Needless to say, I don't consider my position to be rationalistic. Nevertheless, I've also noticed a tendency among people who consider themselves to be Confessional Lutherans to merely be anti-intellectual and then claim to be following Luther by "placing faith above reason." For that reason, I think it's important to have a discussion about what faith and reason are, and how they relate to one another.
To do this, we have to pay attention to several important distinctions that Luther makes: 1) The distinction of that which is above us and that which is below us. 2) The proper distinction between law and gospel, and their function in the Christian's life. 3) The distinction between the theology of glory and the theology of the cross.
1. Contradictory statements in Luther about reason: As Oswald Bayer points out, Luther states two contradictory things about about reason. First he calls reason a "whore" or the "Devil's whore." Secondly he calls it "something divine." These statements, I will argue are not actually contradictory, what they do is to describe two different horizon within which human reason operates.
2. What is reason? In the 16th century, as you will recall, the intellectual tradition that Luther operated in was heavily influenced by Platonism and also (especially) Aristotlianism. To make a long story short, both traditions essentially thought of the human subject as a microcosm of the macrocosm. In other words, there was a certain structure of being presented in created order which the human mind reflected. This is what made the world knowable. Since the human subject participated in these structures intellectually, the structure of the world was discernible by its similitude to the human subject's intellect.
We can observe this sort of thinking in Melanchthon and Gerhard. Gerhard and Melanchthon agree that the human mind possesses in inner light that is something of a remnant of the imago dei. Luther agrees in his Disputation Concerning Man (1536). Human rationality, he states, was confirmed after the Fall, not destroyed. This inner light of reason is still good for discerning earthly goods in two forms. First, being able to figure out the structure of creation in the form of science and technology. And two, making ethical decisions and knowing the law. Of course both of these is weakened by sin, but nevertheless, as earthly things go, reason is a pretty good guide.
3. Reason= Law: As a result, Luther identifies reason with law. This can be observed in a number of writings, not least the Heidelberg Disputation and How Christians Should Regard Moses. Reason is properly identified with law because it's about discerning and conforming to the structure of the world as God has made it. Of course, one needs God's clarification in the form of the revelation of things like the Ten Commandment after the Fall- but nonetheless, the Ten Commandments are nothing but a condensation of what everybody knows in their heart-of-hearts.
4. Where reason goes wrong: As Luther states in Bondage of the Will, the human person exists with two horizons: things below us and things above us. As we have seen, reason is good when it is applied to things below us. It's part of the human vocation in creation from Genesis 1 onwards, that is, to wisely govern the earth. Reason runs into problems though when it is applied to things above us, where God is sovereign and we are not. This happens in two ways.
A. Reason can lead to self-justification: In the Heidelberg Disputation, Luther distinguishes between two sorts of theologians: of the cross and of glory. The theologian of glory uses his or her reason to discern God through is power, wisdom and goodness in the world. Luther states that this is perfectly possible- he isn't Karl Barth- and cites Romans 1 here. The problem with this is that God as he is reflected in the world is inherently law. In other words, God is good and is operative in the structures of creation as law. If one then tries to interact with him through these structures as a sinner, it will only lead to self-justification. God will seem holy and distant. You small and unholy. Hence, in order to bridge this gap, one will enter into a project of self-justification in order to become like God in order to force God to recognize you as being just. This ignores that God has hidden himself in suffering and the cross and therefore demands faith in that hidden, gracious presence made manifest in the flesh of Jesus. Hence, because reason is law, it is bad when applied to things above us because made us self-justify and ignore God's grace and promises.
B. Reason can misfire when it limits God: The second difficulty with reason when it is applied to things above us is that it can misfire. This was the problem with Zwingli and the rest of the Reformed tradition. In other words, reason is meant to operate within the limited structures of creation. Reason is capable of discerning the probability of something being true or untrue because it is able to certain extent discern the limited possibilities of created entities. Thereby it is able to ascertain with a certain probability true and possible outcomes or whether proposition X is probable or not.
With God, this can't work because as an infinite being he has no limitations. Here Luther is true to his training in Nominalism. Nominalism held that because God is infinite and sovereign, you can't limit God to any set of possibilities a prior. The only reliable guide to discovering what God would or wouldn't do is to look at what God promised to do. If God promised to make Jesus flesh present the Eucharist, then it would be. If he said that he was going to make a man born of a Virgin, then he sure as heck was going to do it. There was no limitations that one could put on God and thereby predict what he would or wouldn't do. Hence Zwingli's insistence that God wouldn't make Jesus present in the Eucharist was silly. It was applying this worldly, limiting structure of reason to the wrong horizon, that is, the horizon of divine-human interaction.
