If the Incarnation is actual, then it is possible whether or not we can explain or understand how it is possible. Esse ad posse valet illatio. Necessarily, what is, is really possible, whether or not conceivable by us. It is not for our paltry minds to dictate what is actual and what is possible. On the other hand, if the best and the brightest of our admittedly wretched kind cannot see how a state of affairs is possible, then that is evidence that it is not possible. If, after protracted and sincere effort motivated by a love of truth, the Incarnation keeps coming before the mind as contradictory, and the attempts at defusing the apparent contradiction as so much fancy footwork, then here we have (admittedly non-demonstrative) evidence that the Incarnation really is impossible.
At the Princeton Theological Center, I once heard John Polkinghorne, who is both a theoretical physicist and an Anglican priest, use chaos theory and quantum physics to explain how the Incarnation is altogether possible given our current understanding of things. He was at pains to to add that this did not constitute a proof of the Incarnation, only that such was not impossible.
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