Fallacies and dilemma

# Fallacies and dilemma ## Objectifs et prérequis This chapter aims to equip Form Five students with the ability to identify, analyze, and construct logical arguments by studying formal and informal fallacies and the structure of dilemmas. Students will learn to distinguish valid from invalid reasoning, recognize common errors in argumentation, and apply logical principles to real-world contexts, particularly within Cameroonian and African socio-political discourse. Prerequisites include mastery of basic propositional logic (truth tables, logical connectives, conditional statements) and familiarity with argument forms such as modus ponens and modus tollens, covered in earlier chapters of the Logic syllabus. ## Introduction Logic, as a discipline, is concerned with the principles of valid reasoning. In everyday discourse—especially in public debates, legal proceedings, media commentary, and academic writing—arguments are often undermined not by false premises but by flawed reasoning patterns known as fallacies. A fallacy is an error in reasoning that renders an argument invalid or weak, regardless of the truth of its premises. Simultaneously, dilemmas present structured argument forms where a choice between two alternatives leads to a necessary conclusion, often used in ethical, legal, or policy reasoning. This chapter examines two key types: constructive and destructive dilemmas, and their role in formal logic. It then turns to informal fallacies—errors in content, context, or relevance rather than form—highlighting how they manifest in Cameroonian and African public discourse. Through guided work and structured analysis, students will develop critical thinking skills essential for academic success and informed citizenship. ## I. Guided Work: FALLACY: Affirming one Alternant ### Context This lesson introduces a formal fallacy that arises in the context of disjunctive syllogisms. Students often confuse valid disjunctive reasoning with invalid variants, particularly when dealing with "either/or" statements. The fallacy of affirming one alternant is a common mistake in both academic and public reasoning, especially when individuals mistakenly believe that affirming one option in a disjunction allows them to deny the other, without considering the inclusive nature of "or" in logic. ### Definition and Structure In classical logic, a disjunctive proposition takes the form: "P or Q" (symbolized as P ∨ Q). The valid rule of inference known as **Disjunctive Syllogism** states: If P ∨ Q is true, and P is false, then Q must be true. Equivalently: If P ∨ Q is true, and Q is false, then P must be true. The fallacy of **Affirming one Alternant** occurs when one incorrectly reasons: If P ∨ Q is true, and P is true, then Q must be false. This is invalid because in standard logic, "or" is inclusive unless explicitly stated otherwise (i.e., exclusive or). Thus, both P and Q can be true simultaneously, making the conclusion unjustified. > **Affirming one Alternant is the fallacy of concluding the negation of one disjunct from the affirmation of the other disjunct in an inclusive disjunction.** ### Facts and Logical Analysis - The fallacy violates the truth table for inclusive disjunction (P ∨ Q): | P | Q | P ∨ Q | |---|---|-------| | T | T | T | | T | F | T | | F | T | T | | F | F | F | When P is true and P ∨ Q is true, Q can be either true or false—so concluding ¬Q is not logically necessary. - This fallacy is only valid if the disjunction is explicitly exclusive (i.e., "either P or Q but not both"), symbolized as P ⊕ Q. However, in the absence of such specification, the default interpretation in logic is inclusive. - The error is formal: it depends on the structure of the argument, not the content of P or Q. ### Causes and Consequences **Causes**: - Misinterpretation of natural language "or" as exclusive when it is often inclusive (e.g., "You can have tea or coffee" often implies exclusivity, but "Students who pass Math or English will be promoted" allows both). - Overgeneralization from exclusive contexts to inclusive ones. - Lack of precision in distinguishing logical operators from linguistic usage. **Consequences**: - Leads to false conclusions in argumentation, policy debates, or legal reasoning. - Undermines the credibility of the arguer in academic or professional settings. - Can result in unjust decisions when based on flawed disjunctive reasoning (e.g., assuming that supporting one policy implies opposition to another, when both could be compatible). ### Examples (Cameroonian and African Context) - **Example 1**: A government official states: "We will either increase education funding or improve healthcare infrastructure." A critic responds: "Since they have increased education funding, they