This isn't necessarily the case. If I state the belief that A is A, it would not be possible to regress this more than once, because the justification is the definition of A. The same is true of any statement that is true by necessity.
Well put. This seems to be the sort of brute facts that old school foundationalists were after. But the problem is that these sorts of beliefs have a very hard time justifying things in the actual world. Now, Descartes did provide a means of doing just that, but it involved the existence of God. This project is far beyond the scope of this thread, however.
The bottom line is this. Take the belief that I am looking at a cup of tea in front of me. There seems to be no principled way to go about reducing this belief to beliefs that are necessarily true. And this seems to be the case for all (or nearly all) of our beliefs or knowledge about the external world.
My question is, why do noncognitive state beliefs need to not be justified?
There may be some confusion here in the argument Mage provided, as it involves some rather philosophically 'thick' concepts. Technically, what you just said is a contradiction - or at least, close to one. So let me provide some rough-and-ready definitions.
Doxastic - stuff that has something to do with the notion of belief.
Nondoxastic - stuff that doesn't have anything to do with belief
Cognitive - stuff that has something to do with the notion of cognition (read: thought/thinking)
Noncognitive - stuff that falls outside the realm of cognition
So your question involves noncognitive state beliefs. But beliefs, by definition, are cognitive
So let's look at the first line of the argument again:
(1) Our nondoxastic experiences are either cognitive or noncognitive states.
This is saying that our experiences which have nothing to do with belief either have something to do with cognition or they don't. What kind of experience might this be? Emotions are a nice example of this. There are (or used to be, at least) non-cognitivists about moral opinion. In other words, they thought that moral opinions weren't even beliefs, but rather just emotional responses. Something like "Yay for helping an old lady across the street!" or "Boo for microwaving puppies!".
But this is why a foundationlist might reject premise (2), as I suggested above. There might be non-doxastic, cognitive states that need no justification.
Are we using the word "justify" as "rove?" Or are we using the word justify as its definition, to provide a reasonable explanation or cause?
As with most things in philosophy, the notion of justification is a very difficult one to nail down. Different theories of knowledge often hinge on different notions of justification. Ernie Sosa talks about apt belief rather than justified belief. Timothy Williamson (I think?) talks about warranted belief, rather than justified belief.
The cool thing here is that we can defend foundationalism if we have a notion of justification that works for the theory and is at least plausible. This also gives us another line of attack against foundationalism. Maybe the foundationalist just can't provide a consistent and compelling notion of justification that would even get the theory off the ground.
I would wager it's something along the lines of for example "I exist"
This is a nice example of what some may consider to be a brute fact - one that requires no justification. Some may even argue that it's necessarily true - Descartes certainly thought so! But now we're left wondering what on earth this belief could possible justify. How do get from here to the cup of tea on my desk?