# Antecedent (logic)

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*.

^{[1]}

Examples:

- If , then .

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 implies then is called the **antecedent** and is called the consequent.^{[2]} Antecedent and consequent are connected via logical connective to form a proposition.

- If is a man, then is mortal.

" 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.

Let . If then

## See alsoEdit

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

## ReferencesEdit

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

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