The fallacy of four terms () is the

formal fallacy In logic and philosophical logic, philosophy, a formal fallacy is a pattern of reasoning rendered validity (logic), invalid by a flaw in its logical structure. propositional calculus, Propositional logic, for example, is concerned with the meaning ...

that occurs when a

syllogism A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defin ...

has four (or more) terms rather than the requisite three, rendering it invalid.

Definition

Categorical syllogisms always have three terms: :Major premise: Weapons are dangerous. :Minor premise: Knives are weapons. :Conclusion: Knives are dangerous. Here, the three terms are: "weapon", "dangerous", and "knife". Using four terms invalidates the syllogism: :Major premise: Weapons are dangerous. :Minor premise: Balloons are round. :Conclusion: Balloons are dangerous. Notice that there are four terms: "weapon", "dangerous", "balloon", and "round". The two premises do not connect "balloons" with "dangerous", so the reasoning is invalid. Two premises are not enough to connect four different terms, since in order to establish connection, there must be one term common to both premises. In everyday reasoning, the fallacy of four terms occurs most frequently by

equivocation In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word or expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase ...

: using the same word or phrase but with a different meaning each time, creating a fourth term even though only three distinct words are used. The resulting argument sounds like the (valid) first example above, but is in fact structured like the invalid second example: :Major premise: Nothing is better than eternal happiness. :Minor premise: A ham sandwich is better than nothing. :Conclusion: A ham sandwich is better than eternal happiness. The word "nothing" in the example above has two meanings, as presented: "nothing is better" means the thing being named has the highest value possible (there exists nothing better); "better than nothing" means only that the thing being described has some value (more than the implied zero value of nothing). Therefore, "nothing" acts as two different terms in this example, thus creating the fallacy of four terms. The fallacy of four terms also applies to syllogisms that contain five or six terms.

Reducing terms

Sometimes a syllogism that is apparently fallacious because it is stated with more than three terms can be translated into an equivalent, valid three term syllogism. For example: :Major premise: No humans are immortal. :Minor premise: All Greeks are people. :Conclusion: All Greeks are mortal. This EAE-1 syllogism apparently has five terms: "

humans Humans (''Homo sapiens'') or modern humans are the most common and widespread species of primate, and the last surviving species of the genus ''Homo''. They are Hominidae, great apes characterized by their Prehistory of nakedness and clothing ...

", " immortal", "

Greeks Greeks or Hellenes (; , ) are an ethnic group and nation native to Greece, Greek Cypriots, Cyprus, Greeks in Albania, southern Albania, Greeks in Turkey#History, Anatolia, parts of Greeks in Italy, Italy and Egyptian Greeks, Egypt, and to a l ...

", "

people The term "the people" refers to the public or Common people, common mass of people of a polity. As such it is a concept of human rights law, international law as well as constitutional law, particularly used for claims of popular sovereignty. I ...

", and "mortal". But it can be rewritten as a standard form AAA-1 syllogism by first substituting the synonymous term "humans" for "people" and then by reducing the complementary term "immortal" in the first premise using the

immediate inference An immediate inference is an inference which can be made from only one statement or proposition. For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" ( ...

known as

obversion In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, ...

(that is, the statement "No humans are immortal." is equivalent to the statement "All humans are mortal.").

Classification

The fallacy of four terms is a

syllogistic fallacy A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (define ...

. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and

categorical syllogism A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (define ...

, all of which must have exactly three terms. Because it applies to the argument's form, as opposed to the argument's content, it is classified as a

Equivocation In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word or expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase ...

of the middle term is a frequently cited source of a fourth term being added to a syllogism; both of the equivocation examples above affect the middle term of the syllogism. Consequently this common error itself has been given its own name: the fallacy of the ambiguous middle. An argument that commits the ambiguous middle fallacy blurs the line between formal and informal (material) fallacies, however it is usually considered an informal fallacy because the argument's form appears valid.

References

Notes

Books

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External links

How Logical Fallacy Invalidates Any Argument
Understanding Defectice Arguments, thoughtco.com

onegoodmove.org

fallacyfiles.org

fallacyfiles.org {{Formal fallacy Four terms