually given, commit the fallacies In what follows I will discuss a single named, described. and classified in logic fallacy: that of denying the antecedent. I textbooks? Are these "common fallacies" will offer evidence that this fallacy is less truly common? No, probably they are not. common, at least in print, than is often sug­ That is the provocative claim of Maurice gested. More importantly, I will identify an Finocchiaro. I If we interpret arguments obstacle to charging this fallacy, an obsta­ sensitively and charitably. if we view them cle so serious that I know of no real argu­ as enthymematic and/or non-deductive ment that can justifiably be charged with whenever it is reasonable to do so, then, denying the antecedent. Finocchiaro has argued, we will seldom be I want to stress that I will not be rely­ able to charge them with named fallacies. ing on some very strong principle of ex­ In response, Trudy Govier has disputed the igetical charity. Indeed, I will not rely on adequacy of Finocchiaro's evidence.2 And any principle of charity. I will need only a Ralph Johnson has recorded his conviction, principle prohibiting the opposite of chari­ based on practical experience. that at least ty, one I will call (for want of a better some ofthe named fallacies are indeed com­ name) the principle of fairness. Suppose mon. Johnson cites , , we are choosing between two interpreta­ and .' (Hereafter "the named tions of a passage. And suppose that on in­ fallacies" will be simply "the fallacies.") terpretation A the passage contains a Note that there really are two questions: fallacy, while on interpretation B it does (I) How often are the fallacies committed? not. My principle of fairness requires only 24 Michael B. Burke

this: We should not prefer A to B unless the crash right after the start, so we're ex­ balance of textual, contextual, and other pecting another driver to be the winner. evidence favors A over B. Principles of 3. If the farmers will organize, they have a charity require that we presume, more or good chance of keeping the price less strongly, the absence of fallacy. The supports. But who ever heard of farmers really getting together on anything? principle of fairness requires only that we They are by occupation and conviction not presume the presence of fallacy. Now individualistic to the core. even for the principle of fairness, to which 4. Total pacifism might be a good principle I anticipate no objection, it might prove if everyone were to follow it. But not challenging to provide a fully satisfactory everyone is [following itl, so it isn't. theoretical justification. That is a task I (Gilbert Harman) will not here undertake.s 5. If antiabortionism required the pervert­ ing of natural reason and moral sensibil­ ities by a system of superstitions, then I the liberal could discredit it-but it doesn't, so he can't. (Roger Wertheimer) The fallacy of denying the antecedent 6. "J. J.", I replied, "if it were any of your business, I would have invited you. It is is the fallacy committed by any (semanti­ not, and so I did not." (Paul Erdman) cally invalid) deductive argument that has, when fully stated, the following form. I will come right to the point: These passages cannot fairly be charged with the Premise: If A, then B Premise: Not A fallacy of denying the antecedent, because Conclusion: Not B there is 'no adequate reason to regard the conditionals they contain as premises. It is My bookshelves hold 78 logic text­ anything but unusual for a passage con­ books and 3 theoretical works on fallacies. taining an argument to contain statements Of these, 44 mention the fallacy of denying that are not parts of the argument. Each of the antecedent. And 17 say that the fallacy our passages (except 6) contains an argu­ is common, tempting, or frequently con­ ment. But in no case is there adequate rea­ fused with the valid forms son to consider the conditional a part of the and . In 5, all of them text­ argument. In each case it is at least as plau­ books of formal logic, denying the ante­ sible to ascribe to the conditional some cedent and affirming the consequent are other role. In each case it is at least as plau­ the only fallacies mentioned by name. sible to take the argument to be an My 81 books offer many examples of enthymematic instance of modus ponens denying the antecedent, of which the great (or of modus tollens, depending on the majority are concocted. Below are some of formulation of the unstated conditional). their concoctions, followed by some of Consider passage 1. The "since" ena­ their examples of arguments actually bles us to identify as a premise the claim given. 