Chapter 25: Exercises — Logic, Argumentation, and Fallacy Recognition

Instructions

These exercises progress from identification tasks (recognizing argument structure and fallacies) to analysis and construction tasks (building and evaluating arguments). Work through them in order, as earlier exercises develop skills needed in later ones.

Part A: Argument Structure (Exercises 1–8)

Exercise 1: Distinguishing Arguments from Non-Arguments

Classify each passage as an argument, assertion, explanation, or description. For arguments, identify the premise(s) and conclusion.

(a) "The defendant could not have committed the crime because surveillance footage places him in another city at the time of the offense."

(b) "Climate change is the greatest threat of our time."

(c) "The bridge weakened over decades because road salt accelerated steel corrosion, and winter freeze-thaw cycles expanded micro-cracks in the concrete."

(d) "The senator voted against the bill on Tuesday. The vote was 52-48 in favor."

(e) "We should limit social media use for teenagers, since studies link heavy social media use to increased rates of anxiety and depression in adolescents, and teenagers' developing brains are particularly susceptible to habit formation."

(f) "Scientists have found that regular exercise reduces the risk of cardiovascular disease."

Exercise 2: Identifying Inferential Indicators

Underline the inferential indicator in each sentence and label it as a premise indicator (PI) or conclusion indicator (CI).

(a) "Since the suspect's fingerprints are not at the crime scene, we should look elsewhere for the perpetrator."

(b) "The study used a non-representative sample; consequently, its findings cannot be generalized to the broader population."

(c) "Due to the fact that organic farming prohibits synthetic pesticides, organic produce tends to have lower pesticide residues."

(d) "Governments should fund public health campaigns, for well-designed campaigns have measurably reduced smoking rates, seat belt non-compliance, and drunk driving."

(e) "The experiment failed to replicate, which implies that the original finding may have been a statistical artifact."

Exercise 3: Rewriting in Standard Form

Rewrite the following arguments in standard form (numbered premises followed by conclusion). Identify any implicit premises.

(a) "We know that GMO foods are dangerous because nature didn't design them and anything that isn't natural poses health risks."

(b) "Facebook's recommendation algorithms amplify outrage because outrage content generates more clicks and shares, and the algorithms are optimized for engagement metrics."

(c) "Any information source that has been wrong in the past cannot be trusted. The WHO was wrong about mask guidance early in the pandemic. So we can't trust the WHO."

(d) "There's no point vaccinating against the flu because the vaccine is only about 40-60% effective in most years."

Exercise 4: Validity Assessment

For each argument, determine whether it is valid or invalid. If invalid, explain why the conclusion could be false even if the premises were true. (Do NOT assess whether the premises are true.)

(a) - P1: All peer-reviewed studies are reliable. - P2: This study is peer-reviewed. - C: This study is reliable.

(b) - P1: If a person spreads misinformation, they are irresponsible. - P2: This person is irresponsible. - C: This person spreads misinformation.

(c) - P1: Either the vaccine is safe or there is a government cover-up. - P2: The vaccine is not safe. - C: There is a government cover-up.

(d) - P1: If social media companies cared about truth, they would remove all false content. - P2: Social media companies do not remove all false content. - C: Social media companies do not care about truth.

(e) - P1: Some conspiracy theories turn out to be true. - P2: This claim is a conspiracy theory. - C: This claim might be true.

Exercise 5: Soundness Assessment

For each argument from Exercise 4, assess whether it is sound (valid with true premises). If unsound, identify which premise(s) are false or questionable.

Exercise 6: Reconstructing Implicit Premises

Each argument below has at least one implicit premise. Identify and state the implicit premise(s) that make the argument valid.

(a) "He gets his news from Fox News, so you can't trust what he says about immigration policy."

(b) "People have been growing crops without genetic modification for 10,000 years, so GMO crops should be avoided."

(c) "The COVID vaccine was developed in less than a year, which means it can't be safe."

Exercise 7: Evaluating Analogical Arguments

For each analogical argument, (a) identify the analogy being drawn, (b) list the relevant similarities, (c) list potentially important disanalogies, and (d) rate the argument's strength (strong/moderate/weak) with justification.

(a) "We require drivers to pass a safety test before getting a license. We should require gun owners to pass a safety test before purchasing firearms."

(b) "Restricting speech on social media is just like book burning in Nazi Germany."

(c) "Chemotherapy uses poison to kill cancer cells. Vaccines inject foreign substances into the body to trigger immune responses. Both involve introducing potentially harmful substances — so vaccines are just as risky as chemotherapy."

