Do you "believe" 2+2=4, or do you know that 2+2=4? Do you believe that you are reading this, or do you know you are reading it? The term belief does not apply to that which we can justify as a factual truth -- these items are knowledge and not belief. As we discussed in a previous post, R' Shach and the Brisker Rav were bothered by the use of the term belief with respect to the existance of G-d when this is a "muskal rishon", a point of knowledge that we know is truthful and can justify.
It seems to me that this question is already alluded to in Rishonim. Chazal tell us that unlike the rest of the Torah which was transmitted by G-d to the Jewish people through Moshe, the first 2 dibros were heard directly from G-d. The Rambam (Moreh 2:33) explains this to mean that the philosophical truths of the existance of G-d and the falsehood of idolatry are facts of knowledge that each and every person is innately capable of apprehending. We are hard wired to understand the fundemental philosophical truth of "Anochi" without a lesson from Moshe Rabeinu just as we are hard wired to understand 2+2=4 without a lesson in number theory.
The Rishonim reject this view of the Rambam. I want to focus on one particular question asked by the Derashos haRan (Derush 9, p. 156 in the edition I am using). If the Rambam is correct, writes the Ran, then the exact opposite conclusion as the gemara presents should logically follow. Which would you demand more proof for: if I told you that 2+2=4, or if I told you that tomorrow is a bad day to wear blue on? Obviously the latter -- the former statement needs no proof and is obvious. If the truth of "Anochi" is so obvious and innately part of any rational person's core of knowledge, then why would the gemara tell us that this truth in particular has to be heard directly from G-d? Articulation by G-d himself to all the people is the highest form of proof possible. Does it make sense to demand that highest burden of proof for a statement that is innately obvious to any thinking person, e.g. 2+2=4, while other statements, e.g. the mitzvah of sha'atnez, that are incomprehensible, are left to be articulated by Moshe? The Ran therefore writes that "Anochi" entails more than beleiving what is innately obvious, i.e. G-d's existance, but encompasses belief in Torah min hashamayim as well.
Let's put aside for now how you might defend the Rambam. The point I want to make is that the Ran essentially is raising the same point as R' Shach and the Brisker Rav, namely, that "Anochi" cannot encompass innate knowledge, "muskal rishon" alone. No matter how you slice it, there is more to the belief demanded by "Anochi" than philosophical exercises alone can deliver.