6 When considering the concoctions, that capital punishment does not deter examples 1-3, we will imagine that they murder. And it enables us to identify the are real utterances. conclusion: Capital punishment is not jus­ I. If capital punishment deterred murder, it tified. What it does not tell us is the role of would be justified. Since it doesn't, it isn't. the (stated) conditional. Is the conditional 2. Broc Glover was considered sure to win a part of the argument or a preface to it? Of if he had no bad luck in the early part of course, the conclusion cannot validly be the race. But we have learned that he has inferred solely from the premise flagged had the bad luck to be involved in a by "since." But that is no indication that Denying the Antecedent 25

the conditional is a second premise. since revealing that the arguer accepts the con­ counting it as such would neither validate clusion only because the arguer accepts the the inference nor even strengthen it. If stated premise. there is some non-premisory role we might Similar comments apply to all of our plausibly assign to the conditional, there is passages. In no case is there any textual in­ no apparent obstacle to doing so. dication that the (stated) conditional is a And indeed there is such a role: that of premise. In each case (except 6) it is plau­ clarifying the nature of the arguer's objec­ sible to ascribe to the conditional the dia­ tion to capital punishment, of making clear lectical role I have described. In most cases that the arguer opposes capital punishment the conditional, thus understood, plays only because the arguer believes it doesn't some other role as well. In passage 2, the deter murder. This is a worthy role no mat­ conditional serves to convey the dramatic ter what the circumstances, but it has spe­ significance of the argument: In all proba­ cial importance, rhetorically, if the arguer bility, the favorite has been eliminated. In anticipates resistance to the argument. The passage 3, the conditional serves, via its arguer can use the conditional to "connect" conversational implications, to identify the with the audience. The conditional can unstated premise and, thereby, the unstated serve to communicate, "Look, I'm not op­ conclusion. In passage 5, the conditional posed to capital punishment on principle. may appear to have a polemical role: that I'm a pragmatist, not a moral absolutist. of creating resentment toward the insulting If I thought capital punishment deterred "liberal." (If 5 seems especially weak, murder, I'd be for it." that's not because 5 truly is an instance of But regardless of whether the condi­ denying the antecedent. It's because of the tional is meant to serve the rhetorical func­ doubtfulness of the unstated premise.) In tion of softening resistance, it serves (on passage 6, which I consider to be an expla­ the reading I suggest) the important dialec­ nation and not an argument, the condition­ tical function of indicating that the stated al plays a role analogous to the dialectical premise is, in the opinion of the arguer, role of the other conditionals: that of tell­ crucial to the case for the conclusion: If ing J. J. that he was excluded only for the the audience can cast doubt on the stated stated reason. (His exclusion was not over­ premise, the arguer will not simply substi­ determined.) In addition, the conditional tute another argument for the same conclu­ may be serving to assert the speaker's rec­ sion; the arguer believes that the titude: Neither antipathy toward J. J., nor conclusion stands or falls with the stated an ability to exploit his absence, nor any premise. other unworthy motive would have result­ To sum up my comments on passage I, ed in the omission of an invitation, if the it is plausible to view the passage as con­ matter had been any of J. 1.'s business. sisting of a conditional statement followed Once stated it is obvious, I believe, that by an enthymematic instance of modus po­ the conditionals are naturally and plausibly nens. (Findings reported in Section II sug­ viewed in the way I suggest. Is there any gest that real instances of modus ponens good reason not to view them in this way? are almost always enthymematic.) Thus Is there any good reason to think that the viewed, the argument contains one stated conditionals are indeed parts of the premise and this unstated premise: If capi­ arguments-and that the arguments are tal punishment doesn't deter murder, then therefore formally fallacious? Well, if it isn't justified. The first sentence of the there is some contextual or circumstantial passage, the stated conditional, is not a evidence in favor of such a view, if the ar­ part of the argument. It has, in addition to guers have admitted denying the anteced­ any rhetorical role, the dialectical role of ent, or if it has been determined through 26 Michael B. Burke

