\begin{definition}[Definition:Conditional]
The '''conditional''' or '''implication''' is a binary connective:
:$p \implies q$
defined as:
:'''''If'' $p$ is true, ''then'' $q$ is true.'''
This is known as a '''conditional statement'''.
A '''conditional statement''' is also known as a '''conditional proposition''' or just a '''conditional'''.
$p \implies q$ is voiced:
:'''if $p$ then $q$'''
or:
:'''$p$ implies $q$'''
We are at liberty to write this the other way round. $q \impliedby p$ means the same as $p \implies q$.
$q \impliedby p$ is sometimes known as a '''reverse implication'''.
The rest of this article interprets the '''conditional''' in its usual mathematical sense.
That is, $p \implies q$ is considered to be true whenever:
:$p$ is false
or:
:$q$ is true.
This interpretation of '''implication''' is called '''logical implication''' or '''material implication'''.
Its most important property is that the truth of $p \implies q$ does not {{apriori}} establish a relation of causality between $p$ and $q$.
This allows for the '''conditional''' to be truth-functional, at the price of a slight mismatch with its use in natural language.
\end{definition}