Exercise 8: Inductive Strength

Assess the strength of each inductive argument. Identify any problems with the sample (size, representativeness, selection bias).

(a) A study surveying 12 anti-vaccination Facebook group members finds that 11 of them believe mainstream medicine is corrupt. Conclusion: Most people who reject vaccines believe mainstream medicine is corrupt.

(b) A randomized controlled trial with 25,000 participants across five countries finds that a new drug reduces heart attack risk by 23%. Conclusion: The drug is effective at reducing heart attack risk.

(c) A journalist interviews 20 people in a shopping mall and finds that 15 distrust mainstream news. Conclusion: 75% of the public distrusts mainstream news.

Part B: Fallacy Identification (Exercises 9–20)

Exercise 9: Name That Fallacy

Identify the fallacy (or fallacies) in each example. Choose from the list in Section 25.5 and explain your identification.

(a) "Of course Dr. Fauci says the pandemic is serious — his funding depends on people being scared of disease."

(b) "Critics of homeopathy say it doesn't work. But Western medicine has only existed for a few hundred years. Homeopathy has been practiced for over 200 years and was developed by a trained physician."

(c) "You're either with us or you're with the terrorists."

(d) "A friend of mine took that supplement and lost 30 pounds in two months. It definitely works."

(e) "We gave Johnny the vitamin C supplements and his cold went away. Vitamin C cured his cold."

(f) "If we legalize marijuana, people will move on to harder drugs, and soon the country will be full of heroin addicts."

(g) "Thousands of doctors have signed a petition against mandatory vaccination. If that many medical professionals are skeptical, there must be real safety concerns."

(h) "I don't see why we should take environmental regulations seriously. The senator pushing this legislation was caught lying about his expense reports."

Exercise 10: Fallacy Analysis in Extended Text

Read the following passage and identify every fallacy present, explaining each.

"The establishment is pushing this vaccine on everyone, but we know they're just interested in profit. Natural immunity is the way our bodies have always protected themselves — for thousands of years before vaccines existed, humans survived diseases through natural means. If vaccines were really safe, they wouldn't need to hide the ingredients and give manufacturers legal immunity. Besides, millions of people have serious doubts about vaccines, including many doctors and scientists. Look at how well Sweden did during COVID without lockdowns — clearly natural approaches work. And they haven't even proven that the vaccine doesn't cause long-term problems. Anyone who questions vaccines gets censored, which proves they're afraid of the truth coming out."

Exercise 11: The Straw Man Identification Exercise

Each pair below shows an actual position and a stated counterargument. Identify whether the counterargument attacks the actual position (legitimate response) or a straw man.

(a) - Actual position: "We should implement background checks for all gun purchases, including at gun shows." - Response: "My opponent wants to take away every law-abiding citizen's firearm and leave us defenseless."

(b) - Actual position: "The evidence for homeopathy does not meet the standards required for medical treatments." - Response: "Critics of homeopathy are saying that anything that isn't a pharmaceutical drug is useless, but traditional medicine has cured many people."

(c) - Actual position: "Social media companies should be required to label demonstrably false information." - Response: "My opponent wants the government to control all speech online and decide what's true and false."

Exercise 12: Cherry Picking Analysis

The following statistics are presented in a misinformation article. For each, describe what additional information would be needed to evaluate the full picture.

(a) "VAERS has recorded over 10,000 reports of adverse events following COVID vaccination."

(b) "Six studies have found no link between cellphone radiation and brain cancer."

(c) "GDP grew 4% in the first quarter under the new administration."

(d) "The country with the lowest vaccination rate in Europe reported fewer COVID deaths per capita than [specific highly vaccinated country] during this three-week period."

Exercise 13: False Dichotomy Detection

For each false dichotomy, identify the excluded middle ground options.

(a) "Either you believe everything the government tells you, or you recognize they're all corrupt liars."

(b) "You're either pro-life or pro-death."

(c) "We either accept refugees without restriction or we keep them all out."

(d) "Either science has all the answers, or religion does."

Exercise 14: Appeal to Authority Analysis

Evaluate each appeal to authority as legitimate or fallacious. Explain your reasoning.

(a) A cardiologist testifies about the risks of a specific cardiac procedure they perform regularly.

(b) A Nobel Prize-winning physicist argues that a certain homeopathic remedy works based on his personal experience.

(c) 97% of actively publishing climate scientists agree that human activity is causing current climate change.

(d) A naturopath with a degree from an unaccredited institution claims that a supplement cures cancer.

(e) A former Pfizer employee who now advocates against vaccines claims they have insider knowledge of hidden harms.

