Critical Reasoning – Fallacies of Relevance

Deductive Arguments: Formal vs. Informal

• Basic distinction
  • Formal argument = validity traceable to explicit symbolic form or string-manipulation rules.
  • Informal deductive argument = not written out as a strict proof, yet claimed to be such that, if the premises are true, the conclusion cannot be false.
• Hurley’s suggestion: all deductively valid arguments are formal.
• Counter-claim from IEP logicians: There are genuine deductively valid arguments that cannot (at present) be placed inside any known formal proof-system.

Gödel-style counter-example

• Gödel’s First Incompleteness Theorem:
  • “Any consistent, recursively-axiomatized formal system F that interprets a modicum of arithmetic is incomplete; i.e., there exists a sentence G in the language of F such that neither G nor \neg G is provable in F.”
  • G (the Gödel sentence) is mechanically constructible from a specification of F.
• Informal step: Mathematicians typically say “G is true” on semantic grounds—even though G is unprovable in F.
  • The inference “If F is sound, then G” is deductively valid yet informal, because no string-rewrite derivation for G exists in F.
  • Thus, a deductively valid but non-formal argument.

Halting-problem counter-example

• Halting Problem: There is no Turing-machine procedure that, for every program P, decides whether P halts.
• Decomposition of programs:
  1. Some halt (and can be proved to halt).
  2. Some do not halt and can be proved not to halt.
  3. Some do not halt but cannot be proved (within any sound, complete, formal system) not to halt.
• Let P_{\text{nh}} be a program in the third category.
  • True statement: “P_{\text{nh}} does not halt.”
  • From the axioms of Turing-machine theory one can reason informally to that conclusion, but no formal derivation exists (otherwise the halting problem would be solved).
• Hence another deductively valid yet informal argument.

Fallacies of Relevance – General Profile

• Definition: Premises appear to supply emotional or psychological support but are logically irrelevant to the conclusion.
• Illusion of support: Listener may feel persuaded because the premises trigger fear, pity, admiration, etc.
• Eight central types covered:
  1. Appeal to Force
  2. Appeal to Pity
  3. Appeal to the People
  4. Ad Hominem
  5. Accident
  6. Straw Man
  7. Missing the Point
  8. Red Herring
• Practical import: Recognizing these fallacies safeguards rational dialogue and prevents manipulation.

1. Appeal to Force (Argumentum ad Baculum)

• Structure: “Accept conclusion C, or I/others will harm you.”
• Hidden (false) premise: \text{If threat succeeds} \; \rightarrow \; C\text{ is true}.
• Examples
  • Friend: “‘천원짜리 변호사’ is the best show; if you disagree, my big brother will yell at you!”
  • Lobbyist to senator: “Support our inheritance-tax bill, or the press learns about your NRA donations.”
• Why fallacious?
  • Threats give zero evidence for the truth of C. They only supply prudential reasons for faking assent.
  • Rational belief should track evidence, not fear.

2. Appeal to Pity (Argumentum ad Misericordiam)

• Structure: “Please accept C because something sad/bad will happen to me (or someone) otherwise.”
• Key point: Personal misfortune ≠ logical relevance.
• Illustrative case
  • Tax-evasion defendant: “If I’m found guilty my reputation is ruined, my wife can’t get surgery, kids will starve. Therefore I’m not guilty.”
• Why defective?
  • Guilt or innocence depends on facts about wrongdoing, not on consequences for the wrongdoer.

3. Appeal to the People (Argumentum ad Populum)

• Harnesses social desires: being admired, belonging, status.
• Four sub-varieties:
  1. Bandwagon: “Everybody believes/does X, so you should too.”
  • Eg: “Everyone owns the latest iPhone ⇒ you should buy one.”
  1. Vanity: Link to a celebrity.
  • Eg: “Kylie Jenner uses Kylie LipKit ⇒ you should, to be like her.”
  1. Snobbery: Appeal to an elite subgroup.
  • Eg: “Galaxy S22 Ultra – only for the accomplished. Purchase to signal you’re part of the few.”
  1. Tradition: “We have always done X ⇒ we should keep doing X.”
  • Eg: “Serving turkey at Thanksgiving is traditional ⇒ we should serve turkey this year.”
• Diagnostic test: ask “Does popularity, fame, exclusivity, or age alone ensure truth or desirability?” – answer: no.

4. Ad Hominem (Argument Against the Person)

• Two-party pattern: Person 1 offers argument A ➔ Person 2 attacks Person 1 rather than A.
• Three modes:
  1. Abusive – direct verbal abuse.
  • Eg: “Bill Maher says religion is nonsense; Maher is a self-righteous pig ⇒ his argument is worthless.”
  1. Circumstantial – highlight opponent’s motives or background.
  • Eg: “Erica Evans wants higher minimum wage; she earns minimum wage ⇒ ignore her.”
  1. Tu Quoque (“you too”) – charge of hypocrisy.
  • Eg: “Obama tells us to avoid junk food, yet he eats greasy burgers, so ignore his nutrition advice.”
• Fallacy source: Attributes of a speaker do not logically undermine (or support) the relationship between that speaker’s premises and conclusion.

