But there is nothing ironic, let alone any "contradiction", in either of them using reason to attack the authority of reason. First, reason must be distinguished from reasoning, in the sense of logic - which neither of them question in the slightest. They simply both understand that logic alone - even with the addition of sense experience - doesn't get anyone to certain knowledge of the external world. Logic is contentless, and sense experience alone cannot fill it up. That much is quite true, and has been known since the time of Aristotle. It isn't equivalent to skepticism or questioning reason, however, because that turns on the issue, do we have any other means of knowledge besides logic and our senses? Which is the whole epistomological problem in the whole history of philosophy, with different people taking different positions on it.
Beside the distinction between reason and logic, though, it is an old and venerable philosophic tradition to reason about the limits of reason. The Eleatics did so, and Plato, medieval rationalism and theology, Humean skeptics, Kantean critical philosophy, modern positivism, and modern relativism. So do entire areas of mathematics, come to that, where proving that a given problem is insoluable is an everyday exercise. How sweeping the conclusions are varies from case to case. Most except logic from whatever conclusions they draw, and that is all they need to reason about the matter without putting the status of their premises into "play".
And even if any of them did arrive at a "contradiction" it would still be perfectly sound reasoning. Assume reason's authority is trustworthy, arrive at a conclusion that reason's authority is not trustworthy, contradiction, means only "therefore reject the initial premise, and conclude that reason's authority is not trustworthy". Not that I defend that conclusion, I merely point out there is no error in reasoning involved in drawing such a conclusion, if that is where the chain of reasoning led. The logic of the deduction is perfectly sound. That is only an aside, but meant to make clear that flip dismissals are not sufficient here.
Next you say "there must be an alternative way to knowledge" if reasoning does not arrive at knowledge. This is, to say the least, not obvious. Knowledge might simply be unavailable to us. I don't happen to think so, but again, it is not something that follows from the previous. I take it here you meant your statement as a sort of commentary and criticism of Ghazali, that he turned to revelation because reason wasn't useful. There is some truth to that. But he recognizes that revelation gives truths that are not certain as logic is certain, but instead only propositions accepted by faith. This seperates revelation from both certainty in logic on the one hand, and the vanity of pretended rational merely human knowledge on the other hand, to Ghazali.
In addition, there is an aspect of Ghazali's position I don't think you've quite noticed yet, that is an important part of its strength, as a practical argument I mean. He has removed an independent standard with which to challenge the positive law of one's community. His acceptance of Islamic revelation is not simply a "gee, here is something else" as you pretend. It is literally the law, when and where he was writing.
Without human rational knowledge (with content, beyond mere logic and mathematics), there is no place for an interpreter or legislator, let alone for a rebel, to challenge the established law of his community. The exception for revelation does allow a place for a "higher law" and appeals to it, but only a very narrow one, to the exact letter of the traditional (revealed) law - because of the prohibition against interpretation, as likely to introduce human distortions that have no defensible claim to truth.
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So basically it is in that sense that I call it ironic that Hume et al would reason the practice of logical reasoning to have it's vulnerability in it's sensory nature when the very concept of reason itself, not to mention a concept of what constitutes sensory, is under the ultimate ends of such an argument itself derived from sensory associations, which, for the sake of consistency, must also be inherent with their flaws, or more specifically the sensory defined concept of what constitutes a flaw. - It's simply taking a derived form of skepticism to its end, which is also beyond what most skeptics themselves are willing to admit but nevertheless may be arrived at. In that end exists an internally turned being with certitude in nothing - almost like a psychological reclusiveness for lack of a better phrasing.
As for the turn to revelation, indeed it was a criticism of Al Ghazali, but specifically moreso of what stemmed from him. Though Al Ghazali himself was not the fundamentalist literalism I criticize, he undeniably made the world a better place for those after him who propagated extreme literalism in the Koran. It's also a criticism of convenience in that he took his leap of faith to the revelation that was closest to him. Law or no law of the state at the time, it's a decision of convenience in more ways than one (including the convenience of not upsetting the authorities by contradicting their rule, which is understandable though still the element of choice exists). Needless to say, the presence of that element of choice on the whole as well as a preexisting societal dictate towards one choice over all others makes his choice a weaker one, in that he took the safe route. It's an unfortunate solution to any riddle, even though it may have been the most practical. It's kinda like putting an enormous effort into debunking and completely dismantling somebody else's viewpoint then proposing what is right in front of you as an alternative, for whatever reason be it legal, practical, or political. In that sense, Al Ghazali's alternative route was that which conveniently was in front of him, known to him, and heavily expected of him, meaning it was not an alternative chosen for any particular merit other than that it was there and it was what he knew. It was a convenient piece to complete his puzzle with, and any predetermined societal bias towards that piece just further shows the reasons why it was chosen.
As for our own brand of literalism in western society, sure we have our set of strains. In fact, being a strict constructionist I could arguably be said to subscribe to one of them. A distinction must be made in the extent of literalism. Literalism in reading brief rulebook for legislative government is a lot different than an absurdly literal reading of the Koran that digs itself so deeply behind the words that it finds itself at odds with reality. There are times to be literal, and other times where being literal is absurd. Literally reading a rulebook in a game is practical for society. Literally reading an allegorical abstract defeats the purpose all together, making it absurd.
This is indeed turning into a fun discussion! I look forward to your next set of thoughts on it.