Definition:Conditional/Antecedent

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Definition

In a conditional $p \implies q$, the statement $p$ is the antecedent.


Examples

Arbitrary Example

Consider the compound statement:

If $n$ is divisible by $2$, then $n$ is even.

The antecedent is:

$n$ is divisible by $2$.


Also known as

The terms:

premise
assumption
hypothesis

can often be found in the literature as a word for antecedent, but on $\mathsf{Pr} \infty \mathsf{fWiki}$ we reserve the use of premise, assumption and hypothesis for elements of the structure of logical arguments.


The term antecedent clause can sometimes be seen, particularly when the conditional it is part of consists of a statement in natural language.


The archaic terms implicans and protasis can sometimes be found.


Also defined as

Let $P = a \circ b$ be an expression.

The term $a$ is known as the antecedent of $P$.

The term is usually applied when the expression in question is a ratio.

For example, in $5 : 7$, the number $5$ is the antecedent.


Also see

  • Results about antecedents can be found here.


Linguistic Note

The word antecedent is usually found in classical mathematical literature, notably Euclid's The Elements.

The word comes from the Greek, and literally means leading term, or the thing that comes first.


It is pronounced an-tee-see-dent.


Sources

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