Others: downvotes don't fix what problems might be in myron's thoughts. They make them worse.

Myron: preliminary note, your comment sounds a bit presumptuous and demanding.

Substance: I don't believe that rationality necessarily has a fundamental undeniable metaphysical grounding. I believe every philosophy lacks this. Problems like the problem of induction (knowledge comes from experiences and it's impossible to know that the future will be like the past) and the turtles all the way down problem (assumptions are either unwarranted or dependent on further assumptions, which makes all forms of thought either infinitely regressive or groundless) are basically insurmountable. These are problems that all philosophies face and cannot answer satisfactorily.

However, I think you're asking the wrong question. Instead of starting by looking for fundamental metaphysical justifications, which we know to be impossible, we should look to a more pragmatic and tangible level. The brute fact of our existence is that some things work and others don't, that some things seem right and others seem wrong. If someone is insistent upon denying reality, then that's their affair, but they should know that there are consequences to this rejection. I consider the rejection of reality to be viceful, because those who do so reject their own current values and intutions in favor of an embrace of an abstract form of nihilism. Nihilism is much easier than acknowledging reality, but it's also much worse, in my opinion.

Even if nothing that we see or predict or experience or value is real in an absolute and abstract and irrefutable metaphysical sense, it's real and meaningful and useful in the context of our everyday lives. The reality that we face each day is the one that I care about, not the abstract and irrefutable ideological one. That's why I support rationality even if I don't know why rationality works. The fact that it does work, or that it seems to work, is enough for me.

I also think it's relevant that the alternatives to rationality that I've seen have all been worse, in terms of logical metaphysical justification.