Antecedent (logic)

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An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause.

Examples:

  • If P, then Q.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In an implication, if \phi implies \psi then \phi is called the antecedent and \psi is called the consequent.[1]

  • If X is a man, then X is mortal.

"X is a man" is the antecedent for this proposition.

  • If men have walked on the moon, then I am the king of France.

Here, "men have walked on the moon" is the antecedent.

See also[edit]

References[edit]

  1. ^ Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004