Affirming the consequent
- Form
- P → Q, Q ∴ P
- Example
- If it rained, the pavement is wet. The pavement is wet, so it rained. (It could also have been the sprinkler.)
- Why it fails
- The conditional licenses inferring Q from P, not P from Q.
Informal · I
Fallacies
fallacia · ‘a deception, a trick in argument’
Recurring failure modes of argument. The list below is intentionally bounded — five families, around twenty entries — chosen to cover the cases most likely to appear in real reasoning rather than to be exhaustive.
Index
Five families
The taxonomy below follows Copi's standard division — one block of formal (structural) fallacies, and four of informal ones grouped by the kind of mistake the family shares.
- 01Formal3 entries
- 02Of relevance7 entries
- 03Of defective induction5 entries
- 04Of presumption4 entries
- 05Of ambiguity4 entries
Family 01
Formal
Failures of structure — invalid argument forms in propositional or syllogistic logic. Detectable from the form alone, independent of content.
Denying the antecedent
- Form
- P → Q, ¬P ∴ ¬Q
- Example
- If it rained, the pavement is wet. It did not rain, so the pavement is not wet. (The sprinkler again.)
- Why it fails
- The conditional says nothing about what follows when P is false.
Undistributed middle
- Form
- All A are B; all C are B ∴ all A are C
- Example
- All cats are mammals; all dogs are mammals; therefore all cats are dogs.
- Why it fails
- The middle term (B) must be distributed in at least one premise for the conclusion to follow.
Family 02
Of relevance
The premises, even if true, do not bear on the conclusion. Attention is redirected from the question at issue.
Ad hominem
argumentum ad hominem
- Form
- X is a bad person; therefore X's claim is false.
- Example
- He cheated on his taxes — why should we trust his theory of climate? (His character has no bearing on the theory's correctness.)
- Why it fails
- An argument is sound or unsound on its own; the arguer's biography does not bear on its premises.
Tu quoque (you too)
- Form
- You also do X; therefore your criticism of X is invalid.
- Example
- You tell me to quit smoking, but you smoke yourself — so your advice is worthless.
- Why it fails
- A messenger's failure to live by a principle is independent of whether the principle is correct.
Ad populum
argumentum ad populum
- Form
- Most people believe P; therefore P.
- Example
- Millions of people believe astrology works, so there must be something to it.
- Why it fails
- Truth is not settled by census. Popular belief is evidence of popular belief.
Ad verecundiam
argumentum ad verecundiam
- Form
- Authority X says P; therefore P.
- Example
- A famous actor endorses this medical treatment, so it must work.
- Why it fails
- Appeal to authority is legitimate only when the authority is genuine, relevant, and not exceptional in disagreement. Misuse strips those qualifiers.
Straw man
- Form
- X argues for P; the speaker substitutes P' (a weaker or absurd version) and refutes P'.
- Example
- You want to fund the arts? So you'd rather give money to painters than feed children. (The original position need not require that trade-off.)
- Why it fails
- Refuting a misrepresented position leaves the original position untouched.
Red herring
- Form
- Q is raised in response to P, when Q is irrelevant to P.
- Example
- Asked about the missing funds, the official answers that crime is up in other cities.
- Why it fails
- Argumentative attention is diverted to a topic that does not bear on the question at issue.
Genetic fallacy
- Form
- P originated from a discreditable source; therefore P is false.
- Example
- The idea came from a propaganda pamphlet, so it cannot be true.
- Why it fails
- A claim's origin is independent of its truth. Many true claims have disreputable origins.
Family 03
Of defective induction
Inductive moves whose premises do not warrant the strength of the conclusion. Each of these is a real inductive form gone wrong, not a structural invalidity.
Hasty generalisation
- Form
- A small or unrepresentative sample of P has property Q; therefore all P have Q.
- Example
- The two restaurants I tried in that city were terrible — the city must have bad food.
- Why it fails
- Small or biased samples do not license universal claims. The premise of projectibility requires a sample large and unbiased enough to support the move.
Appeal to ignorance
argumentum ad ignorantiam
- Form
- P has not been proven false; therefore P. (Or: P has not been proven; therefore ¬P.)
- Example
- No one has proved that ghosts do not exist; therefore they probably do.
- Why it fails
- Absence of evidence is evidence of absence only when an investigation that would have found evidence was actually conducted.
