Microsoft Word - 4 Tomic (607-639) - REVIEW1.doc © Taeda Tomić . Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. The Distinction Between False Dilemma and False Disjunctive Syllogism TAEDA TOMIĆ Department of Philosophy Uppsala University Postal Box 627 751 26 Uppsala, Sweden Taeda.tomic@filosofi.uu.se Abstract: Since a clear account of the fallacy of false disjunctive syllogism is missing in the literature, the fallacy is defined and its three types are differentiated after some preliminar- ies. Section 4 further elaborates the differentia specifica for each of the three types by analyzing relevant argument criticism of each, as well as the related profiles of dialogue. After defining false disjunctive syllogisms, it becomes possible to distinguish between a false dilemma and a false disjunctive syllogism: section 5 analyzes their similarities (which explains why the fallacies are often confused with one another) and section 6 explains their differences. Résumé: Puisqu'un compte rendu clair du syllogisme disjonctif falla- cieux est absent dans la littérature, je définis cette erreur et différencie ses trois types. La section 4 décrit en plus de détails les différences spécifiques pour chacun de ces trois types en analysant la critique argumentative pertinente de chacun, ainsi que les profils de dialogue associés. Après avoir défini les syllogismes disjonctifs fallacieux, il devient possible de distinguer entre un faux dilemme et un syllogisme disjonctif fallacieux: la section 5 analyse leurs similitudes (ce qui explique pourquoi ces sophismes sont souvent confondus) et la section 6 explique leurs différences. Keywords: analytical thinking, argument criticism, argument schemas, infor- mal logic, false dilemma, false disjunctive syllogism, fallacies, profiles of dialogue, relevance 1. Introduction In the field of informal logic and argumentation theory, there are almost no works on disjunctive fallacies. In the extensive bibliog- raphy on fallacies (Hansen and Fioret 2016), there are only two articles (Govier 2007; Tomić 2013) on the fallacy “false disjunc- tion (dichotomy, alternatives),” as it is called in the bibliography. 608 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. In contrast, there are 90 works (articles or books) on six different types of ad hominem fallacy in the bibliography. While there is a systematic presentation of false dilemma (Tomić 2013), analysis of the fallacy of false disjunctive syllogism is still missing in the field. Some works contain short considera- tions about affirming a disjunct without placing it into fallacies or explaining how it appears to be a good argument (e.g., Copi et al. 2011, p. 273; Pospesel and Lycan 2000, p. 209), even though affirming a disjunct is only one variant of false disjunctive syllo- gism. Cavender and Kahane (2010, p. 58) briefly mention the “either-or fallacy” calling it a rhetorical device. However, most of the relevant works on fallacies do not consider false disjunctive syllogism (e.g., Hamblin 1970; Hansen 2020; Hansen and Pinto 1995; Johnson and Blair 1994; Tindale 2007). Some formal-logical works analyze the validity of disjunctive syllogism (e.g., Anderson and Belnap 1975, pp. 165, 174–76; Bhave 1997; Mortensen 1983; Routley 1984). According to An- derson and Belnap (1975), disjunctive syllogism is not a tautologi- cally valid form of reasoning because certain ways of using it contain a relevance fallacy. Anderson and Belnap’s discovery, which is only a part of their lucid analysis of entailment, has been very influential in formal logic; for instance, it has initiated devel- opments of relevance logic. Despite their clear and influential analysis, not even that type of false disjunctive syllogism is in- cluded in the contemporary literature on fallacies in informal logic and argumentation theory. Additionally, even the distinction between false dilemma and false disjunctive syllogism is lacking in the field. A current confu- sion between three concepts—false dilemma, false disjunctive syllogism and false dichotomy—makes it even more difficult to differentiate between the two fallacies: false disjunctive syllogism and false dilemma. Tomić (2013) clarifies the distinction between two of the three concepts that are often confused with one anoth- er—false dilemma and false dichotomy—rightly stating that the first is a logically incorrect argument whereas the second is a false statement (even if that kind of statement is one of the premises in certain types of false dilemma). Govier (2001, pp. 234-35, 441, 2007) also points out that false dichotomy is a false belief or False dilemma & false disjunctive syllogism 609 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. statement, and not an argument. However, in many textbooks, and other types of texts, false dichotomy, false dilemma and false disjunctive syllogism are surprisingly confused with one another and presented as one and the same type of reasoning (Bowell and Kemp 2015, pp. 254-55; van Eemeren and Grootendorst 1992, pp. 191-93; van Vleet 2010, pp. 14-15). The aim of the present article is therefore twofold: • to analyze and define the fallacy of false disjunctive syllo- gism, and • to clarify the distinction between false dilemma and false disjunctive syllogism. The article does not aim at an empirical analysis of all uses of either/or reasoning in natural-English. Nor does it attempt an empirical analysis of argumentative discourses containing false disjunctive syllogism. Such a study would be of great benefit, but the space of the article is limited. The article is rather about rea- soning involved in the fallacy as related to the argument schema of disjunctive syllogism. This approach may make upcoming empiri- cal studies easier as a starting-point framework, which in turn can inspire further studies of false disjunctive syllogism. One innovation of the article is the definition of false disjunc- tive syllogism distinguishing between its three types in Section 3. Another new aspect is the guidelines for distinguishing between several types of the same fallacy in Section 2. The fourth section explores a general account of argument criticism and correspond- ing profiles of dialogue (Krabbe 1992, 1999). However, the article demonstrates a new, specific application of the analytical tools to the three types of false disjunctive syllogism, which further elabo- rates the differentia specifica for each of the three types. After defining false disjunctive syllogism, it becomes possible to distin- guish between a false dilemma and a false disjunctive syllogism. This distinction is another new contribution of the article. Section 5 analyzes similarities between the two fallacies, which explains why the fallacies are often confused with one another. Section 6 explains their differences. 