The thirteen rules of interpretation.
The thirteen rules of interpretation serve as introduction and prologue to the Sifra. While in the past it has generally been accepted that these rules were Sinaitic in origin and that without them we would not know how to interpret the Torah (see the eloquent argument for this in Ra'avad's first comments on the Sifra), in more modern times there were attempts to present them as self evident rules of logic or language based interpretation. R. David Nieto in Matteh Dan (end of Dialogue III) represents first approach and Malbim the second.
Explaining the 13 rules as logic presents a difficulty in that they do not appear to follow classic rules of logic. Recall that the Greeks distinguished between logic, a self sufficient science of reasoning, and rhetoric, an ability to construct an argument for a desired position. The former is akin to mathematics in rigor and persuasiveness while the latter, at its worst, deteriorates into sophistry. The 13 rules do not follow classic logical constructs. Contemporary attempts to accrue validity for the 13 rules as logic, invoked the essentially different manner in which Greek and subsequently Western, and Talmudic, or Hebrew mind thinks and reasons. This is a point that has been realized and expounded by dozens of scholars over the past century and it is worth considering at some length, in order to understand how some have approached the difficult task of justifying the 13 rules .
Greek civilization was above all visual. Its gods were concrete and material and so was its conceptual language. Its writers, such as Homer, wrote in long, detail laden paragraphs in order to describe a scene that the readers could visualize, as if it was taking place in front of their very eyes. Homer is famous for the mass of detail and leisurely development of his scenes, dress and deportment of characters, their physical surroundings, their movements and behavior. On the other hand, he is poor in describing their inner states. A picture may be worth a thousand words for an image with all of its attendant detail can be grasped in one glance. On the other hand, a picture is static; it can never be anything more than it is at the moment that it has been grasped. It does not allow for development or progression, only for replacement by another picture. Not so hearing. Although it transmits information but one syllable at a time, speech is dynamic and flexible. Every word and every saying must be actively perceived, related and reconciled with the words, syllables, and units of information that came before and that are yet to come. It is for this reason that Scripture is discontinuous and filled with gaps and apparent contradictions  that must be filled in and reconciled by the Oral Tradition. The Jews were above all a nation devoted to hearing. Their Law was spoken and heard at Sinai; beyond this, the world itself came into being in an act of Divine speech. A Jew is not a passive receiver but an active participant in the act of revelation and Revelation and he is constantly in the process of perception and interpretation.
It is not surprising than that Greek logic sought to establish identity while Jewish thought desired to reason from similarity. One of the basic forms of Greek reasoning was a syllogism. The purpose of syllogism was to reveal an identity relationship between different particulars, as members of the same class. A syllogism goes like this:
1. All men are mortal.
2. Socrates is a man
3. Therefore, Socrates is mortal.
While syllogisms are excellent tools to equate simple entities, they are unable to adequately represent complex relationships of things that are similar in some aspects but different in others. Such "messy logic" requires different logical tools .
The thirteen principles are precisely such tools. What they attempt to do is to establish sufficient similarity between categories that an aspect of one is transferable to the other, without, however, changing the actual nature of either category. Similarity serves not to establish equivalence but to serve as proof that more than aspect of the one also exist in the other. We use this kind of logic in everyday life without stopping to think and formalize it. It may not be Greek logic but it is nevertheless the basis of our daily functioning and we rely on it to make major decisions.
An example may be useful. Imagine that you went to the railway station where you encountered the ticket master in full railroad regalia and wearing a distinctive conductor's cap. As you board the train, you are greeted by ticket checker who is in the same uniform but wearing different pants. After a few hours on the train you make your way across the engine room and see there a man who is loading coal into the heaving furnace. Because of the heat in his compartment he is wearing nothing but shorts and the conductor's hat. Is there any doubt that this one part of the uniform would be sufficient for you to assume that he is an employee of the railroad, just like the others? This example illustrates the kind of logic that enables us to handle shifting and complex categories without recourse to syllogism and formal categories of Greek thought.
It might be instructive to compare Kal V'Chomer and syllogism in its so-called a-fortiori form. Whereas syllogism deals with names and predicates, kal v'chomer deals with sentences. It is not concerned with relationships of classes. Syllogism apply terms such as 'all' and, 'every' but kal v"chomer employs juxtapositions - if an aspect of a law is found in the minor case, so much so must it be present in the major case. In fact, kal v"chomer works just as well for transferring leniencies as stringencies, an aspect not found in syllogism. Kal v'chomer argues that if a lenient aspect is found in the stricter case, it should also pertain in a less strict case. Conversely, if there is strict aspect to a lenient case, we should expect that it should also exist in a stricter case.
