A Rebbi of mine in elementary school told me that me that the Talmud was written with Ru'ach Ha'kodesh, an idea that is accepted by many in the Orthodox world. What does it mean?
In HaYom Yom, entry for 6 Sh'vat:
My father wrote that he heard in the name of the Alter Rebbe that all rabbinic authors until and including the Taz and Shach, composed their works with ruach hakodesh, the Divine Spirit. An individual's ruach hakodesh, as explained by Korban Ha'eida in Tractate Sh'kalim (Talmud Yerushalmi), end of ch. 3, means that the mysteries of Torah are revealed to him. This comes from the aspect of chochma in its pre-revelation state.
I vaguely remember an explanation of this entry also to mean that they were able to find their sources through ruach hakodesh.
It means they had a certain prophetic spirit within them as the Shomer Emunim writes:
Included in Emunah is to believe all the words of our sages, of blessed memory, even though there appears something in their words which appears far and outside nature. We must attribute the lacking on our own understanding rather than theirs. For all their words were said with a prophetic spirit (ruach nevuoh) within them.
Even in the Midrashim where they argued, one sage says this and another says that - both are the words of the living G-d, and there is not in their words anything superfluous. Rather, everything is truth, both lines of reasoning are correct.
from http://dafyomireview.com/456 see there for more
"the primary principle which is obligatory on anyone who is called a Jew is to believe with complete faith that all that is found in the words of chazal in the halachot and agadot of the shas and midrashim are all words of the living God" (Leshem - Niglot Leshem parsha shoftim).
Thus he holds their words are imbued with some kind of prophetic spirit.