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A consequent is the second half of a hypothetical proposition. In the standard form of such a proposition, it is the part that follows "then". In an implication, if \phi implies \psi then \phi is called the antecedent and \psi is called the consequent.[1]


  • If P, then Q.

Q is the consequent of this hypothetical proposition.

  • If X is a mammal, then X is an animal.

Here, "X is an animal" is the consequent.

  • If computers can think, then they are alive.

"They are alive" is the consequent.

The consequent in a hypothetical proposition is not necessarily a consequence of the antecedent.

  • If monkeys are purple, then fish speak Klingon.

"Fish speak Klingon" is the consequent here, but intuitively is not a consequence of (nor does it have anything to do with) the claim made in the antecedent that "monkeys are purple".

See also


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