Therefore, in both cases, reason is problematic when applied to the faith not because we shouldn't think about the articles of the faith, but because it destroys or limits God's promises. It does this by 1. Insisting on interacting with God on the basis of law. 2. By discounting God's promises by inappropriately placing limitations on what God can or can't do.
5. The Reason of Faith: As we have seen, temporal reason cannot be applied to God's promises. Nevertheless, it does not mean that faith itself does not have a kind of rationality unto itself. Luther, with the early Christian tradition, called this the "analogy of faith." That is, it is claimed (based on a rather poor interpretation of Romans 12:6- though there are other texts we can point to) that the articles of the faith represent a kind of inner, coherent system of truth. This system of truth cannot be worked out so that there are no antinomies left over (i.e. predestination vs. the universal will of salvation), but there is a particular rationality to them. Much as in the world the structure of the human mind and its similitude to the structures of creation provides basic principles of this worldly reason, so the clear statements of Scripture centered on the gospel (Sedes Doctrinae) provide the basic axiomatic structure of the reason of faith.
Doctrine therefore can be derived via inference from clear statements of Scripture and discerning the implications of those statement in light of the total shape of the faith (the Lutheran scholastics called this the "type of the faith"). Inference works when it simply draws out the implications of certain statements of the Bible. If it works in such a way that contradicts other clear statements of Scripture (for example, when, as later Lutherans would point out, the Reformed ignore all the statement regarding universal desire of God for salvation on the basis of the Bible's statement about predestination) then it is invalid. We can observe this in Bondage of the Will when Luther distinguishes between the preached God, who does not desire the death of the sinner and the God of law, hiddenness and wrath who certainly does. Both exist based on the implication of statements made in Scripture- the Bible says God hates sinner, the Bible say God loves them. Both statements are within God's own reason coherent, but how they are cannot be know by humans this side of eternity.
One can similarly point to the doctrine of the Trinity. Although the words "one substance, three persons" never appears in the Bible (neither does the word "Trinity") the doctrine can be inferred from the fact that 1) God repeatedly states that he is one 2) Jesus says God the Father is God 3) Jesus says that he himself is God and that he is one with the Father 3) Paul says that the Holy Spirit is the Spirit of the Son 5) Jesus and the whole Bible say that the Holy Spirit is God. Put these clear statements together and you infer "one substance, three persons"-as well as the subsisting relations between the person- even though Bible technically never uses the Nicene formula.
Luther's own exegetical practice suggests this. In The Last Words of David, he infers that certain texts are Trinitarian that do not on their surface appear to be Trinitarian. He can do this because he has other clear propositional statements elsewhere in the Bible that distinguish between persons within the one God on his side. Since God is the author of Scripture, his statements, which are self-consistent, can be used according to the analogy of faith infer the presence of the Trinity in other texts that do not immediately appear to be Trinitarian. Hence the Old Testament is to be read as a fully Trinitarian text, although the doctrine is technically never directly spelled out there.
In Luther's later life he wrote several interesting pieces about this- namely, the Disputation Concerning the Word made Flesh (1535) and the Disputation Concerning Man (1536).
In both of these pieces, he argues that faith and temporal reason possess their own separate and perfectly valid sets of rationality and language. For example, as temporal reason and relations go, humans are properly defined "Rational Animals" as Aristotle had said. As they relate to God, humans are defined by their receptivity to God self-giving. Hence the proper theological definition of humans is "Justified by faith."
In the same way, regarding the kingdom of the world, that is, that which is below us, "Man" means something that is "not God"- just as God means something that is "Not Man." In the language of faith, they mean something else. Though the words obvious have an analogical similitude to how they are used outside the language of faith (Jesus is not some other species of human), they are nevertheless redefined when they are placed in a new relationship to one another in Christ. So, now, in Christ, "Man" means something which "is God" and vice versa.
In a sense, we can again observe the problem with the Reformed position. The Reformed assume that human reason can be projected onto God. It also assumes that the signification of what words mean in ordinary temporal language are what they mean in relation to Christ. Hence they run into all sorts of problems. They define humanity a prior according to human reason and word usage. Then they define God in the same way. Then the proceed to try to put them together. This is a disaster. It's for this reason that they come up with an concept of Incarnation that does really involve, well, Incarnation.
Hence, in order to summarize: For Luther reason is problematic when applied to faith not because we cannot use our minds or discern the meanings of words. He often draws out implications from doctrinal statements of the Bible. He and the rest of the earthly Lutheran tradition hold that we can discern doctrine from inference on the basis of the analogy of faith. His difficulty with reason is 1) it leads to self-justification. 2.) It limits God in fulfilling his promises.