Exercise 15: Post Hoc Reasoning

For each post hoc argument, explain what would need to be established to support a causal claim.

(a) "Crime rates fell in the years after the state adopted concealed carry laws. The concealed carry laws reduced crime."

(b) "After the country began a national reading program in 2015, math test scores improved by 8% over five years. The reading program improved math performance."

(c) "I started using essential oils last year and haven't had a cold since. Essential oils boost my immune system."

Exercise 16: Formal Fallacy Identification

Identify whether each argument commits the fallacy of affirming the consequent, denying the antecedent, or neither.

(a) - If the drug is effective, clinical trials will show improvement over placebo. - Clinical trials show improvement over placebo. - Therefore, the drug is effective.

(b) - If the earth were flat, we would not be able to see ships disappearing hull-first over the horizon. - Ships do disappear hull-first over the horizon. - Therefore, the earth is not flat.

(c) - If the politician is corrupt, they will accept bribes. - The politician does not accept bribes. - Therefore, the politician is not corrupt.

(d) - If this supplement boosts immunity, users will get sick less often. - Users do not get sick less often. - Therefore, this supplement does not boost immunity.

Part C: Applied Analysis (Exercises 17–25)

Exercise 17: Newspaper Argument Reconstruction

Find a recent newspaper opinion article (or use the provided sample below) and: (a) Identify the main conclusion. (b) List all stated premises. (c) List all implicit premises. (d) Evaluate the argument's validity/strength. (e) Identify any fallacies.

Sample article excerpt: "Social media companies should be required to verify user identities. Anonymous posting has enabled harassment campaigns, the spread of coordinated misinformation, and the amplification of hate speech. When people are accountable for their words, they behave more responsibly. Countries like South Korea that have experimented with real-name systems have seen some reductions in online harassment. Protecting public discourse requires accountability."

Exercise 18: Political Speech Analysis

Analyze the following speech excerpt for logical quality. Identify premises, conclusions, implicit assumptions, and fallacies.

"My opponent has been in Washington for 20 years. In those 20 years, your wages have stagnated and your costs have risen. Twenty years of failure. My plan will cut taxes, reduce regulations, and unleash American enterprise. Countries with lower tax rates have seen explosive economic growth. Either we take bold action now, or we accept permanent decline. The choice is clear. Real Americans understand that freedom means less government."

Evaluate the following social media posts for logical quality. For each, identify: the implicit argument, the fallacies, and what evidence would actually be needed to support or refute the underlying claim.

(a) "My cousin's friend is a nurse and she says they're being told to code all deaths as COVID to inflate the numbers. The media won't cover this. SHARE before this gets deleted!"

(b) "THINK ABOUT IT: They spend billions fighting cancer. If they cured it, they'd lose billions. Why would they ever cure cancer? Wake up."

(c) "New study: Coffee linked to 15% lower Alzheimer's risk! Drink up! ☕"

Exercise 20: Argument Construction

Construct a valid deductive argument (minimum 3 premises) for each conclusion. Ensure all premises are plausible and the inference is tight.

(a) Conclusion: Students should be taught media literacy as part of standard K-12 curricula.

(b) Conclusion: Not all claims on the internet deserve equal evidential weight.

(c) Conclusion: Peer review is a necessary but insufficient safeguard against scientific error.

Exercise 21: Rebuttal Construction

For each fallacious argument, write a rebuttal that: (a) names the fallacy, (b) explains why it's fallacious, and (c) indicates what a valid argument for a related conclusion would require.

(a) "Millions of people believe the moon landing was faked, so there must be something to it."

(b) "That research is funded by the government, so it's politically biased and unreliable."

(c) "Herbal medicine has been used for centuries, so it must be effective."

Exercise 22: Gish Gallop Analysis

Below is a summary of 15 claims made in a five-minute portion of an anti-vaccination presentation.

Claims: (1) Vaccines contain aluminum; (2) Vaccines contain formaldehyde; (3) VAERS shows X injuries; (4) The FDA has recalled Y drugs before; (5) Big Pharma pays doctors; (6) Natural immunity is stronger; (7) Some vaccines were pulled due to side effects; (8) Studies are funded by pharma; (9) Doctors don't read package inserts; (10) Japan changed its vaccine schedule; (11) One country delayed a vaccine; (12) A celebrity's child regressed after vaccination; (13) The 1976 swine flu vaccine caused harm; (14) A whistleblower made claims about data manipulation; (15) Vaccine court has paid out billions.

(a) Classify each claim by type (empirical, misleading context, appeal to authority, conspiracy, anecdote, etc.).

