On the contrary - this is precisely faith. Notice, it’s nothing like logic. Logic is a coherent set of necessary linguistic rules, hence the laws of non-contradiction, excluded middle and identity are always true by the very nature of their definitions (i.e. language).
Should I also say: “on the contrary”? Here is the analysis.
Universal skeptic (US) says: We don’t know if the senses are reliable, we must accept it on faith.
Regular skeptic (RS) says: Why so? We rely on our senses every second in life.
US: But you cannot
be sure that they give you an accurate picture of reality.
RS: How do you know that the picture is not accurate? What
epistemological method do you use to ascertain that the “
actual reality” and the “
perceived reality” are different? Do you have direct access to the “actual reality”, which does not include the sensory data?
US: No, I don’t. But I can point out that the senses give “inconsistent” information about reality.
RS: For example?
US: Well, here is this glass of water. I place a pencil into it. I look at it, and the pencil seems to be broken, but when I touch it, I can feel that it is not broken.
RS. Actually I look at it, too, but it does not seem “broken” at all.
US: Well, not where you stand… but come over to me and you will see that it seems broken.
RS: So your “proof” that the senses are unreliable is
contingent upon the exact position where you stand? Strange! By the way, the pencil is not broken, it seems to be disjointed. And the real reason for that it that the speed of light in air and in water are different. Nevertheless your “proof” that the senses are unreliable is
contingent upon the assumption that the senses ARE reliable. After all you assume that your touch gives you correct information about the pencil not being broken, while your eyes also give you correct information, that the pencil is broken. So you say that the senses are unreliable but your method to prove this relies on the assumption that the senses are reliable. Are you serious?
US: ??? (please continue

)
(By the way, this is a perfect example of a self-refuting proposition…)
Disclaimer: this example was taken (not verbatim) from the book of George Smith: “Atheism, A Case against God”.
But “that the senses are reliable” cannot be a properly basic belief since it need not be true. It isn’t logically necessary, nor does it rest on either a logically necessary presupposition or else be based on evidence.
Again, on the contrary, it is a properly basic principle, since its denial
requires the assumption that the senses are reliable, as explained above - and this is a contradiction. There is no logical necessity that a physical object cannot move faster than speed of light. Yet, as Einstein’s famous thought experiment showed, from the assumption that any physical object can go faster than the speed of light we arrive at a logical contradiction. Just because a proposition
ITSELF is not a logical contradiction per se, it does not follow that it will never lead to logical contradiction. Also, there is no logical necessity that the zero Kelvin should be the “absolute zero”. It is simply a brute fact, without any reason. There is no logical necessity that the virtual size of the Sun and the Moon (when viewed from Earth) should be almost identical. Another “brute fact”. (Since there is no logical necessity, do you contend that we must accept this fact on “faith”?)
The method we use here is called “indirect proof” in mathematics. The principle is again simple: “in order to prove that a proposition is true, one can start with the negation of the proposition, and if this negation leads to contradiction, the original proposition is proven to be true”. There is no logical reason for this principle. There is no logical reason for the “direct proof” either. There is no logical reason that “mathematical induction” should lead to true propositions. None of these proving methods are the corollary of the axioms of mathematics. These are all properly basic principles - and no faith is needed in accepting them, even with your definition of “faith”, which I reject.
But there’s no logical reason why it’s the final arbiter of truth.
Brute facts need no logical reason for what they are. Also you keep using the word “truth”. As long as you use it as an abbreviation for “a sufficiently correct model of reality”, I have no problem with it. But I suspect that your usage is different.
Now, I’m not a universal sceptic at all. All I’m arguing is that you need a particular metaphysical background in order to justify the reliability of the senses.
You may not like the label, but what you keep saying is exactly what a US says. I hate to repeat it so many times, but the denial of the reliability of the senses leads to a contradiction, therefore the principle cannot be denied.
You cannot “prove” that the universe exists - in a logical fashion. Therefore in your verbiage one must accept the existence of the universe “on faith”. There is a huge problem with your usage of this word: “everything, except the axioms in a formal system must be accepted on faith”. And that makes “faith” a meaningless word.
But notice that survival doesn’t have to be based on the truth.
On the short run, in some lucky circumstances yes, it is possible. I already agreed to that. But on the long run reality (which you call truth) will catch up with you. And when your model will be
seriously at odds with reality, you will die.