610 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 2. Some preliminaries There are at least three ways in which disjunctive syllogism may be used falsely. One is known as affirming a disjunct, the second may be titled using an irrelevant disjunction, the third may be called unsound disjunctive syllogism. It is necessary to distinguish between the three types of false disjunctive syllogism for the following reasons: • This may improve the ability to deal with the fallacy in argumentative discourses, such as those concerning deci- sion making, diagnostic practices, political debates or im- provement of mental health (e.g. handling implicit argu- ments on the allegedly positive effects of excessive worry used by patients with GAD [Dugas and Robichaud 2007, pp. 124, 128]). • Knowing their characteristics improves the ability to dis- tinguish them from other related fallacies, i.e., false di- lemma. • Distinguishing between the three types of false disjunc- tive syllogism contributes to a clear analytical definition of the fallacy and thus to further systematization of falla- cies in the literature of informal logic and argumentation. • The distinction shows that some fallacies can manifest both as formal and informal fallacies. Characteristics that distinguish the three types of false disjunc- tive syllogism are described generally, below. They are elaborated in Sections 3 and 4. i) Each of the three types demonstrates a distinctive way of falsely appealing to the valid argument schemas of dis- junctive syllogism, shown in Figures 2 and 3. Some of them do this by ways of formal fallacies and are non- valid arguments. Others contain informal fallacies, i.e., ir- relevance or false/incomplete premises, thus faulty argu- False dilemma & false disjunctive syllogism 611 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. mentation, despite being truth-functionally valid argu- ments. This justifies the contention that different ways of reasoning are used in the three types of the fallacy. This is analyzed in Section 3. ii) Different strategies of argument criticisms are required to deal with each of the three types of the fallacy, which also confirms the difference in the reasoning explored in them. This is analyzed in Section 4. iii) Different profiles of dialogue are required to graphically present the structure of the corresponding argument criti- cisms, strengthening (ii). This is analyzed in Section 4. iv) Different argument evaluations are applicable to each of the three types of the fallacy. This also justifies the need to differentiate between them. This is analyzed in Sec- tions 3 and 4. To guide the reader in what to focus on in the analyses and the examples provided in Sections 3 and 4, the guidelines and the general characteristics are summarized in Figure 1. 612 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. The guide- lines Affirming the disjunct Using an irrele- vant disjunction Unsound disjunctive syllogism Different false appeals to the argument schemas of disjunctive syllogism Confusing the schemas for including and excluding disjunctive syllogism, and the related truth- functionality The truth- functionally valid schema of includ- ing disjunctive syllogism turns into a not relevant- ly valid1 argument and faulty argu- mentation, due to the irrelevance between the disjuncts Using the valid schemas of disjunctive syllogism and respecting the truth- functionality of disjunc- tion and with relevance between the disjuncts, but with false/incomplete disjunctive premise Different strategies for argument criticism Refuting by using inadmis- sibility criti- cism Questioning or refuting by using relevance criticism - Questioning or refuting by using tenability criti- cism - Refuting by using active criticism Different profiles of dialogue for the corre- sponding argument criticisms See Figure 5 See Figure 6 and 7 - See Figures 8 and 9 (the profile of dialogue for the tenability criticism) - See Figures 10, 11 and 12 (the profile of dialogue for the active criticism) Different argument evaluations Truth- functionally non-valid argument, due to equivocation and to not- following the truth- functionality Truth-functionally but not relevantly valid argument, and faulty argu- mentation - due to the irrelevance between the disjuncts Truth-functionally and relevantly valid argument, but faulty argumentation due to the false/incomplete disjunc- tive premise Figure 1: The guidelines and characteristics for distinguishing between the three types of disjunctive syllogism 1 See section 3.2 False dilemma & false disjunctive syllogism 613 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 3. False disjunctive syllogism One valid argument schema of disjunctive syllogism (Figure 2) has including disjunction in one of the premises, that is, a disjunc- tive claim in which both disjuncts can be true but cannot both be false (according to the truth conditions of including disjunction). A good example of including disjunction is the statement: “We allow immigration to the country to the same extent as now, or we help the refugees in the immediate area around the conflict hotspots (or both).” Figure 2: Argument schema of disjunctive syllogism with including disjunction The other valid argument schema (Figure 3) has excluding dis- junction in one of the premises, that is, a disjunctive claim in which only one of the disjuncts can be true, but not both of them, according to the truth conditions of excluding disjunction. A good example of excluding