## Frequent Links

# Antecedent (logic)

An **antecedent** is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. It is also known for a person's principles to a possible or hypothetical issue.

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 <math>\phi</math> implies <math>\psi</math> then <math>\phi</math> is called the **antecedent** and <math>\psi</math> 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

- Affirming the consequent (fallacy)
- Denying the antecedent (fallacy)
- Necessity and sufficiency

## References

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

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