The fallacy of four terms ( la, quaternio terminorum) is the

formal fallacy In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic syst ...

that occurs when a

syllogism A syllogism ( grc-gre, συλλογισμός, ''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. ...

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

invalid Invalid may refer to: * Patient, a sick person * one who is confined to home or bed because of illness, disability or injury (sometimes considered a politically incorrect term) * .invalid, a top-level Internet domain not intended for real use As t ...

Definition

Categorical syllogisms always have three terms: :Major premise: All fish have fins. :Minor premise: All goldfish are fish. :Conclusion: All goldfish have fins. Here, the three terms are: "goldfish", "fish", and "fins". Using four terms invalidates the syllogism: :Major premise: All fish have fins. :Minor premise: All goldfish are fish. :Conclusion: All humans have fins. The premises do not connect "humans" with "fins", so the reasoning is invalid. Notice that there are four terms: "fish", "fins", "goldfish" and "humans". 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/expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase havin ...

: 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: :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", "immortal", "Greeks", "people", 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 A complement is something that completes something else. Complement may refer specifically to: The arts * Complement (music), an interval that, when added to another, spans an octave ** Aggregate complementation, the separation of pitch-class ...

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 ( grc-gre, συλλογισμός, ''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. ...

. Types of syllogism to which it applies include

statistical syllogism A statistical syllogism (or proportional syllogism or direct inference) is a non- deductive syllogism. It argues, using inductive reasoning, from a generalization true for the most part to a particular case. Introduction Statistical syllogisms may ...

hypothetical syllogism In classical logic, a hypothetical syllogism is a valid argument form, a syllogism with a conditional statement for one or both of its premises. An example in English: :If I do not wake up, then I cannot go to work. :If I cannot go to work, then ...

, and

categorical syllogism A syllogism ( grc-gre, συλλογισμός, ''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 ...

, 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/expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase havin ...

of the

middle term In logic, a middle term is a term that appears (as a subject or predicate of a categorical proposition) in both premises but not in the conclusion of a categorical syllogism. Example: :Major premise: All men are mortal. :Minor premise A syllogi ...

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