disjunction is the statement: “We either allow immigration to the country to the same extent as now, or we help the refugees in the immediate area around the conflict hotspots (but not both).” Figure 3: Argument schema of disjunctive syllogism with excluding dis- junction The different ways in which the three types of false disjunctive syllogism falsely appeal to the valid argument schemas of disjunc- tive syllogism show that different perspectives on defining a falla- cy are applicable for each of the three types. Affirming the dis- junct is a formal fallacy because it is not a truth-functionally valid argument but attempts to be. Using an irrelevant disjunction is a 614 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. fallacy of irrelevance: it contains a truth functionally valid argu- ment, but due to the irrelevance between the disjuncts, it turns into a not relevantly valid argument and thus also into faulty argumen- tation. Unsound disjunctive syllogism is an informal fallacy: it is both truth-functionally and relevantly valid argument, but the incomplete disjunctive premise with all false disjuncts turns it into faulty argumentation. In the continuance of Section 3 and in Sec- tion 4, the differentia specifica for each of the three types is elabo- rated. 3.1. Affirming a disjunct This type of false disjunctive syllogism is a formal fallacy: it is not a valid argument but attempts to be. It uses a logically incor- rect mixture of the two valid argument schemas for disjunctive syllogism: the one with including disjunction, and the one with excluding disjunction (Figure 4). It therefore involves logically improper mixture of truth conditions for the two different types of disjunction. Figure 4: Argument scheme for affirming a disjunct Even if affirming a disjunct is not a deductively valid argument, it appears to be deductively valid due to its equivocal use of the disjunctive premise. The equivocation consists of using including disjunction in the disjunctive premise but presenting it as if it were an excluding one, as shown in Figure 4 and in Example 1. (P1) We allow immigration to the country to the same extent as now, or we help the refugees in the immediate area around the conflict hotspots. (P2) We help the refugees in the immediate area around the conflict hotspots. (C) We do not allow immigration to the country to the same extent as now. Example 1: An argument with affirming a disjunct False dilemma & false disjunctive syllogism 615 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. The argument is not valid because it does not specify that the first premise would be an excluding disjunction. The premise is structurally formulated as an including disjunction because the expression “but not both” is missing, but is used as if it were ex- cluding. Even as a matter of fact the disjuncts in the disjunctive premise both can be true – they actually do not exclude each other. Therefore, claiming one of the disjuncts does not logically imply the negation of the other one. 3.2. Using an irrelevant disjunction Using an irrelevant disjunction is a fallacy of relevance. It is a truth-functionally valid argument, but the irrelevance between the disjuncts turns it into a not relevantly valid argument (where the truth-functional validity still holds). In other words, using an irrelevant disjunction respects the truth conditions of an including disjunction and is therefore a truth-functionally valid argument. Nevertheless, it presents a disjunctive syllogism with an including disjunction (Figure 2) as logically valid only due to its logical form, irrespective of the relevance between the disjuncts. Howev- er, as Anderson and Belnap have explained, a disjunctive syllo- gism is a relevantly valid argument only when the intensional sense of ”or” is used so that there is a true relevance between the disjuncts in the claim “A-or-B” (1975, pp. 166, 176). This is dif- ferent from the truth-functional sense of “or” in the symbolic schema. When the intensional sense of “or” is used, the disjuncts share the propositional content which makes a disjunctive syllo- gism valid, as in Example 2 where the disjuncts share the proposi- tional content of referring to the diseases with similar symptoms. Some related analyses of the concept of relevant validity may be found in Lavers (1988), and Schurz (1991). 616 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. (P1) The symptoms indicate that it is either COVID-19 or seasonal influenza (and if it is not the one, then it is the other). (P2) The laboratory results confirm that it is not COVID-19. (C) It is seasonal influenza. Example 2: Relevantly valid disjunctive syllogism (truth- functionally valid and with the relevance between the dis- juncts) (following Anderson and Belnap 1975, p. 176). However, when truth-functional disjunction without relevance between the disjuncts is used in the premise of disjunctive syllo- gism, we get using an irrelevant disjunction in which the conclu- sion does not logically follow from the premises, despite the ar- gument’s truth-functional validity. This is then a not relevantly valid argument (Anderson and Belnap 1975, pp. 162-67, 176-77, 296-300). This is the case in Example 3, where the disjuncts do not share the propositional content. (P1) It is Friday today or the techniques of healthy living will be included in the curriculum. (P2) It is not Friday today. (C) The techniques of healthy living will be included in the curriculum. Example 3: Using an irrelevant disjunction: disjunctive syllo- gism without relevance between the disjuncts At first glance, it is not clear why anybody would accept the reasoning presented in Example 3 in any way: it is obvious that the disjuncts do not share the propositional content and that therefore the negation of one of them does not imply the assertion of the other. According to Anderson and Belnap, the reason why such an argument may still seem acceptable is the truth-functionally valid form of the argument that is usually presented as unequivocally valid, even when applied in arguments in which the intensional and not truth functional “or” is required. It should be pointed out