The "middoth" were Rabbi Hillel's rules for interpretation. There are seven of them. What are they? Please list them and include one or two clear examples for each.

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1. “Light and heavy” (קל וחומר) - "kal vachomer", i.e. a minori ad majus and vice versa.

The first of Hillel’s rules was known as the rule of “light and heavy” and was simply an application of the usual argument of “from the lesser to the greater.” (cf. Gen. 44:8; Ex. 6:12; Num. 12:14 – not explicit but see BK 25a; Deut. 31:27; I Sam. 23:3; Jer. 12:5; Ezek. 15:5; Prov. 11:31; Esth. 9:12

2. “Equivalence” -"gezerah shavah"

The second rule dealt with an inferred relation between two subjects from identical expressions of reference; for instance, it was written that both the Sabbath and the Passover sacrifice must be “at the due season,” and if this meant that the “daily” sacrifice must be offered on a Sabbath, then the Passover sacrifice may also be offered on a Sabbath. It is probable that etymologically the word gezerah means "law" – as in Daniel 4:4, 14 – so that gezerah shavah would mean a comparison of two similar laws (Beẓah 1:6; see however S. Lieberman, Hellenism in Jewish Palestine, 193ff.); if the same word occurs in two Pentateuchal passages, then the law applying in the one should be applied to the other. Bergman argues (Sinai 71, 1972) that a gezerah shavah is the application of the laws in one instance to a second instance to achieve a unified legal principle, irrespective of the differences between the cases, more often than not by finding a word that appears in both instances. For example, the word be-mo'ado ("in its appointed time") is used both in regard to the Paschal lamb (Num. 9:2) and to the tamid, the daily offering (Num. 28:2), which is offered on the Sabbath as well. Thus it can be inferred that the term be-mo'ado includes the Sabbath and hence the Paschal lamb may be offered even on the Sabbath, although work normally forbidden on the Sabbath is entailed (Pes. 66a). The gezerah shavah, as may be seen from the above example, was originally a purely logical principle. It is reasonable to suppose that a law clearly stated in one passage can shed light on a similar law in a different passage. In the schools, however, the gezerah shavah threatened to become a formal principle whereby a mere similarity in words was sufficient warrant for positing similar laws in the respective passages. To prevent the abuse of this method, rules were laid down to qualify its use. A man cannot advance a gezerah shavah independently, but must receive it by tradition from his teachers (Pes. 66a); both passages must be from the Pentateuch (BK 2b); the words of the gezerah shavah must not only be similar but also superfluous (mufneh, "free") in the context in which they appear, so that it can be argued that they were placed there for the express purpose of the gezerah shavah (Shab. 64a). It would appear that the school of R. Akiva disagrees with that of R. Ishmael and does not require mufneh (TJ, Yoma 8:3, 45a).

3. Deduction from special to general.

The third rule was the “extension from the special to the general”; for example, necessary work on a Sabbath became authorized work on any holy day..

Examples: (a) "He shall pour out the blood thereof and cover it with dust" (Lev. 17:13) – just as the pouring out of the blood (the act of slaughter) is performed with the hand, so must the covering be done with the hand, not with the foot (hekkesh). R. Joseph derives from this that no precept may be treated disrespectfully. He observes: "The father of all of them is blood," i.e., from the law that the precept of covering the blood must be carried out in a respectful manner it is learnt that all precepts must be so carried out (Shab. 22a).

(b) According to the rabbinic interpretation of Deuteronomy 23:25f., a farm laborer, when working in the field, may eat of his employer's grapes and standing corn. May he likewise eat of other things growing in the field? This cannot be derived from the case of the vineyard, for the owner of a vineyard is obliged to leave the gleanings to the poor (Lev. 19:10), and it may be that since the owner has this obligation, he also has the other. Nor can it be derived from the case of standing corn, for the owner of standing corn is obliged to give ḥallah, the priest's portion of the dough (Num. 15:17–21). Taking the two cases together, however, others can be derived from them. For the decisive factor in the case of the vineyard cannot be the gleanings, since the law of gleanings does not apply to standing corn. Nor can the decisive factor in the case of standing corn be ḥallah since ḥallah does not apply to a vineyard. The factor common to both vines and standing corn is that they are plants, from which it may be inferred that the law applies to all plants (BM 87b).

4. An inference from several passages -" binyan av"

The fourth rule was the explanation of two passages by a third two verses contradict one another until a third verse reconciles them. For example, one verse states that God came down to the top of the mountain (Ex. 19:20), another that His voice was heard from heaven (Deut. 4:36). A third verse (Ex. 20:19) provides the reconciliation. He brought the heavens down to the mount and spoke (Sifra 1:7).

