Talmudical hermeneutics

Talmudical hermeneutics defines the rules and methods for investigation and exact determination of meaning of the scriptures in the Hebrew Bible, within the framework of Rabbinic Judaism. This includes, among others, the rules by which the requirements of the Oral Law and the Halakha are derived from and established by the written law.
These rules relate to:

grammar and exegesis
the interpretation of certain words and letters and superfluous and/or missing words or letters, and prefixes and suffixes
the interpretation of those letters which, in certain words, are provided with points
the interpretation of the letters in a word according to their numerical value
the interpretation of a word by dividing it into two or more words
the interpretation of a word according to its consonantal form or according to its vocalization
the interpretation of a word by transposing its letters or by changing its vowels
the logical deduction of a halakhah from a Scriptural text or from another law
Classes of rules

Compilations of such hermeneutic rules were made in the earliest times. The tannaitic tradition recognizes three such collections, namely:

the 7 Rules of Hillel
the 13 Rules of Rabbi Ishmael
the 32 Rules of Rabbi Eliezer ben Jose. These last-mentioned rules are contained in an independent baraita which has been incorporated and preserved only in later works. They are intended for aggadic interpretation, but many of them are valid for the Halakah as well, coinciding with the rules of Hillel and Ishmael.

For list of rules see List of Talmudic principles.
For exhaustive list and examples from the Talmud, see Hillel Bakis.
It must be borne in mind, however, that neither Hillel, Ishmael, nor Eliezer ben Jose sought to give a complete enumeration of the rules of interpretation current in his day. For some reason they restricted themselves to a compilation of the principal methods of logical deduction, which they called "middot", although the other rules also were known by that term.
Those rules are traditionally studied and applied to the religious texts of some biblical canon, which were commonly believed to be inspired by God himself, through the words and the actions of human people. Therefore, those rules were related in coordination with the four independent level of biblical reading, as in the acronym pardes.

Dates of the rules

All the hermeneutic rules scattered through the Talmudim and Midrashim have been collected by Malbim in Ayyelet HaShachar, the introduction to his commentary on the Sifra, and have been reckoned at 613, to correspond with the 613 commandments. The antiquity of the rules can be determined only by the dates of the authorities who quote them, meaning that they cannot safely be declared older than the tanna to whom they are first ascribed. It is certain, however, that the seven middot of Hillel and the 13 of Rabbi Ishmael are from earlier than the time of Hillel himself, who was the first to transmit them. In any event, he did not invent them, but merely collected them as current in his day, though he possibly amplified them. They were not immediately recognized by all as valid and binding. Different schools interpreted and modified them, restricting or expanding them, in various ways.
The Talmud itself gives no information concerning the origin of the middot, although the Geonim regarded them as Sinaitic.

Rules of Rabbi Akiva and Rabbi Ishmael

and Rabbi Ishmael and their scholars especially contributed to the development or establishment of these rules. Rabbi Akiva devoted his attention particularly to the grammatical and exegetical rules, while Rabbi Ishmael developed the logical. The rules laid down by one school were frequently rejected by another because the principles which guided them in their respective formulations were essentially different.

Superfluity in the text

According to Rabbi Akiva, the divine language of the Torah is distinguished from the speech of men by the fact that in the former no word or sound is superfluous. He established two principles broadening the scope of the rule of his teacher Nahum Ish Gamzu, who had declared that certain particles, like את, גם and או, were inclusive and certain others, such as אך, רק and מן, were exclusive. These two principles are:

אין רבוי אחר רבוי אלא למעט
לשונות רבויין הן

Hence he interprets the following forms of expression as amplifications: an infinitive before a finite verb, e.g., הכרת תכרת ; the doubling of a word, e.g., איש איש ; and the repetition of a term by a synonym, e.g., ודבר ואמר. Ishmael, on the contrary, lays down the principle "the Torah speaks in the language of men", and thus may have employed superfluous words and sounds; and forced values should not be assigned to them for the purpose of deducing new rules therefrom.
The same statement holds with regard to the repetition of an entire section. Ishmael is of the opinion that "the Torah at times repeats a whole section of the Law in order to give a new application to it". It is unnecessary, therefore, to draw a new inference from every repetition. Thus, for instance, in Numbers 5:5-8 the Torah repeats the laws of Leviticus 5:20-26 for the purpose of teaching the new ruling that in certain cases recompense for sin shall be made directly to the priests. Akiva asserts, on the other hand, that "Everything that is said in a section so repeated must be interpreted", and that new deductions may be drawn from it. According to this view, in Numbers 5:5-8 a new meaning must be sought in the repetition of the Law.

Vocalization of words

In cases where the consonantal spelling of a word differs from the traditional vowelization by which the word is pronounced, Akiva derives laws from the word's pronunciation, while Ishmael derives laws from the written spelling.
For example: In Leviticus 21:11, the word נַפְשֹׁת is written without the letter vav. The vowelization indicates that the word should be translated as "bodies", but the unvowelled consonants would normally be translated as "body". Since the vowelization indicates the plural, Akiva concludes that a quarter-log of blood also defiles him when it issues from two bodies. According to Ishmael, however, this minimum quantity defiles a priest only when it issues from a single corpse.

