# Why is a statement such as, “It's 5 o'clock” excluded from propositions?

From MIT notes:

A proposition excludes statements whose truth varies with circumstance such as, “It’s five o’clock”.

And:

A predicate is a proposition whose truth depends on the value of one or more variables.

If a proposition excludes statements whose truth varies with circumstance, why is a predicate considered as a proposition whose truth depends on the value of one or more variables?

In other words, why can't I just write a statement like "It's 5 o'clock" as:

$P(x) ::=$ "$x$ is equal to 5"

Thanks!

But there is another confusion. A predicate is not a proposition, even in the second broad sense. And a predicate need contain no variable (it seems that the notes confuse a predicate with an open sentence). Thus compare the formal expressions $Fx$, an open wff, and its predicate $F$. Or compare the ordinary language expressions "She is a logician"' corresponding to an open sentence, and its predicate "... is a logician".