an additional reason why the reasoning may appear relevantly valid: the disjuncts in using an irrelevant False dilemma & false disjunctive syllogism 617 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. disjunction may be chosen so as to seem to share propositional content, when they actually do not. In such cases, the disjuncts are not relevant to one another but people may wrongly believe that they are. This is the case in Example 4 presenting a truth- functionally valid argument, often used by people suffering from excessive worry (following Dugas and Robichaud 2007, pp. 126- 28). Still, the actual argument is not relevantly valid because there is no relevance between the disjuncts: regular worry about one’s performance getting wrong is in itself not relevant to the quality of the performance. However, a person who is advancing such an argument and behaving accordingly may have observed that some- times, coincidentally, her good performance follows the worry. Therefore, and due to her intolerance of uncertainty, she wrongly believes that there is relevance between the worry and the perfor- mance – in her attempt to reduce uncertainty. One of the strategies in treatment of excessive worry is to assist clients in challenging the beliefs about a concrete worry being relevant to a concrete outcome, such as the wrong belief about the relevance between the disjuncts in (P1) (Dugas and Robichaud 2007, pp. 129-33). (P1) I always worry beforehand that something I’m working on will get wrong, or the thing I’m working on will get wrong. (P2) I don’t always worry beforehand that something I’m working on will get wrong. (C1) The thing I’m working on will get wrong. Example 4: Using an irrelevant disjunction: a not relevantly valid reasoning that seems to be relevantly valid due to the seeming relevance between the disjuncts According to Anderson and Belnap, a disjunctive syllogism with irrelevant disjunction (what is here titled using an irrelevant disjunction), makes obvious that it is not always possible to distin- guish clearly between the formal fallacies (in which something is wrong with the logical form of an argument independently of its content) and the material (informal) fallacies (depending on misin- terpretations, mis-presentations or omissions of the content of the 618 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. argument). This is because the validity of the logical form of reasoning in disjunctive syllogism is dependent on the very con- tent of the disjunctive premise and the relevance between the disjuncts (Anderson and Belnap 1975, pp. 164-65, 176-77, 236-37, 296-300). 3.3. Unsound disjunctive syllogism The unsound disjunctive syllogism is an informal fallacy. It is a truth functionally and relevantly valid argument that still involves faulty argumentation due to (intentionally or unintentionally) not making obvious the falsity of the disjunctive premise and thus focusing on the argument’s validity when the argument actually also attempts at soundness. The two ways in which the disjunctive premise may be false in effect amount to the same thing. All the disjuncts in the disjunctive premise may be false, which indicates that there are other, true, disjuncts of relevance; this shows that the initial premise was incomplete. On the other hand, in the incom- plete disjunctive premise of the unsound disjunctive syllogism, the (seemingly) true disjuncts become obviously false when the other relevant disjuncts are included. In both ways, the disjuncts are false and the disjunctive premise is incomplete.2 In what follows, the falsity of the disjunctive premise is still approached from the two different perspectives briefly presented above. The perspective in section 3.3.1. focuses on the falsity of each of the given disjuncts; the perspective in section 3.3.2. focus- es on the incomplete disjunctive premise. Describing these two different perspectives is important because it shows that the un- sound disjunctive syllogism may be handled by different strategies of argument criticism and thus by different dialogue approaches discussed in Section 4. 3.3.1. The perspective with focus on the falsity of the disjuncts in the disjunctive premise Take the unsound disjunctive syllogism with including disjunction and with relevance between the disjuncts. This truth functionally 2 The author is grateful to the anonymous referee for the insight in the sentence. False dilemma & false disjunctive syllogism 619 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. and relevantly valid argument is a fallacy due to the faulty argu- mentation when the argument is presented as if at least one of the disjuncts in the disjunctive premise is true in a given situation; whereas, as a matter of fact neither of them is. Examples 5 and 6 contain such reasoning. Example 5: (P1) We have to be materially very rich and also high per- forming, or we are unworthy as human beings. (P2) We are worthy as human beings. (C) We have to be materially very rich and also high performing. Example 6: (P1) We have to achieve a high social status or we have to look sexually attractive. (P2) We do not have to look sexually attractive. (C) We have to achieve a high social status. In both examples, the relevance between the disjuncts, and the truth-functionality is respected, and the arguments are thus rele- vantly and truth-functionally valid. However, neither of the two arguments is sound, because none of the disjuncts in each of the arguments is true. That is, they all have a false disjunctive premise suggesting two options that are both, as a matter of fact, false: • We do not have to be materially very rich and also high per- forming, and we are worthy as human beings. • We do not have to achieve a high social status, and we do not have to look sexually attractive. However, by focusing the listeners’ attention only on the validity of the argument, the use of the unsound disjunctive syllogism can lead to not noticing the falsity of the disjunctive premise in the situations in which soundness is attempted; the argument may thus 620 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. be accepted. This confusing and faulty argumentation is the reason why it is a variant of the fallacy of false disjunctive syllogism. 