cleverly designed experiments that these the passage is a premise and that the pas­ arguers are highly susceptible to that falla­ sage, therefore, is an instance of denying cy, then the answer is yes. But no such evi­ the antecedent. Otherwise we will call it an dence has been adduced. And none is "A" pattern. (Thus an argumentative pas­ apparent when one examines the sources? sage with an A pattern might or might not Absent such evidence, there is no apparent be an instance of denying the antecedent. basis for charging the arguers with denying One with a B pattern almost surely is.) the antecedent. To do so would be unfair­ Below are some patterns of each type. unless their arguments would be no better A Patterns (relatively common) at all on the interpretation I have suggest­ (a) If A, then B. Not A. So, not B. it ed. And for this condition to be met, (b) If A, then B. But not A. So, not B. would not be enough, at least from a dia­ (c) If A, then B. Since not A, not B. lectical perspective, for the validating con­ (d) If A, then B. But since not A, not B. ditional to be less than certain, for it to be less than acceptable, or even for it to be B Patterns (uncommon) downright implausible. It would have to be (e) Not A. If A, then B. So, not B. indisputably indefensible, that is, indisput­ (f) If A. then B. And not A. So, not B. (g) Not A. Since B if A, not B. ably incapable of being made acceptable. (h) If A. then B. And since not A. not B. After all, denying the antecedent is an in­ 0) Not A. But if A. then B. So, not B. disputably indefensible form of argument. (j) Not A. But since B if A, not B. This stiff (but fair) requirement is satisfied (k) Not B, since not A. And if A, then B. in none of the examples we have (I) Not B, since B if A. And not A. considered-and in none of which I am (m) If A, then B. So not B, since not A. aware. But for any example in which it is Patterns (a)-(d) are A patterns. In pat­ satisfied. I would allow that the charge of terns (a) and (b), "so" immediately follows denying the antecedent is not unfair, even "not A." In (c) and (d), "since" immediate­ if, given the availability of an equally plau­ ly precedes "not A." These placements in­ sible interpretation, the charge is not dicate that "not A" is serving to support differentially justified. "not B." But none of the four patterns con­ tains a textual indication that "If A. then B" is playing the same role. None contains II a textual obstacle to assigning to that con­ ditional the dialectical and other roles that Are examples 1-6 in some way unrep­ I have described. resentative? Do we commonly encounter Patterns (e)-(m) are B patterns. In pat­ passages that are best viewed as instances terns (e), (g), (i), (j), (1), and (m), the posi­ of denying the antecedent? Is it likely that tions of "so" and "since" indicate that "If this fallacy is commonly committed, even A, then B" (or "B if A") is serving to sup­ in published writings. however hard it may port "not B." In (f), (h) and (k), the "and" be to justify charging the fallacy? In this indicates the same thing, although some­ section, I will offer some evidence in sup­ what less strongly. (By contrast, the "but" port of negative answers to these questions. in A patterns (b) and (d) creates no pre­ The fallacy of denying the antecedent sumption that the statements preceding it is instantiable by passages of many differ­ are premises.8) ent patterns. We will call any such pattern Now what is telling is that A patterns a HB" pattern just in case any (argumenta­ are relatively common and their instantia­ tive) passage instantiating it will contain a tions sound natural, while B patterns are textual feature indicating (even if not con­ uncommon and their instantiations sound clusively) that the conditional contained by unnatural. (Return to Section I and hear Denying the Antecedent 27 what happens when passage 6 is changed ponens. (Yes, only I!) It does not exhibit from an (a) pattern to an (f) pattern by the the "preferred" order. addition of an "and." Hear what happens Now I am not suggesting that the fallacy when passages 