When I was a student, we had an assignment: "Prove or disprove the existence of God" in ten pages.  One clever answer used less than a page, and got top marks for the effort.  The student wrote to the effect that the assignment was not possible using the rules of logical proof.  For in using the available conventional starting point, we would only be able to use the things that can be observed and verified by human senses within the known created world.  All one could do, the argument supposed, in that instance is prove that something in the created world was God.  In other words, you could prove that something was God that could not possibly be God.  The second part of the argument suggested that in order for such a "proof" to be valid, a student would have to be objective, from the start, about that answer.  A student would need not to care if there was or was not a "God".  Since everyone has a stake in the answer, one way or another, it was reasoned that such a proof was impossible to attempt.

How would you prove the existence of God? The point of the exercise was to get the students to think about who or what God is. The reality of the exercise, at least for the student in question, is that we cannot approach the answer through logical thought, through reason alone.  Now this is not to say that reason and logic do not have their place in the realm of faith. It is just to say that they alone cannot do the job.  The IS-ness of God is just too different from our experience to be able to fathom.  So the language of the Trinity in the Christian witness may serve mostly to humble us.  It serves to remind us that God is indeed beyond our complete comprehension.  All the language that we have about God must be metaphor.  Most of the language in the bible is just that, with one notable exception: "God is love."