What is a fallacy?
An argument gives reasons (premises) to support a claim (conclusion). A fallacy is a mistake in reasoning: the premises do not really support the conclusion, even if the argument sounds good.
A fallacy is not the same as a false fact. "The Moon is made of cheese" is just false. A fallacy is a bad link between reasons and conclusion. A fallacious argument can even have a true conclusion by luck.
To evaluate an argument, ask: (1) Are the premises true? (2) Do they support the conclusion (valid or strong)? (3) Is anything relevant left out?
Formal and informal fallacies
Formal fallacies are errors in the logical form of a deductive argument. You can spot them by replacing statements with letters; the content does not matter.
- Affirming the consequent: If p then q; q; so p. ("If it rains, the road is wet. The road is wet, so it rained." A water tanker could have wet it.)
- Denying the antecedent: If p then q; not p; so not q.
- Undistributed middle: All cats are animals; all dogs are animals; so all dogs are cats.
Informal fallacies have an acceptable-looking form but fail because of what is said: irrelevant points, unclear words, weak evidence or hidden assumptions. Most everyday fallacies are informal.
Fallacies of relevance: attacking the wrong target
- Ad hominem ("to the person"): attacking the speaker's character, looks or background instead of their reasons. "Ignore his idea about recycling, he is only 14."
- Straw man: twisting the other side's claim into a weaker one, then defeating that. "You want less homework? So you want no school at all!"
- Red herring: changing the subject to distract.
- Appeal to popularity (bandwagon): "Everyone believes it, so it is true."
- False authority: quoting someone who is famous but not an expert on the topic.
- Appeal to emotion / fear: using feelings instead of reasons.
In a fair discussion you answer the strongest version of the other person's view (the opposite of a straw man) and judge ideas, not people.
Fallacies of weak evidence and hidden assumptions
- False dilemma: offering only two options when there are more. "Either you agree with me or you are against the country."
- Slippery slope: claiming one small step will lead to a chain of disasters without evidence for each link.
- Hasty generalisation: a big rule from too few cases.
- Post hoc ("after this, therefore because of this"): assuming that because B came after A, A caused B.
- Circular reasoning (begging the question): the conclusion is already assumed in a premise.
- Equivocation: using one word in two meanings. "A feather is light; what is light cannot be dark; so a feather cannot be dark."
How to detect a seemingly good argument: rewrite it as premises and conclusion, name the link, and ask for a counterexample or the missing options.
Try it: a fallacy hunt
Collect five adverts or social-media posts at home. For each one write the conclusion, the reason given, and which fallacy (if any) it uses. Then rewrite one of them as a fair argument with real evidence.
Key formulas and definitions
- Fallacy = an error in the link between premises and conclusion
- Formal fallacy = bad form (e.g. affirming the consequent: p → q, q ∴ p)
- Informal fallacy = bad content: relevance, evidence, language or assumptions
- Ad hominem: attack the person, not the argument
- Straw man: attack a distorted, weaker version of a claim
- False dilemma: only two options shown; slippery slope: unproved chain of consequences
Worked examples
1. Name the fallacy: "My neighbour's son smoked for years and lived to 90, so smoking is harmless."
Hasty generalisation: one case cannot overturn large studies.
2. Name the fallacy: "You can't trust her opinion on climate; she flies to conferences."
Ad hominem (a 'you too' type): her behaviour does not change whether her evidence is correct.
3. Name the fallacy: "If it is a dog, it has four legs. My cat has four legs, so it is a dog."
Affirming the consequent, a formal fallacy.
4. Name the fallacy: "We must either cut down the forest or let the town starve."
False dilemma: other choices exist (other land, better farming, other jobs).
Common mistakes
- Calling every argument you dislike a fallacy. An argument can be correct even if you disagree with it.
- Thinking that if an argument contains a fallacy, its conclusion must be false (this is itself called the fallacy fallacy).
- Mixing up ad hominem with fair criticism of someone's expertise when expertise is actually relevant.
- Confusing slippery slope with a real, evidence-backed chain of causes.