1) If the Trinity doctrine can neither be proved nor disproved, then it is not falsifiable.
2) If the Trinity doctrine is not falsifiable, then it is neither true nor false.
3) Therefore, if the Trinity doctrine can neither be proved nor disproved, then it is neither true nor false.
Proof here refers to rational argumentation (a logical demonstration) as opposed to proving the doctrine from biblical texts or from creation, although reasoning is also used when one attempts to make a case from scripture for one doctrine or another.
Karl Popper is known for advocating falsification when it comes to scientific hypotheses. He evidently thought: "The adherents of a pseudo-science are able to cling to its hypotheses no matter how events turn out, because the hypotheses are not testable." So if the Trinity doctrine is not logically testable or falsifiable, that would seem to make us question its overall truth-value or its claims pertaining to deity.