Antecedent (logic)

Template:Short description An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the protasis.<ref>See Conditional sentence.</ref>

Examples:

• If <math>P</math>, then <math>Q</math>.

This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication "<math>\phi</math> implies <math>\psi</math>", <math>\phi</math> is called the antecedent and <math>\psi</math> is called the consequent.<ref>Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004</ref> Antecedent and consequent are connected via logical connective to form a proposition.

• If <math>X</math> is a man, then <math>X</math> is mortal.

"<math>X</math> is a man" is the antecedent for this proposition while "<math>X</math> is mortal" is the consequent of the 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 and "I am the king of France" is the consequent.

Let <math>y=x+1</math>.

• If <math>x=1</math> then <math>y=2</math>,.

"<math>x=1</math>" is the antecedent and "<math>y=2</math>" is the consequent of this hypothetical proposition.

See also

• Consequent
• Affirming the consequent (fallacy)
• Denying the antecedent (fallacy)
• Necessity and sufficiency

References

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