The underlying principle underlying the thirteen rules of interpretation is the principle of unity of the Torah. In some ways it is similar to the scientific method; when different phenomena evidence similar characteristics, one looks of for common mechanisms. This is known after J.S. Mills as the Method of Agreement, which states: "If two or more instances of a phenomenon under investigation have one circumstance in common, the circumstance in which alone all the instances agree is the cause of the phenomena". R. Adin Steinsaltz wrote in the Essential Talmud (p. 97) that "Rabbis anticipated modern science while endeavoring to employ an empirical approach without having recourse to theoretical structures that did not derive from tested facts". They applied this most modern logic to texts and linguistic structures, in the world of hearing and reception, as scientists apply them to the world of visible and natural phenomena.
Attempting to explain the logical underpinnings of the 13 rules is good apologetics but I have a question. It should be evident that the more these rules can be proven to be based on pure logic, the less they need to have been Divinely revealed. Why, after all do we need Sinaitic rules, if we could have figured them out by ourselves. On the other hand, as decoding tools they hardly need to be logical at all. For those who believe that the Divine Author encrypted multiple meanings into the Torah and that the thirteen rules are the code with which to comprehend them, the supposition that they are pure logic to be nothing but a distraction.
Let us restate the traditional majority opinion about the 13 rule. It is that that the thirteen principles are themselves received at Sinai . In this view, the Divine Author intentionally encrypted multiple meanings in his Torah and also provided the keys with which they may be comprehended or decoded. In addition, certain limitations on how these rules work, such as that an individual may not derive a gzeirah shava on his own, or that principle of D'yo for a Kal V'Chomer, fit best with this approach. There should be no limitations on use of pure logic, if that is what the 13 rules are.
There is a third approach - one that sees some of the rules as logic and others as received decoding devices. This is, for example, the approach of the Shela  who considers the first 10 rules as being received and the last three as purely logical. The Ra'vad also writes that 12 rules are received and the last (bringing a 3rd verse to reconcile two conflicting verses) is logical. This approach deserves farther explication and study.
Much of this research has been summarized by Susan Handelman, a professor of English and seminary teacher of Tanach in The slayers of Moses: The emergence of Rabbinic interpretation in modern literary theory, SUNY Press, 1982
2 This point has become widely accepted after Erich Auerbach in Mimesis.
3 Classic Greek thinkers attempted to surmount this problem by characterizing the 'metaphor' as the way to deal with comparison of things that are not susceptible to use of syllogism. Metaphor is essentially a device that language uses to speak of two different entities as if they essentially the same, without them becoming same. Thus one can speak of one beloved's eyes as being as bright as stars without them actually being stars. While concepts such as metaphor and simile enable Greek logicians to surmount some of the difficulties they faced, they led to another unfortunate development in the realm of hermeneutics, or science of interpretation. Western thinkers became unable to allow that Scripture may have more than one 'true' meaning. A biblical verse could have either a literal meaning or be an allegory, with the 'real' meaning hidden and the literal meaning being no more than a metaphor. When applied to a living, dynamic, multi-level work written for Jews and in their language and pattern of thought, it led to more than two millennia of grievous misinterpretation of Scripture in Christian thought.
4 The minority view, that the Sages extracted the thirteen rules of interpretation from the mass of received precedent may be represented by Meiri in Kidddushin 24 and views of those early authorities who allowed any individual to apply these rules, with the exception of gzerah shava, without a pre-existent tradition. In the same vein, Maimonides wrote that gzerah shavah was restricted for use by the High Court only in order to prevent widespread confusion, implying its non-Sianitic origin (See Encyclopedia Talmudit, entry gzerah shavah, and middot, when available). One may explain, however, that gzerah shavah could on occasion be used without a pre-existent tradition (to prove meaning, giluy milta) and that his remarks pertain only to such a case (See Halichot Olam, Beit Yosef's Klalei Hagmara, Techilat Chochma 11, Margaliyot Hayam to Sanhedrin 16). As R. Nieto points out, in such cases the rules of interpretation were used to confirm or support established received traditions. Maimonides himself uses the term "words of scribes" for laws derived from rules of interpretation. Virtually every commentator explains that he does not mean that these laws are of Rabbinic origin; however, his response (#444) that were subsequently published appear explicit in this regard (See Sefer Hamitsvot and commentaries to Shoresh 2).
In modern times, the first one to argue that gzeirah shava was only a giluy milsa was Zechariah Frankel in Darchei Hamishna. Standard editions of Sifro have a nice response to this by the publisher who appears to have been a great scholar. R. S.R. Hirsch argues forcefully against this as well in Vol. 5 of Collected Writings.
5 See Kitzur Piskei Shela, Klalei Hatalmud