Definition

1. Noun:
   • A form of deductive reasoning: A syllogism is a logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions (premises) that are asserted or assumed to be true.
   • A specific logical structure: It is a classic structure in logic consisting of a major premise, a minor premise, and a conclusion. For example: All humans are mortal (major premise). Socrates is a human (minor premise). Therefore, Socrates is mortal (conclusion).

Examples of Usage

• Noun:
  • The philosopher explained the classic syllogism about mortality.
  • Her argument was built on a flawed syllogism, so the conclusion was invalid.
  • Understanding basic syllogisms is fundamental to studying logic.

Advanced Usage

• "Categorical syllogism": The most common type, where the premises and conclusion are categorical statements (e.g., All A are B, No A are B).
  • Aristotle's theory of the categorical syllogism laid the groundwork for formal logic.
• "Hypothetical syllogism": A form of argument where at least one premise is a conditional ("if-then") statement.
  • "If it rains, the ground gets wet. If the ground gets wet, it becomes slippery. Therefore, if it rains, it becomes slippery" is a hypothetical syllogism.
• "Disjunctive syllogism": An argument where one premise is a disjunction ("either-or") and the other premise denies one of the alternatives.
  • "Either the keys are in the car or in the house. They are not in the car. Therefore, the keys are in the house."

Variants and Related Words

• Syllogistic (adj): Pertaining to or of the nature of a syllogism.
  • Syllogistic logic was a primary focus of ancient philosophers.
• Syllogize (verb, rare): To reason or argue by means of syllogisms.
  • The debater attempted to syllogize his position clearly.

Synonyms

• Deductive argument: A broader term for reasoning from general premises to a specific conclusion.
• Logical deduction: The process of reaching a necessary conclusion from given premises.

Related Phrases

• "Enthymeme": A rhetorical syllogism, often with an unstated premise that is assumed by the audience.
  • Political speeches often use enthymemes, relying on the audience to fill in the missing premise.
• "Valid syllogism": A syllogism where the conclusion logically follows from the premises, regardless of the truth of the premises.
  • A valid syllogism can have false premises but a logically sound structure.
• "Sound syllogism": A syllogism that is both valid and has true premises.
  • For a conclusion to be definitively true, it must come from a sound syllogism.

Noun

1. deductive reasoning in which a conclusion is derived from two premises