3.3.2. The perspective with focus on the incomplete disjunctive premise Taking this perspective, the unsound disjunctive syllogism is initially presented as a sound argument: it is truth-functionally and relevantly valid, and it seemingly has all the premises factually true, but the fact that the disjunctive premise is incomplete is, intentionally or unintentionally, concealed. However, additional disjuncts (additional information) are relevant for what is consid- ered in the argument. Due to the additional information, the initial disjuncts may all turn false and lead to another conclusion than the one in the originally given argument. When the premise (P1) in Example 7 is presented as if it con- tains all the alternatives of relevance for reasoning about the con- clusion, the conclusion is derived on the basis of faulty argumenta- tion, and may be wrong, despite the truth-functional and the rele- vant validity of the argument. (P1) The physician should prescribe pills or the symptoms will remain. (P2) The symptoms will not remain. (C1) The physician should prescribe pills. Example 7: Disjunctive syllogism with incomplete disjunctive premise (P2) is true given that the patient is concerned about her/his health. However, additional options are relevant for reasoning about how the physician should act if she/he wants to help the patient to get rid of the symptoms. The relevant information is thus (intentional- ly or unintentionally) hidden in the argument which is thus a falla- cy due to the confusing and faulty argumentation. Adding relevant additional information to the first premise might refute the argu- ment in Example 7: due to the additional information the conclu- sion (C1) would not have to be chosen among several possible False dilemma & false disjunctive syllogism 621 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. conclusions (e.g., C2, C3 and C4) which would all logically follow from the augmented true premise. The refuting argument is pre- sented in Example 8. (P3) The physician should prescribe pills, or regular physical exercise, or regularly doing mental exercise, or a course in improvement of a new skill that the patient always wanted to learn, or coaching to diminish the patient’s everyday stress, or the symptoms will remain. (P2) The symptoms will not remain. (P4) The physician should not prescribe pills (in the light of the new alternatives). (C2) The physician should prescribe regular physical exercise. (C3) The physician should prescribe a course for improvement of a new skill that the patient always wanted to learn. (C4) The physician should prescribe coaching to diminish the patient’s everyday stress. Example 8: An argument that refutes the unsound disjunc- tive syllogism in Example 7 4. Argument criticism for false disjunctive syllogism This section explores a general account of argument criticism and corresponding profiles of dialogue (Krabbe 1992, 1999). However, the section demonstrates a new, specific application of the analyti- cal tools to the three types of false disjunctive syllogism. Thus, it further elaborates the differentia specifica for each of these three types of the fallacy (described in Section 3), implements the guide- lines for distinguishing them (provided in Section 2), and graph- ically systematizes the differences between these three types. 622 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 4.1. Refutation by using inadmissibility criticism Affirming the disjunct is best approached by refutation based on inadmissibility-criticism (Krabbe 1999, p. 10), due to equivoca- tion. When applied to affirming the disjunct, this type of criticism points out the following: - There is ambiguity between the including and the excluding disjunction in the disjunctive premise; and - ambiguity makes affirming the disjunct seem to be valid when it actually is not (the conclusion does not follow from the premises, because the disjunctive premise is not exclud- ing disjunction, neither formal-logically nor actually). To further clarify the inadmissibility criticism, we first sym- bolize the main claims in the argument from Example 1 by propo- sitional letters A and B, where: A: We allow immigration to the country to the same extent as now. B: We help the refugees in the immediate area around the conflict hotspots. We then apply the general profile of dialogue for inadmissibility criticism (Krabbe 1999) to affirming the disjunct from Example 1, as represented in Figure 5. False dilemma & false disjunctive syllogism 623 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. Figure 5: The profile of dialogue for inadmissibility criticism of affirming a disjunct. Of course, refutation by using inadmissibility criticism can be expressed in a form that simply states the reasoning, without fol- lowing the question-answer dialectical structure of the argumenta- tive dialogue. However, the profile of dialogue makes the reason- ing and the steps of refutation clearer. 624 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 4.2. Relevance criticism for using an irrelevant disjunction Two general types of relevance criticism, the connection criticism and the narrow-type relevance criticism (Krabbe 1992, pp. 278, 279; 1999, pp. 6, 10), are the most suitable to deal with using an irrelevant disjunction. The connection criticism questions the logical connection between on the one hand the disjunctive prem- ise with irrelevant disjuncts and the negation of one of them and, on the other hand, the conclusion. It thus asks for additional rea- sons for the claimed entailment between the premises and the conclusion. The narrow-type relevance criticism points out that the relevant logical connection is lacking and provides the reasons why. In other words, both types of the relevance criticism chal- lenge the relevant validity of the advanced argument; the connec- tion criticism asks for additional reasons to claim the validity, and the narrow-type of relevance criticism provides the reasons why the conclusion does not follow from the premises, despite the