I wonder whether mysterianism in defense of such theological doctrines as the Trinity does not in the end backfire by making possible the philosophical justification of philosophical theses incompatible with it. To ease our way into this line of inquiry, let us consider materialist mysterianism.
1. If mysterianism is an acceptable approach in theology, why can't a materialist make use of it in the philosophy of mind? The (positive) mysterian maintains that there are true propositions which appear (and presumably must appear given our 'present' cognitive make-up) contradictory. This is not to be confused with dialetheism, the view that there are some true contradictions. For the mysterian there are no true contradictions, but there are some truths that must appear to us as contradictory due to our cognitive limitations.
2. Now consider token-token materialism in the philosophy of mind. This is the view that every token mental state, whether or not exhibiting intentionality, is identical to some token physical state. And because mental states, if identical to physical states, are in the head and not in the gluteus maximus, we can substitute for present purposes 'brain state' for 'physical state.' We needn't be concerned whether mental states are type-identical to brain states. Identity at the level of tokens is to be understood as absolute numerical identity, which is an equivalence relation (reflexive, symmetrical and transitive) governed by the Indiscernibility of Identicals (InId) and the Necessity of Identity. InId is commonly (mis)called 'Leibniz's Law.'
3. We now consider a line of argument that motivates and makes plausible the token-token identity materialism just sketched:
a. Anti-Eliminativism: There really are mental states. If some eliminativist denies this, kick him in the cojones and invite him to focus on the sensory qualia he is now enduring. Repeat as necessary. You should be able to get through to him unless he is a philosophical zombie or a sophist. If he's a sophist, show him the door and apply your boot to his glutes on his way out.
b. One-Worldism: There is exactly one world and it is physical all the way down and all the way up. Everything in it is physical through and through. We are in it. So all of our states, including our mental states, are material states of a material thing. How do we know this? We know it because Science tells us so. (in truth, it tells us no such thing, but play along.)
c. Therefore: Mental states are brain states. What else could they be? Spook states? They exist by (a) and given (b) they cannot be identified as anything other than states of a material thing. This argument is not compelling but it does render the materialism under discussion somewhat 'reasonable.'
4. The line of argument just sketched, however, collides with a principle than which no more luminous can be conceived, to wit, the Indiscernibility of Identicals. InId, roughly, states that if two things are identical, then whatever is true of one is true of the other and vice versa. Not surprising: if the antecedent is satisfied, there is really only one thing. So if a particular mental state is identical to a particular brain state, then everything true of the first must be true of the second, and vice versa. But while some mental states are intentional, no physical states are. So no mental state featuring intentionality can be a physical state. And while some mental states have a qualitative feel about them, a Nagelian what-it-is-like, no physical states do. So no non-intentional mental state is identical to a brain state. These arguments can be spelled out and objections can be answered. The arguments are very simple but very powerful.
5. Now suppose we have a materialist who, convinced by the considerations in #4, refuses to abandon either his materialism or his anti-eliminativism. It is open to him to make the mysterian move along the following lines. He knows or thinks he knows from Science that mental functioning cannot be anything other than brain functioning. And yet he cannot understand how mental states could be identical to brain states. He cannot understand how two things can be identical if they differ property-wise. And yet they are identical in the case of mental and brain states. So the mysterian concludes that the noncontradictory truth of materialism appears contradictory to us, and must appear contradictory to us, because of our cognitive limitations. We don't understand how it could be true, and it must appear impossible to us given our cognitive limitations, but it is true all the same. It is in that sense a mystery that we must accept with 'natural piety.'
6. Now I don't believe that Science -- the capitalization is ironic -- can reveal truths to us that must appear contradictory to us: I take the materialist position sketched above to be decisively refuted by the considerations in #4. But if mysterianism were a legitimate approach to such theological mysteries as Trinity and Incarnation, if it were a legitimate way to justify or defend these doctrines, then it would also be a legitimate way to justify or defend materialism about the mind. Now materialism and theism are arguably incompatible. (This needs arguing but I can't argue it here; I do so elsewhere: "Could a Classical Theist be a Physicalist?" Faith and Philosophy, April 1998.) So it looks as if appeal to mysterianism can be used to defend incompatible doctrines. This suggests that mysterianism is not effective for defending either theological claims or materialist claims.