(If the reader is inclined to think Calvinists are not committed to this kind of determinism, then there is even less of a problem for them, and the following argument's response need not even be offered).
Does determinism undermine our ability to know anything?
Some advocates of libertarian free will have argued that if our abilities to form beliefs and make
decisions on matters of truth are determinist, then we have a reason not to trust them. We have a reason to think that they are not reliable, since they are simply the natural outworking of causes applied to our brains, and the beliefs which they form are only the results of electric impulses, fully determined by their input. This charge, if successful, is a serious problem, because it means that if determinism is true, we have a reason to doubt the very ability with which we form all our beliefs, including the belief in determinism itself, and therefore we have a reason to doubt it. That would render determinism literally self-refuting. This argument against determinism is proposed by William Lane Craig in the following words:
Universal causal determinism cannot be rationally affirmed. There is a sort of dizzying, self-defeating character to determinism. For if one comes to believe that determinism is true, one has to believe that the reason he has come to believe it is simply that he was determined to do so. One has not in fact been able to weigh the arguments pro and con and freely make up one’s mind on that basis. The difference between the person who weighs the arguments for determinism and rejects them and the person who weighs them and accepts them is wholly that one was determined by causal factors outside himself to believe and the other not to believe. When you come to realize that our decision to believe in determinism was itself determined and that even your present realization of that fact right now is likewise determined, a sort of vertigo sets in, for everything that you think, even this very thought itself, is outside your control. Determinism could be true; but it is very hard to see how it could ever be rationally affirmed, since its affirmation undermines the rationality of its affirmation.So what should Calvinists make of this argument?
They should maintain that this argument is both entertaining and sound, but that it is shooting at the wrong target. This argument is not aiming at Calvinist determinism (as I will explain below); it is aiming at naturalism, or the view which says that the natural world is all that exists. It is not an argument against mere determinism; it is one against naturalistic determinism. In all essentials, it is the so-called 'evolutionary argument against naturalism' crafted by Alvin Plantinga and evidently offered against naturalism. It is a good argument against atheistic naturalism, arguing that if naturalism is true, then we have a reason to disbelieve it. Plantinga’s basic contentions are as follows:
From a theistic point of view, we’d expect that our cognitive faculties would be (for the most part, and given certain qualifications and caveats) reliable. God has created us in his image, and an important part of our image bearing is our resembling him in being able to form true beliefs and achieve knowledge. But from a naturalist point of view the thought that our cognitive faculties are reliable (produce a preponderance of true beliefs) would be at best naïve hope. The naturalist can be reasonably sure that the neurophysiology underlying belief formation is adaptive, but nothing follows about the truth of the beliefs depending on that neurophysiology. In fact he’d have to hold that it is unlikely, given unguided evolution, that our cognitive faculties are reliable. It’s as likely, given unguided evolution, that we live in a sort of dream world as that we actually know something about ourselves and the world.Calvinists can and should affirm this fun argument, but why does it not apply to their Christian understanding of determinism? It is because contrary to what Craig affirms, the inability to be confident in the process of knowledge acquisition resides not in the determinism of the process, but in its destination; in its purpose, or lack thereof. Think about it. What matters for the reliability of the process of knowledge acquisition is where we are going, not how we get there. We want to land on true beliefs, regardless of how we travel toward them. In an atheistic naturalistic worldview, the reason why cognitive faculties are not to be trusted is not that they are determinist, but it is that they were designed by evolution and natural selection for survival, and not for the purpose of forming true beliefs. However, the Calvinist who does hold to determinism can perfectly defend the reliability of his cognitive faculties on the basis that they do result from the design of God who intended us to form typically true beliefs about the world, albeit in a determinist way.
If this is so, the naturalist has a defeater for the naturalist assumption that his cognitive faculties are reliable – a reason for rejecting that belief, for no longer holding it. (Example of a defeater: suppose someone once told me that you were born in Michigan and I believed her; but now I ask you, and you tell me you were born in Brazil. That gives me a defeater for my belief that you were born in Michigan.) And if he has a defeater for that belief, he also has a defeater for any belief that is the product of his cognitive faculties. But of course, that would be all of his beliefs –including naturalism itself. So the naturalist has a defeater for naturalism; natural-ism, therefore, is self-defeating and cannot be rationally believed.
Whether Calvinist or Arminian, whether compatibilist or libertarian, in Christianity we have a mind designed by God to access truth (albeit in a fallible way); in atheism we have a brain designed by chance and natural selection to save our skin. That, is the relevant difference. So as long as God exists—which I think a lot of Calvinists believe—Calvinist determinism stands the charge.
For the Lord will give you understanding in everything (2 Tim. 2:7)
“None comprehend the mysteries of God save those to whom it is given.” –John Calvin 
The above response satisfyingly does away with the “rational self-defeat” objection against Calvinist determinism, but I want to add the following theological commentary: –these conclusions about cognitive faculties and determinism actually provide Calvinists with excellent grounds for humility about their knowledge, including their theological knowledge. On Calvinism, as theological determinism is true, it is the all-decreeing God who providentially decrees not only just how good our choices shall be, but also just how true our beliefs end up being. Craig’s words above are exactly right; the difference between a Calvinist and a non-Calvinist is “wholly that one was determined by causal factors outside himself to believe and the other not to believe.” And of course on Calvinism, the “causal factor” is put in place by the Lord Almighty. What follows from this, is that if Calvinism is true, then the Arminian is mistaken alright, but the Calvinist who decries the irrationality of Arminianism must understand that he can no more brag about his being right, than about his being saved. On Calvinism, the reason why anyone is saved is the same reason why he is a knowledgeable, sound Calvinist theologian: –God gave him the grace to be so. Let it be the ground for a good, solid, Calvinist, theological humility. It will do much good to the Calvinist case in this debate.
 William Lane Craig, “Response to Paul Kjoss Helseth” in Four Views on Divine Providence, ed. Stanley N. Gundry, Dennis W. Jowers (Grand Rapids, MI: Zondervan), 60.
 Alvin Plantinga, “The Dawkins Confusion: Naturalism ‘ad absurdum,’” Christianity Today, http://www.christianitytoday.com/bc/2007/marapr/1.21.html.
 John Calvin, Institutes of the Christian Religion, Book First, Chapter 7, Section 5, trans. Henry Beveridge (Peabody, MA: Hendrickson Publishers, 2008), 34.