must not be improving healthcare." This commits the fallacy if the original statement allowed for both actions to occur simultaneously (which is plausible in a national budget). - **Example 2**: In a university debate, a student argues: "Either the curriculum should be decolonized, or it should remain unchanged. Since the ministry has introduced new African literature courses, the curriculum must not be unchanged." This is valid only if the disjunction is exclusive—but if the reform allows for both change and retention of some elements, the conclusion is unwarranted. - **Example 3**: A Cameroonian farmer says: "I will plant maize or cassava this season." If he plants maize, it does not logically follow that he did not plant cassava—he might have planted both, especially in intercropping systems common in African agriculture. ### Vocabulary to Retain - Disjunction (P ∨ Q): A logical connective meaning "or", inclusive unless specified otherwise. - Disjunctive Syllogism: Valid inference: P ∨ Q, ¬P ∴ Q. - Affirming one Alternant: Invalid inference: P ∨ Q, P ∴ ¬Q. - Exclusive Disjunction (P ⊕ Q): "Either P or Q but not both". - Inclusive Disjunction: Standard logical "or", allowing both disjuncts to be true. ### Example of Exam-Type Question with Plan **Question**: Identify the fallacy in the following argument: "The government will either build a new hospital in Bamenda or upgrade the existing one in Yaoundé. Since they have announced the construction of the new hospital in Bamenda, it follows that they will not upgrade the hospital in Yaoundé." Explain why this reasoning is fallacious, and state under what condition it would be valid. **Plan**: 1. Identify the logical form: Premise: H_b ∨ H_y (H_b = hospital in Bamenda built, H_y = hospital in Yaoundé upgraded). Premise: H_b. Conclusion: ¬H_y. 2. Recognize the structure as Affirming one Alternant: P ∨ Q, P ∴ ¬Q. 3. Explain that this is invalid under inclusive disjunction (default in logic), as both H_b and H_y could be true. 4. State that the reasoning would be valid only if the disjunction were exclusive (i.e., "either... but not both"), which is not indicated in the premise. 5. Conclude that the argument commits the fallacy of Affirming one Alternant unless exclusivity is explicitly stated. ## II. Structure of Dilemma ### Context This lesson introduces the dilemma as a valid argument form in propositional logic. A dilemma presents a situation where an agent must choose between two alternatives, each leading to the same conclusion. Unlike fallacies, dilemmas, when properly structured, are logically sound and are used to force a conclusion regardless of which disjunct is true. Understanding the structure of dilemmas is essential for analyzing arguments in ethics, law, and public policy, where choices are often framed as unavoidable. ### Definition and Structure A **Constructive Dilemma** has the following form: (P → Q) ∧ (R → S) P ∨ R ∴ Q ∨ S In words: If P implies Q, and R implies S, and either P or R is true, then either Q or S must be true. A **Destructive Dilemma** has the form: (P → Q) ∧ (R → S) ¬Q ∨ ¬S ∴ ¬P ∨ ¬R In words: If P implies Q, and R implies S, and either Q is false or S is false, then either P is false or R is false. These forms are valid because they preserve truth: if the premises are true, the conclusion must be true. > **Constructive Dilemma**: From (P → Q) ∧ (R → S) and P ∨ R, infer Q ∨ S. > **Destructive Dilemma**: From (P → Q) ∧ (R → S) and ¬Q ∨ ¬S, infer ¬P ∨ ¬R. ### Facts and Logical Analysis - Both forms are valid argument forms, verifiable via truth tables or proof by cases. - Constructive Dilemma is analogous to a disjunctive syllogism applied to conditionals. - Destructive Dilemma is the contrapositive-based counterpart, relying on modus tollens within each conditional. - The dilemma structure is powerful in argumentation because it does not require knowing which disjunct (P or R, or ¬Q or ¬S) is true—only that at least one is. ### Causes and Consequences **Causes**: - Dilemmas arise naturally in decision-making contexts where two conditions lead to the same outcome. - They are used rhetorically to limit perceived options and compel acceptance of a conclusion. **Consequences**: - When used correctly, dilemmas strengthen arguments by showing that a conclusion follows regardless of which premise holds. - When misapplied (e.g., false dilemma), they become fallacious by artificially restricting choices. - In Cameroonian legal or policy debates, dilemmas are often invoked to justify decisions under constraints (e.g., resource allocation, security vs. liberty). ### Examples (Cameroonian and African Context) - **Example 1 (Constructive Dilemma)**: Premise 1: If the government increases teacher salaries (P), then education quality improves (Q). Premise 2: If the government invests in school infrastructure (R), then education quality improves (S). Premise 3: The government will either increase teacher salaries or invest in school infrastructure (P ∨ R). Conclusion: Therefore, education quality will improve (Q ∨ S). This is a valid Constructive Dilemma. Even if we do not know which policy is chosen, the outcome is guaranteed. - **Example 2 (Destructive Dilemma)**: Premise 1: If corruption is widespread (P), then public trust in government is low (Q). Premise 2: If electoral fraud occurs (R), then public trust in government is low (S). Premise 3: Public trust in government is not low in some regions (¬Q) OR election results are accepted as legitimate in some areas (¬S). Conclusion: Therefore, either corruption is not widespread (¬P) OR electoral fraud did not occur (¬R). This reflects a real-world scenario where advocates use lack of declining trust to argue against systemic corruption or fraud. - **Example 3 (Policy Dilemma in Cameroon)**: "If we impose strict lockdowns (P), then economic activity declines (Q). If we do not impose lockdowns (R), then infections rise (S). We must either impose lockdowns or not (P ∨ R). Therefore, either economic activity declines or infections rise (Q ∨ S)." This Constructive Dilemma illustrates the unavoidable trade-off faced during the COVID-19 pandemic, a context familiar to students. ### Vocabulary to Retain - Constructive Dilemma: Valid form: (P → Q) ∧ (R → S), P ∨ R ∴ Q ∨ S. - Destructive Dilemma: Valid form: (P → Q) ∧ (R → S), ¬Q ∨ ¬S ∴ ¬P ∨ ¬R. - Antecedent: The "if" clause in a conditional (P in P → Q). - Consequent: The "then" clause in a conditional (Q in P → Q). - Disjunctive Premise: The "either/or" statement (P ∨ R or ¬Q ∨ ¬S) that fuels the dilemma. - Horns of the Dilemma: The two conditional premises (P → Q and R → S) representing the choices. ### Example of Exam-Type Question with Plan **Question**: Consider the following argument: "If the road to Douala is repaired (P), then travel time decreases (Q). If the road remains unrepaired (R), then vehicle maintenance costs increase (S). It is either the case that the road is repaired or it is not repaired (P ∨ R). Therefore, either travel time decreases or vehicle maintenance costs increase (Q ∨ S)." Identify the argument form, state whether it is valid, and justify your answer. **Plan**: 1. Identify the structure: Two conditionals (P → Q) and (R → S), a disjunctive premise (P ∨ R), and a disjunctive conclusion (Q ∨ S). 2. Recognize this as the pattern of a Constructive Dilemma. 3. State that Constructive Dilemma is a valid argument form in propositional logic. 4. Justify by noting that if P is true, Q follows by modus ponens; if R is true, S follows by modus ponens; since at least one of P or R is true, at least one of Q or S must be true. 5. Conclude that the argument is valid and exemplifies a Constructive Dilemma. ## III. Destructive Dilemma ### Context This lesson focuses specifically on the Destructive Dilemma, a valid argument form that is less intuitive than its constructive counterpart but equally important in logical analysis. While the Constructive Dilemma moves from affirming antecedents to affirming consequents, the Destructive Dilemma moves from denying consequents to denying antecedents. It is particularly useful in refuting arguments or showing that certain conditions cannot hold if outcomes are not as expected. Students must master this form to evaluate counterarguments and engage in critical reasoning, especially in debates about governance, justice, and social policy in Cameroon and Africa. ### Definition and Structure The **Destructive Dilemma** has the following logical form: (P → Q) ∧ (R → S) ¬Q ∨ ¬S ∴ ¬P ∨ ¬R In words: - If P implies Q, and R implies S, - And either Q is false or S is false (or both), - Then either P is false or R is false (or both). This form is valid because it relies on the contrapositive of each conditional: (P → Q) is logically equivalent to (¬Q → ¬P), (R → S) is logically equivalent to (¬S → ¬R). Thus, from ¬Q ∨ ¬S, we can infer ¬P ∨ ¬R via Constructive Dilemma applied to the contrapositives, or directly by cases. > **Destructive Dilemma**: From (P → Q) ∧ (R → S) and ¬Q ∨ ¬S, infer ¬P ∨ ¬R. > This form is valid: if the premises are true, the conclusion must be true. ### Facts and Logical Analysis - The Destructive Dilemma is the mirror image of the Constructive Dilemma, using denial instead of affirmation. - It can be proven valid by: a) Applying the law of contraposition to each conditional to get (¬Q → ¬P) ∧ (¬S → ¬R), b) Then using Constructive Dilemma on ¬Q ∨ ¬S to derive ¬P ∨ ¬R. - Alternatively, a truth table or proof by cases (assuming ¬Q, then ¬P; assuming ¬S, then ¬R) confirms validity. - It is a rule