One of his works is a little treatise usually known as "On the Method of the Knowledge of God", which raises some interesting ideas with regard to theological epistemology. In this work he suggests that there are four ways by which something can be known:
(1) through being seen;
(2) through its effects;
(3) through something like it;
(4) through something contrary to it.
God is obviously not seen, so this can be set aside. The other three, however, are still viable, and Theodore insists that it is important to use all three, and to use all three in appropriate ways, in order to know God properly.
The basic principle of knowledge through effect, he says, is "If we see anything in a state that is not in accord with its nature, we infer that there is something that caused it to be in that state" (p. 158 / B76) Thus, for instance, if it is in the nature of earth to sink and fall, and we find it established in place, we know that something must be causing it to stay, whether it be a material or immaterial power. If, however, we say that a body is causing it to stay in place, this gets us into an infinite regress of bodies caused to stay in place due to bodies that are caused to stay in place by other bodies. Thus there must be an immaterial power holding it up, which could be called 'God'. This would be an example of knowing something by its effect. Theodore suggests that it is possible to have many proofs of God's existence, "from anything that is observed to have different aspects" (p. 159 / B78).
Beyond God's existence, however, one wishes to know things about Him; and this, Theodore suggests, arises primarily from resemblance as a method for knowing God. It could be, of course, that nothing resembles Him, in which case we could never know much about Him, but in practice people do recognize things as resembling God in some way. We recognize, for instance, that it would be appropriate to take things that are excellent to resemble God, somehow; and likewise people of all kinds detest it if anyone tries to attribute to God the names of resembling things that are less than excellent.
Further, we must hold that if there is a God there are things that somehow resemble Him, because there would only be two ways He could be known -- through His self-description and through creation, but both cases require that there be some kind of resemblance. God could only describe Himself to us by means of resemblances, and so if there are none, we would have to say that He describes Himself improperly; and if creatures did not resemble Him in any way, we would not be able to say anything about God on the basis of them. This resemblance, however, is necessarily not complete. God is known by what resembles Him in something like the way a person is known by way of his image in the mirror.
This brings us to knowledge by contrary:
Whenever we say that a created being resembles God, even as we say this we take it back, and as soon as we note the resemblance we deny it, lest the minds of those who hear stop there and fall into error. (p. 161 / B79)
This is not self-contradiction; instead, whenever we describe God in terms of creatures, we have to recognize that God is different even with respect to how creatures resemble Him. Thus, for instance, God is living and human beings are living; there is a resemblance. But treating this as all there is to it is merely anthropomorphism. In recognizing the resemblance we need also to recognize the differences: the lives of human beings have beginnings and endings, but God's living could not possibly begin and end; human life is filled with change, but God is unchanging; human life is vulnerable and fragile, but divine life could not be. By recognizing that some aspects of the resemblance are inconsistent with other things known about God, we learn more about God.
The astute reader will notice that Theodore's account of the ways of knowing God is an account of the triplex via, in at least one of its possible orders: we start with the way of causation, thus establishing that God exists, and then through this travel the way of eminence, by recognizing that he super-excels the excellences of creatures; and then end with the way of negation or remotion, in which we learn what God is not.
Abu Qurrah does not stop here, however, and goes on to argue that this triple method supports the Christian doctrine of the Trinity. Begetting one like oneself is an excellence of human nature; indeed, there are few things about us that are more honorable and excellent. Thus by the way of resemblance, we should be able to say that God begets someone like Himself. If one were to object that this means that there was then before and after in God, however, we would see that this is ruled out by the way of contraries: fathers are before sons in human beings for reasons directly attributable to the defects and limitations of our natures, since this happens because we are always born incomplete. We can therefore eliminate this aspect of the resemblance from our discussion. We can see in a similar way that there can only be one Begotten, since if there needed to be more than one this would indicate that the first was insufficient, which brings us again to defect and limitation. Thus Theodore ends with the Nicene-Constantinopolitan Creed, which shows in its very structure the triple method of knowing God.
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Quotations are from Theodore Abu Qurrah, Theodore Abu Qurrah, John C. Lamoreaux, tr. and ed., Brigham Young University Press (Provo, UT: 2005).