5. Accident (Over-generalization)

• Definition: Rigidly applying a general rule to an exceptional case whose relevant features (“accidents”) remove it from the rule’s scope.
• Prototype
  • P1: “Whoever thrusts a knife into another person commits a crime.”
  • P2: “Surgeons thrust knives into people.”
  • \therefore “Surgeons are criminals.”
• Why wrong?
  • The general norm is designed for malicious stabbing, not for medically sanctioned surgery; context alters moral/legal status.

6. Straw Man

• Mechanism
  1. Misrepresent opponent’s actual position (weaker, distorted, exaggerated).
  2. Refute this caricature.
  3. Claim victory over original argument.
• Classic example
  • “Mr. Goldberg argued against prayer in public schools ⇒ obviously he advocates atheism which leads to suppressing religion and an omnipotent state ⇒ absurd, therefore Goldberg is wrong.”
  • Real argument = separation of church and state, not atheism.
• Contemporary US case – “War on Christmas”
  • Switch cups from “Merry Christmas” to “Happy Holidays.”
  • Critics: Starbucks (and inclusive language) are anti-Christian, waging war on Christmas.
  • Misrepresents the inclusive side’s aim; sets up an easier target (anti-Christian hostility) to knock down.

7. Missing the Point (Ignoratio Elenchi)

• Pattern: Premises logically imply conclusion C1, but speaker draws loosely-related conclusion C2.
• Model case
  • Premise: “Theft and robbery rates are skyrocketing.”
  • Drawn conclusion: “We must reinstate the death penalty.”
  • More natural conclusions: strengthen policing, address root causes, etc.
• Key diagnostic: Is there a more fitting conclusion that flows directly from the given evidence?

8. Red Herring

• Tactic: Divert the conversation onto a different issue (often subtly related) so that attention leaves the original question.
• Etymology: Trainers dragged smelly red herrings across a fox-trail; dogs (listeners) lose scent of fox (original issue).
• Canonical examples
  1. “Need to eliminate pesticides from produce ⇒ But carrots give vitamin A, broccoli iron, oranges vitamin C.”
  • Focus shifts from pesticides to nutritional value.
  1. “Opponent: Reduce greenhouse gases to curb global warming ⇒ Reply: The real threat is nuclear terrorism—focus there.”
• Relation to straw man: Every straw man is a red herring (change of track) but not every red herring involves misrepresentation; sometimes it’s just topic-switching without caricature.

Exercise Items & Official Answers (Page 37-39)

• 1. Give job to Frank; he has six hungry kids, wife needs surgery → Appeal to pity.
• 2. Dismiss Erica’s minimum-wage argument because she earns minimum wage → Ad hominem circumstantial.
• 3. School repairs debated; arguer shifts to too much computer time → Red herring.
• 4. Arrest whoever thrusts knife → therefore arrest surgeons → Accident.
• Additional key codes from instructor list:
  • 5. Appeal to the people (indirect).
  • 6. Ad hominem abusive.
  • 7. Appeal to force.
  • 8. Straw man (Social Security ↔ socialism).
  • 9. Missing the point (solution = improve schools, not close them).
  • 10. Tu quoque.
  • 11. No fallacy (argument deductively valid & sound).

Connection Map & Broader Significance

• Ethical Implication: Fallacies of relevance often exploit non-rational factors—fear, compassion, peer pressure, prejudice—highlighting moral responsibility to argue in good faith.
• Cognitive Bias Links:
  • Bandwagon ↔ conformity bias.
  • Snobbery ↔ status-seeking bias.
  • Appeal to force ↔ authority gradient.
• Historical tie-ins:
  • Ancient sophists cataloged similar tricks; Aristotle’s Sophistical Refutations prefigures many of these.
• Practical tools for defense
  1. Keep the logical question (“Do premises ⇒ conclusion?”) in focus.
  2. Ask “Would the conclusion be any less (or more) true if the emotional component vanished?”
  3. Demand evidence, not pressure.

Compact Checklist for Spotting Relevance Fallacies

• Does the arguer resort to threats? → Appeal to force.
• Play on sympathy? → Appeal to pity.
• Cite popularity, celebrity, exclusivity, or tradition? → Appeal to the people (identify subtype).
• Attack arguer, not argument? → Ad hominem (abusive, circumstantial, tu quoque).
• Misapply a general rule to an exception? → Accident.
• Beat up a distorted version of the view? → Straw man.
• Draw an ill-fitting conclusion? → Missing the point.
• Change subject mid-stream? → Red herring.

Summary Take-Home

• Fallacies of relevance simulate support rather than supply it.
• Understanding them :
  • enhances critical-thinking and debate skills,
  • immunizes against manipulation in advertising, politics, and media,
  • refines our ability to construct sound, cogent arguments.
• Remember: Good reasoning requires that premises be relevant and sufficient for the conclusion—nothing more, nothing less.