4 and 5 are changed to (f) of denying the antecedent is never or almost patterns by substituting "and" for "but." never committed. I do have the impression Hear what happens when any of the six that a non-negligible percentage of stu­ passages is recast into any B pattern.) dents taking introductory logic are at least In examining 81 books, as well as nu­ somewhat susceptible to this fallacy. For merous articles on fallacies, I found 9 real this reason (and others), I think it worth­ passages said to be instances of denying while for logic texts to distinguish modus the antecedent. (Textbook examples of fal­ ponens and modus tollens from the invalid lacies are mostly concocted.) With one forms denying the antecedent and affirm­ near exception, to be discussed below, ing the consequent. But the evidence I have none is an instance of any B pattern. That cited, limited though it is, does suggest is, none is an instance of any pattern in that the fallacy of denying the antecedent which indicator words make it reasonably is not common in published writings. clear that the passage is an instance of the Rather more strongly the evidence sug­ fallacy of denying the antecedent.9 gests that published passages cannot often Assuming that my small (but labori­ be charged with denying the antecedent. ously collected) sample is representative, Passages exhibiting A patterns are relative­ one question is this. If the fallacy of deny­ ly common. But as we have seen, they ing the antecedent truly is a common one, even among arguers sufficiently mature to readily admit of an alternative interpreta­ have published writings, why is it that the tion. It would be unfair to view them as fallacy generally is instantiated by passag­ formally fallacious unless there were some es exhibiting patterns (A patterns) that special reason for doing so. And in none of present no obstacle to a different interpre­ the cases known to me does either the con­ tation? Why is it that the fallacy generally text of the passage or any other salient cir­ is not instantiated by passages exhibiting cumstance supply such a reason. By the many patterns (B patterns) that virtual­ contrast, passages exhibiting B patterns ly preclude a different interpretation? can fairly be viewed as instances of deny­ Perhaps it will be suggested that the ing the antecedent. But real passages ex­ answer lies simply in our preference, evi­ hibiting those patterns evidently are rare: I dent also with regard to the valid forms found none. modus ponens and modus toliens, for plac­ The closest thing I found to such a pas­ ing the conditional premise first, the un­ sage is one cited, as an example of denying conditional premise second, and the the antecedent, by Rolf George,IO who conclusion last. In reply, two points: First, identifies its source only as John 8:47. The even if there were such a preference, it speaker is Jesus: wouldn't explain a dispreference for B pat­ He that is of God heareth God's words: (f) terns and (h), which do feature that or­ ye therefore hear them not. because ye are der. Second, a survey of my sources did not of God. not confirm that the logician's preference when presenting argument forms is The position of "therefore" indicates matched by the preferences of real-life ar­ that the first statement, "He that is of God guers. I found 22 non-enthymematic, real heareth God's words," is a part of the argu­ examples of modus tollens. Only 8 exhibit ment (or explanation), not merely a pref­ the "preferred" order. I found I non­ ace to it. The passage has a pattern closely enthymematic, real example of modus related to B pattern (m). 28 Michael B. Burke

Now I have not claimed that the charge He who has God for his father listens to the of denying the antecedent is never justi­ words of God. fied. So I could cheerfully accept this as You are not God's children, and that is why one case where it is. But there are three you do not listen. reasons not to. First, denying the anteced­ To summarize: An argumentative ent is a sentential fallacy, whereas Jesus is passage exhibiting a B pattern is a guilty, if at all, of the predicate-logic ana­ presumptive instance of denying the ante­ logue of that fallacy. Second, it is clear from the context (the preceding ten verses) cedent. But in Section II, I offered that the passage is an explanation and not evidence that B patterns are uncommon in an argument. So again, the passage con­ published writings: I found not a single tains, at most, a logical error analogous to real instance. This, taken together with denying the antecedent. Third, and most the results of Section I, suggests that pub­ important, the passage is probably a mis­ lished arguments can seldom be charged translation. 