truth-functional validity of the argument. The profile of dialogue for relevance criticism (Krabbe 1992, 1999), when applied to the fallacy of using an irrelevant disjunction, makes even clearer the missing relevant validity of the argument from Example 3, as shown in figure 6 below. Figure 6: The profile of dialogue for relevance criticism of using an irrelevant disjunction in the argument of Example 3 False dilemma & false disjunctive syllogism 625 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. Let us symbolize the simple statements from Example 3 by propositional letters F and T, where F: It is Friday today. T: The techniques of healthy living will be included in the curriculum. Then we get the general profile of dialogue for relevance criticism of using an irrelevant disjunction, as presented in Figure 7. Figure 7: The profile of dialogue for relevance criticism of using an irrelevant disjunction 626 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 4.3. Tenability criticism of unsound disjunctive syllogism with focus on the falsity of the disjuncts in the disjunctive premise Here, the most suitable argument criticism is tenability criticism that questions the actual truth of the disjuncts, or refutes the argu- ment by asserting the falsity of the disjuncts. This type of criticism acknowledges the truth functional and the relevant validity of the argument but points out that the argument also aims at soundness which is why the soundness of the argument is questioned or opposed. General profile for tenability criticism (Krabbe 1999, p. 6) may suitably be applied to analyze the tenability criticism of the argu- ment in Example 5, as shown in Figure 8 be- low. Figure 8: The profile of dialogue for questioning and for refuting unsound disjunctive syllogism with focus on the false disjuncts in the argument from Example 5, by using tenability criticism False dilemma & false disjunctive syllogism 627 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. Let us symbolize the simple statements used in Example 5 by propositional letters M and W, where M: We have to be materially very rich and also high performing. W: We are unworthy as human beings. Then we get the general profile of dialogue for tenability criticism of unsound disjunctive syllogism with focus on the false disjuncts in the disjunctive premise, as presented in Figure 9. Figure 9: The profile of dialogue for tenability criticism of unsound disjunctive syllogism with focus on the false disjuncts in the disjunctive premise 4.4. Active criticism of unsound disjunctive syllogism with focus on the incomplete disjunctive premise Here, it is best to use active criticism to show that the argument is truth functionally and relevantly valid but not all relevant disjuncts are included in the disjunctive premise. By adding the additional relevant disjuncts, both the initial disjuncts turn false and the conclusion no longer follows from the augmented set of premises. The argument in Example 7 has an incomplete disjunctive premise because there are other alternatives of importance for the 628 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. reasoning. Thus, in Example 8, the disjunctive premise is aug- mented by additional information contained in the added disjuncts. The additional information shows that both the initial disjuncts are false, which thus refutes the conclusion of the initial argument and leads to other conclusions (e.g., (C2), (C3) and (C4) in Example 8). So, the active criticism advanced in Example 8 refutes the argument in Example 7. This type of criticism may be analyzed by the general profile of dialogue for active criticism (Krabbe 1999, pp. 7, 10), which is presented in figure 10 with regard to the argument advanced in Example 8. Figure 10: The profile of dialogue for active criticism of argument advanced in Example 7 (see also Example 8) False dilemma & false disjunctive syllogism 629 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. Let us symbolize the simple propositions used in Example 7 and 8 in the following way: A: The physician should prescribe pills. B: The symptoms will remain. C: The physician should prescribe regular physical exercise. D: The physician should prescribe doing mental exercise regularly. E: The physician should prescribe a course in improvement of a new skill that the patient always wanted to learn. F: The physician should prescribe coaching to diminish the patient’s everyday stress. With this symbolization, the argument schema for active criticism of unsound disjunctive syllogism, focus on the incomplete disjunc- tive premise, is presented in Figure 11, where the additional rele- vant information and the new relevant conclusions are written in brackets. A Ú B [ Ú C Ú D Ú E Ú F Ú … F+n ] ¬B [¬A (because of C Ú D Ú E Ú F Ú … F+n )] [C] [E] [F] […] Figure 11: Active criticism for unsound disjunctive syllogism, focusing on the incomplete disjunctive premise In using the propositional letters given above, we also obtain the general profile of dialogue for active criticism of unsound disjunc- tive syllogism, focusing on the incomplete disjunctive premise (Figure 12). 630 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. Figure 12: General structure of the profile of dialogue for active criticism of unsound disjunctive syllogism, focusing on the incomplete disjunctive premise The types of false disjunctive syllogism and the related argument criticisms are summarized in Figure 13. Types of false disjunctive syllogism Corresponding argument criticism Affirming a disjunct Refuting by using inadmis- sibility criticism Using an irrelevant disjunction Questioning or refuting by using irrelevance criticism Unsound dis- junctive syllo- gism with the perspective that emphasizes the falsity of the disjuncts Questioning or refuting by using tenability criticism with the perspective that emphasizes the incom- plete disjunctive premise Refuting by using active criticism Figure 13: Three types of false disjunctive syllogism and the corresponding argument criticisms False dilemma & false disjunctive syllogism 631 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 5. Similarities between