of inference in formal logic systems and is used in automated theorem proving. ### Causes and Consequences **Causes**: - Arises when attempting to refute a position by showing that its expected outcomes are not observed. - Common in scientific reasoning, legal defense, and policy critique: if a theory predicts certain outcomes, and those outcomes are absent, the theory may be challenged. **Consequences**: - When used correctly, it is a powerful tool for critical thinking and argument refutation. - If misapplied (e.g., denying the consequent fallaciously within each conditional), it can lead to error—but the dilemma form itself avoids this by requiring only one consequent to be false. - In Cameroonian contexts, it helps evaluate claims about governance, development, or human rights where predicted improvements are not observed. ### Examples (Cameroonian and African Context) - **Example 1 (Public Health)**: Premise 1: If the vaccination campaign is effective (P), then measles cases decrease (Q). Premise 2: If health education programs are widespread (R), then measles cases decrease (S). Premise 3: Measles cases have not decreased in the North Region (¬Q) OR they have not decreased in the East Region (¬S). Conclusion: Therefore, either the vaccination campaign is not effective (¬P) OR health education programs are not widespread (¬R). This reflects a real epidemiological assessment where lack of decline in cases prompts investigation into program efficacy. - **Example 2 (Education Policy)**: Premise 1: If free primary education is implemented (P), then enrollment increases (Q). Premise 2: If community schools are built (R), then enrollment increases (S). Premise 3: Enrollment has not increased in some subdivisions (¬Q) OR dropout rates remain high in others (¬S — interpreted as failure to increase enrollment). Conclusion: Therefore, either free primary education is not fully implemented (¬P) OR community schools are not sufficiently built (¬R). This mirrors critiques of Cameroon’s education policy where enrollment gains are uneven. - **Example 3 (Agricultural Development)**: Premise 1: If subsidized fertilizers are distributed (P), then crop yields rise (Q). Premise 2: If extension services are accessible (R), then crop yields rise (S). Premise 3: Crop yields have not risen in the West Highlands (¬Q) OR they have not risen in the Littoral zone (¬S). Conclusion: Therefore, either fertilizer distribution is ineffective (¬P) OR extension services are not reaching farmers (¬R). This aligns with field reports from Cameroonian agricultural extension services. ### Vocabulary to Retain - Destructive Dilemma: Valid form: (P → Q) ∧ (R → S), ¬Q ∨ ¬S ∴ ¬P ∨ ¬R. - Contrapositive: The equivalent form ¬Q → ¬P of a conditional P → Q. - Denying the Consequent: Valid inference: P → Q, ¬Q ∴ ¬P (used implicitly in each arm of the dilemma). - Disjunctive Denial: The premise ¬Q ∨ ¬S, stating that at least one expected outcome is absent. - Refutational Structure: The argument’s function in challenging a position by showing its predicted outcomes are missing. - Burden of Proof Shift: In using this form, the arguer shifts the burden to defend why both conditionals might still hold despite failed outcomes. ### Example of Exam-Type Question with Plan **Question**: A civil society group argues: "If the government had truly decentralized power (P), then local councils would have greater autonomy (Q). If traditional authorities had been formally integrated into governance (R), then local decision-making would be more inclusive (S). However, local councils still lack real autonomy (¬Q) OR decision-making remains dominated by state appointees (¬S). Therefore, either power has not been truly decentralized (¬P) OR traditional authorities have not been formally integrated (¬R)." Identify the argument form, state whether it is valid, and explain its logical basis. **Plan**: 1. Identify the structure: Two conditionals (P → Q) and (R → S), a disjunctive premise of denied consequents (¬Q ∨ ¬S), and a disjunctive conclusion of denied antecedents (¬P ∨ ¬R). 2. Recognize this as the Destructive Dilemma form. 3. State that Destructive Dilemma is a valid argument form in propositional logic. 4. Explain the logical basis: Each conditional implies its contrapositive (¬Q → ¬P and ¬S → ¬R); from ¬Q ∨ ¬S, Constructive Dilemma yields ¬P ∨ ¬R. Alternatively, by cases: if ¬Q, then ¬P by modus tollens; if ¬S, then ¬R by modus tollens; thus ¬P ∨ ¬R follows. 