Justification for Foundational Belief

[Perhaps]

We should constantly question those principles regardless of what reality we may find ourselves in -don't you think? Why, btw, are we assuming that a self generated reality would be so easily subject to change? How adept are you at exploiting and controlling your dreams (since that example was used)?

...yes, I agree and have always held that we ought to question foundational principals regardless of reality. A proposed idea questioning foundational beliefs is silly, because to evaluate the idea is to accept the truth of said beliefs. That isn't to say that they are set in stone, however. If a discrepancy is found between observed reality and foundational beliefs, it would seem that they are false or teetering on false.

To determine falsity requires an understanding of truth. If you were to question the fact of your existence, something self-evidently true, you've just stated that it would be "silly" because you are already accepting the truth value of the original belief. This is perhaps the most accurate definition of self-evident truth - something which must be true to even begin to analyze its falsity (thus, not allowing it to be false.)

The interesting turn comes in when observing your italicized sentence. I would be more careful when determining truth based on observed reality. The objective of fundamental beliefs is to capture truth, which is why we base the rest of our beliefs on the fundamental ones. If we observe something which contradicts a fundamental belief then it may be evidence that the fundamental belief was originally wrongly categorized as being fundamental. This is why we have so few fundamental beliefs - namely the self-evident ones. The problem with the axioms of existence (number 3 specifically) are that they may reach past self-evident truths to useful assumptions.

Descartes ran into this problem when beginning his journey on absolute doubt, eventually only being able to rationally assert cogito ergo sum. It is sometimes referred to as Descartes' lonely island because his extreme doubt could only get him this far. We must make basic assumptions on which the utility value surpasses their possible falsity. When we analyze these assumptions our only method though which to find fault is rationalism or empiricism, both of which are equally dependent on assumption - namely of what is true and how we know its true.

We strive to understand truth, but it is something which evades us. Perhaps there is none, then the nihilist is correct, or perhaps there is one, then the rationalists are correct, or perhaps there are many, then the empiricists are correct. Like I said earlier, foundationalism is a nice compromise of the three, allowing for correction over time and accountability, but in order to actually attain truth one must pursue it farther than the basic assumptions of fundamental beliefs.

In short, perhaps a deeper question would bring light to your search for justification: what is truth? From there you can base all other claims on a strong foundation.