The Book of Hebrews in the Newer Testament has several "binyan av" arguments, which strongly suggests a rabbinic authorship to the book [though deduction lets one know with certainty it was not Paul]. In Hebrews 1:5-14, the author quotes the following passages in order to build an extensive argument that Moshiach is superior to the angels: 1:5 = Psalms 2:7 [In Judaism, Psalms 2 has been held to refer to Aaron, David, AmIsrael in Messianic times, Moshiach ben Yosef, and the oldest reference in Psalms of Solomon 17:21-27 and b.Succah 62a it refers to Moshiach ben David] 1:5 = 2 Samuel 7:14 [This is been midrashically applied to Am Israel, but the Newer Testament’s application is a chiddush , an innovation, showing that not only is Moshiach (G-d’s firstborn) better than the angels, but that all prophecy is fulfilled in Yeshua as David haMelech’s physical descendant] 1:6 = Psalms 97:7 [Since Judaism allows for “ elohim ” to be used in reference to

angels, the LXX translation and its use in Hebrews is compatible; yet here it is used to suggest that the angels of Heaven worship Moshiach.] 1:7 = Psalms 104:4 [This text is crediting deeds to Moshiach that Tanach and Jewish Tradition attribute to Hashem. The use of “ fire ” and “ wind ” come from Jewishtradition: Yalchut Shimoni 2.11.3 state “ sometimes he makes us fire and sometimes winds ,” elsewhere in 4 Ezra 8:20-21 it states, “ O L-rd, before whom your hosts stand trembling at your word, change to fire and wind .”] 1:8-9 = Psalms 45:8-9 [The Soncino Tanach states, “ This psalm came to be understood as referring to King Messiah and his marriage as an allusion to his redemption of Israel .”] 1:10-12 = Psalms 102:25-27 [The LXX version of this passage has Hashem speaking to someone whom He addresses as “ L-rd .” The MT does not paint the samepicture; instead no one is specifically addressed.] 1:13 = Psalms 110:1 [Psalms 110, visualizes a Priest-King.]

5. Inference from the general to the special.- "Kelal uferat uferat ukelal"

The fifth rule allowed drawing from a general situation an inference that governed special situations. you may derive only things similar to those specified. Example: "Thou shalt bestow the money for whatsoever thy soul desireth [kelal] for oxen, or for sheep, or for wine, or for strong drink [perat] or for whatsoever thy soul asketh of thee [kelal]" (Deut. 14:26). Other things than those specified may be purchased, but only if they are food or drink like those specified (Sifra, introd. 8).

6. Analogy of another passage.

The sixth rule was the explanation of a passage from the analogy of other passages. Often called, “ Like that in another place ,” Hillel’s Sixth Rule [while very similar to R’Ishmael’sThirteenth rule, does not require the verses to be contradictory], allows one Biblical passage toexplain another through their similar content. For instance, in 1 Samuel 1:11, Hannah prayed atthe Mishkan while it was stationed in Shiloh and she said, “ Give your maidservant a male offspring, then I shall give him to Hashem all the days of his life and a razor shall not come upon his head .” Hannah’s prayer can be explained using Numbers 6:5. In Numbers 6:1-21, thetorah of the Nazir is provided, and within that passage it states, “ A razor shall not pass over his head ” [Numbers 6:5]. The similarity between Hannah’s prayer and the laws of Nazirus clueus in that the prophet Samuel was a lifelong Nazir.

7. An inference from the context.

Rule seven was an application of inferences from passages that were self-evident. In the hands of the scribes these simple rules became the basis for much unwarranted interpretation.

the meaning of a passage may be deduced: (a) from its context (mi-inyano), (b) from a later reference in the same passage (mi-sofo). As an example of (a), "Thou shalt not steal" in the Decalogue (Ex. 20:13) must refer to the capital offense of kidnapping, since the two other offenses mentioned in the same verse, "Thou shalt not murder" and "Thou shalt not commit adultery," are both capital offenses (Mekh., Ba-Ḥodesh, 8, 5). In example of (b), "I put the plague of leprosy in a house of the land of your possession" (Lev. 14:34), refers only to a house built with stones, timber, and mortar, since these materials are mentioned later in verse 45 (Sifra, introd. 1:6).

thanks to this pdf document , http://www.academia.edu/4489668/The_Middot_of_Hillel_Hillels_Hermeneutical_Rules and http://www.jewishvirtuallibrary.org/jsource/judaica/ejud_0002_0009_0_08805.html

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