5. Conclude that the argument is valid and exemplifies how logical forms can be used to critique public policy in Cameroonian contexts. ## IV. Guided Work: Informal Fallacies ### Context This lesson shifts from formal to informal fallacies—errors in reasoning that stem not from invalid logical structure, but from irrelevant content, ambiguous language, emotional manipulation, or faulty assumptions about context. Unlike formal fallacies (e.g., Affirming one Alternant), informal fallacies can occur even when the argument’s form is valid, because the premises fail to support the conclusion in a meaningful way. In Cameroonian and African public discourse—where debates on ethnicity, governance, tradition, and development are often emotionally charged—informal fallacies are prevalent. Recognizing them is crucial for critical thinking, media literacy, and responsible citizenship. ### Definition and Characteristics An **informal fallacy** is a mistake in reasoning that arises due to the content, context, or manner of presentation of an argument, rather than its logical form. The argument may appear persuasive but fails because of irrelevance, ambiguity, presumption, or emotional appeal. Key categories include: - **Fallacies of Relevance**: Premises are logically irrelevant to the conclusion (e.g., ad hominem, appeal to emotion). - **Fallacies of Presumption**: Premises assume what they aim to prove or rely on unwarranted assumptions (e.g., begging the question, false dilemma). - **Fallacies of Ambiguity**: Arise from vague or equivocal language (e.g., equivocation, amphiboly). > **Informal Fallacy**: A defect in an argument’s content, context, or expression that undermines its rational force, even if the form appears correct. ### Facts and Classification Informal fallacies are not captured by formal logic alone because they depend on meaning, pragmatics, and context. However, they are systematically studied in logic and critical thinking curricula. Common types include: - **Ad Hominem**: Attacking the person instead of the argument. - **Appeal to Emotion (Ad Populum, Ad Baculum, Ad Misericordiam)**: Using fear, pity, or popularity to persuade. - **Begging the Question (Petitio Principii)**: Assuming the conclusion in the premises. - **False Dilemma (Either/Or Fallacy)**: Presenting only two options when more exist. - **Equivocation**: Using a word with two different meanings in the same argument. - **Straw Man**: Misrepresenting an opponent’s position to make it easier to attack. - **Appeal to Authority (Ad Verecundiam)**: Citing an authority outside their expertise or as decisive proof. - **Hasty Generalization**: Drawing a broad conclusion from insufficient evidence. These are not exhaustive but represent the core set taught in Form Five Logic. ### Causes and Consequences **Causes**: - Cognitive biases (e.g., confirmation bias, in-group favoritism). - Rhetorical training that prioritizes persuasion over truth. - Cultural norms where respect for authority or elders discourages questioning. - Media environments that reward sensationalism over nuance. - Lack of training in critical analysis and argument evaluation. **Consequences**: - Distorts public debate and hinders consensus-building. - Leads to poor policy decisions based on manipulated perceptions. - Undermines trust in institutions and democratic processes. - Can exacerbate ethnic, regional, or religious tensions when fallacies exploit identity. - In academic settings, results in weak essays and inability to engage with counterarguments. ### Examples (Cameroonian and African Context) - **Example 1 (Ad Hominem)**: During a debate on land reform, a politician says: "We shouldn’t listen to Dr. Ngozi’s proposal because she is from the Northwest and has always opposed government projects." This attacks the person’s regional identity rather than addressing the merits of the land reform proposal—classic ad hominem. - **Example 2 (Appeal to Emotion – Fear)**: A radio broadcast claims: "If we allow Anglophone schools to use the GCE system, Cameroon will break apart—just like Sudan did." This invokes fear of secession without evidence, using emotional manipulation to oppose educational autonomy. - **Example 3 (Begging the Question)**: A government statement: "Our policies are effective because they are designed by experts, and experts only design effective policies." The premise assumes the conclusion: effectiveness is assumed in the definition of expert design. - **Example 4 (False Dilemma)**: A campaign poster: "Either you support the President’s vision for Cameroon, or you are against national unity." This ignores middle positions—such as supporting unity while criticizing specific policies—thereby falsely restricting choice. - **Example 5 (Equivocation)**: A speaker says: "We must have faith in our leaders. After all, faith moves mountains, and our leaders have promised to build a new bridge." Here, "faith" shifts from religious trust to confidence in promises—two different meanings—making the argument misleading. - **Example 6 (Straw Man)**: In a discussion about customary