Here is one critique of the book that purports to show that if you believe a set of theological claims that together entail a paradox (note: X is paradoxical if X amounts to a set of claims which taken in conjunction appear to be logically inconsistent), and you do not resolve the paradox, then continued belief in the set is irrational. Here's why:
My argument is fairly straight forward. In order for one to claim propositions appear to be contradictory, you have to show why you believe it is apparent that the truth of one proposition implies the falsity of the other. That’s simply the definition of a contradiction. So if it appears to you that both propositions can not be true at the same time, then it’s irrational to believe both propositions are true at the same time … unless you can provide a reasonable resolution to the apparent contradiction.
There’s no escape from the charge of irrationalism simply by saying that you don’t believe the contradiction is real, even though it seems real - if you can not demonstrate that there is an reasonable solution to the appearance of a contradiction. Which is what Van Til said we could not do. And which brings us full circle. What do you say? Is there a reasonable solution to the “apparent” paradoxes?
Now, this is addressed by following the argument in the book, mainly in chapters 5 and 6. The import of the Creator/creature distinction, the doctrine of incomprehensibility, the doctrine of analogy, our epistemic situation, etc., all bear on the answer.
Nevertheless, it won't hurt to answer this briefly since it comes from one who says he has read the review. So perhaps I did a poor job at communicating how a simple grasp of a few basic points undercuts this objection without further thought on the matter.
The fastest way around this objection is that on the model Anderson presents, one doesn't take it that the component propositions are false.
Anderson views theological paradox (with the constraints Anderson sets on what kind of doctrines make the cut) as merely apparent contradictions, MACs. Thus they are not real contradictions.
They result from unarticulated equivocations in the metaphysical expressions of the doctrines (though they can be expressed formally in an non-contradictory way). Hence they are merely apparent contradictions resulting from unarticulated equivocations, MACRUEs.
Now, granting that Anderson shows that we are warranted in taking the paradoxical doctrines as MACRUEs, then it follows that we do not believe that any of component the claims are false. We can believe all of the component claims are true. (How we can be warranted in our beliefs of the component claims is demonstrated in chapter 5.)
We can write the doctrines out in such a way as to avoid explicit or formal contradictions. We can even think about them in a formally or explicitly consistent way.
Anderson uses the example of the two-dimensional Flatlander FL and the three-dimensional Spacelander SL. Say that FL gets propositional revelation from SL regarding a cone (which is a three-dimensional object). FL cannot grasp the entire truth of the matter; indeed, FL's very conceptual limitations mean that he can only conceive of the object (cone) two-dimensionally. SL wants to reveal to FL about the nature of the cone. SL thus does it this way:
 The object O is shaped triangularly.
 The object O is shaped circularly.
This is not an explicit contradiction, but when FL conjoins the above with this other belief:
 No object is both such that it is shaped triangularly and circularly, he obtains his apparent contradiction because he can only think two-dimensionally.
But say that FL is independently warranted in believing both  and  (how the Christian can be was shown in ch.5). For example, say that FL knows that SL cannot lie and cannot make errors and would not deceive FL about something like this. Given that, then FL is warranted in believing  and . If he is, then he is rational in believing  and . This is based on the tradition of warrant Anderson stands in.
So, FL also has this belief:
  and  are both true.
Thus, though they appear to contradict for FL, he can nevertheless believe that they are not contradictory (because two propositions that are really contradictory cannot both be true, and given what FL knows, they cannot be false because a being that can‘t make an error told him they are true…just not the whole truth, perhaps!).
So he takes it that because of his limitations, the vast distinction between a three-dimensional being and a two-dimensional one, the accommodated or analogical language SL employs, etc., there is a term he doesn't fully understand. So, he takes this as an instance of a MACRUE. In so doing he does not believe any of the claims are false. Now, in so doing he realizes that there is some sense in which the object is both triangular and circular, even though he can't grasp how this can be. He might nevertheless be humbled at his epistemic situation and grant that this is all possible in a three-dimensional world.
FL can also render the doctrine formally consistent. Say he had other revelation where he knew that terms were being used differently. So, he would write it out like this, for instance:
[1*] The object O is shaped1 triangularly.
[2*] The object O is shaped2 circularly.
The 1 and 2 might indicate horizontal and vertical, respectively.
Still FL might not be able to concretely conceive of how this cone looks, or could exist. This cone-doctrine is rendered formally consistent, not metaphysically or concretely.
At any rate, say the Christian is in a situation like this with the doctrine of the Trinity. Say that they are warranted in believing the doctrine to be a MACRUE. In this case he does not need to believe that any of the component claims are false.
Now, this removes the fangs of the objection. the objection received was that the Christian was irrational because he had to believe the one of the component claims were false. I have shown that this is not the case.
So, the only other move the objector could make is this:
 Even if you can believe the paradoxical doctrine to be a MACRUE, and even if you don't have to believe any of the component claims are false, you still have to be able to specify where, precisely, the unarticulated equivocation lay. Which term it is, otherwise you are irrational.
Well, given that 'irrational' or 'rational' hasn't been defined, I totally deny the intuitions behind  and don't see why I must accept it, at all.
One more thing. The above objection doesn't really help matters out much. If Anderson has shown the orthodox expressions of the doctrines to indeed be paradoxical, then the only choice for the objector is to embrace what he calls irrationality, or to embrace heterodoxy.
Without overcoming the objections and analysis made in chapters 1 and 2, then by the objector claiming that belief in the paradigm paradoxical doctrines is irrational, and he will not be an irrationalist, he has just said he's going to opt for heterodoxy. This is hardly a consolation prize for orthodox Christians.