1 checked four editions of the with denying the antecedent. Somewhat Bible and found four translations of the less strongly it suggests that published ar­ verse in question, all different from one an­ guments seldom commit this fallacy. other, and all different from the translation In Section I, I argued, in effect, that it found by George. None contains the generally is unfair to regard a passage ex­ "therefore" or any other expression that hibiting one of the relatively common A identifies the generalization as a part of the patterns as an instance of denying the ante­ explanans. None exhibits (an explanatory analogue ot) a B pattern. Here are the cedent. Such a passage can very plausibly be taken to contain an enthymematic in­ translations 1 found. I! (In each case, the verse is preceded by this question or its stance of modus ponens (or modus tollens), equivalent: "If 1 speak the truth, why do unless there is some contextual or circum­ you not believe meT' Jesus then proceeds stantial obstacle to doing so. And I know to answer his own question.) of no case in which there is such an obsta­ He who belongs to God, listens to the cle. The conditional contained by the pas­ words of God; sage can very plausibly be viewed as a you do not listen to them, because you do preface to the argument, not as a part of not belong to God. the argument. Thus viewed, the condition­ Whoever is of God hears every word God al has, in addition to any rhetorical or other speaks. extra-dialectical purpose, the dialectical The reason you do not hear is that you are not of God. function of conceding that the acceptabili­ ty of the stated premise is a necessary A child of God listens to the words of God; if you refuse to listen, it is because you are condition of the acceptability of the not God's children. conclusion. 12

Notes

I "Fallacies and the Evaluation of Reasoning," upon ... the fallaciousness of an argument is American Philosophical Quarterly 18, Janu­ not seen as an objectively verifiable fact ..." ary 1981. In a later article, "Six Types of Falla­ (pp. 264-65). ciousness," Argumentation 1, 1987, Finocchiaro offers his own list of six fallacies, but on the 2 "Four Reasons There are No Fallacies," Ch. 9, understanding that "we have a fallacy only Problems in A rgument Analysis and Evalua­ within the framework of a given practitioner's tion, Dordrecht: Foris Publications, 1987, pp. conception of the argument he is commenting 190-99. Denying the Antecedent 29

3 "The Blaze of Her Splendors: Suggestions is [following it], so it isn't." (Gilbert Harman, About Revitalizing Fallacy Theory," Argumen­ The Nature of Morality, New York: Oxford tation, Vol. I, No.3, 1987, p. 244. University Press, 1977, pp. 76-77.) Is the con­ ditional statement a premise? Or is it a pref­ 4 There is no difficulty in understanding how we ace? I see nothing in the context that favors the could have reason for believing the former to former interpretation over the latter. exceed the latter, providing the latter means something like "the frequency with which a S The conjunctions "and" and "but" differ prag­ given fallacy can justifiably be charged on the matically, if not semantically. When state­ basis of information readily available." ments are conjoined with a "but" instead of an "and," often it is because the speaker takes the 5 For a survey of attempts to justify principles of statements to have opposing or contrasting im­ charity, and for objections to strong principles plications. Compare these passages: (I) "John of charity, see Trudy Govier, "A New was then in New York. And Sally was then in Approach to Charity," Ch. 7, Problems in Toronto. So, Fred is lying." (2) "John was then Argument Analysis and Evaluation, Dor­ in New York. But Sally was then in Toronto. drecht: Foris Publications, 1987. So, Fred is lying." In (I), the use of "and" sug­ gests that the statement preceding it is part of 6 Example I is my own concoction, one I've the basis for the conclusion. In (2), the use of given several times to my students as an exam­ "but" suggests the opposite. ple of denying the antecedent. But essentially the same example is given in Jerry Cederblom 9 Also significant is that very few even of the and David W. Paulsen, Instructor's Manual to concocted examples exhibit B patterns, no accompany Critical Reasoning, 3rd ed., Bel­ doubt because passages exhibiting those mont, California: Wadsworth Publishing Com­ patterns lack the naturalness we prize when pany, 1991, p. 185. Example 2 is given in contriving examples. Brooke Noel Moore and Richard Parker, Criti­ 10 "A Postscript on Fallacies," Journal of Philo­ cal Thinking, 3rd ed., Mountain View, Califor­ sophical Logic, Vol. 12, 1983, p. 323. nia: Mayfield Publishing Co., 19<12, p. 247. Example 3 is given in W. Ward Fearnside and II The sources, in corresponding order, are these: William Holther, Fallacy: The Counterfeit of James Moffatt, trans. A New Translation of the Argument, Englewood Cliffs: Prentice-Hall, Bible, New York: Harper & Row, 1954, p. 126. Inc., 1959, p. 156. Example 5 is given in Members of the Catholic Biblical Association Lilly-Marlene Russow and Martin Curd, Prin­ of America, trans. The New American Bible, ciples of Reasoning, New York: St. Martin's Saint Joseph Edition, New York: Catholic Press, 1989, pp. 99-100. Examples 4 and 6 are Book Publishing Co., 1970, p. 118. Alexander given in Irving M. Copi and Carl Cohen, Intro­ Jones, cd. The New Jerusalem Bible, Garden duction to Logic. 8th ed., New York: Macmil­ City, New York: Doubleday & Co., Inc., p. lan, 1990, p. 244 and p. 241. 1 consider 166. The Revised English Bible, New example 6 to be an explanation and not an Rochelle, New York: Oxford University Press argument (even if some explanations are also and Cambridge University Press, 1989, p. 89 arguments). But Copi and Cohen present it as of "The New Testament." an example of denying the antecedent. 12 1 am not the first to note that what might 7 Take passage 5, for example, which comes at appear to be an instance of denying the the end of a paragraph. Here is as much of the antecedent may instead be an enthymematic context as seems pertinent to its interpretation. instance of modus ponens or modus tollens. "Furthermore, even apart from the question Robert Fogelin and Timothy Duggan whether moral principles are laws of reason, it ("Fallacies," Argumentation, Vol. I, No.3, cannot be true that the correct moral principles 1987, p. 258) suggest that in some apparent in­ are limited to those principles that would ap­ stances of the fallacy (they don't say which, or ply in a Kingdom of Ends, where everyone how many-they devote only a paragraph to acted morally and no one ever did anything the point), the stated conditional serves to wrong. In the real world not everyone acts imply, conversationally, its converse, which morally and moral principles must allow for then serves as an unstated premise. Two brief that. Total pacifism might be a good principle comments: (I) This suggestion leaves if everyone were to follow it. But not everyone unexplained why the arguer didn't simply state 30 Michael B. Burke

the converse instead. (So would any sugges­ conversational implicature, argue that we need tion that the stated conditional is intended to not take the boy to be denying the antecedent. bear the meaning of a biconditional.) (2) It is We may take him to be relying on a premise true that the use of the stated conditional may conversationally implied by the stated condi­ imply that the arguer believes the unstated tional. (Argumentation, Communication, and converse of that conditional. But what makes Fallacies, Hillsdale, New Jersey: Lawrence the unstated converse an unstated premise, and Erlbaum Associates, Publishers. 1992, pp. what generally suffices to identify it as such. is 181-82.) In this sort of case, in which the rea­ the arguer's inferring of the conclusion from soner is someone other than the stater of the the stated, unconditional premise. When the conditional, I agree that the stated conditional stated conditional is not itself a premise, its may be seen as supplying. via conversational primary purpose is to play the dialectical, implicature. a premise. rhetorical, and/or other roles that I have I am grateful for the many comments and described. helpful suggestions of John Tilley, Kim Frans H. van Eemeren and Rob Grooten­ Margason. and two referees for this journal, dorst. while discussing the importance in argu­ Jerry Cederblom and Rolf George. ment analysis of pragmatic considerations, give a case in which a boy is told that he may MICHAEL B. BURKE not go to a movie if he does not tidy his room. DEPARTMENT OF PHILOSOPHY The boy promptly tidies his room and then ex­ INDIANA UNIVERSITY pects to be allowed to go to the movie. Van 425 UNIVERSITY BOULEVARD Eemeren and Grootendorst, also appealing to INDIANAPOLIS, IN 46202 o