(b) Estimate how long a thorough rebuttal to each claim would require. Sum the total time needed.

(c) What does this tell us about the epistemology of the Gish Gallop?

(d) Write a brief meta-rebuttal (naming the tactic without addressing each claim individually) that could be delivered in 90 seconds.

Exercise 23: Abductive Reasoning Practice

For each observation, generate two competing hypotheses that could explain it, then identify which is preferable under Occam's Razor and why.

(a) Observation: A popular YouTube channel's videos critical of a pharmaceutical company are repeatedly removed by the platform.

(b) Observation: Several independent studies from different countries find the same effect size for a new treatment.

(c) Observation: A news story about a vaccine injury goes viral but is not covered by mainstream news outlets.

Exercise 24: Burden of Proof Allocation

For each scenario, determine where the burden of proof lies and explain your reasoning.

(a) Someone claims that a supplement cures cancer.

(b) A researcher claims that a specific chemical, previously considered safe, causes liver damage at high doses.

(c) Someone claims that 5G towers do not cause cancer.

(d) A historian claims that a widely accepted historical event did not occur as recorded.

Exercise 25: Comprehensive Argument Evaluation

Evaluate the following extended argument. Apply all relevant tools from this chapter: identify structure, assess validity, evaluate premises, identify fallacies, name implicit assumptions, and write a 200-word critical assessment.

"We shouldn't trust the consensus on climate change. The same experts who now claim consensus once told us that fat was bad for us, that ulcers were caused by stress, and that thalidomide was safe. Scientific consensus has been wrong before. Besides, climate scientists receive government funding, so they have every reason to exaggerate the threat to keep their grants coming. In 1970, environmentalists predicted an ice age — they were wrong. And if climate change were real and man-made, why have global temperatures paused for periods in the recent record? Natural variation explains everything we see just as well as human activity does. Many ordinary people — the real experts in how the climate has changed in their lifetimes — notice that winters seem perfectly normal. The climate alarmists want to destroy our economy and return us to the Stone Age. We should trust common sense over computer models that have consistently over-predicted warming."

Part D: Synthesis Exercises (Exercises 26–33)

Exercise 26: Building a Misinformation Argument Anatomy

Choose a piece of misinformation you have encountered (online, in conversation, or in media). Write a 400-word analysis that: - States the misinformation claim - Reconstructs it in standard argument form - Identifies all fallacies it contains - Explains its psychological appeal - Proposes a fact-based rebuttal

Exercise 27: Debate Simulation

Debate partners: one argues for, one against, the following claim using only valid argument forms and factual premises. After 10 minutes, switch sides. Reflection: which fallacies were you tempted to use? Did you notice any?

Claim: "Schools should teach logic and critical thinking as a required subject."

Exercise 28: Fallacy Diary

Over one week, record every logical fallacy you encounter in media, conversation, or advertising. At the end of the week, analyze: Which fallacies were most common? In what contexts? What emotions did they typically appeal to?

Exercise 29: Argument Repair

Each argument below is invalid or contains a fallacy. Repair each by modifying premises to make a valid, sound (or cogent) argument for a related conclusion.

(a) "Everyone on Twitter supports this policy, so it's clearly the right approach."

(b) "That remedy has been used for centuries, therefore it works."

(c) "He's not a real doctor, so his health claims are worthless."

Exercise 30: Comparative Fallacy Analysis

Compare and contrast the following pairs of fallacies. How are they similar? How are they different? Give an original example of each.

(a) Ad hominem vs. genetic fallacy

(b) Straw man vs. false equivalence

(c) Appeal to authority vs. appeal to popular opinion

(d) Post hoc vs. false cause

Exercise 31: Valid Arguments for False Conclusions

Construct a valid deductive argument for each false conclusion using one false premise. Identify which premise is false and explain its falsity.

(a) Conclusion: Vaccines are more dangerous than the diseases they prevent.

(b) Conclusion: Climate scientists are motivated to exaggerate findings.

Exercise 32: Implicit Premise Excavation

The following arguments are missing crucial implicit premises. Make explicit all hidden premises, then evaluate whether the argument works with those premises stated.

(a) "It's natural, so it must be good for you."

(b) "If the government is involved, I don't trust it."

(c) "It hasn't been proven safe."

Exercise 33: Meta-Analysis — Fallacy Patterns in Misinformation

Across the fallacies you have studied, identify three common patterns or themes. For each pattern, explain: (a) why it is cognitively appealing, (b) what psychological bias it exploits, and (c) what kind of evidence would help overcome it.