It seems that the Trinity doctrine cannot be formulated or stated adequately with fully intelligible sentences.
William Hasker maintains that an intelligible statement "must be expressible in grammatically well-formed sentences" and it "should not be contradictory or otherwise logically impossible" (God, Time, and Knowledge, p. 146-147). He also observes that an intelligible proposition is an assertion that can be rationally accounted for, by means of inferential or non-trivial relations of ideas.
The Trinity doctrine does not appear to be "intelligible," when judged by Hasker's definition. Admittedly, he claims that "intelligibility" is person-relative (not the same for everybody). While I agree with Hasker to an extent, since what some people think is intelligible might not be readily understood by others, the idea of person-relative intelligibility is questionable on another front. After all, most everybody can agree that some utterances simply are not intelligible, no matter what anyone thinks. For instance, that a2 + b2 = f2. Additionally, are there not some utterances that might be intelligible in se even though most of us fail to make sense of them?
In Logic and the Nature of God, a Trinitarian logician named Stephen T. Davis who believes that the Trinity is orthodox still voices these concerns:
"So I am not saying that the mystery of 'three in one' cannot in principle be explained or rationalized or is such that for any phi, the Trinity is not phi. Perhaps even some future theologian will be able to produce conceptual categories adequate to explain it. All I claim is that it is mysterious to us now" (p. 142).
Davis suggests that the Trinity might not be opaque to humans forever. One day, he insists, we could understand the doctrine fully, as God now completely understands us. But at present, Davis asserts, there are evidently no satisfactory conceptual categories that facilitate how to articulate the Trinity doctrine intelligibly; therefore, it seems that the doctrine might not be intelligible now. Most importantly, the Bible is completely silent respecting God's so-called triune being. It presents a contrary view throughout its many inspired pages.