Well, Aristotle qualifies as quite "humanities oriented" according to the modern way of classifying subject areas, but up until recently plenty of usage history can get traced back to him. Actually, there still exists some usage history traceable back to him.
That said, you might want to see this page, which indicates that perhaps no real inventor existed. Shosky tried to argue that Russell did so. Anellis, though, if his evidence is correct clearly enough indicates that C. S. Peirce had them before that. So, unless historians have missed something in Frege, Peirce gets the prize here:
... the discovery by
Zellweger of Peirce’s manuscript of 1902 does permit us to unequivocally declare
with certitude that the earliest, the first recorded, verifiable, cogent, attributable
and complete truth-table device in modern logic attaches to Peirce, rather than to
Wittgenstein’s 1912 jottings and Eliot’s notes on Russell’s 1914 Harvard lectures
One might also ask here, "who first used numbers for truth-values in the context of truth tables?" I'm not so sure here, but I would think Łukasiewicz did that first, though when he wrote a truth table he wrote them horizontally instead of vertically. ${}$
Suppose $\mathcal{U}$ was some arbitrary set of infinite cardinality.
I think the issue that the book is touching on is that for some arbitrary statement containing a universal quantifier (like $\forall x \in \mathcal{U} \ p(x)$), although it does have a truth value, you cannot use a truth table to find that value directly by testing all values of $x$. (since you would have to have an infinitely large table to get all of the cases)
What made your example doable with a truth table was that in that particular case, you did not have to consider every possible $x$ (which could be infinite), you only needed to care about $p(x), q(x), p(x) \vee q(x)$, which can only take on finitely many values.
Best Answer
The semantics for quantifiers are more complicated than truth tables can deal with. If $\forall x$ was defined via truth table, you would have to give meaning to the formula $P(x)$, so that $(\forall x)P(x)$ can have a truth value. But, $x$ is a variable, so, $P(x)$ isn't a claim that it makes sense to assign a truth value to, without a way of interpreting that variable.