The idea that there are a set of beliefs which we must privilege is mistaken. The idea that one set of premises supply warrant to a proposition only if they cannot lead to other conclusions is mistaken as well. The idea that warrant is absent from beliefs about brute facts is mistaken. Here’s why:
If we take “I exist” as a belief that I must take axiomatically, on faith, and that there is no warrant for such a belief, then there are no other warrantable beliefs which arise from it. In other words, as an axiom, all ideas related to it are tautology. Tautology only proves other tautology and certainly we don’t mean by “warrant”, “proof”, because real states of affairs are our concerns rather than simple rational thinking. It may be true that all of the same “reasons to assert” “I exist” can be the same reasons for the idea that I am all that exists, there are no other minds, reality isn’t real, and so on, but the “reasons to assert” are “warrant” and it simply turns out that there are many conclusions that are warranted using the same “reasons to assert”.
So, is the belief that “I exist” taken on faith since I can believe something else? No! Again, you have warrant for the belief and for additional reasons aside from the shared “reasons to assert” something else, you cannot believe alternatives otherwise. They honestly do not seem to be the case. Being convinced, being certain, or some other psychological state has no bearing on the fact that you believe “I exist” is the case. That is to say that I may have doubts, psychologically, when confronted with some other argument against my belief that I exist, but I do not doubt in any genuine epistemological sense that the actual state of affairs is that I exist.
Since doubt and reserving judgment and belief all require warrant, then my belief that “I exist” is immediately a justified, warranted belief because it occurs naturally, uncontrived, and obviously to me more than any other thing I may wish to believe about reality. It cannot be said that this belief lacks justification because I have not deliberated the matter. The fact that I may be wrong about “I exist” isn’t justified grounds for me to doubt “I exist”. There is no place then for faith with respect to my existence. It is from experience that the idea has occurred to me and experience is the reason the belief is justified, as it sustains the belief “I exist” rather than defeats it or casts genuine doubt on it.
This is true of all such primitive “brute facts”; whether or not I have blind faith in my senses, or that my trust in my senses does in fact have warrant; whether it is a matter of faith that the next moment will be consistent with previous moments; whether there are other minds, and so on.
The object of faith is belief. The object of belief is a state of affairs. One need no faith at all in these beliefs about these states of affairs because each has warrant. And, even if we simply assume these propositions without committing to believing them true or false, we still are not acting on faith. We have simply adopted a set of propositions, provisionally, in order to ferret out a full sense of what the implications of them could be.
I personally do not take these things provisionally but as matters of fact that I know as fact and that I have complete justification for in spite of competing ideas. I do not take any of these on faith as my confidence about my belief relies on objective reality, not hope, and empirical experience affirms rather than conflicts with my belief. I need not privilege this belief because it is just as open to revision as any other belief that I have, and all of those are revisable because of the fact that there is an objective reality. How do I know there’s an objective reality? Well, non circularly, I just explained it. The key is, knowledge is not privileged either. It is a collection of justified beliefs. I know there is an objective reality because to doubt there is is to literally pretend for the sake of doubt.
Quite simply, there are no beliefs about any other states of affairs that have more grounding than these which have in this conversation been named “properly basic”. They require no faith to believe. We can accept them provisionally or adopt them and induct them into the realm of human knowledge. Either would be done through, and only through, warrant. However, they are still beliefs and should be given no special privilege, open to the same revision as any and all other beliefs should.
“Let us now return to our biconditional (T): the assertion that p is true if and only if (really) p. The intuition that this sentence expresses could also be reformulated as such: an assertion is true if and only if it is the case as was asserted. We can now think what ‘place’ such an explanation of the concept of truth can have in our practice of making assertions. This practice is of a ‘normative’ kind: assertions are moves in a language game that are “justified” or “unjustified”. We are entitled to assertions if we have good reasons to assert that p, or if we have convinced ourselves through our perception that p — or also if someone whom we have good reason to trust has said to us that p (i.e., reason for the assumption that this Someone could provide good reasons). What we learn when we learn a language is — among other things — to judge in a reasoned way and to distinguish between justified and unjustified assertions (convictions). This suggests a new interpretation of the biconditional (T), which no longer frames it as an attempt to interpret truth as an agreement between statements and states of affairs, but rather as an attempt to determine the place the word “true” has in our assertive and justificatory praxis. Accordingly, we could now read the biconditional as such: someone is justified in asserting that p is true precisely when he or she is justified in asserting that p. And this could now be further interpreted as saying: to say that an assertion is true is nothing other than to say that the assertion is legitimate (grounded, justified). Truth would then become no more than “warranted assertability” or “rational acceptability.” The concept of truth would consequently be drawn back into justification.”
(Albrecht Wellmer, “The Pragmatic Turn In Philosophy: Contemporary Engagements Between Analytic And Continental Thought”, State University Of New York, 2004, Page 96)
“There is no property of truth intrinsic to the explanation, but only a vast array of explanatory stories of the identical form, none of which need use the predicate (Truth) and none of which, therefore, requires the identification of any mysterious property or relation to which the predicate might supposed to refer.”
(Pederson & Wright, Truth And Pluralism: Current Debates, pg. 264)
“According to model-dependent realism, it is pointless to ask whether a model is real, only whether it agrees with observation. If there are two models that both agree with observation … then one cannot say that one is more real than another. One can use whichever model is more convenient in the situation under consideration.”
(Mlodinow/Hawking, The Grand Design)
“We cannot begin with complete doubt. We must begin with all the prejudices which we actually have when we enter upon the study of philosophy. These prejudices are not to be dispelled by a maxim, for they are things which it does not occur to us can be questioned. Hence this initial skepticism will be a mere self-deception, and not real doubt; and no one who follows the Cartesian method will ever be satisfied until he has formally recovered all those beliefs which in form he has given up. It is, therefore, as useless a preliminary as going to the North Pole would be in order to get to Constantinople by coming down regularly upon a meridian. A person may, it is true, in the course of his studies, find reason to doubt what he began by believing; but in that case he doubts because he has a positive reason for it, and not on account of the Cartesian maxim. Let us not pretend to doubt in philosophy what we do not doubt in our hearts.”
(C.S. Peirce, Some Consequences Of Four Incapacities, Journal of Speculative Philosophy  2, 140-157)