Greg Bahnsen has already showed that atheistic empiricism cannot account for most of what we consider knowledge, and I covered his argument pretty well in Atheism and the Problem of Knowledge. Edward John Carnell has a series of arguments against theistic empiricism.
Empiricist theologians such as Thomas Aquinas and Maimonedes argued that we do not have innate knowledge. Everything that we know begins in sense experience. The empiricist cannot know that knowledge of the past gives us knowledge about the future. The theistic empiricist has that difficulty plus the problem of how we can possibly have knowledge of God, who is not perceived by the senses.
To an empiricist, all concepts must come from experience, but all that experience tells us is what is not God. If we do not have innate knowledge of God, then we cannot know the essence of God.
Problem of Predication
When we take a look at what sense perception delivers to us, the problem gets worse. All concepts are useless when applied to God, for God occupies a different realm of being than the world of sense experience. On empiricism, our concepts cannot apply univocally to God.
This would lead us to conclude that a proposition about a creature necessarily loses all meaning when applied to God. It follows from such a principle that if we take our starting point from the world of sense experience, we can know nothing of God nor prove anything concerning him without continual equivocations.
Might we not come to God by way of negation? Can we build a theology using only negations such as "God is not ignorant" and "God is not mortal"? Such an endeavor cannot be sufficient to know anything about God. We must know God to be able to say that he is not this or that. How could we tell him from this or that if we did not first know him? To say that a piano is not a banana is to give us no clues as to what a piano has which separates it from all other things which are also not bananas.
For example, we know that a piano is not a banana, but that does not distinguish it from a yacht, which is also not a banana. We need more than negation to help us. Negative theology alone leads to skepticism and agnosticism.
Aquinas admitted that from the knowledge of sensible things the whole power of God cannot be known. Still, because creation is an effect with God as the cause, we can be led from creation to the creator. Remember that a term can be used in three ways: with the same meaning (univocally), with a different meaning (equivocally), and with a meaning that is partially the same and partially different.
The term "animal" can be predicated univocally of a cat, a dog, and a horse. The term "Greek" is predicated equivocally when we apply it to the language and then to the philosopher Socrates. The term "loud" is analogical when we apply it to both sound and to the color of one's shirt.
Analogy is based on a comparison which can only be obtained when there is neither complete agreement nor complete disagreement between two things. There are two glaring fallacies in analogy when prevents it from being a way that the empiricist can know about God based on experience.
First, it is built on a contradiction. Aquinas says there is no univocal element in the terms that we apply both to the world and to God, yet he affirms that we understand God through analogy. The one and only thing that separates analogy from equivocation is its univocal element. When we say that the mind is to the soul as the eye is to the body, the univocal element is "light" or "guide." When we say "the foundation is to the house as the heart is to the organism," the univocal element is "sustaining basis." The success of any analogy is non-analogical. IF there is no univocal element, it is just like comparing two unrelated things, and this is equivocation. No meaning is conveyed. Without meaning, there is no truth, for truth is properly construed meaning.
If there are no terms which apply univocally to God, then there can be no element from which we can draw analogies. Hence, we are no better off than verificationists. Where, in the whole gamut of our sensory experience, can we find that univocal element which a successful analogy requires, that we may use it in making a comparison between God and man? How can the non-spatial be abstracted from the spatial, the spiritual from the material, the eternal from the temporal, the changeless form the flux? The intellect may be active ,but cannot take from sensory experience what is not there.
There is one way to complete an abstraction from nature: bu setting aside the differentiating aspects of each item and retaining the aspects which are common. For example, if I examine all animals, such as cats, cows, worms, and sardines, as long as I examine vertebrates, I can arrive at the abstract idea of vertebrates. When I take in worms, I then have to take a more abstract concept. When I add plants to the list, I need the further abstract notion of a living being. As long as animation is common to all of the items examined, I cannot discard it.
If I know all of being by way of sensible beings, I can never discard from my final abstract ideas the element of sensible being, for all my knowledge is loaded with it. By abstraction, therefore ,I have no basis for believing that from sense perception I can rise to a knowledge of the necessary, eternal, and immaterial in God. Wherever my ideas go, there trails along the notion of the sensible being, in common to all concepts abstracted from sensation which cannot be discarded.
To admit simultaneously that we have no univocal knowledge of God, that all our knowledge comes from sensation, and that we can avoid ambiguity and equivocation by referring predication to the analogy of being, is a contradiction in terms. The only element in analogy which distinguishes it from equivocation is the univocal. If the univocal element is admitted, then how do we account for it if there is nothing in the intellect that is not first in the senses? We either give up empiricism or admit that talk about God is meaningless.
Secondly, analogy alone makes God unknowable. If God's essence is unknown (as Thomists admit), then it follows that his existence is equally unknowable (since God's existence is supposed to be the same as his essence). The Thomist will quote Romans in response.
For his invisible attributes, namely, his eternal power and divine nature, have been clearly perceived, ever since the creation of the world, in the things that have been made. So they are without excuse. (Romans 1:20)To argue that Romans 1:20 supports empiricism is to argue in a circle. If this view can be coherently explained from any non-empiricist standpoint, then the argument loses all of its force. God may be known through sense perception, but this does not rescue empiricism. May it not be equally true that having innate knowledge of God, we are reminded of him by his works?
Empiricists believe that the principles of proof originate in sense perception. It follows from this that all that exceeds the sensible worlds is unamenable to proof. God exceeds all our senses and sensible objects, but his effects are often sense objects. Yet the fact remains that under theistic empiricism, any knowledge that we could have of the supersensible comes solely from our knowledge of the sensible. But we msut remember that in the argument where we argue for the existence of God, we cannot take as a principle the essence of God, which is unknown to us. The proof being impossible, the only road that can lead us to a knowledge of the creator must cut through the things of sense.
Thomists also argue that God has two sides: as he is eternally in himself, and also as he appears to us in our examination of the content of our sense perceptions. This does not help. How can we possibly know that a thing exists when we do not know what it is? What is it that we are talking about? If we cannot first know him as he is, then how can we draw any connection between God in himself, and God as he appears to us? It does not even seem meaningful to speak of God's essence, for we have no known means of ascertaining what the term "God" even means. Without meaning, truth is absent. So this position is contradictory.
For the Thomist who bites the bullet and states that we can know God even if we do not know his essence, then this opens the gate to other unknowables when one defends an unknown God. If we can talk about God whose essence we do not know, then we can talk of blarps and blegs and splinth and other nonsensical terms with equal clarity. No one knows enough to assert the existence of an object of which they know nothing. The assertion that an object of which nothing can be known reduces to total skepticism. The right of each of us to assert this kind of unknowable throws all objectivity into confusion; and the implicit contradiction contained in asserting that something cannot be known cuts the foundation out from any and all knowledge.
The end of empiricism is verificationism, and the end of positivism is Cratylus, who could not so much as speak, but only waved his hands.