Is the proposition $\forall x: P(x)$ a tautology? If $P(x)$ is a predicate and for all x: $P(x)$ is true, does that make the proposition $(\forall x: P(x))$ a tautology? Or is it not a tautology because P(x) can be defined to be false, in which case $(\forall x: P(x))$ can also be a contradiction since it always evaluates to false? Edit: Mistook tautology for 'totality'

No. Putting it crudely, a necessary condition for a sentence counting as a tautology is that it is true as a matter of logic alone (some would require more). But for a given $P$ with a given interpretation, if could be the case that $\forall xPx$ because of how things just happen to be.

If $P$ means "is male", and the domain is Presidents of the US, past and present, then $\forall xPx$ is true: but that's not a tautology on any account but a regrettable contingent fact!