The fervor and dedication applied to the interpretation of the Torah was a lot like a thousand-year chess tournament of International Grand Masters in which every square and every piece and every move and every conceivable arrangement of pieces carried enormous weight. The approach to the process pre-dates the Mishna and was developed by many divergent schools of thought over a long period of time.
Eilu v'eilu divrei Elohim Chayim, "This and also this are the words of the living God" (Eruvin 13b). Eilu v'eilu emphasizes the incompleteness of any single opinion. The v', which means 'and,' is essential, uniting and complementing the two opinions without choosing one or compromising the integrity of either. "Nobody's right if everybody's wrong" (Stephen Stills, 1966) - from the book Great is Peace
Commencing with the belief that the Torah comes directly from God, the rabbis determined that nothing in it could possibly be superfluous. They attributed significance to inflections, repetitions, forms of usage, and omissions in the language. No word, sound, verb tense, repetition of a passage, or letter was regarded as accidental. The rabbis investigated the gematria (numerological value of the words) to reveal information suggested by, but not explicit in, the Torah. For example, they infer that Eliezer, Abraham’s servant, took part in the battle at Damascus because the number of soldiers in the battle and the numerical value of the letters in his name are the same (318). There is a belief that Torah was God’s blueprint for the creation of the universe. In Tractate Eruvin 13a, Rabbi Yishmael cautions his student Meir, as Meir is transcribing a new Torah scroll, "My son, be careful in your work, for your work is Heavenly. If you delete even one letter or add even one letter, you may destroy the whole world!"
What follows is a brief excerpt from a much longer discussion, which, while ostensibly about an egg, is actually, by way of analogy, about the 13 rules of Talmudic hermeneutics, which I have included to give you a sense of the flavor of the process (as Mike Meyers so famously advised in an old Saturday Night Live skit, "Discuss amongst yourselves!")
TRACT BETZAH (rules about YOM TOV [holidays])
CHAPTER I. REGULATIONS CONCERNING EATABLES AND BEVERAGES: PREPARATIONS FROM THE FIRST DAY OF FESTIVALS TO THE SECOND, FROM THE FESTIVALS TO THE SABBATH, AND VICE VERSA.
MISHNA:
An egg laid on a festival may be eaten on the same day. So says the school of Shammai; the school of Hillel, however, says it must not.
GEMARA:
To what kind of hen does the Mishna refer? If to a hen designed for eating, why then does the school of Hillel prohibit the eating of the egg? Is it not a part of the eatables which were prepared (for the festival)? If to a hen kept for laying eggs only, what is the reason of the school of Shammai, who permit to eat it? Is this not Muktzah [non-permitted object to even have around on shabbat or yom tov]?
If we suppose that the school of Shammai does not hold the theory of Muktzah, even then the eating of it could not be permitted, as it is a newborn thing, and even one who denies the theory of Muktzah should hold to the theory of Nolad (newborn thing). No, R’ Na'hman has declared that one who denies the theory of Muktzah denies also the theory of Nolad.
If so, then the school of Shammai will be in accordance with R’ Simeon (who denies the theory of Muktzah), and the school of Hillel will be in accordance with R’ Jehudah (who holds it); but this would not be the case, because did not R’ Na'hman state (in Tractate Sabbath) that the school of Hillel is always in accordance with R’ Simeon and the school of Shammai with R’ Jehudah?
R’ Na'hman may say: Because we found an anonymous Mishna (in Tract Sabbath, p. 375) which is in accordance with R’ Simeon, therefore he declares that concerning the Sabbath the school of Hillel holds with R’ Simeon, and concerning the festivals we found an anonymous Mishna (Sabbath, p. 375) in accordance with R’ Jehudah, therefore he declares that the school of Hillel is in accordance with R’ Jehudah, who is more rigorous.
Let us see: Who makes the Mishna anonymous? Rabbi (its editor). Why does he make it anonymous in regard to Sabbath in accordance with R’ Simeon, and in regard to festivals (makes it anonymous) according to R’ Jehudah? This is no question. Relating to Sabbath, which is so rigorous that it has a capital punishment and there is no fear that anyone will dare to disregard its rules, therefore Rabbi made an anonymous Mishna in accordance with the more lenient R’ Simeon; but relating to festivals, which have no capital punishment at all, and the rules are lenient, for fear that otherwise they may be disregarded, Rabbi made an anonymous Mishna in accordance with R’ Jehudah.
Now, then, if the Mishna means a hen which is kept for laying eggs, and the reason that the school of Hillel prohibits it is because the egg is Muktzah, why do they not differ about the hen itself? (whether it is permitted to eat it or not).
Therefore said Rabba: The Mishna refers to a hen kept for eating, and to a festival which falls after Sabbath; and the teaching of the school of Hillel is not for the reason of Muktzah, but of preparation; i.e., an egg which is laid today. Rabba is certain that it was ripe the preceding day, and it is in accordance with his theory, thus: It is written [Ex. xvi. 5]: "And it shall come to pass on the sixth day, when they prepare what they shall have brought in"; i.e., only on a week day shall anything be prepared for the Sabbath or for festivals, but nothing should be prepared on a festival for the Sabbath, and vice versa.
They go on like this for quite some time, expanding into a discussion of parallels between rules about fruit trees and fallen branches, and the relative sanctitude of different holidays, the time and circumstances under which eggs were laid, and whether or not the hen crossed the road on a plank, but the real subject is how to think. And, you may notice, they always,
always credit the source of any comment. We don't take credit for other people's ideas - this is a really big deal, and a sign of respect to teachers and the tradition.