law, one says: "Those who want to reform customary law just want to abolish all tradition and impose Western values." This misrepresents the reform position as total rejection, when in fact advocates may seek to harmonize tradition with human rights. - **Example 7 (Hasty Generalization)**: After seeing two incidents of corruption in a single ministry, a commentator declares: "All civil servants in Cameroon are corrupt." This draws a sweeping conclusion from a tiny, unrepresentative sample. ### Vocabulary to Retain - Informal Fallacy: Error in reasoning due to content, context, or expression, not logical form. - Ad Hominem: Attacking the person rather than the argument. - Appeal to Emotion: Using fear, pity, or popularity to persuade instead of evidence. - Begging the Question: Assuming the conclusion in the premises (circular reasoning). - False Dilemma: Presenting only two options when more exist. - Equivocation: Using a word with multiple meanings in different senses within the argument. - Straw Man: Misrepresenting an opponent’s view to make it easier to attack. - Hasty Generalization: Drawing a broad conclusion from insufficient or biased evidence. ### Example of Exam-Type Question with Plan **Question**: Identify the informal fallacy in each of the following statements: (a) "The minister’s proposal to reduce university fees must be wrong—he failed his own exams." (b) "If we don’t ban motorcycle taxis in Yaoundé, the city will become ungovernable, just like Lagos." (c) "Traditional rulers should not be questioned because they are the custodians of our culture, and custodians of culture are beyond reproach." (d) "Either we adopt French as the sole official language, or we risk ethnic fragmentation." (e) "The law says everyone is equal before the court, so this verdict must be fair." For each, name the fallacy and explain why it applies. **Plan**: For each part: 1. Identify the reasoning pattern. 2. Match it to a known informal fallacy from the curriculum. 3. Explain why the fallacy applies, focusing on content, context, or language rather than form. 4. Avoid confusing with formal fallacies (e.g., do not call (d) Affirming one Alternant—it is a False Dilemma). **Answers**: (a) Ad Hominem: Attacks the minister’s personal academic failure instead of addressing the proposal’s merits. (b) Appeal to Emotion (Fear): Uses fear of chaos (comparing to Lagos) to argue for a policy without evidence of causal link. (c) Begging the Question: Assumes traditional rulers are beyond reproach in the premise to conclude they should not be questioned. (d) False Dilemma: Presents only two options (French monolingualism or fragmentation), ignoring bilingualism or multilingual solutions. (e) Equivocation: "Equal before the court" shifts from legal equality (equal treatment under law) to assuming verdict fairness—two different meanings of "equal". ## Synthèse du chapitre - The chapter covers both formal and informal dimensions of logical reasoning. - **Formal Focus**: The fallacy of Affirming one Alternant (invalid disjunctive reasoning), and the valid argument forms of Constructive and Destructive Dilemma. - **Informal Focus**: Identification and analysis of common informal fallacies in public discourse, with emphasis on Cameroonian and African relevance. - Students learn to distinguish valid from invalid structures, and sound from manipulative content in arguments. - Mastery enables critical engagement with media, policy debates, and academic texts. - The dilemmas illustrate how logic can model unavoidable choices or refute positions based on absent outcomes. - Informal fallacies reveal how rhetoric can subvert reason, even when logic appears intact. ## Glossaire - **Affirming one Alternant**: The fallacy of inferring the negation of one disjunct from the affirmation of the other in an inclusive disjunction (P ∨ Q, P ∴ ¬Q). - **Constructive Dilemma**: A valid argument form: (P → Q) ∧ (R → S), P ∨ R ∴ Q ∨ S. - **Destructive Dilemma**: A valid argument form: (P → Q) ∧ (R → S), ¬Q ∨ ¬S ∴ ¬P ∨ ¬R. - **Disjunction (P ∨ Q)**: A logical connective meaning "or", inclusive by default in formal logic. - **Equivocation**: An informal fallacy arising from the use of a word with two different meanings in different parts of an argument. - **False Dilemma**: An informal fallacy that presents only two alternatives when more exist. - **Informal Fallacy**: A defect in an argument’s content, context, or expression that undermines its rational force. - **Modus Tollens**: Valid inference: P → Q, ¬Q ∴ ¬P (used implicitly in Destructive Dilemma). - **Straw Man**: An informal fallacy that misrepresents an opponent’s position to make it easier to attack. - **Valid Argument Form**: A structure where, if the premises are true, the conclusion must be true.