False cause
post hoc ergo propter hoc; cum hoc ergo propter hoc
- Form
- A precedes (or co-occurs with) B; therefore A caused B.
- Example
- I wore my lucky socks and my team won — the socks helped.
- Why it fails
- Temporal succession and correlation are necessary but not sufficient for causation. Common causes and coincidence are not excluded.
Slippery slope
- Form
- If P, then Q; if Q, then R; … if Y, then catastrophe. Therefore ¬P.
- Example
- Allow this, and next we'll have to allow that, and then everything will collapse.
- Why it fails
- Each link in the chain requires its own warrant. A long chain of unsupported conditionals does not produce a sound argument.
False analogy
- Form
- A is like B in respect R; B has property Q; therefore A has Q.
- Example
- The brain is like a computer; computers can crash, so brains can too.
- Why it fails
- Analogical inference is only as strong as the relevance of the shared respects to the property in question.
Family 04
Of presumption
An undefended assumption is built into the argument, so the conclusion is reached without doing the argumentative work.
Begging the question
petitio principii
- Form
- The conclusion is assumed (often in a paraphrase) among the premises.
- Example
- Reading is beneficial because reading is good for you.
- Why it fails
- An argument that assumes its conclusion provides no support for it. Strict petitio is rare; near-petitio (where a premise covertly requires the conclusion) is common.
Complex question
plurium interrogationum
- Form
- A question presupposes a controversial answer to a prior question.
- Example
- Have you stopped beating your spouse? (Presupposes that you started.)
- Why it fails
- Answering directly concedes the presupposition. Reject the question, not the answer.
False dichotomy
- Form
- Either P or Q; ¬P; therefore Q. (Where in fact other alternatives exist.)
- Example
- Either you support the policy or you don't care about the country.
- Why it fails
- Disjunctive syllogism is valid only when the disjunction is exhaustive. Pretending two options are exhaustive forces an unwarranted choice.
Accident (sweeping generalisation)
a dicto simpliciter ad dictum secundum quid
- Form
- A general rule is applied to a case that is a recognised exception.
- Example
- Lying is wrong; therefore you should not lie to the murderer about where his victim is hiding.
- Why it fails
- Most general rules are defeasible. Applying them mechanically to exceptional cases misuses the rule.
Family 05
Of ambiguity
Language is used loosely enough that a term or structure shifts meaning between premises and conclusion.
Equivocation
- Form
- A term is used in two senses across the premises and conclusion.
- Example
- All laws have lawmakers; the laws of nature are laws; therefore the laws of nature have a lawmaker.
- Why it fails
- The term 'law' shifts from prescriptive (civil law) to descriptive (regularity). Two terms wearing the same word.
Amphiboly
- Form
- A premise's grammatical structure is ambiguous and admits readings on which the inference fails.
- Example
- The general read the report quickly, then dismissed it — meaning the dismissal was quick? Or the reading?
- Why it fails
- The argument relies on a particular reading without disambiguating; an opposing reader can refuse it.
Composition
- Form
- Each part of a whole has property Q; therefore the whole has Q.
- Example
- Every brick in the wall is light; therefore the wall is light.
- Why it fails
- Properties of parts do not always survive aggregation. Light bricks compose a heavy wall.
Division
- Form
- The whole has property Q; therefore each part has Q.
- Example
- The orchestra is famous; therefore each musician is famous.
- Why it fails
- The inverse of composition. Properties of a whole are not always inherited by its parts.
A note on the catalogue
What this list is, and is not
A fallacy index is a sharpening tool, not a moral one. Naming a fallacy in an argument is the beginning of the criticism, not its conclusion: the move that looks like ad hominem may turn out to be a relevant point about the source's reliability, and the move that looks like hasty generalisation may rest on a large sample one had not noticed. The catalogue helps one see what is happening; the judgement remains.
The boundaries between fallacy families are loose. Hasty generalisation belongs equally to defective induction and presumption, depending on which feature one stresses; the slippery slope can be read as a defective inductive chain or as a complex of false-cause links. The taxonomy is a convenience.
The canonical source is Aristotle's Sophistical Refutations(c. 350 BC). The modern standardisation in English-language textbooks is from Irving Copi's Introduction to Logic(since 1953, fourteen editions). Douglas Walton's body of work, from the 1980s onward, treats fallacies dialogically rather than structurally, and is the most influential refinement of the tradition since Copi.