There really is no reason to think that "reason" is infallible.
Let's say we are learning the Critique of Pure Reason or Hegel which deal with what pure reason can tell us. [That is  where Kant says that pure reason can tell us more than when there are self contradictions [as per Hume]. He shows  reason can show us synthetic a priori which is the same things as universals.]
But there is no claim that reason is infallible.
So how does reason recognize things. Not by implanted knowledge, nor by recollection but by probability. [The implanted knowledge was refuted by Husserl].
The kind of probability here was discovered by Thomas Bayes.
Dr Michael Huemer shows this in his web site 

In Yore Deah the Rema brings that learning Physics and metaphysics is a part of learning Torah,. Even though the is a famous note from the Gra on this  Rema in Yore Deah, I was one day in the Yeshiva of the Gra in the old city of Jerusalem and saw an extended commentary on the notes of the Gra. On that note it was brought that it was inserted and not at all from the Gra. [Before the notes went to the printer someone inserted this comment that supposedly shows that the Gra disagreed with the Rema on that point.] 

One surprising things the Gra wrote is "The root of the souls of gentiles is from heaven and the root of souls of Israel is from the earth." From what I recall this is from his commentary on Shir Hashirim chapter two [right at the start of the chapter]. So the idea of superiority because of birth seems to be in accurate.

I saw a similar idea in Rav Luria on Genesis in a verse on the three sons on Noah.I.e., that their root was from the three names "I will be" אלף הי יוד הי. אלף הא יוד הי. אלף הה יוד הה.

Even though I learned a lot of very great lessons from the teachings of Rav Nahman of Breslov still I have to admit that the only way to get to the pure essence of Torah is through the Gra [Rav Eliyahu the Gaon of Vilna]. And you can see this yourself any time you talk to anyone in Breslov. When anyone in Breslov wants to show that so and so is a great Torah scholar, they never say "he is so great and you know this because he learned in a  Breslov yeshiva". Rather they say "he is a great Torah scholar, and you know this to be so because he learned in the Mir." [Or they say it in present tense as in reference to people that are at present in the Mir either in the Mir in NY or the Mir in Israel.] 

w87 E Flat Major

Philosophy is supposed to give some direction in life. It is meant to apply reason to questions about life and the universe in general. Yet is it has not been providing much direction for a long time. So instead of philosophy people would look into different religions.
Now in the Middle Ages there actually was direction one could gain from philosophy since the general line then was Faith with Reason. But since then this balance has been lost.

That balance and synthesis was lost to some degree I would guess because of the Enlightenment that meant to push out priest and princes and replace them with intellectuals [as Allan Bloom points out in his Closing of the American Mind].
 But Kant and Hegel meant to find a balance. Kant on one hand looked towards Newton as a paradigm of what a rigorous logical philosophy ought to be, [as  Nataliya Palatnik in Kant's Moral System points out in her PhD.] Kant however knows there are no experiments that can be done. So he substitutes the idea that certain kinds of things, dinge an sich [things beyond the capability of experience] if reason goes into them comes up with self contradictions. And Hegel simply stretched that idea further to come to the conclusion that reason (--no matter what it is applied to) will come up with self contradictions until it rises up one level to a higher level where that contradiction disappears and then at  that level the process is continued until one gets to God.
However Kant and Hegel only lasted until the 1900's. Then came "analytic philosophy". That Robert Hanna has shown well is overdue for the trash bin. So people are waking up again to Kant and Hegel. [But I have no idea what kind of approach to Kant and Hegel, Robert Hanna would take. Which Neo Kant school? If any? Which approach to Hegel? McTaggart? Maybe someone would start to look at them afresh?]

in the path of the Gra is the pure essence of Torah.

I knew the head of the Aderet Eliyahu a yeshiva in the old city of Jerusalem that goes totally by the Gra. And I used to eat the third meal of Shabat every week with him and his family. That is Rav Eliyahu Silverman.
But I was at the time not going totally by the Gra in all respects.
But there was a time that I was  trying to go by the Gra in every way. But that path was too pure and too hard for me, so I got sidetracked. But even so, I remain with the conviction that in the path of the Gra is the pure essence of Torah.
So here I would like to bring a few of the important points of the Gra. But before I do I would like to reiterate the idea: that as much and as well one can follow the Gra in every single detail, all the better.

One of the first ideas of the Gra [as is well known] is that every word of Torah is worth as much as  all the other commandments of Torah put together. [I have to say that I became aware of this right at the start of my time at Shar Yashuv in NY and that lit a fuse underneath me.] I am sure everyone knows the Mishna "Learning Torah is equal to them all"   תלמוד תורה כנגד כולם. Now in the Mishna itself when it says ""equal to all of them" it is not actually referring to all the commandments, but rather to the other commandments mentioned above in the Mishna. [So there is not contradiction here between this mishna and other places in the Torah itself which make it clear that coming to love and fear of God and attachment with God is the purpose of the commandments.]

However the Yerushalmi actually explains that mishna to mean in fact that every word of Torah is worth more than all the other commandments, and the Gra simply quotes the Yerushalmi.

Also in terms of actually keeping what the Gra says here there are two aspects. One is Torah in depth. The other is getting through the entire set, the Babylonian Gemara and Yerushalmi, and the Midrash Raba and all the midrashim. That is all the books written by the sages of the Gemara.
[He probably would not hold that Physics and Metaphysics are in the category of learning Torah. But like I said before, my own path diverges from the Gra and there does not seem to be any way to reconnect. So I try just to do the best I can in my own situation. But even if I can not walk fully in the Gra's path, I at least try to hang on the the knowledge of how special and important it is. And I even remember how that path helped me to get to Israel  and also the a special kind of feeling of attachment with God which i think is a fulfillment of those two verses that command one to be attached to God.]

Now Litvak yeshivas are based on the Litvak yeshivas in Lithuania which all stemmed from the Gra. But they do not follow the Gra in every detail. That is sad. That the reason they are not very effective. If they would be more loyal and straightforward about going with the Gra in every detail they would be doing a lot better. So why do they not follow the Gra in every respect? Because of the fifth column--the traitors in their midst. The insincere people that are there using Torah simply as a way to make money. The traitors are often the top people. It is like the idea of the "Against Professional Philosophy" blog. But here the idea is, "Against Professional Torah."


The problem with diverging from the path of the Gra is that one can easily fall as I have seen many times. [Side note: Rav Nahman I considered not to have been under the excommunication, so I feel free to quote him.]