false dilemma and false disjunctive syllogism One similarity between the two fallacies is that they have a dis- junctive premise among their premises. Further, both fallacies use deductively valid argument schemas but still involve faulty argu- mentation. False dilemma explores the valid argument schemas of constructive and destructive dilemma (Figure 14), widely and rightly accepted as valid forms of inference in textbooks on formal logic. For instance, Copi et al. (2011, p. 320) rightly include sim- ple constructive dilemma among the common argument forms; Kelley (1998, pp. 372-73; 2014, p. 318) and Pospesel and Lycan (2000, p. 108) correctly include constructive and destructive di- lemmas in the standard rules of inference. As previously pointed out, false disjunctive syllogism explores the valid schemas of disjunctive syllogism (Figure 15). A Ú B A ® C B ® C C A Ú B A ® Q B ® R Q Ú R E ® G E ® H ¬G Ú ¬H ¬E F ® J K ® L ¬J Ú ¬L ¬ F Ú ¬K Simple Con- structive Di- lemma Complex Con- structive Di- lemma Simple De- structive Di- lemma Complex Destructive Dilemma Figure 14: Valid argument schemas for constructive and destructive dilemma A Ú B ¬A B A Ú B ¬B A (A Ú B) Ù ¬ (A Ù B) A ¬B (A Ú B) Ù ¬ (A Ù B) B ¬A Disjunctive syllogism with in- cluding disjunction Disjunctive syllogism with in- cluding disjunction Disjunctive syllogism with excluding dis- junction Disjunctive syllo- gism with excluding disjunction Figure 15: Valid argument schemas for disjunctive syllogism (provided that there is relevance between A and B) 632 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. The ways in which the valid dilemma-arguments turn into the related types of false dilemmas are analyzed in detail in Tomić (2013). The same work also shows that the relevant literature is currently lacking other types of false dilemma than those systema- tized by Tomić. Below, the false dilemmas are presented that are sufficient for the analysis of the similarities and differences be- tween false disjunctive syllogism and false dilemma (see Exam- ples 9 and 10 and Section 6). Another similarity is that in some of their variants, both false dilemma and false disjunctive syllogism, even though logically valid arguments, turn into faulty argumentation, due to the false disjuncts or incomplete information in the disjunctive premise. This is true for the unsound disjunctive syllogism (see section 3.3. in this article), as well as for simple and complex false quandary (two variants of false dilemma; see Example 9 and 10, and Tomić 2013, pp. 351-53). Both types of arguments appeal to soundness and not only to validity, which turns them into faulty argumenta- tion, best approached by using tenability criticism or active criti- cism. Let us consider Example 9. (P1) You talk to your boss about the unfair way in which he treats your colleague, or you avoid the discussion. (P2) If you talk to your boss about the unfair way in which he treats your colleague, the boss will continue to treat the colleague unfairly (because you dared to talk about his bad behavior). (P3) If you avoid the discussion, the boss will continue to treat your colleague unfairly (because nobody challenges that type of behavior). (C) The boss will continue to treat your colleague unfairly. Example 9: The simple false quandary (a variant of false dilemma) As in the unsound disjunctive syllogism, the disjunctive premise in the valid argument of the simple false quandary is typically False dilemma & false disjunctive syllogism 633 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. false/incomplete. In Example 9, (P1) is false because neither of the disjuncts is true: you can both not talk to your boss, and also not avoid the discussion. There is at least one additional option: you may talk to a person from the department of human resources and ask her to discuss with the boss his unfair behavior towards your colleague. This will, presumably, lead to his stopping that type of behavior because he will understand that people in charge have been informed of the behavior, which thus leads to a different conclusion than the one deduced in the original argument. The similarity holds also for the complex false quandary (Tomić 2013, pp. 351–53), as illustrated by Example 10. (P1) You talk to your boss about the unfair way in which he treats your colleague, or you avoid the discussion. (P2) If you talk to your boss about the unfair way in which he treats your colleague, the boss will start to treat you in the same unfair way. (P3) If you avoid the discussion, you will lose your friend’s trust. (C) The boss will start to treat you in the same unfair way, or you will lose your friend’s trust. Example 10: The complex false quandary (a variant of false dilemma) In both the unsound disjunctive syllogism, and the valid argument of the complex false quandary the false/incomplete disjunctive premise leads to faulty argumentation. In Example 10, (P1) is false: you neither talk to your boss, nor the discussion is avoided. There is at least one additional option: you and your friend find another job, which leads to depriving the boss of the possibility of treating either one of you unfairly and you also keep your friend’s trust. The conclusion of the first argument is thus refuted and a new conclusion is deduced from the augmented disjunctive prem- ise. 634 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 6. Differences between false dilemma and false disjunctive syllogism The main difference is that the fallacies appeal to different argu- ment schemas, which clearly demonstrates that they are different kinds of reasoning. As shown in Figure 14, the argument schemas used in the four types of false dilemma analyze the logical relation between a disjunctive claim and the consequents implied by each of the disjuncts, which then leads to a corresponding conclusion. In contrast, as shown in Figure 15, the argument schema appealed to in a false disjunctive syllogism analyzes the logical relation between the two mutually including disjuncts in relation to a situa- tion in which one of them is negated (which leads to affirming the other in the conclusion); or the logical relation