Fallacy of four terms

Last updated

The fallacy of four terms (Latin : quaternio terminorum) is the formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three, rendering it invalid.

Contents

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: 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. [1]

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. [2] 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 term "immortal" in the first premise using the immediate inference known as obversion (that is, the statement "No humans are immortal." is equivalent to the statement "All humans are mortal."). [3]

Classification

The fallacy of four terms is a syllogistic fallacy. Types of syllogism to which it applies include statistical syllogism, hypothetical syllogism, and categorical syllogism, 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 formal fallacy.

Equivocation 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. [4] 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. [5]

Related Research Articles

<span class="mw-page-title-main">False dilemma</span> Informal fallacy involving falsely limited alternatives

A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false premise. This premise has the form of a disjunctive claim: it asserts that one among a number of alternatives must be true. This disjunction is problematic because it oversimplifies the choice by excluding viable alternatives, presenting the viewer with only two absolute choices when in fact, there could be many.

In logic, equivocation is an informal fallacy resulting from the use of a particular word/expression in multiple senses within an argument.

<span class="mw-page-title-main">Syllogism</span> Type of logical argument that applies deductive reasoning

A syllogism 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.

A fallacy, also known as paralogia in modern psychology, is the use of invalid or otherwise faulty reasoning in the construction of an argument that may appear to be well-reasoned if unnoticed. The term was introduced in the Western intellectual tradition by the Aristotelian De Sophisticis Elenchis.

Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false.

Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from an original statement. It is a type of mixed hypothetical syllogism in the form:

The fallacy of the undistributed middle is a formal fallacy that is committed when the middle term in a categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy.

An enthymeme is a form of rational appeal, or deductive argument. It is also known as a rhetorical syllogism and is used in oratorical practice. While the syllogism is used in dialectic, or the art of logical discussion, the enthymeme is used in rhetoric, or the art of public speaking. Enthymemes are usually developed from premises that accord with the audience's view of the world and what is taken to be common sense. However, where the general premise of a syllogism is supposed to be true, making the subsequent deduction necessary, the general premise of an enthymeme is merely probable, which leads only to a tentative conclusion. Originally theorized by Aristotle, there are four types of enthymeme, at least two of which are described in Aristotle's work.

Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion.

<span class="mw-page-title-main">Illicit minor</span> Type of formal fallacy in syllogism

Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion.

The fallacy of exclusive premises is a syllogistic fallacy committed in a categorical syllogism that is invalid because both of its premises are negative.

Informal fallacies are a type of incorrect argument in natural language. The source of the error is not just due to the form of the argument, as is the case for formal fallacies, but can also be due to their content and context. Fallacies, despite being incorrect, usually appear to be correct and thereby can seduce people into accepting and using them. These misleading appearances are often connected to various aspects of natural language, such as ambiguous or vague expressions, or the assumption of implicit premises instead of making them explicit.

In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated. It is the inference from the truth of "A implies B" to the truth of "Not-B implies not-A", and conversely. It is very closely related to the rule of inference modus tollens. It is the rule that

<span class="mw-page-title-main">Logical form</span> Form for logical arguments, obtained by abstracting from the subject matter of its content terms

In logic, logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning of a logical form can be determined unambiguously from syntax alone. Logical forms are semantic, not syntactic constructs; therefore, there may be more than one string that represents the same logical form in a given language.

In logic and philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.

A premise or premiss is a proposition—a true or false declarative statement— an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion.

An argument is a series of sentences, statements or propositions some of which are called premises and one is the conclusion. The purpose of an argument is to give reasons for one's conclusion via justification, explanation, and/or persuasion.

In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false. It is not required for a valid argument to have premises that are actually true, but to have premises that, if they were true, would guarantee the truth of the argument's conclusion. Valid arguments must be clearly expressed by means of sentences called well-formed formulas.

Negative conclusion from affirmative premises is a syllogistic fallacy committed when a categorical syllogism has a negative conclusion yet both premises are affirmative. The inability of affirmative premises to reach a negative conclusion is usually cited as one of the basic rules of constructing a valid categorical syllogism.

References

Notes

  1. ↑ Copi & Cohen 1990, pp. 206–207.
  2. ↑ Copi & Cohen 1990, pp. 214–217.
  3. ↑ Cogan 1998, pp. 95–96.
  4. ↑ Copi & Cohen 1990, p. 206.
  5. ↑ Coffey 1912, pp. 302–304.

Books

  • Coffey, Peter (1912). The Science of Logic. Vol. 1. Longmans, Green and Co.
  • Cogan, Robert (1998). Critical Thinking . University Press of America. ISBN   978-0-7618-1067-4.
  • Copi, Irving M.; Cohen, Carl (1990). Introduction to Logic (8th ed.). Macmillan. ISBN   978-0-02-325035-4.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.