Four-term fallacy

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The four-term fallacy is a logical fallacy that occurs when an argument that was intended to be a syllogism improperly uses four terms instead of three.

A valid syllogism contains three terms (here A, B, and C):

  1. Every A is a B.
  2. Every B is a C.
  3. Therefore every A is a C.

If a single instance of any of these terms is replaced by a fourth term, X, an invalid form results. For example:

  1. Every A is a B.
  2. Every B is a C.
  3. Therefore every A is an X.

Or:

  1. Every A is a B.
  2. Every X is a C.
  3. Therefore every A is a C.

And so forth.

The introduction of the extraneous term makes the argument fallacious. When done as transparently as in the examples above, it is generally easy to see that the argument does not hold. When done using some form of equivocation, the fallacy can be harder to spot.

Example

Consider the following argument:

  1. Evolution is a theory.
  2. A theory is a speculation.
  3. Evolution is a speculation.

The proponent of this argument is attempting to discredit the theory of evolution by conflating the everyday use of theory as a mere hypothesis with the scientific use of the word as a well-established, thoroughly tested explanation. In this case the extraneous fourth term is the second use of the word theory.


v · d Logical fallacies
v · d Formal fallacies
Propositional logic   Affirming a disjunct · Affirming the consequent · Argument from fallacy · False dilemma · Denying the antecedent
Quantificational logic   Existential fallacy · Illicit conversion · Proof by example · Quantifier shift
Syllogistic   Affirmative conclusion from a negative premise · Exclusive premises · Necessity · Four-term fallacy · Illicit major · Illicit minor · Undistributed middle


v · d Faulty generalisations
General   Begging the question · Gambler's fallacy · Slippery slope · Equivocation · argumentum verbosium
Distribution fallacies   Fallacy of composition · Fallacy of division
Data mining   Cherry picking · Accident fallacy · Spotlight fallacy · Hasty generalization · Special pleading
Causation fallacies   Post hoc ergo propter hoc · Retrospective determinism · Suppressed correlative · Wrong direction
Ontological fallacies   Fallacy of reification · Pathetic fallacy · Loki's Wager
v · d False relevance
Appeals   Appeal to authority · Appeal to consequences · Appeal to emotion · Appeal to motive · Appeal to novelty · Appeal to tradition · Appeal to pity · Appeal to popularity · Appeal to poverty · Appeal to spite · Appeal to wealth · Sentimental fallacy · Argumentum ad baculum
Ad hominem   Ad hominem abusive · Reductio ad Hitlerum · Judgmental language · Straw man · Tu quoque · Poisoning the well
Genetic Fallacies   Genetic fallacy · Association fallacy · Appeal to tradition · Texas sharpshooter fallacy
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