Definition

Noun: 1. The term in a syllogism that appears in both premises but not in the conclusion. In formal logic, a syllogism is a form of reasoning where a conclusion is drawn from two given or assumed propositions (premises). The middle term is the concept that links the two premises, allowing a relationship to be established between the other two terms (the major and minor terms) in the conclusion.

Examples of Usage

• Noun:
  • In the syllogism "All humans are mortal. Socrates is human. Therefore, Socrates is mortal," the word "human" is the middle term.
  • A valid syllogism requires the middle term to be distributed in at least one of the premises.
  • Identifying the middle term is the first step in analyzing the logical structure of a syllogism.

Advanced Usage

• "To serve as the middle term": To function as the linking concept in a logical argument.
  • In his analogy, trust serves as the middle term connecting the idea of friendship with loyalty.
• Undistributed middle term: A common logical fallacy where the middle term is not applied to all members of the category it denotes in at least one premise, leading to an invalid conclusion.
  • The argument "All cats are mammals. All dogs are mammals. Therefore, all dogs are cats" is flawed due to an undistributed middle term ("mammals").

Variants and Related Words

• Syllogism (n): A form of deductive reasoning consisting of a major premise, a minor premise, and a conclusion.
• Major Term (n): The predicate of the conclusion of a syllogism, which also appears in the major premise.
• Minor Term (n): The subject of the conclusion of a syllogism, which also appears in the minor premise.
• Term (n): In logic, a word or phrase that represents a class or concept within a proposition.

Synonyms

• Linking term
• Mediating term

Related Phrases

• Fallacy of the undistributed middle: A formal fallacy where the conclusion of a categorical syllogism is invalid because the middle term is not distributed.
• Distribution of a term: In logic, the property of a term that indicates whether a statement makes a claim about members of the class denoted by the term.

Noun

1. the term in a syllogism that is common to both premises and excluded from the conclusion