Juxtaposition of sections

According to Rabbi Akiva, laws may be deduced from the juxtaposition of two legal sections, since "every passage which stands close to another must be explained and interpreted with reference to its neighbor". According to Ishmael, on the contrary, nothing may be inferred from the position of the individual sections, since it is not at all certain that every single portion now stands in its proper place. Many a paragraph which forms, strictly speaking, the beginning of a book and should stand in that position, has been transposed to the middle. Ishmael explains the occurrence of a section in a place where it does not properly belong by declaring that "there is no first or last in the Scriptures", not as due to any special reason. Eliezer ben Jose expanded this rule in his baraita and divided it into two parts.
Nonetheless, this method is used in many instances, for example: Deuteronomy 22:11 forbids the wearing of shaatnez, while 22:12 commands the wearing of tzitzit. The juxtaposition of these two verses is used to teach that the transgression of shaatnez is not violated when one wears a four-cornered linen garment bearing tzitzit of wool.
Juxtaposition through "exemplification" or משל has recently been described by Talmudist Daniel Boyarin as the sine qua non of Talmudic hermeneutics, for "until Solomon invented the mashal, no one could understand Torah at all". The phenomenon has been compared to the more recent phenomenon of sampling in modern popular music, especially hip-hop.

Fusion of methodologies

The opposition between the schools of Ishmael and Akiva lessened gradually, and finally vanished altogether, so that the later tannaim apply the axioms of both indiscriminately, although the hermeneutics of Akiva predominated.

Detailed rules

Kal va-chomer (קל וחומר)

The first rule of Hillel and of Rabbi Ishmael is "kal va-chomer", called also "din". This is the argument "a minori ad majus" or "a majori ad minus". In the Baraita on the Thirty-two Rules this rule is divided into two, since a distinction is made between a course of reasoning carried to its logical conclusion in the Holy Scriptures themselves and one merely suggested there. The completed argument is illustrated in ten examples given in Genesis Rabbah xcii.
The full name of this rule should be "kal va-chomer, chomer ve-kal", since by it deductions are made from the simple to the complex or vice versa, according to the nature of the conclusion required. The major premise on which the argument is based is called "nadon", or, at a later period, "melammed" ; the conclusion resulting from the argument is termed בא מן הדין or, later, "lamed". The process of deduction in the kal va-chomer is limited by the rule that the conclusion may contain nothing more than is found in the premise. This is the so-called "dayyo" law, which many teachers, however, ignored. It is formulated thus: דיו לבא מן הדין להיות כנדון.
There is a dispute regarding the thirteen principles: Either the kal va-chomer is unique among the thirteen rules in that it may be applied by anyone in any circumstance in which it logically applies and the remaining twelve rules may only be applied with a tradition of application descending from Moses or all thirteen except a gezerah shava are open to all and only the latter is restricted in its application.
For example, one may make the following logical reasoning and support it using the basis of this rule: If, as a given, a parent will punish his or her child should the latter return home with scuffed shoes, surely the parent will punish his or her child should the latter return home with scuffed shoes, ripped pants and a torn shirt. The reasoning is based on pure logic: if the parent is so upset about one item of clothing, surely he or she will be at least that upset about the child's entire ensemble. A somewhat easier construct would be to assert "if a junior varsity basketball player can make a three-pointer, surely an excellent professional basketball player could make the same three-pointer," but this might be attacked as a poor analogy because not everyone can make every shot.
However, one must be careful of falling into the trap of an illogical deduction, as explained above by "dayyo". An example of this would be as follows: If a parent will punish his or her child with a minor punishment should the latter return home with scuffed shoes, surely the parent will punish his or her child with a major punishment should the latter return home with scuffed shoes, ripped pants and a torn shirt. This is an illogical deduction; although it might be a fair speculation, it cannot be proven with logic. All that can be proven is at least the result of the lesser offense. This would be akin to asserting "if a junior varsity basketball player can make a three-pointer, surely an excellent professional basketball player could make a half-court shot."
The discovery of a fallacy in the process of deduction is called "teshuvah", or, in the terminology of the amoraim, "pirka". The possibility of such an objection is never wholly excluded, hence the deduction of the kal va-chomer has no absolute certainty. The consequences of this are: that the conclusions have, according to many teachers, no real value in criminal procedure, a view expressed in the axiom that the conclusion is insufficient to punish the violator of an inferred prohibition ; that very often a passage is interpreted to mean something which may be inferred by means of a kal va-chomer.
An example of a situation in which transgressions are specifically not punished according to
kal va-chomer is as follows: Leviticus 18:21 speaks of the prohibition of worshiping Molech, a form of worship in which children were passed through fire. Now, one would assume that if it were prohibited to pass some of one's children through the fire, surely it would be prohibited to pass all of one's children through the fire –- a kal va-chomer. However, it is derived from the verse's use of the word "ומזרעך", lit. "and from your seed", that this prohibition is only when some of one's children are sacrificed in this worship; when all of one's children are sacrificed, this is not punishable. This is explained with the reasoning that the intention of the Molech worship is to improve the health and well-being of one's remaining children, whereas complete sacrifice defeats the purported purpose of the service, rendering it unpunishable by lack of intent to perform it properly.