This is the first of a multi-part delivery featuring the Middot of Hillel. Since it’s a sixteen-page document this far, I felt it was best to provide this in smaller, more palatable chunks. I will provide the bibliography at the end of the series.
Hillel, a Rabbi known for his liberal approach to Torah interpretation, is accredited for codifying the seven basic principles of Interpretation. R’Ishmael took these seven and expanded them to thirteen rules. R’Eliezer b. Yose haGalili expanded these further to 32. The origin of the Middot is very old. The Talmud provides no information upon their origin, but the Geonim regard them as originating at Sinai. While Hillel is accredited with the compilation of the seven rules [and he may well have amplified them], they predate him by countless years.
Once compiled, they were not considered minhag immediately. In fact, Rabbis Akiva and Ishmael contributed to their development and expansion. While Akiva [as did his teacher Nahum of Gizmo] concentrated on grammatical rules [cf. y.Shabbat 19 17a, b.Sanhedrin 64b, y.Sotah 8 22b, Sifre Numbers 131], Ishmael developed the logical arguments [cf. Sifre Numbers 2, 112, b.Sanhedrin 4a-b & Tosefot, b.Chullin 72a & Tosefot] .
 Kal Vachomer [#1 Ishmael, #5 and #6 Eliezer]
The full name of this rule is Kal vachomer chomer vekal, which can be translated as simple and complex, complex and simple. Simply described, a kal vachomer applies as such: If a rule or fact is applicable in a situation where there is little reason for it to apply, it will apply all the more in a situation where the rule or fact has more reason to apply even when the rule or fact is not expressed in the text. For example, in Exodus 6:12, Moshe says to Hashem, “Bnei Israel did not listen to me, so how will Pharaoh listen to me?” Mitzrachi understands the text to say, If Israel, for whom the message is favorable, will not listen; how much less will Pharaoh heed when the message is disadvantageous. Additionally the phrase, I am of blocked lips, provides an added dimension to the kal vachomer, for if Bnei Israel, now suffering from a slave mentality would not listen to a man with blocked lips, how much more would Pharaoh who had the world’s finest courtiers, would find Moshe’s presentation distasteful.
We must be cautious with the use of this principle. The kal vachomer is never certain because variances exist in everyday life. For instance, one may say, “If a junior-high school [American] football player can make a safety in the fourth quarter to win the game, surely a professional NFL player can make a safety in the fourth quarter to win the game,” but variances in play and the worthiness of competition are variances that could make the NFL player incapable of completing a safety. Therefore, the kal vachomer of the football players is not only invalid but also illogical. As demonstrated, care must be taken to make sure the kal vachomer is not used to create illogical conclusions. This also means that a Kal vachomer argument is not a sure thing. It can be overturned by a more assured logical argument.
The Kal vachomer, according to Genesis.R 92:7 traces its first use to the Bible. In the Midrash Rabbah, the passage lists ten such arguments scattered throughout the Torah, the Prophets, and the Writings [Genesis 44:8, Exodus 6:12, Numbers 12:14, Deuteronomy 31:27, I Samuel 23:3, Jeremiah 12:5 (twice), Ezekiel 15:5, Proverbs 11:31, Esther 9:12]. Due to its simplicity, the kal vachomer is also known as din [conclusion].
[1a] Kal vachomer meforash [#5 Eliezer]
This kal vachomer [whether it is an a minori ad majus (light to heavy) or a majus ad minori (heavy to light)] is an argument made directly from the text. It is not implied in any way.
[1b] Kal vachomer satun [#6 Eliezer]
This kal vachomer is implied from a text; it is not explicitly declared. Often, a passage can be interpreted to mean something inferred through the use of a kal vachomer [b.Pesach 18b, b.Yoma 43a].