I gave the last word in my dissertation to G. K. Chesterton. Part of the borrowed inscription was: "The ordinary man ... has always cared more for truth than for consistency. If he saw two truths that seemed to contradict each other, he would take the two truths and the contradiction along with them."This strikes me as a dangerous idea. In the first place, there’s a world of difference between seeming contradiction (as in the Chesterton quote) and actual contradiction—the latter being something which I do not expect God would want us to embrace. (And by 'contradiction' I mean two claims such that at least one, but only one, is true. So, for example, "God exists" and "God doesn't exist" together produce a contradiction: one of them is true, but they can't both be true.)
I have always believed this; one cannot believe the Bible otherwise, nor can he be a Christian, for our faith is built upon the ultimate contradiction: the God-Man, and many others besides. [emphasis mine]
At any rate, regarding the God-man: There is nothing inherently contradictory about someone being both God and man. There would, of course, be a contradiction inherent in someone claiming to be solely God while being solely man. But nowhere does the Bible claim that about Jesus, and the apparent contradiction of the God-man, I would argue, can be resolved through careful study and theology (with a little help from philosophy).
I think Chesterton is right that we hold on to two things we know to be true; but instead of endorsing the idea that our faith is built upon a contradiction, let us look for a way to resolve the contradiction, while staying true to the received theological tradition, and so strengthen our witness to those who face intellectual barriers to the faith.