Talmudic discussion seldom has recourse to abstract terms.
Instead, it constructs various hypothetical situations, from the analysis of which the inherent abstract principle comes to the fore.
Since these situations do not necessarily stem from real life, these cases may deal with unrealistic or nearly impossible problems; as we have already observed, however, the main function of the Talmud is to serve not as a compendium of practical law but as a vehicle of theoretical explication.
The theoretical character of the Talmud also influenced the method of discussion and of proof.
Even though the axiomatic framework of the discussion is not explicit in the Talmud itself, such a framework, which bears considerable similarity to that used in mathematics, nevertheless does exist.
The statements of the mishnaic sages are discussed as though they were geometrical theorems, both in terms of the precision and compactness of their expression and in the search for convincing arguments by which they may be proven or disproven.
At times, the law may be decided in practice on the basis of inadequate or incomplete proofs, but this is never the case in the theoretical discussion.
Even though there was a need to rule in practice among different options within the halachah, on the theoretical plane (which constitutes the bulk of the Talmud) the halachah is best understood by comparison to a complex equation with a number of possible solutions.
From this follows the talmudic saying, "Both of these are the words of the living God, and the halachah follows so-and-so" (Babylonian Talmud, Eruvin 13b).
Each solution is deserving of full clarification in its own right.
The fact that a given approach is not accepted for purposes of halachic decision-making does not deny its truth value or its importance in principle.
The determination of the halachah is understood primarily as the application of one of the true solutions to a given actual situation, and not as an absolute statement concerning the truth of the argument per se or the validity of an approach that has not been accepted in practice.
–Rabbi Adin Steinsaltz
From an essay, "Talmud," in The Strife of the Spirit by Rabbi Adin Steinsaltz