between the two mutually excluding disjuncts in relation to the situation when one of them is affirmed (which leads to negating the other disjunct in the conclusion). No analyses of the consequents implied from each of the disjuncts is at all involved in the argument schema of dis- junctive syllogism. Yet another difference is that false dilemma is always grounded in the truth-functionally valid argument of a constructive or de- structive dilemma, whereas only two variants of false disjunctive syllogism are truth-functionally valid according to the schema of disjunctive syllogism. The third one, affirming a disjunct, seems to be valid due to the ambiguity between the including and excluding disjunction. On the other hand, the ambiguity between the includ- ing and excluding disjunction is completely irrelevant for false constructive dilemmas. In a simple constructive dilemma, it does not matter if the disjuncts exclude each other or not; if they imply the same consequents, the result would be the consequent that both of them imply. Equally for the complex constructive dilemma: if we know that one of the disjuncts implies a consequent different from the consequent that the other disjunct implies, the conclusion would be the disjunction between the consequents, no matter if the disjunction in the disjunctive premise of the dilemma argument is including or excluding. An additional difference between the fallacies is that relevance between disjuncts is crucial for one type of false disjunctive syllogism (using an irrelevant disjunction), but is not vital for any type of false dilemma. This makes relevance False dilemma & false disjunctive syllogism 635 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. criticism adequate for one type of false disjunctive syllogism but is not required for any type of false dilemma. The final difference consists in different strategies for the active criticism of defeasible false dilemma and, on the other hand, for the active criticism of the unsound disjunctive syllogism with focus on the incomplete disjunctive premise. Even if both types of arguments obscure the relevant information in the premises, they still obscure different information. Unsound disjunctive syllogism strongly focuses only on some selected possibilities in the disjunc- tive premise and thus obscures relevant information about addi- tional disjunctive possibilities. The related active criticism adds the information about the additional disjuncts in the disjunctive premise, which refutes the initial argument in making obvious its unsoundness and brings in other possible conclusions (see Figures 10, 11 and 12). In contrast, defeasible sound constructive dilem- mas (which are variants of false dilemma) obscure relevant infor- mation about additional relevant consequents from the given dis- juncts in the disjunctive premise (see columns 1 and 2 in Figure 16, where the additional information that the active criticism makes explicit is written in the brackets). Corresponding differ- ences hold even regarding the active criticism of defeasible sound destructive dilemmas (see columns 3 and 4 in Figure 16, with the additional information made explicit by the active criticism written in brackets; for details about this type of active criticism see (Tomić 2013, pp. 356-64, 366). A ∨ B A → C B → C [A → D] [B → D] C [D] A ∨ B A → Q B → R [A → Z] [B → W] Q ∨ R [Z ∨ W] E→ G E → H ¬G ∨ ¬H [E → M] [E → T] ¬E [E → (M ∧ T)] F → J K → L ¬J ∨ ¬L [F ∨ K] ¬F ∨ ¬K [ J ∨ L] Active criticism of sound simple constructive dilemma Active criticism of sound com- plex constructive dilemma Active criticism of sound simple destructive dilemma Active criticism of sound com- plex destructive dilemma Figure 16: Argument schemas for active criticism of the four variants of defea- sible sound dilemma (Tomić 2013) 636 Tomić © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. 7. Conclusion After providing an analysis and a definition of false disjunctive syllogism, the article has distinguished it clearly from false di- lemma; this is summarized in Figure 17. Figure 17: Similarities and differences between false dilemma and false dis- junctive syllogism: a summary Similarities Differences Both have a disjunctive premise in their argument schema. Both are (in all or in some of their variants) grounded in deductively valid argu- ments/argument schemas, but still involve faulty argumentation. They explore different argument sche- mas (and thus involve different types of reasoning). They require different strategies for active criticism (which also shows their different type of reasoning). False dilemma is always grounded in a logically valid argument (still with the faulty argumentation), whereas false disjunctive syllogism involves one variant of truth-functionally non-valid argument, and one variant of truth- functionally, though not relevantly valid argument. Relevance between disjuncts is crucial for one type of false disjunctive syllo- gism, whereas it is not vital for any type of false dilemma. Relevance criticism is adequate for one type of false disjunctive syllogism (using an irrelevant disjunction), but is not required for any type of false dilemma. False dilemma & false disjunctive syllogism 637 © Taeda Tomić. Informal Logic, Vol. 41, No. 4 (2021), pp. 607–639. The following results of the article contribute to informal-logical studies of disjunctive fallacies: • A definition of false disjunctive syllogism and its three types; • guidelines for distinguishing between several types of one and the same fallacy (e.g. for making difference between several types of false disjunctive syllogism); • guidelines for distinguishing between similar though differ- ent fallacies (e.g. for making difference between false dis- junctive syllogism and false dilemma); • insight that one and the same fallacy can manifest as both formal and informal fallacy; • an application of the general strategies of argument criticism and profiles of dialogue to the related analyses of false dis- junctive syllogisms; • and a distinction between false dilemma and false disjunc- tive syllogism. 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